Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.58874\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58874 | −1.83051 | −0.915257 | − | 0.402871i | \(-0.868012\pi\) | ||||
−0.915257 | + | 0.402871i | \(0.868012\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.70156 | 2.35078 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.58874 | −1.05685 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −6.99364 | −2.47262 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.58874 | 0.818631 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.70156 | 1.35722 | ||||||||
\(13\) | −2.40490 | −0.666999 | −0.333499 | − | 0.942750i | \(-0.608229\pi\) | ||||
−0.333499 | + | 0.942750i | \(0.608229\pi\) | |||||||
\(14\) | 2.58874 | 0.691869 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 8.70156 | 2.17539 | ||||||||
\(17\) | −3.70156 | −0.897761 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(18\) | −2.58874 | −0.610171 | ||||||||
\(19\) | 4.15641 | 0.953545 | 0.476773 | − | 0.879027i | \(-0.341807\pi\) | ||||
0.476773 | + | 0.879027i | \(0.341807\pi\) | |||||||
\(20\) | −4.70156 | −1.05130 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.58874 | 0.551921 | ||||||||
\(23\) | −0.0692417 | −0.0144379 | −0.00721895 | − | 0.999974i | \(-0.502298\pi\) | ||||
−0.00721895 | + | 0.999974i | \(0.502298\pi\) | |||||||
\(24\) | −6.99364 | −1.42757 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.22565 | 1.22095 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.70156 | −0.888512 | ||||||||
\(29\) | 0.703336 | 0.130606 | 0.0653031 | − | 0.997865i | \(-0.479199\pi\) | ||||
0.0653031 | + | 0.997865i | \(0.479199\pi\) | |||||||
\(30\) | 2.58874 | 0.472637 | ||||||||
\(31\) | 5.22742 | 0.938873 | 0.469436 | − | 0.882966i | \(-0.344457\pi\) | ||||
0.469436 | + | 0.882966i | \(0.344457\pi\) | |||||||
\(32\) | −8.53879 | −1.50946 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 9.58237 | 1.64336 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 4.70156 | 0.783594 | ||||||||
\(37\) | 7.95005 | 1.30698 | 0.653490 | − | 0.756935i | \(-0.273304\pi\) | ||||
0.653490 | + | 0.756935i | \(0.273304\pi\) | |||||||
\(38\) | −10.7598 | −1.74548 | ||||||||
\(39\) | −2.40490 | −0.385092 | ||||||||
\(40\) | 6.99364 | 1.10579 | ||||||||
\(41\) | 2.31773 | 0.361969 | 0.180984 | − | 0.983486i | \(-0.442072\pi\) | ||||
0.180984 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(42\) | 2.58874 | 0.399451 | ||||||||
\(43\) | 4.24849 | 0.647889 | 0.323944 | − | 0.946076i | \(-0.394991\pi\) | ||||
0.323944 | + | 0.946076i | \(0.394991\pi\) | |||||||
\(44\) | −4.70156 | −0.708787 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0.179249 | 0.0264288 | ||||||||
\(47\) | 13.3532 | 1.94776 | 0.973881 | − | 0.227061i | \(-0.0729117\pi\) | ||||
0.973881 | + | 0.227061i | \(0.0729117\pi\) | |||||||
\(48\) | 8.70156 | 1.25596 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.58874 | −0.366103 | ||||||||
\(51\) | −3.70156 | −0.518322 | ||||||||
\(52\) | −11.3068 | −1.56797 | ||||||||
\(53\) | −8.51136 | −1.16912 | −0.584562 | − | 0.811349i | \(-0.698734\pi\) | ||||
−0.584562 | + | 0.811349i | \(0.698734\pi\) | |||||||
\(54\) | −2.58874 | −0.352283 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 6.99364 | 0.934564 | ||||||||
\(57\) | 4.15641 | 0.550530 | ||||||||
\(58\) | −1.82075 | −0.239076 | ||||||||
\(59\) | −4.47414 | −0.582483 | −0.291242 | − | 0.956650i | \(-0.594068\pi\) | ||||
−0.291242 | + | 0.956650i | \(0.594068\pi\) | |||||||
\(60\) | −4.70156 | −0.606969 | ||||||||
\(61\) | 5.02107 | 0.642882 | 0.321441 | − | 0.946930i | \(-0.395833\pi\) | ||||
0.321441 | + | 0.946930i | \(0.395833\pi\) | |||||||
\(62\) | −13.5324 | −1.71862 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 4.70156 | 0.587695 | ||||||||
\(65\) | 2.40490 | 0.298291 | ||||||||
\(66\) | 2.58874 | 0.318652 | ||||||||
\(67\) | 4.72263 | 0.576961 | 0.288481 | − | 0.957486i | \(-0.406850\pi\) | ||||
0.288481 | + | 0.957486i | \(0.406850\pi\) | |||||||
\(68\) | −17.4031 | −2.11044 | ||||||||
\(69\) | −0.0692417 | −0.00833572 | ||||||||
\(70\) | −2.58874 | −0.309413 | ||||||||
\(71\) | 4.40490 | 0.522765 | 0.261383 | − | 0.965235i | \(-0.415822\pi\) | ||||
0.261383 | + | 0.965235i | \(0.415822\pi\) | |||||||
\(72\) | −6.99364 | −0.824208 | ||||||||
\(73\) | −14.2129 | −1.66350 | −0.831748 | − | 0.555153i | \(-0.812660\pi\) | ||||
−0.831748 | + | 0.555153i | \(0.812660\pi\) | |||||||
\(74\) | −20.5806 | −2.39245 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 19.5416 | 2.24158 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 6.22565 | 0.704916 | ||||||||
\(79\) | −4.40490 | −0.495590 | −0.247795 | − | 0.968813i | \(-0.579706\pi\) | ||||
−0.247795 | + | 0.968813i | \(0.579706\pi\) | |||||||
\(80\) | −8.70156 | −0.972864 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 5.56308 | 0.610627 | 0.305314 | − | 0.952252i | \(-0.401239\pi\) | ||||
0.305314 | + | 0.952252i | \(0.401239\pi\) | |||||||
\(84\) | −4.70156 | −0.512982 | ||||||||
\(85\) | 3.70156 | 0.401491 | ||||||||
\(86\) | −10.9982 | −1.18597 | ||||||||
\(87\) | 0.703336 | 0.0754055 | ||||||||
\(88\) | 6.99364 | 0.745524 | ||||||||
\(89\) | 15.1968 | 1.61085 | 0.805427 | − | 0.592695i | \(-0.201936\pi\) | ||||
0.805427 | + | 0.592695i | \(0.201936\pi\) | |||||||
\(90\) | 2.58874 | 0.272877 | ||||||||
\(91\) | 2.40490 | 0.252102 | ||||||||
\(92\) | −0.325544 | −0.0339403 | ||||||||
\(93\) | 5.22742 | 0.542058 | ||||||||
\(94\) | −34.5679 | −3.56540 | ||||||||
\(95\) | −4.15641 | −0.426438 | ||||||||
\(96\) | −8.53879 | −0.871487 | ||||||||
\(97\) | −8.24494 | −0.837147 | −0.418574 | − | 0.908183i | \(-0.637470\pi\) | ||||
−0.418574 | + | 0.908183i | \(0.637470\pi\) | |||||||
\(98\) | −2.58874 | −0.261502 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 4.70156 | 0.470156 | ||||||||
\(101\) | 11.0354 | 1.09807 | 0.549034 | − | 0.835800i | \(-0.314996\pi\) | ||||
0.549034 | + | 0.835800i | \(0.314996\pi\) | |||||||
\(102\) | 9.58237 | 0.948796 | ||||||||
\(103\) | −2.84182 | −0.280013 | −0.140006 | − | 0.990151i | \(-0.544712\pi\) | ||||
−0.140006 | + | 0.990151i | \(0.544712\pi\) | |||||||
\(104\) | 16.8190 | 1.64924 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 22.0337 | 2.14010 | ||||||||
\(107\) | −15.3567 | −1.48459 | −0.742295 | − | 0.670073i | \(-0.766263\pi\) | ||||
−0.742295 | + | 0.670073i | \(0.766263\pi\) | |||||||
\(108\) | 4.70156 | 0.452408 | ||||||||
\(109\) | 12.8597 | 1.23174 | 0.615870 | − | 0.787848i | \(-0.288805\pi\) | ||||
0.615870 | + | 0.787848i | \(0.288805\pi\) | |||||||
\(110\) | −2.58874 | −0.246826 | ||||||||
\(111\) | 7.95005 | 0.754586 | ||||||||
\(112\) | −8.70156 | −0.822220 | ||||||||
\(113\) | 16.5114 | 1.55326 | 0.776629 | − | 0.629958i | \(-0.216928\pi\) | ||||
0.776629 | + | 0.629958i | \(0.216928\pi\) | |||||||
\(114\) | −10.7598 | −1.00775 | ||||||||
\(115\) | 0.0692417 | 0.00645682 | ||||||||
\(116\) | 3.30678 | 0.307026 | ||||||||
\(117\) | −2.40490 | −0.222333 | ||||||||
\(118\) | 11.5824 | 1.06624 | ||||||||
\(119\) | 3.70156 | 0.339322 | ||||||||
