Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1002,2,Mod(1,1002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1002, 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("1002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1002 = 2 \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1002.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: | \(8.00101028253\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2777.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.679643\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.416566 | 0.186294 | 0.0931469 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931469 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.65960 | 1.76116 | 0.880582 | − | 0.473893i | \(-0.157152\pi\) | ||||
0.880582 | + | 0.473893i | \(0.157152\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.416566 | 0.131730 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.283116 | 0.0785223 | 0.0392611 | − | 0.999229i | \(-0.487500\pi\) | ||||
0.0392611 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(14\) | 4.65960 | 1.24533 | ||||||||
\(15\) | −0.416566 | −0.107557 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.640714 | 0.155396 | 0.0776979 | − | 0.996977i | \(-0.475243\pi\) | ||||
0.0776979 | + | 0.996977i | \(0.475243\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −5.88544 | −1.35021 | −0.675106 | − | 0.737720i | \(-0.735902\pi\) | ||||
−0.675106 | + | 0.737720i | \(0.735902\pi\) | |||||||
\(20\) | 0.416566 | 0.0931469 | ||||||||
\(21\) | −4.65960 | −1.01681 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.88544 | 1.22720 | 0.613600 | − | 0.789617i | \(-0.289721\pi\) | ||||
0.613600 | + | 0.789617i | \(0.289721\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.82647 | −0.965295 | ||||||||
\(26\) | 0.283116 | 0.0555236 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.65960 | 0.880582 | ||||||||
\(29\) | 5.16687 | 0.959463 | 0.479732 | − | 0.877415i | \(-0.340734\pi\) | ||||
0.479732 | + | 0.877415i | \(0.340734\pi\) | |||||||
\(30\) | −0.416566 | −0.0760542 | ||||||||
\(31\) | 1.22584 | 0.220167 | 0.110083 | − | 0.993922i | \(-0.464888\pi\) | ||||
0.110083 | + | 0.993922i | \(0.464888\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.640714 | 0.109881 | ||||||||
\(35\) | 1.94103 | 0.328094 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.82816 | −1.12254 | −0.561271 | − | 0.827632i | \(-0.689688\pi\) | ||||
−0.561271 | + | 0.827632i | \(0.689688\pi\) | |||||||
\(38\) | −5.88544 | −0.954745 | ||||||||
\(39\) | −0.283116 | −0.0453349 | ||||||||
\(40\) | 0.416566 | 0.0658648 | ||||||||
\(41\) | 12.4116 | 1.93837 | 0.969183 | − | 0.246343i | \(-0.0792288\pi\) | ||||
0.969183 | + | 0.246343i | \(0.0792288\pi\) | |||||||
\(42\) | −4.65960 | −0.718993 | ||||||||
\(43\) | −3.07617 | −0.469112 | −0.234556 | − | 0.972103i | \(-0.575364\pi\) | ||||
−0.234556 | + | 0.972103i | \(0.575364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.416566 | 0.0620980 | ||||||||
\(46\) | 5.88544 | 0.867761 | ||||||||
\(47\) | 7.82647 | 1.14161 | 0.570804 | − | 0.821086i | \(-0.306632\pi\) | ||||
0.570804 | + | 0.821086i | \(0.306632\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 14.7119 | 2.10170 | ||||||||