\(120\) | 6.99364 | 0.638429 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −12.9982 | −1.17680 | ||||||||
\(123\) | 2.31773 | 0.208983 | ||||||||
\(124\) | 24.5771 | 2.20708 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.58874 | 0.230623 | ||||||||
\(127\) | −0.248490 | −0.0220500 | −0.0110250 | − | 0.999939i | \(-0.503509\pi\) | ||||
−0.0110250 | + | 0.999939i | \(0.503509\pi\) | |||||||
\(128\) | 4.90647 | 0.433675 | ||||||||
\(129\) | 4.24849 | 0.374059 | ||||||||
\(130\) | −6.22565 | −0.546026 | ||||||||
\(131\) | 12.6178 | 1.10242 | 0.551212 | − | 0.834365i | \(-0.314166\pi\) | ||||
0.551212 | + | 0.834365i | \(0.314166\pi\) | |||||||
\(132\) | −4.70156 | −0.409218 | ||||||||
\(133\) | −4.15641 | −0.360406 | ||||||||
\(134\) | −12.2256 | −1.05614 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 25.8874 | 2.21982 | ||||||||
\(137\) | 9.40312 | 0.803363 | 0.401682 | − | 0.915779i | \(-0.368426\pi\) | ||||
0.401682 | + | 0.915779i | \(0.368426\pi\) | |||||||
\(138\) | 0.179249 | 0.0152587 | ||||||||
\(139\) | 22.4934 | 1.90787 | 0.953934 | − | 0.300016i | \(-0.0969921\pi\) | ||||
0.953934 | + | 0.300016i | \(0.0969921\pi\) | |||||||
\(140\) | 4.70156 | 0.397355 | ||||||||
\(141\) | 13.3532 | 1.12454 | ||||||||
\(142\) | −11.4031 | −0.956929 | ||||||||
\(143\) | 2.40490 | 0.201108 | ||||||||
\(144\) | 8.70156 | 0.725130 | ||||||||
\(145\) | −0.703336 | −0.0584088 | ||||||||
\(146\) | 36.7935 | 3.04505 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 37.3777 | 3.07243 | ||||||||
\(149\) | −13.9001 | −1.13874 | −0.569370 | − | 0.822081i | \(-0.692813\pi\) | ||||
−0.569370 | + | 0.822081i | \(0.692813\pi\) | |||||||
\(150\) | −2.58874 | −0.211370 | ||||||||
\(151\) | 2.95183 | 0.240216 | 0.120108 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120108 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(152\) | −29.0684 | −2.35776 | ||||||||
\(153\) | −3.70156 | −0.299254 | ||||||||
\(154\) | −2.58874 | −0.208606 | ||||||||
\(155\) | −5.22742 | −0.419877 | ||||||||
\(156\) | −11.3068 | −0.905267 | ||||||||
\(157\) | 5.15463 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(158\) | 11.4031 | 0.907184 | ||||||||
\(159\) | −8.51136 | −0.674995 | ||||||||
\(160\) | 8.53879 | 0.675051 | ||||||||
\(161\) | 0.0692417 | 0.00545701 | ||||||||
\(162\) | −2.58874 | −0.203390 | ||||||||
\(163\) | 2.32128 | 0.181817 | 0.0909083 | − | 0.995859i | \(-0.471023\pi\) | ||||
0.0909083 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(164\) | 10.8970 | 0.850910 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −14.4014 | −1.11776 | ||||||||
\(167\) | 17.7581 | 1.37416 | 0.687081 | − | 0.726581i | \(-0.258892\pi\) | ||||
0.687081 | + | 0.726581i | \(0.258892\pi\) | |||||||
\(168\) | 6.99364 | 0.539571 | ||||||||
\(169\) | −7.21647 | −0.555113 | ||||||||
\(170\) | −9.58237 | −0.734934 | ||||||||
\(171\) | 4.15641 | 0.317848 | ||||||||
\(172\) | 19.9745 | 1.52304 | ||||||||
\(173\) | 20.2094 | 1.53649 | 0.768245 | − | 0.640156i | \(-0.221130\pi\) | ||||
0.768245 | + | 0.640156i | \(0.221130\pi\) | |||||||
\(174\) | −1.82075 | −0.138031 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −8.70156 | −0.655905 | ||||||||
\(177\) | −4.47414 | −0.336297 | ||||||||
\(178\) | −39.3404 | −2.94869 | ||||||||
\(179\) | −5.95005 | −0.444728 | −0.222364 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222364 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(180\) | −4.70156 | −0.350434 | ||||||||
\(181\) | −5.54161 | −0.411904 | −0.205952 | − | 0.978562i | \(-0.566029\pi\) | ||||
−0.205952 | + | 0.978562i | \(0.566029\pi\) | |||||||
\(182\) | −6.22565 | −0.461476 | ||||||||
\(183\) | 5.02107 | 0.371168 | ||||||||
\(184\) | 0.484251 | 0.0356995 | ||||||||
\(185\) | −7.95005 | −0.584499 | ||||||||
\(186\) | −13.5324 | −0.992246 | ||||||||
\(187\) | 3.70156 | 0.270685 | ||||||||
\(188\) | 62.7808 | 4.57876 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 10.7598 | 0.780601 | ||||||||
\(191\) | 25.8966 | 1.87381 | 0.936905 | − | 0.349585i | \(-0.113677\pi\) | ||||
0.936905 | + | 0.349585i | \(0.113677\pi\) | |||||||
\(192\) | 4.70156 | 0.339306 | ||||||||
\(193\) | −1.31596 | −0.0947248 | −0.0473624 | − | 0.998878i | \(-0.515082\pi\) | ||||
−0.0473624 | + | 0.998878i | \(0.515082\pi\) | |||||||
\(194\) | 21.3440 | 1.53241 | ||||||||
\(195\) | 2.40490 | 0.172218 | ||||||||
\(196\) | 4.70156 | 0.335826 | ||||||||
\(197\) | −4.44212 | −0.316488 | −0.158244 | − | 0.987400i | \(-0.550583\pi\) | ||||
−0.158244 | + | 0.987400i | \(0.550583\pi\) | |||||||
\(198\) | 2.58874 | 0.183974 | ||||||||
\(199\) | −25.7453 | −1.82504 | −0.912520 | − | 0.409033i | \(-0.865866\pi\) | ||||
−0.912520 | + | 0.409033i | \(0.865866\pi\) | |||||||
\(200\) | −6.99364 | −0.494525 | ||||||||
\(201\) | 4.72263 | 0.333109 | ||||||||
\(202\) | −28.5679 | −2.01003 | ||||||||
\(203\) | −0.703336 | −0.0493645 | ||||||||
\(204\) | −17.4031 | −1.21846 | ||||||||
\(205\) | −2.31773 | −0.161877 | ||||||||
\(206\) | 7.35672 | 0.512567 | ||||||||
\(207\) | −0.0692417 | −0.00481263 | ||||||||
\(208\) | −20.9264 | −1.45098 | ||||||||
\(209\) | −4.15641 | −0.287505 | ||||||||
\(210\) | −2.58874 | −0.178640 | ||||||||
\(211\) | −24.2129 | −1.66689 | −0.833443 | − | 0.552605i | \(-0.813634\pi\) | ||||
−0.833443 | + | 0.552605i | \(0.813634\pi\) | |||||||
\(212\) | −40.0167 | −2.74836 | ||||||||
\(213\) | 4.40490 | 0.301819 | ||||||||
\(214\) | 39.7545 | 2.71756 | ||||||||
\(215\) | −4.24849 | −0.289745 | ||||||||
\(216\) | −6.99364 | −0.475857 | ||||||||
\(217\) | −5.22742 | −0.354861 | ||||||||
\(218\) | −33.2905 | −2.25472 | ||||||||
\(219\) | −14.2129 | −0.960420 | ||||||||
\(220\) | 4.70156 | 0.316979 | ||||||||
\(221\) | 8.90188 | 0.598805 | ||||||||
\(222\) | −20.5806 | −1.38128 | ||||||||
\(223\) | 8.38697 | 0.561633 | 0.280817 | − | 0.959761i | \(-0.409395\pi\) | ||||
0.280817 | + | 0.959761i | \(0.409395\pi\) | |||||||
\(224\) | 8.53879 | 0.570522 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −42.7436 | −2.84326 | ||||||||
\(227\) | 2.79542 | 0.185538 | 0.0927692 | − | 0.995688i | \(-0.470428\pi\) | ||||
0.0927692 | + | 0.995688i | \(0.470428\pi\) | |||||||
\(228\) | 19.5416 | 1.29417 | ||||||||
\(229\) | 9.95360 | 0.657752 | 0.328876 | − | 0.944373i | \(-0.393330\pi\) | ||||
0.328876 | + | 0.944373i | \(0.393330\pi\) | |||||||
\(230\) | −0.179249 | −0.0118193 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −4.91887 | −0.322940 | ||||||||
\(233\) | −2.77612 | −0.181870 | −0.0909350 | − | 0.995857i | \(-0.528986\pi\) | ||||
−0.0909350 | + | 0.995857i | \(0.528986\pi\) | |||||||
\(234\) | 6.22565 | 0.406983 | ||||||||
\(235\) | −13.3532 | −0.871065 | ||||||||
\(236\) | −21.0354 | −1.36929 | ||||||||
\(237\) | −4.40490 | −0.286129 | ||||||||
\(238\) | −9.58237 | −0.621133 | ||||||||
\(239\) | −14.6034 | −0.944618 | −0.472309 | − | 0.881433i | \(-0.656579\pi\) | ||||
−0.472309 | + | 0.881433i | \(0.656579\pi\) | |||||||
\(240\) | −8.70156 | −0.561683 | ||||||||
\(241\) | 10.5385 | 0.678842 | 0.339421 | − | 0.940635i | \(-0.389769\pi\) | ||||
0.339421 | + | 0.940635i | \(0.389769\pi\) | |||||||
\(242\) | −2.58874 | −0.166410 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 23.6069 | 1.51127 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −9.99573 | −0.636013 | ||||||||
\(248\) | −36.5587 | −2.32148 | ||||||||
\(249\) | 5.56308 | 0.352546 | ||||||||
\(250\) | 2.58874 | 0.163726 | ||||||||
\(251\) | −19.3904 | −1.22391 | −0.611955 | − | 0.790892i | \(-0.709617\pi\) | ||||
−0.611955 | + | 0.790892i | \(0.709617\pi\) | |||||||
\(252\) | −4.70156 | −0.296171 | ||||||||
\(253\) | 0.0692417 | 0.00435319 | ||||||||
\(254\) | 0.643276 | 0.0403627 | ||||||||
\(255\) | 3.70156 | 0.231801 | ||||||||
\(256\) | −22.1047 | −1.38154 | ||||||||
\(257\) | 2.71771 | 0.169526 | 0.0847631 | − | 0.996401i | \(-0.472987\pi\) | ||||
0.0847631 | + | 0.996401i | \(0.472987\pi\) | |||||||
\(258\) | −10.9982 | −0.684720 | ||||||||
\(259\) | −7.95005 | −0.493992 | ||||||||
\(260\) | 11.3068 | 0.701216 | ||||||||
\(261\) | 0.703336 | 0.0435354 | ||||||||
\(262\) | −32.6642 | −2.01800 | ||||||||
\(263\) | −14.4548 | −0.891324 | −0.445662 | − | 0.895201i | \(-0.647032\pi\) | ||||
−0.445662 | + | 0.895201i | \(0.647032\pi\) | |||||||
\(264\) | 6.99364 | 0.430428 | ||||||||
\(265\) | 8.51136 | 0.522849 | ||||||||
\(266\) | 10.7598 | 0.659729 | ||||||||
\(267\) | 15.1968 | 0.930027 | ||||||||
\(268\) | 22.2037 | 1.35631 | ||||||||
\(269\) | −17.2677 | −1.05283 | −0.526414 | − | 0.850228i | \(-0.676464\pi\) | ||||
−0.526414 | + | 0.850228i | \(0.676464\pi\) | |||||||
\(270\) | 2.58874 | 0.157546 | ||||||||
\(271\) | 15.7051 | 0.954017 | 0.477009 | − | 0.878899i | \(-0.341721\pi\) | ||||
0.477009 | + | 0.878899i | \(0.341721\pi\) | |||||||
\(272\) | −32.2094 | −1.95298 | ||||||||
\(273\) | 2.40490 | 0.145551 | ||||||||
\(274\) | −24.3422 | −1.47057 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −0.325544 | −0.0195955 | ||||||||
\(277\) | 15.9837 | 0.960369 | 0.480184 | − | 0.877168i | \(-0.340570\pi\) | ||||
0.480184 | + | 0.877168i | \(0.340570\pi\) | |||||||
\(278\) | −58.2296 | −3.49238 | ||||||||
\(279\) | 5.22742 | 0.312958 | ||||||||
\(280\) | −6.99364 | −0.417950 | ||||||||
\(281\) | −5.50302 | −0.328283 | −0.164141 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164141 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(282\) | −34.5679 | −2.05849 | ||||||||
\(283\) | −8.09208 | −0.481024 | −0.240512 | − | 0.970646i | \(-0.577315\pi\) | ||||
−0.240512 | + | 0.970646i | \(0.577315\pi\) | |||||||
\(284\) | 20.7099 | 1.22891 | ||||||||
\(285\) | −4.15641 | −0.246204 | ||||||||
\(286\) | −6.22565 | −0.368130 | ||||||||
\(287\) | −2.31773 | −0.136811 | ||||||||
\(288\) | −8.53879 | −0.503153 | ||||||||
\(289\) | −3.29844 | −0.194026 | ||||||||
\(290\) | 1.82075 | 0.106918 | ||||||||
\(291\) | −8.24494 | −0.483327 | ||||||||
\(292\) | −66.8229 | −3.91052 | ||||||||
\(293\) | 6.51490 | 0.380605 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(294\) | −2.58874 | −0.150978 | ||||||||
\(295\) | 4.47414 | 0.260494 | ||||||||
\(296\) | −55.5998 | −3.23167 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 35.9837 | 2.08448 | ||||||||
\(299\) | 0.166519 | 0.00963006 | ||||||||
\(300\) | 4.70156 | 0.271445 | ||||||||
\(301\) | −4.24849 | −0.244879 | ||||||||
\(302\) | −7.64150 | −0.439719 | ||||||||
\(303\) | 11.0354 | 0.633970 | ||||||||
\(304\) | 36.1672 | 2.07433 | ||||||||
\(305\) | −5.02107 | −0.287505 | ||||||||
\(306\) | 9.58237 | 0.547788 | ||||||||
\(307\) | −22.5679 | −1.28802 | −0.644008 | − | 0.765019i | \(-0.722730\pi\) | ||||
−0.644008 | + | 0.765019i | \(0.722730\pi\) | |||||||
\(308\) | 4.70156 | 0.267896 | ||||||||
\(309\) | −2.84182 | −0.161665 | ||||||||
\(310\) | 13.5324 | 0.768590 | ||||||||
\(311\) | 0.0513177 | 0.00290996 | 0.00145498 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145498 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(312\) | 16.8190 | 0.952187 | ||||||||
\(313\) | −3.44224 | −0.194567 | −0.0972835 | − | 0.995257i | \(-0.531015\pi\) | ||||
−0.0972835 | + | 0.995257i | \(0.531015\pi\) | |||||||
\(314\) | −13.3440 | −0.753045 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −20.7099 | −1.16502 | ||||||||
\(317\) | 31.6582 | 1.77810 | 0.889050 | − | 0.457810i | \(-0.151366\pi\) | ||||
0.889050 | + | 0.457810i | \(0.151366\pi\) | |||||||
\(318\) | 22.0337 | 1.23559 | ||||||||
\(319\) | −0.703336 | −0.0393792 | ||||||||
\(320\) | −4.70156 | −0.262825 | ||||||||
\(321\) | −15.3567 | −0.857129 | ||||||||
\(322\) | −0.179249 | −0.00998914 | ||||||||
\(323\) | −15.3852 | −0.856055 | ||||||||
\(324\) | 4.70156 | 0.261198 | ||||||||
\(325\) | −2.40490 | −0.133400 | ||||||||
\(326\) | −6.00918 | −0.332818 | ||||||||
\(327\) | 12.8597 | 0.711145 | ||||||||
\(328\) | −16.2094 | −0.895013 | ||||||||
\(329\) | −13.3532 | −0.736184 | ||||||||
\(330\) | −2.58874 | −0.142505 | ||||||||
\(331\) | −3.55953 | −0.195650 | −0.0978248 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978248 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(332\) | 26.1552 | 1.43545 | ||||||||
\(333\) | 7.95005 | 0.435660 | ||||||||
\(334\) | −45.9710 | −2.51542 | ||||||||
\(335\) | −4.72263 | −0.258025 | ||||||||
\(336\) | −8.70156 | −0.474709 | ||||||||
\(337\) | 4.23221 | 0.230543 | 0.115272 | − | 0.993334i | \(-0.463226\pi\) | ||||
0.115272 | + | 0.993334i | \(0.463226\pi\) | |||||||
\(338\) | 18.6815 | 1.01614 | ||||||||
\(339\) | 16.5114 | 0.896774 | ||||||||
\(340\) | 17.4031 | 0.943817 | ||||||||
\(341\) | −5.22742 | −0.283081 | ||||||||
\(342\) | −10.7598 | −0.581826 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −29.7124 | −1.60198 | ||||||||
\(345\) | 0.0692417 | 0.00372785 | ||||||||
\(346\) | −52.3168 | −2.81257 | ||||||||
\(347\) | 15.6160 | 0.838313 | 0.419157 | − | 0.907914i | \(-0.362326\pi\) | ||||
0.419157 | + | 0.907914i | \(0.362326\pi\) | |||||||
\(348\) | 3.30678 | 0.177262 | ||||||||
\(349\) | 2.24357 | 0.120096 | 0.0600479 | − | 0.998195i | \(-0.480875\pi\) | ||||
0.0600479 | + | 0.998195i | \(0.480875\pi\) | |||||||
\(350\) | 2.58874 | 0.138374 | ||||||||
\(351\) | −2.40490 | −0.128364 | ||||||||
\(352\) | 8.53879 | 0.455119 | ||||||||
\(353\) | 11.9965 | 0.638507 | 0.319253 | − | 0.947669i | \(-0.396568\pi\) | ||||
0.319253 | + | 0.947669i | \(0.396568\pi\) | |||||||
\(354\) | 11.5824 | 0.615596 | ||||||||
\(355\) | −4.40490 | −0.233788 | ||||||||
\(356\) | 71.4486 | 3.78677 | ||||||||
\(357\) | 3.70156 | 0.195907 | ||||||||
\(358\) | 15.4031 | 0.814080 | ||||||||
\(359\) | 24.6743 | 1.30226 | 0.651131 | − | 0.758966i | \(-0.274295\pi\) | ||||
0.651131 | + | 0.758966i | \(0.274295\pi\) | |||||||
\(360\) | 6.99364 | 0.368597 | ||||||||
\(361\) | −1.72428 | −0.0907514 | ||||||||
\(362\) | 14.3458 | 0.753997 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 11.3068 | 0.592636 | ||||||||
\(365\) | 14.2129 | 0.743938 | ||||||||
\(366\) | −12.9982 | −0.679428 | ||||||||
\(367\) | 22.2808 | 1.16305 | 0.581524 | − | 0.813529i | \(-0.302457\pi\) | ||||
0.581524 | + | 0.813529i | \(0.302457\pi\) | |||||||
\(368\) | −0.602511 | −0.0314081 | ||||||||