\(50\) | −4.82647 | −0.682566 | ||||||||
\(51\) | −0.640714 | −0.0897179 | ||||||||
\(52\) | 0.283116 | 0.0392611 | ||||||||
\(53\) | −5.46888 | −0.751208 | −0.375604 | − | 0.926780i | \(-0.622565\pi\) | ||||
−0.375604 | + | 0.926780i | \(0.622565\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.65960 | 0.622666 | ||||||||
\(57\) | 5.88544 | 0.779546 | ||||||||
\(58\) | 5.16687 | 0.678443 | ||||||||
\(59\) | 3.20962 | 0.417857 | 0.208928 | − | 0.977931i | \(-0.433002\pi\) | ||||
0.208928 | + | 0.977931i | \(0.433002\pi\) | |||||||
\(60\) | −0.416566 | −0.0537784 | ||||||||
\(61\) | −1.16687 | −0.149402 | −0.0747011 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747011 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(62\) | 1.22584 | 0.155681 | ||||||||
\(63\) | 4.65960 | 0.587055 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.117936 | 0.0146282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.29863 | −0.280822 | −0.140411 | − | 0.990093i | \(-0.544842\pi\) | ||||
−0.140411 | + | 0.990093i | \(0.544842\pi\) | |||||||
\(68\) | 0.640714 | 0.0776979 | ||||||||
\(69\) | −5.88544 | −0.708524 | ||||||||
\(70\) | 1.94103 | 0.231998 | ||||||||
\(71\) | −8.60401 | −1.02111 | −0.510554 | − | 0.859846i | \(-0.670560\pi\) | ||||
−0.510554 | + | 0.859846i | \(0.670560\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.26690 | 0.265321 | 0.132660 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132660 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(74\) | −6.82816 | −0.793758 | ||||||||
\(75\) | 4.82647 | 0.557313 | ||||||||
\(76\) | −5.88544 | −0.675106 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.283116 | −0.0320566 | ||||||||
\(79\) | −7.69302 | −0.865533 | −0.432766 | − | 0.901506i | \(-0.642462\pi\) | ||||
−0.432766 | + | 0.901506i | \(0.642462\pi\) | |||||||
\(80\) | 0.416566 | 0.0465735 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.4116 | 1.37063 | ||||||||
\(83\) | 9.27646 | 1.01822 | 0.509112 | − | 0.860700i | \(-0.329974\pi\) | ||||
0.509112 | + | 0.860700i | \(0.329974\pi\) | |||||||
\(84\) | −4.65960 | −0.508405 | ||||||||
\(85\) | 0.266899 | 0.0289493 | ||||||||
\(86\) | −3.07617 | −0.331712 | ||||||||
\(87\) | −5.16687 | −0.553946 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.94103 | 0.417749 | 0.208874 | − | 0.977943i | \(-0.433020\pi\) | ||||
0.208874 | + | 0.977943i | \(0.433020\pi\) | |||||||
\(90\) | 0.416566 | 0.0439099 | ||||||||
\(91\) | 1.31921 | 0.138291 | ||||||||
\(92\) | 5.88544 | 0.613600 | ||||||||
\(93\) | −1.22584 | −0.127113 | ||||||||
\(94\) | 7.82647 | 0.807239 | ||||||||
\(95\) | −2.45167 | −0.251536 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.99334 | 0.913135 | 0.456568 | − | 0.889689i | \(-0.349079\pi\) | ||||
0.456568 | + | 0.889689i | \(0.349079\pi\) | |||||||
\(98\) | 14.7119 | 1.48613 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.82647 | −0.482647 | ||||||||
\(101\) | −12.3364 | −1.22752 | −0.613759 | − | 0.789493i | \(-0.710344\pi\) | ||||
−0.613759 | + | 0.789493i | \(0.710344\pi\) | |||||||
\(102\) | −0.640714 | −0.0634401 | ||||||||
\(103\) | −12.3448 | −1.21637 | −0.608183 | − | 0.793797i | \(-0.708101\pi\) | ||||
−0.608183 | + | 0.793797i | \(0.708101\pi\) | |||||||