\(369\) | 2.31773 | 0.120656 | ||||||||
\(370\) | 20.5806 | 1.06993 | ||||||||
\(371\) | 8.51136 | 0.441888 | ||||||||
\(372\) | 24.5771 | 1.27426 | ||||||||
\(373\) | 13.6389 | 0.706195 | 0.353097 | − | 0.935587i | \(-0.385128\pi\) | ||||
0.353097 | + | 0.935587i | \(0.385128\pi\) | |||||||
\(374\) | −9.58237 | −0.495493 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −93.3872 | −4.81608 | ||||||||
\(377\) | −1.69145 | −0.0871141 | ||||||||
\(378\) | 2.58874 | 0.133150 | ||||||||
\(379\) | 14.1985 | 0.729330 | 0.364665 | − | 0.931139i | \(-0.381183\pi\) | ||||
0.364665 | + | 0.931139i | \(0.381183\pi\) | |||||||
\(380\) | −19.5416 | −1.00246 | ||||||||
\(381\) | −0.248490 | −0.0127305 | ||||||||
\(382\) | −67.0394 | −3.43003 | ||||||||
\(383\) | −10.1244 | −0.517332 | −0.258666 | − | 0.965967i | \(-0.583283\pi\) | ||||
−0.258666 | + | 0.965967i | \(0.583283\pi\) | |||||||
\(384\) | 4.90647 | 0.250382 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 3.40667 | 0.173395 | ||||||||
\(387\) | 4.24849 | 0.215963 | ||||||||
\(388\) | −38.7641 | −1.96795 | ||||||||
\(389\) | −20.9342 | −1.06141 | −0.530703 | − | 0.847558i | \(-0.678072\pi\) | ||||
−0.530703 | + | 0.847558i | \(0.678072\pi\) | |||||||
\(390\) | −6.22565 | −0.315248 | ||||||||
\(391\) | 0.256303 | 0.0129618 | ||||||||
\(392\) | −6.99364 | −0.353232 | ||||||||
\(393\) | 12.6178 | 0.636485 | ||||||||
\(394\) | 11.4995 | 0.579335 | ||||||||
\(395\) | 4.40490 | 0.221634 | ||||||||
\(396\) | −4.70156 | −0.236262 | ||||||||
\(397\) | −24.5679 | −1.23303 | −0.616513 | − | 0.787345i | \(-0.711455\pi\) | ||||
−0.616513 | + | 0.787345i | \(0.711455\pi\) | |||||||
\(398\) | 66.6479 | 3.34076 | ||||||||
\(399\) | −4.15641 | −0.208081 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | −38.4180 | −1.91850 | −0.959252 | − | 0.282551i | \(-0.908819\pi\) | ||||
−0.959252 | + | 0.282551i | \(0.908819\pi\) | |||||||
\(402\) | −12.2256 | −0.609760 | ||||||||
\(403\) | −12.5714 | −0.626227 | ||||||||
\(404\) | 51.8838 | 2.58132 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 1.82075 | 0.0903624 | ||||||||
\(407\) | −7.95005 | −0.394069 | ||||||||
\(408\) | 25.8874 | 1.28162 | ||||||||
\(409\) | −1.17748 | −0.0582224 | −0.0291112 | − | 0.999576i | \(-0.509268\pi\) | ||||
−0.0291112 | + | 0.999576i | \(0.509268\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | 9.40312 | 0.463822 | ||||||||
\(412\) | −13.3610 | −0.658249 | ||||||||
\(413\) | 4.47414 | 0.220158 | ||||||||
\(414\) | 0.179249 | 0.00880959 | ||||||||
\(415\) | −5.56308 | −0.273081 | ||||||||
\(416\) | 20.5349 | 1.00681 | ||||||||
\(417\) | 22.4934 | 1.10151 | ||||||||
\(418\) | 10.7598 | 0.526281 | ||||||||
\(419\) | −37.2585 | −1.82020 | −0.910098 | − | 0.414393i | \(-0.863994\pi\) | ||||
−0.910098 | + | 0.414393i | \(0.863994\pi\) | |||||||
\(420\) | 4.70156 | 0.229413 | ||||||||
\(421\) | 3.10469 | 0.151313 | 0.0756566 | − | 0.997134i | \(-0.475895\pi\) | ||||
0.0756566 | + | 0.997134i | \(0.475895\pi\) | |||||||
\(422\) | 62.6809 | 3.05126 | ||||||||
\(423\) | 13.3532 | 0.649254 | ||||||||
\(424\) | 59.5253 | 2.89081 | ||||||||
\(425\) | −3.70156 | −0.179552 | ||||||||
\(426\) | −11.4031 | −0.552483 | ||||||||
\(427\) | −5.02107 | −0.242986 | ||||||||
\(428\) | −72.2006 | −3.48995 | ||||||||
\(429\) | 2.40490 | 0.116110 | ||||||||
\(430\) | 10.9982 | 0.530382 | ||||||||
\(431\) | −13.5452 | −0.652447 | −0.326224 | − | 0.945293i | \(-0.605776\pi\) | ||||
−0.326224 | + | 0.945293i | \(0.605776\pi\) | |||||||
\(432\) | 8.70156 | 0.418654 | ||||||||
\(433\) | −33.7904 | −1.62386 | −0.811931 | − | 0.583754i | \(-0.801583\pi\) | ||||
−0.811931 | + | 0.583754i | \(0.801583\pi\) | |||||||
\(434\) | 13.5324 | 0.649577 | ||||||||
\(435\) | −0.703336 | −0.0337224 | ||||||||
\(436\) | 60.4609 | 2.89555 | ||||||||
\(437\) | −0.287797 | −0.0137672 | ||||||||
\(438\) | 36.7935 | 1.75806 | ||||||||
\(439\) | 11.6052 | 0.553887 | 0.276943 | − | 0.960886i | \(-0.410679\pi\) | ||||
0.276943 | + | 0.960886i | \(0.410679\pi\) | |||||||
\(440\) | −6.99364 | −0.333408 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −23.0446 | −1.09612 | ||||||||
\(443\) | −24.7226 | −1.17461 | −0.587304 | − | 0.809367i | \(-0.699811\pi\) | ||||
−0.587304 | + | 0.809367i | \(0.699811\pi\) | |||||||
\(444\) | 37.3777 | 1.77387 | ||||||||
\(445\) | −15.1968 | −0.720396 | ||||||||
\(446\) | −21.7117 | −1.02808 | ||||||||
\(447\) | −13.9001 | −0.657452 | ||||||||
\(448\) | −4.70156 | −0.222128 | ||||||||
\(449\) | 31.5275 | 1.48788 | 0.743938 | − | 0.668249i | \(-0.232956\pi\) | ||||
0.743938 | + | 0.668249i | \(0.232956\pi\) | |||||||
\(450\) | −2.58874 | −0.122034 | ||||||||
\(451\) | −2.31773 | −0.109138 | ||||||||
\(452\) | 77.6292 | 3.65137 | ||||||||
\(453\) | 2.95183 | 0.138689 | ||||||||
\(454\) | −7.23660 | −0.339631 | ||||||||
\(455\) | −2.40490 | −0.112743 | ||||||||
\(456\) | −29.0684 | −1.36125 | ||||||||
\(457\) | −13.3874 | −0.626235 | −0.313118 | − | 0.949714i | \(-0.601373\pi\) | ||||
−0.313118 | + | 0.949714i | \(0.601373\pi\) | |||||||
\(458\) | −25.7673 | −1.20402 | ||||||||
\(459\) | −3.70156 | −0.172774 | ||||||||
\(460\) | 0.325544 | 0.0151786 | ||||||||
\(461\) | 3.87070 | 0.180276 | 0.0901382 | − | 0.995929i | \(-0.471269\pi\) | ||||
0.0901382 | + | 0.995929i | \(0.471269\pi\) | |||||||
\(462\) | −2.58874 | −0.120439 | ||||||||
\(463\) | 29.2484 | 1.35929 | 0.679643 | − | 0.733543i | \(-0.262135\pi\) | ||||
0.679643 | + | 0.733543i | \(0.262135\pi\) | |||||||
\(464\) | 6.12012 | 0.284119 | ||||||||
\(465\) | −5.22742 | −0.242416 | ||||||||
\(466\) | 7.18666 | 0.332915 | ||||||||
\(467\) | 14.2551 | 0.659645 | 0.329823 | − | 0.944043i | \(-0.393011\pi\) | ||||
0.329823 | + | 0.944043i | \(0.393011\pi\) | |||||||
\(468\) | −11.3068 | −0.522656 | ||||||||
\(469\) | −4.72263 | −0.218071 | ||||||||
\(470\) | 34.5679 | 1.59450 | ||||||||
\(471\) | 5.15463 | 0.237513 | ||||||||
\(472\) | 31.2905 | 1.44026 | ||||||||
\(473\) | −4.24849 | −0.195346 | ||||||||
\(474\) | 11.4031 | 0.523763 | ||||||||
\(475\) | 4.15641 | 0.190709 | ||||||||
\(476\) | 17.4031 | 0.797671 | ||||||||
\(477\) | −8.51136 | −0.389708 | ||||||||
\(478\) | 37.8045 | 1.72914 | ||||||||
\(479\) | −32.2339 | −1.47280 | −0.736401 | − | 0.676545i | \(-0.763476\pi\) | ||||
−0.736401 | + | 0.676545i | \(0.763476\pi\) | |||||||
\(480\) | 8.53879 | 0.389741 | ||||||||
\(481\) | −19.1191 | −0.871754 | ||||||||
\(482\) | −27.2813 | −1.24263 | ||||||||
\(483\) | 0.0692417 | 0.00315061 | ||||||||
\(484\) | 4.70156 | 0.213707 | ||||||||
\(485\) | 8.24494 | 0.374384 | ||||||||
\(486\) | −2.58874 | −0.117428 | ||||||||
\(487\) | 5.27382 | 0.238980 | 0.119490 | − | 0.992835i | \(-0.461874\pi\) | ||||
0.119490 | + | 0.992835i | \(0.461874\pi\) | |||||||
\(488\) | −35.1155 | −1.58960 | ||||||||
\(489\) | 2.32128 | 0.104972 | ||||||||
\(490\) | 2.58874 | 0.116947 | ||||||||
\(491\) | 35.6647 | 1.60953 | 0.804764 | − | 0.593595i | \(-0.202292\pi\) | ||||
0.804764 | + | 0.593595i | \(0.202292\pi\) | |||||||
\(492\) | 10.8970 | 0.491273 | ||||||||
\(493\) | −2.60344 | −0.117253 | ||||||||
\(494\) | 25.8763 | 1.16423 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 45.4867 | 2.04242 | ||||||||
\(497\) | −4.40490 | −0.197587 | ||||||||
\(498\) | −14.4014 | −0.645340 | ||||||||
\(499\) | −39.0083 | −1.74625 | −0.873127 | − | 0.487494i | \(-0.837911\pi\) | ||||
−0.873127 | + | 0.487494i | \(0.837911\pi\) | |||||||
\(500\) | −4.70156 | −0.210260 | ||||||||
\(501\) | 17.7581 | 0.793372 | ||||||||
\(502\) | 50.1966 | 2.24039 | ||||||||
\(503\) | −32.6821 | −1.45722 | −0.728612 | − | 0.684926i | \(-0.759834\pi\) | ||||
−0.728612 | + | 0.684926i | \(0.759834\pi\) | |||||||
\(504\) | 6.99364 | 0.311521 | ||||||||
\(505\) | −11.0354 | −0.491071 | ||||||||
\(506\) | −0.179249 | −0.00796857 | ||||||||
\(507\) | −7.21647 | −0.320495 | ||||||||
\(508\) | −1.16829 | −0.0518346 | ||||||||
\(509\) | 3.25808 | 0.144412 | 0.0722058 | − | 0.997390i | \(-0.476996\pi\) | ||||
0.0722058 | + | 0.997390i | \(0.476996\pi\) | |||||||
\(510\) | −9.58237 | −0.424315 | ||||||||
\(511\) | 14.2129 | 0.628743 | ||||||||
\(512\) | 47.4103 | 2.09526 | ||||||||
\(513\) | 4.15641 | 0.183510 | ||||||||
\(514\) | −7.03544 | −0.310320 | ||||||||
\(515\) | 2.84182 | 0.125226 | ||||||||
\(516\) | 19.9745 | 0.879330 | ||||||||
\(517\) | −13.3532 | −0.587272 | ||||||||
\(518\) | 20.5806 | 0.904260 | ||||||||
\(519\) | 20.2094 | 0.887093 | ||||||||
\(520\) | −16.8190 | −0.737561 | ||||||||
\(521\) | 7.75506 | 0.339755 | 0.169878 | − | 0.985465i | \(-0.445663\pi\) | ||||
0.169878 | + | 0.985465i | \(0.445663\pi\) | |||||||
\(522\) | −1.82075 | −0.0796921 | ||||||||
\(523\) | 27.1647 | 1.18783 | 0.593916 | − | 0.804527i | \(-0.297581\pi\) | ||||
0.593916 | + | 0.804527i | \(0.297581\pi\) | |||||||
\(524\) | 59.3235 | 2.59156 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 37.4198 | 1.63158 | ||||||||
\(527\) | −19.3496 | −0.842883 | ||||||||
\(528\) | −8.70156 | −0.378687 | ||||||||
\(529\) | −22.9952 | −0.999792 | ||||||||
\(530\) | −22.0337 | −0.957082 | ||||||||
\(531\) | −4.47414 | −0.194161 | ||||||||
\(532\) | −19.5416 | −0.847236 | ||||||||
\(533\) | −5.57391 | −0.241433 | ||||||||
\(534\) | −39.3404 | −1.70243 | ||||||||
\(535\) | 15.3567 | 0.663929 | ||||||||
\(536\) | −33.0284 | −1.42661 | ||||||||
\(537\) | −5.95005 | −0.256764 | ||||||||
\(538\) | 44.7014 | 1.92722 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −4.70156 | −0.202323 | ||||||||
\(541\) | 36.2087 | 1.55673 | 0.778366 | − | 0.627811i | \(-0.216049\pi\) | ||||
0.778366 | + | 0.627811i | \(0.216049\pi\) | |||||||
\(542\) | −40.6564 | −1.74634 | ||||||||
\(543\) | −5.54161 | −0.237813 | ||||||||
\(544\) | 31.6069 | 1.35513 | ||||||||
\(545\) | −12.8597 | −0.550851 | ||||||||
\(546\) | −6.22565 | −0.266433 | ||||||||
\(547\) | −11.1160 | −0.475288 | −0.237644 | − | 0.971352i | \(-0.576375\pi\) | ||||
−0.237644 | + | 0.971352i | \(0.576375\pi\) | |||||||
\(548\) | 44.2094 | 1.88853 | ||||||||
\(549\) | 5.02107 | 0.214294 | ||||||||
\(550\) | 2.58874 | 0.110384 | ||||||||
\(551\) | 2.92335 | 0.124539 | ||||||||
\(552\) | 0.484251 | 0.0206111 | ||||||||
\(553\) | 4.40490 | 0.187315 | ||||||||
\(554\) | −41.3777 | −1.75797 | ||||||||
\(555\) | −7.95005 | −0.337461 | ||||||||
\(556\) | 105.754 | 4.48498 | ||||||||
\(557\) | 34.4772 | 1.46084 | 0.730422 | − | 0.682996i | \(-0.239323\pi\) | ||||
0.730422 | + | 0.682996i | \(0.239323\pi\) | |||||||
\(558\) | −13.5324 | −0.572873 | ||||||||
\(559\) | −10.2172 | −0.432141 | ||||||||
\(560\) | 8.70156 | 0.367708 | ||||||||
\(561\) | 3.70156 | 0.156280 | ||||||||
\(562\) | 14.2459 | 0.600926 | ||||||||
\(563\) | 16.2129 | 0.683293 | 0.341647 | − | 0.939829i | \(-0.389015\pi\) | ||||
0.341647 | + | 0.939829i | \(0.389015\pi\) | |||||||
\(564\) | 62.7808 | 2.64355 | ||||||||
\(565\) | −16.5114 | −0.694638 | ||||||||
\(566\) | 20.9483 | 0.880522 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −30.8062 | −1.29260 | ||||||||
\(569\) | 3.64807 | 0.152935 | 0.0764675 | − | 0.997072i | \(-0.475636\pi\) | ||||
0.0764675 | + | 0.997072i | \(0.475636\pi\) | |||||||
\(570\) | 10.7598 | 0.450680 | ||||||||
\(571\) | −36.7563 | −1.53820 | −0.769102 | − | 0.639126i | \(-0.779296\pi\) | ||||
−0.769102 | + | 0.639126i | \(0.779296\pi\) | |||||||
\(572\) | 11.3068 | 0.472760 | ||||||||
\(573\) | 25.8966 | 1.08184 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | −0.0692417 | −0.00288758 | ||||||||
\(576\) | 4.70156 | 0.195898 | ||||||||
\(577\) | −2.17433 | −0.0905186 | −0.0452593 | − | 0.998975i | \(-0.514411\pi\) | ||||
−0.0452593 | + | 0.998975i | \(0.514411\pi\) | |||||||
\(578\) | 8.53879 | 0.355167 | ||||||||
\(579\) | −1.31596 | −0.0546894 | ||||||||
\(580\) | −3.30678 | −0.137306 | ||||||||
\(581\) | −5.56308 | −0.230795 | ||||||||
\(582\) | 21.3440 | 0.884737 | ||||||||
\(583\) | 8.51136 | 0.352504 | ||||||||
\(584\) | 99.4000 | 4.11320 | ||||||||
\(585\) | 2.40490 | 0.0994303 | ||||||||
\(586\) | −16.8654 | −0.696702 | ||||||||
\(587\) | 13.9501 | 0.575780 | 0.287890 | − | 0.957663i | \(-0.407046\pi\) | ||||
0.287890 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(588\) | 4.70156 | 0.193889 | ||||||||
\(589\) | 21.7273 | 0.895258 | ||||||||
\(590\) | −11.5824 | −0.476839 | ||||||||
\(591\) | −4.44212 | −0.182724 | ||||||||
\(592\) | 69.1779 | 2.84319 | ||||||||
\(593\) | −10.9483 | −0.449592 | −0.224796 | − | 0.974406i | \(-0.572172\pi\) | ||||
−0.224796 | + | 0.974406i | \(0.572172\pi\) | |||||||
\(594\) | 2.58874 | 0.106217 | ||||||||
\(595\) | −3.70156 | −0.151749 | ||||||||
\(596\) | −65.3522 | −2.67693 | ||||||||
\(597\) | −25.7453 | −1.05369 | ||||||||
\(598\) | −0.431075 | −0.0176280 | ||||||||
\(599\) | −41.1998 | −1.68338 | −0.841689 | − | 0.539963i | \(-0.818438\pi\) | ||||
−0.841689 | + | 0.539963i | \(0.818438\pi\) | |||||||
\(600\) | −6.99364 | −0.285514 | ||||||||
\(601\) | 21.5110 | 0.877450 | 0.438725 | − | 0.898621i | \(-0.355430\pi\) | ||||
0.438725 | + | 0.898621i | \(0.355430\pi\) | |||||||
\(602\) | 10.9982 | 0.448254 | ||||||||
\(603\) | 4.72263 | 0.192320 | ||||||||
\(604\) | 13.8782 | 0.564696 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −28.5679 | −1.16049 | ||||||||
\(607\) | −13.8580 | −0.562478 | −0.281239 | − | 0.959638i | \(-0.590745\pi\) | ||||
−0.281239 | + | 0.959638i | \(0.590745\pi\) | |||||||
\(608\) | −35.4907 | −1.43934 | ||||||||
\(609\) | −0.703336 | −0.0285006 | ||||||||
\(610\) | 12.9982 | 0.526283 | ||||||||
\(611\) | −32.1130 | −1.29915 | ||||||||
\(612\) | −17.4031 | −0.703480 | ||||||||
\(613\) | −32.0223 | −1.29337 | −0.646684 | − | 0.762758i | \(-0.723845\pi\) | ||||
−0.646684 | + | 0.762758i | \(0.723845\pi\) | |||||||
\(614\) | 58.4223 | 2.35773 | ||||||||
\(615\) | −2.31773 | −0.0934600 | ||||||||
\(616\) | −6.99364 | −0.281782 | ||||||||
\(617\) | −3.39958 | −0.136862 | −0.0684309 | − | 0.997656i | \(-0.521799\pi\) | ||||
−0.0684309 | + | 0.997656i | \(0.521799\pi\) | |||||||
\(618\) | 7.35672 | 0.295931 | ||||||||
\(619\) | −1.91638 | −0.0770259 | −0.0385129 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385129 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(620\) | −24.5771 | −0.987038 | ||||||||