\(104\) | 0.283116 | 0.0277618 | ||||||||
\(105\) | −1.94103 | −0.189425 | ||||||||
\(106\) | −5.46888 | −0.531184 | ||||||||
\(107\) | −19.0867 | −1.84518 | −0.922591 | − | 0.385779i | \(-0.873933\pi\) | ||||
−0.922591 | + | 0.385779i | \(0.873933\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 17.2553 | 1.65276 | 0.826378 | − | 0.563116i | \(-0.190398\pi\) | ||||
0.826378 | + | 0.563116i | \(0.190398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.82816 | 0.648100 | ||||||||
\(112\) | 4.65960 | 0.440291 | ||||||||
\(113\) | 2.91099 | 0.273843 | 0.136921 | − | 0.990582i | \(-0.456279\pi\) | ||||
0.136921 | + | 0.990582i | \(0.456279\pi\) | |||||||
\(114\) | 5.88544 | 0.551222 | ||||||||
\(115\) | 2.45167 | 0.228620 | ||||||||
\(116\) | 5.16687 | 0.479732 | ||||||||
\(117\) | 0.283116 | 0.0261741 | ||||||||
\(118\) | 3.20962 | 0.295469 | ||||||||
\(119\) | 2.98547 | 0.273678 | ||||||||
\(120\) | −0.416566 | −0.0380271 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −1.16687 | −0.105643 | ||||||||
\(123\) | −12.4116 | −1.11912 | ||||||||
\(124\) | 1.22584 | 0.110083 | ||||||||
\(125\) | −4.09337 | −0.366122 | ||||||||
\(126\) | 4.65960 | 0.415111 | ||||||||
\(127\) | −21.2636 | −1.88684 | −0.943421 | − | 0.331599i | \(-0.892412\pi\) | ||||
−0.943421 | + | 0.331599i | \(0.892412\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.07617 | 0.270842 | ||||||||
\(130\) | 0.117936 | 0.0103437 | ||||||||
\(131\) | −14.2030 | −1.24092 | −0.620459 | − | 0.784239i | \(-0.713054\pi\) | ||||
−0.620459 | + | 0.784239i | \(0.713054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.4238 | −2.37795 | ||||||||
\(134\) | −2.29863 | −0.198571 | ||||||||
\(135\) | −0.416566 | −0.0358523 | ||||||||
\(136\) | 0.640714 | 0.0549407 | ||||||||
\(137\) | −10.5484 | −0.901213 | −0.450606 | − | 0.892723i | \(-0.648792\pi\) | ||||
−0.450606 | + | 0.892723i | \(0.648792\pi\) | |||||||
\(138\) | −5.88544 | −0.501002 | ||||||||
\(139\) | 11.9550 | 1.01401 | 0.507003 | − | 0.861944i | \(-0.330753\pi\) | ||||
0.507003 | + | 0.861944i | \(0.330753\pi\) | |||||||
\(140\) | 1.94103 | 0.164047 | ||||||||
\(141\) | −7.82647 | −0.659108 | ||||||||
\(142\) | −8.60401 | −0.722033 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.15234 | 0.178742 | ||||||||
\(146\) | 2.26690 | 0.187610 | ||||||||
\(147\) | −14.7119 | −1.21342 | ||||||||
\(148\) | −6.82816 | −0.561271 | ||||||||
\(149\) | 3.58343 | 0.293566 | 0.146783 | − | 0.989169i | \(-0.453108\pi\) | ||||
0.146783 | + | 0.989169i | \(0.453108\pi\) | |||||||
\(150\) | 4.82647 | 0.394080 | ||||||||
\(151\) | −3.74074 | −0.304417 | −0.152209 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152209 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(152\) | −5.88544 | −0.477372 | ||||||||
\(153\) | 0.640714 | 0.0517986 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.510642 | 0.0410157 | ||||||||
\(156\) | −0.283116 | −0.0226674 | ||||||||
\(157\) | −13.7709 | −1.09904 | −0.549518 | − | 0.835482i | \(-0.685189\pi\) | ||||
−0.549518 | + | 0.835482i | \(0.685189\pi\) | |||||||
\(158\) | −7.69302 | −0.612024 | ||||||||
\(159\) | 5.46888 | 0.433710 | ||||||||
\(160\) | 0.416566 | 0.0329324 | ||||||||