\(621\) | −0.0692417 | −0.00277857 | ||||||||
\(622\) | −0.132848 | −0.00532672 | ||||||||
\(623\) | −15.1968 | −0.608846 | ||||||||
\(624\) | −20.9264 | −0.837725 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.91106 | 0.356158 | ||||||||
\(627\) | −4.15641 | −0.165991 | ||||||||
\(628\) | 24.2348 | 0.967075 | ||||||||
\(629\) | −29.4276 | −1.17336 | ||||||||
\(630\) | −2.58874 | −0.103138 | ||||||||
\(631\) | −37.4019 | −1.48895 | −0.744473 | − | 0.667653i | \(-0.767299\pi\) | ||||
−0.744473 | + | 0.667653i | \(0.767299\pi\) | |||||||
\(632\) | 30.8062 | 1.22541 | ||||||||
\(633\) | −24.2129 | −0.962377 | ||||||||
\(634\) | −81.9547 | −3.25484 | ||||||||
\(635\) | 0.248490 | 0.00986104 | ||||||||
\(636\) | −40.0167 | −1.58676 | ||||||||
\(637\) | −2.40490 | −0.0952855 | ||||||||
\(638\) | 1.82075 | 0.0720842 | ||||||||
\(639\) | 4.40490 | 0.174255 | ||||||||
\(640\) | −4.90647 | −0.193945 | ||||||||
\(641\) | 8.52928 | 0.336886 | 0.168443 | − | 0.985711i | \(-0.446126\pi\) | ||||
0.168443 | + | 0.985711i | \(0.446126\pi\) | |||||||
\(642\) | 39.7545 | 1.56899 | ||||||||
\(643\) | 36.3615 | 1.43396 | 0.716979 | − | 0.697095i | \(-0.245524\pi\) | ||||
0.716979 | + | 0.697095i | \(0.245524\pi\) | |||||||
\(644\) | 0.325544 | 0.0128282 | ||||||||
\(645\) | −4.24849 | −0.167284 | ||||||||
\(646\) | 39.8282 | 1.56702 | ||||||||
\(647\) | 42.2551 | 1.66122 | 0.830609 | − | 0.556856i | \(-0.187993\pi\) | ||||
0.830609 | + | 0.556856i | \(0.187993\pi\) | |||||||
\(648\) | −6.99364 | −0.274736 | ||||||||
\(649\) | 4.47414 | 0.175625 | ||||||||
\(650\) | 6.22565 | 0.244190 | ||||||||
\(651\) | −5.22742 | −0.204879 | ||||||||
\(652\) | 10.9136 | 0.427411 | ||||||||
\(653\) | −21.8110 | −0.853532 | −0.426766 | − | 0.904362i | \(-0.640347\pi\) | ||||
−0.426766 | + | 0.904362i | \(0.640347\pi\) | |||||||
\(654\) | −33.2905 | −1.30176 | ||||||||
\(655\) | −12.6178 | −0.493019 | ||||||||
\(656\) | 20.1679 | 0.787424 | ||||||||
\(657\) | −14.2129 | −0.554499 | ||||||||
\(658\) | 34.5679 | 1.34760 | ||||||||
\(659\) | −46.8164 | −1.82371 | −0.911853 | − | 0.410516i | \(-0.865348\pi\) | ||||
−0.911853 | + | 0.410516i | \(0.865348\pi\) | |||||||
\(660\) | 4.70156 | 0.183008 | ||||||||
\(661\) | −17.1113 | −0.665551 | −0.332775 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332775 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(662\) | 9.21469 | 0.358139 | ||||||||
\(663\) | 8.90188 | 0.345720 | ||||||||
\(664\) | −38.9061 | −1.50985 | ||||||||
\(665\) | 4.15641 | 0.161179 | ||||||||
\(666\) | −20.5806 | −0.797482 | ||||||||
\(667\) | −0.0487002 | −0.00188568 | ||||||||
\(668\) | 83.4907 | 3.23035 | ||||||||
\(669\) | 8.38697 | 0.324259 | ||||||||
\(670\) | 12.2256 | 0.472318 | ||||||||
\(671\) | −5.02107 | −0.193836 | ||||||||
\(672\) | 8.53879 | 0.329391 | ||||||||
\(673\) | −48.3707 | −1.86455 | −0.932277 | − | 0.361746i | \(-0.882181\pi\) | ||||
−0.932277 | + | 0.361746i | \(0.882181\pi\) | |||||||
\(674\) | −10.9561 | −0.422013 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −33.9287 | −1.30495 | ||||||||
\(677\) | 26.6463 | 1.02410 | 0.512050 | − | 0.858956i | \(-0.328886\pi\) | ||||
0.512050 | + | 0.858956i | \(0.328886\pi\) | |||||||
\(678\) | −42.7436 | −1.64156 | ||||||||
\(679\) | 8.24494 | 0.316412 | ||||||||
\(680\) | −25.8874 | −0.992736 | ||||||||
\(681\) | 2.79542 | 0.107121 | ||||||||
\(682\) | 13.5324 | 0.518183 | ||||||||
\(683\) | 5.94514 | 0.227484 | 0.113742 | − | 0.993510i | \(-0.463716\pi\) | ||||
0.113742 | + | 0.993510i | \(0.463716\pi\) | |||||||
\(684\) | 19.5416 | 0.747192 | ||||||||
\(685\) | −9.40312 | −0.359275 | ||||||||
\(686\) | 2.58874 | 0.0988385 | ||||||||
\(687\) | 9.95360 | 0.379754 | ||||||||
\(688\) | 36.9685 | 1.40941 | ||||||||
\(689\) | 20.4689 | 0.779805 | ||||||||
\(690\) | −0.179249 | −0.00682388 | ||||||||
\(691\) | 7.72867 | 0.294012 | 0.147006 | − | 0.989136i | \(-0.453036\pi\) | ||||
0.147006 | + | 0.989136i | \(0.453036\pi\) | |||||||
\(692\) | 95.0156 | 3.61195 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | −40.4258 | −1.53454 | ||||||||
\(695\) | −22.4934 | −0.853225 | ||||||||
\(696\) | −4.91887 | −0.186449 | ||||||||
\(697\) | −8.57923 | −0.324961 | ||||||||
\(698\) | −5.80802 | −0.219837 | ||||||||
\(699\) | −2.77612 | −0.105003 | ||||||||
\(700\) | −4.70156 | −0.177702 | ||||||||
\(701\) | −4.70334 | −0.177643 | −0.0888213 | − | 0.996048i | \(-0.528310\pi\) | ||||
−0.0888213 | + | 0.996048i | \(0.528310\pi\) | |||||||
\(702\) | 6.22565 | 0.234972 | ||||||||
\(703\) | 33.0437 | 1.24627 | ||||||||
\(704\) | −4.70156 | −0.177197 | ||||||||
\(705\) | −13.3532 | −0.502910 | ||||||||
\(706\) | −31.0557 | −1.16880 | ||||||||
\(707\) | −11.0354 | −0.415031 | ||||||||
\(708\) | −21.0354 | −0.790560 | ||||||||
\(709\) | 21.8822 | 0.821803 | 0.410901 | − | 0.911680i | \(-0.365214\pi\) | ||||
0.410901 | + | 0.911680i | \(0.365214\pi\) | |||||||
\(710\) | 11.4031 | 0.427952 | ||||||||
\(711\) | −4.40490 | −0.165197 | ||||||||
\(712\) | −106.281 | −3.98304 | ||||||||
\(713\) | −0.361956 | −0.0135553 | ||||||||
\(714\) | −9.58237 | −0.358611 | ||||||||
\(715\) | −2.40490 | −0.0899381 | ||||||||
\(716\) | −27.9745 | −1.04546 | ||||||||
\(717\) | −14.6034 | −0.545375 | ||||||||
\(718\) | −63.8754 | −2.38381 | ||||||||
\(719\) | −19.2875 | −0.719302 | −0.359651 | − | 0.933087i | \(-0.617104\pi\) | ||||
−0.359651 | + | 0.933087i | \(0.617104\pi\) | |||||||
\(720\) | −8.70156 | −0.324288 | ||||||||
\(721\) | 2.84182 | 0.105835 | ||||||||
\(722\) | 4.46370 | 0.166122 | ||||||||
\(723\) | 10.5385 | 0.391930 | ||||||||
\(724\) | −26.0542 | −0.968297 | ||||||||
\(725\) | 0.703336 | 0.0261212 | ||||||||
\(726\) | −2.58874 | −0.0960771 | ||||||||
\(727\) | 35.4877 | 1.31616 | 0.658082 | − | 0.752946i | \(-0.271368\pi\) | ||||
0.658082 | + | 0.752946i | \(0.271368\pi\) | |||||||
\(728\) | −16.8190 | −0.623353 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −36.7935 | −1.36179 | ||||||||
\(731\) | −15.7261 | −0.581649 | ||||||||
\(732\) | 23.6069 | 0.872535 | ||||||||
\(733\) | 49.4163 | 1.82523 | 0.912615 | − | 0.408819i | \(-0.134059\pi\) | ||||
0.912615 | + | 0.408819i | \(0.134059\pi\) | |||||||
\(734\) | −57.6791 | −2.12898 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0.591240 | 0.0217934 | ||||||||
\(737\) | −4.72263 | −0.173960 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | 18.1095 | 0.666168 | 0.333084 | − | 0.942897i | \(-0.391911\pi\) | ||||
0.333084 | + | 0.942897i | \(0.391911\pi\) | |||||||
\(740\) | −37.3777 | −1.37403 | ||||||||
\(741\) | −9.99573 | −0.367202 | ||||||||
\(742\) | −22.0337 | −0.808882 | ||||||||
\(743\) | −45.0972 | −1.65445 | −0.827227 | − | 0.561868i | \(-0.810083\pi\) | ||||
−0.827227 | + | 0.561868i | \(0.810083\pi\) | |||||||
\(744\) | −36.5587 | −1.34031 | ||||||||
\(745\) | 13.9001 | 0.509260 | ||||||||
\(746\) | −35.3075 | −1.29270 | ||||||||
\(747\) | 5.56308 | 0.203542 | ||||||||
\(748\) | 17.4031 | 0.636321 | ||||||||
\(749\) | 15.3567 | 0.561122 | ||||||||
\(750\) | 2.58874 | 0.0945273 | ||||||||