\(161\) | 27.4238 | 2.16130 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 11.2398 | 0.880366 | 0.440183 | − | 0.897908i | \(-0.354914\pi\) | ||||
0.440183 | + | 0.897908i | \(0.354914\pi\) | |||||||
\(164\) | 12.4116 | 0.969183 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.27646 | 0.719993 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | −4.65960 | −0.359496 | ||||||||
\(169\) | −12.9198 | −0.993834 | ||||||||
\(170\) | 0.266899 | 0.0204702 | ||||||||
\(171\) | −5.88544 | −0.450071 | ||||||||
\(172\) | −3.07617 | −0.234556 | ||||||||
\(173\) | 1.16687 | 0.0887154 | 0.0443577 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443577 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(174\) | −5.16687 | −0.391699 | ||||||||
\(175\) | −22.4895 | −1.70004 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.20962 | −0.241250 | ||||||||
\(178\) | 3.94103 | 0.295393 | ||||||||
\(179\) | 7.77088 | 0.580823 | 0.290412 | − | 0.956902i | \(-0.406208\pi\) | ||||
0.290412 | + | 0.956902i | \(0.406208\pi\) | |||||||
\(180\) | 0.416566 | 0.0310490 | ||||||||
\(181\) | 10.2570 | 0.762394 | 0.381197 | − | 0.924494i | \(-0.375512\pi\) | ||||
0.381197 | + | 0.924494i | \(0.375512\pi\) | |||||||
\(182\) | 1.31921 | 0.0977863 | ||||||||
\(183\) | 1.16687 | 0.0862574 | ||||||||
\(184\) | 5.88544 | 0.433880 | ||||||||
\(185\) | −2.84438 | −0.209123 | ||||||||
\(186\) | −1.22584 | −0.0898827 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.82647 | 0.570804 | ||||||||
\(189\) | −4.65960 | −0.338936 | ||||||||
\(190\) | −2.45167 | −0.177863 | ||||||||
\(191\) | −13.5630 | −0.981381 | −0.490690 | − | 0.871334i | \(-0.663255\pi\) | ||||
−0.490690 | + | 0.871334i | \(0.663255\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −2.56623 | −0.184721 | −0.0923607 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923607 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(194\) | 8.99334 | 0.645684 | ||||||||
\(195\) | −0.117936 | −0.00844561 | ||||||||
\(196\) | 14.7119 | 1.05085 | ||||||||
\(197\) | −2.92383 | −0.208314 | −0.104157 | − | 0.994561i | \(-0.533214\pi\) | ||||
−0.104157 | + | 0.994561i | \(0.533214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.43377 | −0.243413 | −0.121707 | − | 0.992566i | \(-0.538837\pi\) | ||||
−0.121707 | + | 0.992566i | \(0.538837\pi\) | |||||||
\(200\) | −4.82647 | −0.341283 | ||||||||
\(201\) | 2.29863 | 0.162133 | ||||||||
\(202\) | −12.3364 | −0.867987 | ||||||||
\(203\) | 24.0756 | 1.68977 | ||||||||
\(204\) | −0.640714 | −0.0448589 | ||||||||
\(205\) | 5.17025 | 0.361106 | ||||||||
\(206\) | −12.3448 | −0.860100 | ||||||||
\(207\) | 5.88544 | 0.409066 | ||||||||
\(208\) | 0.283116 | 0.0196306 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.94103 | −0.133944 | ||||||||
\(211\) | −21.8854 | −1.50666 | −0.753328 | − | 0.657645i | \(-0.771553\pi\) | ||||
−0.753328 | + | 0.657645i | \(0.771553\pi\) | |||||||
\(212\) | −5.46888 | −0.375604 | ||||||||
\(213\) | 8.60401 | 0.589537 | ||||||||
\(214\) | −19.0867 | −1.30474 | ||||||||
\(215\) | −1.28143 | −0.0873926 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.71191 | 0.387750 | ||||||||
\(218\) | 17.2553 | 1.16867 | ||||||||
\(219\) | −2.26690 | −0.153183 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.181396 | 0.0122020 | ||||||||