\(751\) | 47.9495 | 1.74970 | 0.874851 | − | 0.484391i | \(-0.160959\pi\) | ||||
0.874851 | + | 0.484391i | \(0.160959\pi\) | |||||||
\(752\) | 116.193 | 4.23714 | ||||||||
\(753\) | −19.3904 | −0.706625 | ||||||||
\(754\) | 4.37872 | 0.159464 | ||||||||
\(755\) | −2.95183 | −0.107428 | ||||||||
\(756\) | −4.70156 | −0.170994 | ||||||||
\(757\) | 13.8158 | 0.502145 | 0.251073 | − | 0.967968i | \(-0.419217\pi\) | ||||
0.251073 | + | 0.967968i | \(0.419217\pi\) | |||||||
\(758\) | −36.7563 | −1.33505 | ||||||||
\(759\) | 0.0692417 | 0.00251331 | ||||||||
\(760\) | 29.0684 | 1.05442 | ||||||||
\(761\) | 12.2221 | 0.443051 | 0.221525 | − | 0.975155i | \(-0.428896\pi\) | ||||
0.221525 | + | 0.975155i | \(0.428896\pi\) | |||||||
\(762\) | 0.643276 | 0.0233034 | ||||||||
\(763\) | −12.8597 | −0.465554 | ||||||||
\(764\) | 121.754 | 4.40492 | ||||||||
\(765\) | 3.70156 | 0.133830 | ||||||||
\(766\) | 26.2094 | 0.946983 | ||||||||
\(767\) | 10.7598 | 0.388516 | ||||||||
\(768\) | −22.1047 | −0.797634 | ||||||||
\(769\) | 29.3013 | 1.05663 | 0.528316 | − | 0.849048i | \(-0.322823\pi\) | ||||
0.528316 | + | 0.849048i | \(0.322823\pi\) | |||||||
\(770\) | 2.58874 | 0.0932916 | ||||||||
\(771\) | 2.71771 | 0.0978760 | ||||||||
\(772\) | −6.18706 | −0.222677 | ||||||||
\(773\) | 43.2356 | 1.55508 | 0.777539 | − | 0.628835i | \(-0.216468\pi\) | ||||
0.777539 | + | 0.628835i | \(0.216468\pi\) | |||||||
\(774\) | −10.9982 | −0.395323 | ||||||||
\(775\) | 5.22742 | 0.187775 | ||||||||
\(776\) | 57.6621 | 2.06995 | ||||||||
\(777\) | −7.95005 | −0.285207 | ||||||||
\(778\) | 54.1931 | 1.94292 | ||||||||
\(779\) | 9.63344 | 0.345154 | ||||||||
\(780\) | 11.3068 | 0.404848 | ||||||||
\(781\) | −4.40490 | −0.157620 | ||||||||
\(782\) | −0.663500 | −0.0237267 | ||||||||
\(783\) | 0.703336 | 0.0251352 | ||||||||
\(784\) | 8.70156 | 0.310770 | ||||||||
\(785\) | −5.15463 | −0.183977 | ||||||||
\(786\) | −32.6642 | −1.16509 | ||||||||
\(787\) | −20.1489 | −0.718230 | −0.359115 | − | 0.933293i | \(-0.616921\pi\) | ||||
−0.359115 | + | 0.933293i | \(0.616921\pi\) | |||||||
\(788\) | −20.8849 | −0.743993 | ||||||||
\(789\) | −14.4548 | −0.514606 | ||||||||
\(790\) | −11.4031 | −0.405705 | ||||||||
\(791\) | −16.5114 | −0.587076 | ||||||||
\(792\) | 6.99364 | 0.248508 | ||||||||
\(793\) | −12.0752 | −0.428801 | ||||||||
\(794\) | 63.5998 | 2.25707 | ||||||||
\(795\) | 8.51136 | 0.301867 | ||||||||
\(796\) | −121.043 | −4.29027 | ||||||||
\(797\) | −7.08676 | −0.251026 | −0.125513 | − | 0.992092i | \(-0.540058\pi\) | ||||
−0.125513 | + | 0.992092i | \(0.540058\pi\) | |||||||
\(798\) | 10.7598 | 0.380894 | ||||||||
\(799\) | −49.4276 | −1.74862 | ||||||||
\(800\) | −8.53879 | −0.301892 | ||||||||
\(801\) | 15.1968 | 0.536951 | ||||||||
\(802\) | 99.4542 | 3.51185 | ||||||||
\(803\) | 14.2129 | 0.501563 | ||||||||
\(804\) | 22.2037 | 0.783065 | ||||||||
\(805\) | −0.0692417 | −0.00244045 | ||||||||
\(806\) | 32.5441 | 1.14632 | ||||||||
\(807\) | −17.2677 | −0.607850 | ||||||||
\(808\) | −77.1779 | −2.71511 | ||||||||
\(809\) | −12.5391 | −0.440852 | −0.220426 | − | 0.975404i | \(-0.570745\pi\) | ||||
−0.220426 | + | 0.975404i | \(0.570745\pi\) | |||||||
\(810\) | 2.58874 | 0.0909590 | ||||||||
\(811\) | −8.27697 | −0.290644 | −0.145322 | − | 0.989384i | \(-0.546422\pi\) | ||||
−0.145322 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(812\) | −3.30678 | −0.116045 | ||||||||
\(813\) | 15.7051 | 0.550802 | ||||||||
\(814\) | 20.5806 | 0.721350 | ||||||||
\(815\) | −2.32128 | −0.0813109 | ||||||||
\(816\) | −32.2094 | −1.12755 | ||||||||
\(817\) | 17.6585 | 0.617791 | ||||||||
\(818\) | 3.04817 | 0.106577 | ||||||||
\(819\) | 2.40490 | 0.0840339 | ||||||||
\(820\) | −10.8970 | −0.380538 | ||||||||
\(821\) | 50.1133 | 1.74897 | 0.874483 | − | 0.485056i | \(-0.161201\pi\) | ||||
0.874483 | + | 0.485056i | \(0.161201\pi\) | |||||||
\(822\) | −24.3422 | −0.849032 | ||||||||
\(823\) | −52.3851 | −1.82603 | −0.913014 | − | 0.407927i | \(-0.866252\pi\) | ||||
−0.913014 | + | 0.407927i | \(0.866252\pi\) | |||||||
\(824\) | 19.8746 | 0.692366 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −11.5824 | −0.403002 | ||||||||
\(827\) | 27.7003 | 0.963234 | 0.481617 | − | 0.876382i | \(-0.340050\pi\) | ||||
0.481617 | + | 0.876382i | \(0.340050\pi\) | |||||||
\(828\) | −0.325544 | −0.0113134 | ||||||||
\(829\) | −7.51970 | −0.261170 | −0.130585 | − | 0.991437i | \(-0.541686\pi\) | ||||
−0.130585 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(830\) | 14.4014 | 0.499878 | ||||||||
\(831\) | 15.9837 | 0.554469 | ||||||||
\(832\) | −11.3068 | −0.391992 | ||||||||
\(833\) | −3.70156 | −0.128252 | ||||||||
\(834\) | −58.2296 | −2.01633 | ||||||||
\(835\) | −17.7581 | −0.614544 | ||||||||
\(836\) | −19.5416 | −0.675861 | ||||||||
\(837\) | 5.22742 | 0.180686 | ||||||||
\(838\) | 96.4524 | 3.33189 | ||||||||
\(839\) | −41.0385 | −1.41681 | −0.708403 | − | 0.705809i | \(-0.750584\pi\) | ||||
−0.708403 | + | 0.705809i | \(0.750584\pi\) | |||||||
\(840\) | −6.99364 | −0.241303 | ||||||||
\(841\) | −28.5053 | −0.982942 | ||||||||
\(842\) | −8.03722 | −0.276981 | ||||||||
\(843\) | −5.50302 | −0.189534 | ||||||||
\(844\) | −113.839 | −3.91848 | ||||||||
\(845\) | 7.21647 | 0.248254 | ||||||||
\(846\) | −34.5679 | −1.18847 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −74.0621 | −2.54330 | ||||||||
\(849\) | −8.09208 | −0.277720 | ||||||||
\(850\) | 9.58237 | 0.328673 | ||||||||
\(851\) | −0.550475 | −0.0188700 | ||||||||
\(852\) | 20.7099 | 0.709509 | ||||||||
\(853\) | 42.8693 | 1.46782 | 0.733909 | − | 0.679248i | \(-0.237694\pi\) | ||||
0.733909 | + | 0.679248i | \(0.237694\pi\) | |||||||
\(854\) | 12.9982 | 0.444790 | ||||||||
\(855\) | −4.15641 | −0.142146 | ||||||||
\(856\) | 107.399 | 3.67083 | ||||||||
\(857\) | 18.7354 | 0.639988 | 0.319994 | − | 0.947420i | \(-0.396319\pi\) | ||||
0.319994 | + | 0.947420i | \(0.396319\pi\) | |||||||
\(858\) | −6.22565 | −0.212540 | ||||||||
\(859\) | −47.5569 | −1.62262 | −0.811310 | − | 0.584616i | \(-0.801245\pi\) | ||||
−0.811310 | + | 0.584616i | \(0.801245\pi\) | |||||||
\(860\) | −19.9745 | −0.681126 | ||||||||
\(861\) | −2.31773 | −0.0789881 | ||||||||
\(862\) | 35.0649 | 1.19431 | ||||||||
\(863\) | −49.6177 | −1.68901 | −0.844503 | − | 0.535551i | \(-0.820104\pi\) | ||||
−0.844503 | + | 0.535551i | \(0.820104\pi\) | |||||||
\(864\) | −8.53879 | −0.290496 | ||||||||
\(865\) | −20.2094 | −0.687139 | ||||||||
\(866\) | 87.4744 | 2.97250 | ||||||||
\(867\) | −3.29844 | −0.112021 | ||||||||
\(868\) | −24.5771 | −0.834200 | ||||||||
\(869\) | 4.40490 | 0.149426 | ||||||||
\(870\) | 1.82075 | 0.0617293 | ||||||||
\(871\) | −11.3574 | −0.384832 | ||||||||
\(872\) | −89.9364 | −3.04563 | ||||||||
\(873\) | −8.24494 | −0.279049 | ||||||||
\(874\) | 0.745030 | 0.0252010 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −66.8229 | −2.25774 | ||||||||
\(877\) | 29.0962 | 0.982510 | 0.491255 | − | 0.871016i | \(-0.336538\pi\) | ||||
0.491255 | + | 0.871016i | \(0.336538\pi\) | |||||||
\(878\) | −30.0429 | −1.01390 | ||||||||