\(222\) | 6.82816 | 0.458276 | ||||||||
\(223\) | −4.65960 | −0.312030 | −0.156015 | − | 0.987755i | \(-0.549865\pi\) | ||||
−0.156015 | + | 0.987755i | \(0.549865\pi\) | |||||||
\(224\) | 4.65960 | 0.311333 | ||||||||
\(225\) | −4.82647 | −0.321765 | ||||||||
\(226\) | 2.91099 | 0.193636 | ||||||||
\(227\) | −22.4467 | −1.48984 | −0.744920 | − | 0.667154i | \(-0.767512\pi\) | ||||
−0.744920 | + | 0.667154i | \(0.767512\pi\) | |||||||
\(228\) | 5.88544 | 0.389773 | ||||||||
\(229\) | 12.3715 | 0.817533 | 0.408766 | − | 0.912639i | \(-0.365959\pi\) | ||||
0.408766 | + | 0.912639i | \(0.365959\pi\) | |||||||
\(230\) | 2.45167 | 0.161659 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.16687 | 0.339222 | ||||||||
\(233\) | 19.5940 | 1.28364 | 0.641822 | − | 0.766854i | \(-0.278179\pi\) | ||||
0.641822 | + | 0.766854i | \(0.278179\pi\) | |||||||
\(234\) | 0.283116 | 0.0185079 | ||||||||
\(235\) | 3.26024 | 0.212675 | ||||||||
\(236\) | 3.20962 | 0.208928 | ||||||||
\(237\) | 7.69302 | 0.499716 | ||||||||
\(238\) | 2.98547 | 0.193519 | ||||||||
\(239\) | 3.43377 | 0.222112 | 0.111056 | − | 0.993814i | \(-0.464577\pi\) | ||||
0.111056 | + | 0.993814i | \(0.464577\pi\) | |||||||
\(240\) | −0.416566 | −0.0268892 | ||||||||
\(241\) | 14.4861 | 0.933130 | 0.466565 | − | 0.884487i | \(-0.345491\pi\) | ||||
0.466565 | + | 0.884487i | \(0.345491\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.16687 | −0.0747011 | ||||||||
\(245\) | 6.12848 | 0.391534 | ||||||||
\(246\) | −12.4116 | −0.791334 | ||||||||
\(247\) | −1.66626 | −0.106022 | ||||||||
\(248\) | 1.22584 | 0.0778407 | ||||||||
\(249\) | −9.27646 | −0.587872 | ||||||||
\(250\) | −4.09337 | −0.258888 | ||||||||
\(251\) | −26.8576 | −1.69524 | −0.847618 | − | 0.530607i | \(-0.821964\pi\) | ||||
−0.847618 | + | 0.530607i | \(0.821964\pi\) | |||||||
\(252\) | 4.65960 | 0.293527 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −21.2636 | −1.33420 | ||||||||
\(255\) | −0.266899 | −0.0167139 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.57846 | −0.223218 | −0.111609 | − | 0.993752i | \(-0.535600\pi\) | ||||
−0.111609 | + | 0.993752i | \(0.535600\pi\) | |||||||
\(258\) | 3.07617 | 0.191514 | ||||||||
\(259\) | −31.8165 | −1.97698 | ||||||||
\(260\) | 0.117936 | 0.00731411 | ||||||||
\(261\) | 5.16687 | 0.319821 | ||||||||
\(262\) | −14.2030 | −0.877462 | ||||||||
\(263\) | 5.52517 | 0.340697 | 0.170348 | − | 0.985384i | \(-0.445511\pi\) | ||||
0.170348 | + | 0.985384i | \(0.445511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.27815 | −0.139945 | ||||||||
\(266\) | −27.4238 | −1.68146 | ||||||||
\(267\) | −3.94103 | −0.241187 | ||||||||
\(268\) | −2.29863 | −0.140411 | ||||||||
\(269\) | 29.0039 | 1.76840 | 0.884199 | − | 0.467110i | \(-0.154705\pi\) | ||||
0.884199 | + | 0.467110i | \(0.154705\pi\) | |||||||
\(270\) | −0.416566 | −0.0253514 | ||||||||
\(271\) | −24.0301 | −1.45973 | −0.729863 | − | 0.683593i | \(-0.760416\pi\) | ||||
−0.729863 | + | 0.683593i | \(0.760416\pi\) | |||||||
\(272\) | 0.640714 | 0.0388490 | ||||||||
\(273\) | −1.31921 | −0.0798422 | ||||||||
\(274\) | −10.5484 | −0.637254 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.88544 | −0.354262 | ||||||||