\(879\) | 6.51490 | 0.219742 | ||||||||
\(880\) | 8.70156 | 0.293330 | ||||||||
\(881\) | 10.8454 | 0.365390 | 0.182695 | − | 0.983170i | \(-0.441518\pi\) | ||||
0.182695 | + | 0.983170i | \(0.441518\pi\) | |||||||
\(882\) | −2.58874 | −0.0871673 | ||||||||
\(883\) | 12.4000 | 0.417293 | 0.208646 | − | 0.977991i | \(-0.433094\pi\) | ||||
0.208646 | + | 0.977991i | \(0.433094\pi\) | |||||||
\(884\) | 41.8527 | 1.40766 | ||||||||
\(885\) | 4.47414 | 0.150397 | ||||||||
\(886\) | 64.0004 | 2.15014 | ||||||||
\(887\) | 19.7823 | 0.664224 | 0.332112 | − | 0.943240i | \(-0.392239\pi\) | ||||
0.332112 | + | 0.943240i | \(0.392239\pi\) | |||||||
\(888\) | −55.5998 | −1.86581 | ||||||||
\(889\) | 0.248490 | 0.00833410 | ||||||||
\(890\) | 39.3404 | 1.31869 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 39.4319 | 1.32028 | ||||||||
\(893\) | 55.5012 | 1.85728 | ||||||||
\(894\) | 35.9837 | 1.20348 | ||||||||
\(895\) | 5.95005 | 0.198888 | ||||||||
\(896\) | −4.90647 | −0.163914 | ||||||||
\(897\) | 0.166519 | 0.00555992 | ||||||||
\(898\) | −81.6164 | −2.72358 | ||||||||
\(899\) | 3.67663 | 0.122623 | ||||||||
\(900\) | 4.70156 | 0.156719 | ||||||||
\(901\) | 31.5053 | 1.04959 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | −4.24849 | −0.141381 | ||||||||
\(904\) | −115.474 | −3.84062 | ||||||||
\(905\) | 5.54161 | 0.184209 | ||||||||
\(906\) | −7.64150 | −0.253872 | ||||||||
\(907\) | −9.96278 | −0.330809 | −0.165404 | − | 0.986226i | \(-0.552893\pi\) | ||||
−0.165404 | + | 0.986226i | \(0.552893\pi\) | |||||||
\(908\) | 13.1428 | 0.436160 | ||||||||
\(909\) | 11.0354 | 0.366023 | ||||||||
\(910\) | 6.22565 | 0.206378 | ||||||||
\(911\) | 57.6869 | 1.91125 | 0.955627 | − | 0.294580i | \(-0.0951799\pi\) | ||||
0.955627 | + | 0.294580i | \(0.0951799\pi\) | |||||||
\(912\) | 36.1672 | 1.19762 | ||||||||
\(913\) | −5.56308 | −0.184111 | ||||||||
\(914\) | 34.6564 | 1.14633 | ||||||||
\(915\) | −5.02107 | −0.165991 | ||||||||
\(916\) | 46.7975 | 1.54623 | ||||||||
\(917\) | −12.6178 | −0.416677 | ||||||||
\(918\) | 9.58237 | 0.316265 | ||||||||
\(919\) | 19.2033 | 0.633460 | 0.316730 | − | 0.948516i | \(-0.397415\pi\) | ||||
0.316730 | + | 0.948516i | \(0.397415\pi\) | |||||||
\(920\) | −0.484251 | −0.0159653 | ||||||||
\(921\) | −22.5679 | −0.743637 | ||||||||
\(922\) | −10.0202 | −0.329998 | ||||||||
\(923\) | −10.5933 | −0.348684 | ||||||||
\(924\) | 4.70156 | 0.154670 | ||||||||
\(925\) | 7.95005 | 0.261396 | ||||||||
\(926\) | −75.7163 | −2.48819 | ||||||||
\(927\) | −2.84182 | −0.0933376 | ||||||||
\(928\) | −6.00564 | −0.197145 | ||||||||
\(929\) | 39.9422 | 1.31046 | 0.655231 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655231 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(930\) | 13.5324 | 0.443746 | ||||||||
\(931\) | 4.15641 | 0.136221 | ||||||||
\(932\) | −13.0521 | −0.427536 | ||||||||
\(933\) | 0.0513177 | 0.00168007 | ||||||||
\(934\) | −36.9026 | −1.20749 | ||||||||
\(935\) | −3.70156 | −0.121054 | ||||||||
\(936\) | 16.8190 | 0.549745 | ||||||||
\(937\) | 29.7826 | 0.972954 | 0.486477 | − | 0.873693i | \(-0.338282\pi\) | ||||
0.486477 | + | 0.873693i | \(0.338282\pi\) | |||||||
\(938\) | 12.2256 | 0.399182 | ||||||||
\(939\) | −3.44224 | −0.112333 | ||||||||
\(940\) | −62.7808 | −2.04768 | ||||||||
\(941\) | 26.5208 | 0.864554 | 0.432277 | − | 0.901741i | \(-0.357710\pi\) | ||||
0.432277 | + | 0.901741i | \(0.357710\pi\) | |||||||
\(942\) | −13.3440 | −0.434771 | ||||||||
\(943\) | −0.160484 | −0.00522607 | ||||||||
\(944\) | −38.9320 | −1.26713 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 10.9982 | 0.357583 | ||||||||
\(947\) | −34.6659 | −1.12649 | −0.563245 | − | 0.826290i | \(-0.690447\pi\) | ||||
−0.563245 | + | 0.826290i | \(0.690447\pi\) | |||||||
\(948\) | −20.7099 | −0.672626 | ||||||||
\(949\) | 34.1806 | 1.10955 | ||||||||
\(950\) | −10.7598 | −0.349096 | ||||||||
\(951\) | 31.6582 | 1.02659 | ||||||||
\(952\) | −25.8874 | −0.839015 | ||||||||
\(953\) | −31.9451 | −1.03480 | −0.517402 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517402 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(954\) | 22.0337 | 0.713366 | ||||||||
\(955\) | −25.8966 | −0.837993 | ||||||||
\(956\) | −68.6590 | −2.22059 | ||||||||
\(957\) | −0.703336 | −0.0227356 | ||||||||
\(958\) | 83.4450 | 2.69599 | ||||||||
\(959\) | −9.40312 | −0.303643 | ||||||||
\(960\) | −4.70156 | −0.151742 | ||||||||
\(961\) | −3.67405 | −0.118518 | ||||||||
\(962\) | 49.4942 | 1.59576 | ||||||||
\(963\) | −15.3567 | −0.494864 | ||||||||
\(964\) | 49.5472 | 1.59581 | ||||||||
\(965\) | 1.31596 | 0.0423622 | ||||||||
\(966\) | −0.179249 | −0.00576723 | ||||||||
\(967\) | 5.97781 | 0.192233 | 0.0961167 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961167 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(968\) | −6.99364 | −0.224784 | ||||||||
\(969\) | −15.3852 | −0.494244 | ||||||||
\(970\) | −21.3440 | −0.685314 | ||||||||
\(971\) | −6.61617 | −0.212323 | −0.106161 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106161 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(972\) | 4.70156 | 0.150803 | ||||||||
\(973\) | −22.4934 | −0.721106 | ||||||||
\(974\) | −13.6525 | −0.437456 | ||||||||
\(975\) | −2.40490 | −0.0770184 | ||||||||
\(976\) | 43.6911 | 1.39852 | ||||||||
\(977\) | 14.9276 | 0.477577 | 0.238788 | − | 0.971072i | \(-0.423250\pi\) | ||||
0.238788 | + | 0.971072i | \(0.423250\pi\) | |||||||
\(978\) | −6.00918 | −0.192152 | ||||||||
\(979\) | −15.1968 | −0.485691 | ||||||||
\(980\) | −4.70156 | −0.150186 | ||||||||
\(981\) | 12.8597 | 0.410580 | ||||||||
\(982\) | −92.3267 | −2.94626 | ||||||||
\(983\) | −15.6774 | −0.500030 | −0.250015 | − | 0.968242i | \(-0.580436\pi\) | ||||
−0.250015 | + | 0.968242i | \(0.580436\pi\) | |||||||
\(984\) | −16.2094 | −0.516736 | ||||||||
\(985\) | 4.44212 | 0.141538 | ||||||||
\(986\) | 6.73962 | 0.214633 | ||||||||
\(987\) | −13.3532 | −0.425036 | ||||||||
\(988\) | −46.9956 | −1.49513 | ||||||||
\(989\) | −0.294173 | −0.00935415 | ||||||||
\(990\) | −2.58874 | −0.0822755 | ||||||||
\(991\) | −33.8504 | −1.07529 | −0.537647 | − | 0.843170i | \(-0.680687\pi\) | ||||
−0.537647 | + | 0.843170i | \(0.680687\pi\) | |||||||
\(992\) | −44.6359 | −1.41719 | ||||||||
\(993\) | −3.55953 | −0.112958 | ||||||||
\(994\) | 11.4031 | 0.361685 | ||||||||
\(995\) | 25.7453 | 0.816182 | ||||||||
\(996\) | 26.1552 | 0.828758 | ||||||||
\(997\) | −6.45130 | −0.204315 | −0.102157 | − | 0.994768i | \(-0.532575\pi\) | ||||
−0.102157 | + | 0.994768i | \(0.532575\pi\) | |||||||
\(998\) | 100.982 | 3.19654 | ||||||||
\(999\) | 7.95005 | 0.251529 |
(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 | 1155.2.a.u.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 3465.2.a.bl.1.4 | 4 | |||
5.4 | even | 2 | 5775.2.a.bz.1.4 | 4 | |||
7.6 | odd | 2 | 8085.2.a.bn.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.u.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3465.2.a.bl.1.4 | 4 | 3.2 | odd | 2 | |||
5775.2.a.bz.1.4 | 4 | 5.4 | even | 2 | |||
8085.2.a.bn.1.1 | 4 | 7.6 | odd | 2 |