\(277\) | 2.99382 | 0.179881 | 0.0899406 | − | 0.995947i | \(-0.471332\pi\) | ||||
0.0899406 | + | 0.995947i | \(0.471332\pi\) | |||||||
\(278\) | 11.9550 | 0.717010 | ||||||||
\(279\) | 1.22584 | 0.0733889 | ||||||||
\(280\) | 1.94103 | 0.115999 | ||||||||
\(281\) | 1.72523 | 0.102919 | 0.0514593 | − | 0.998675i | \(-0.483613\pi\) | ||||
0.0514593 | + | 0.998675i | \(0.483613\pi\) | |||||||
\(282\) | −7.82647 | −0.466060 | ||||||||
\(283\) | 18.5372 | 1.10192 | 0.550960 | − | 0.834531i | \(-0.314262\pi\) | ||||
0.550960 | + | 0.834531i | \(0.314262\pi\) | |||||||
\(284\) | −8.60401 | −0.510554 | ||||||||
\(285\) | 2.45167 | 0.145225 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 57.8331 | 3.41378 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.5895 | −0.975852 | ||||||||
\(290\) | 2.15234 | 0.126390 | ||||||||
\(291\) | −8.99334 | −0.527199 | ||||||||
\(292\) | 2.26690 | 0.132660 | ||||||||
\(293\) | 14.8331 | 0.866561 | 0.433280 | − | 0.901259i | \(-0.357356\pi\) | ||||
0.433280 | + | 0.901259i | \(0.357356\pi\) | |||||||
\(294\) | −14.7119 | −0.858016 | ||||||||
\(295\) | 1.33702 | 0.0778442 | ||||||||
\(296\) | −6.82816 | −0.396879 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.58343 | 0.207583 | ||||||||
\(299\) | 1.66626 | 0.0963625 | ||||||||
\(300\) | 4.82647 | 0.278657 | ||||||||
\(301\) | −14.3337 | −0.826183 | ||||||||
\(302\) | −3.74074 | −0.215256 | ||||||||
\(303\) | 12.3364 | 0.708708 | ||||||||
\(304\) | −5.88544 | −0.337553 | ||||||||
\(305\) | −0.486077 | −0.0278327 | ||||||||
\(306\) | 0.640714 | 0.0366272 | ||||||||
\(307\) | −31.9927 | −1.82592 | −0.912961 | − | 0.408047i | \(-0.866210\pi\) | ||||
−0.912961 | + | 0.408047i | \(0.866210\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3448 | 0.702269 | ||||||||
\(310\) | 0.510642 | 0.0290025 | ||||||||
\(311\) | −7.07884 | −0.401404 | −0.200702 | − | 0.979652i | \(-0.564322\pi\) | ||||
−0.200702 | + | 0.979652i | \(0.564322\pi\) | |||||||
\(312\) | −0.283116 | −0.0160283 | ||||||||
\(313\) | 23.6496 | 1.33675 | 0.668376 | − | 0.743823i | \(-0.266990\pi\) | ||||
0.668376 | + | 0.743823i | \(0.266990\pi\) | |||||||
\(314\) | −13.7709 | −0.777136 | ||||||||
\(315\) | 1.94103 | 0.109365 | ||||||||
\(316\) | −7.69302 | −0.432766 | ||||||||
\(317\) | −13.7007 | −0.769506 | −0.384753 | − | 0.923020i | \(-0.625713\pi\) | ||||
−0.384753 | + | 0.923020i | \(0.625713\pi\) | |||||||
\(318\) | 5.46888 | 0.306679 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.416566 | 0.0232867 | ||||||||
\(321\) | 19.0867 | 1.06532 | ||||||||
\(322\) | 27.4238 | 1.52827 | ||||||||
\(323\) | −3.77088 | −0.209818 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.36645 | −0.0757971 | ||||||||
\(326\) | 11.2398 | 0.622513 | ||||||||
\(327\) | −17.2553 | −0.954219 | ||||||||
\(328\) | 12.4116 | 0.685316 | ||||||||
\(329\) | 36.4683 | 2.01056 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.40991 | −0.517215 | −0.258608 | − | 0.965982i | \(-0.583264\pi\) | ||||
−0.258608 | + | 0.965982i | \(0.583264\pi\) | |||||||
\(332\) | 9.27646 | 0.509112 | ||||||||
\(333\) | −6.82816 | −0.374181 | ||||||||
\(334\) | −1.00000 | −0.0547176 | ||||||||
\(335\) | −0.957530 | −0.0523155 | ||||||||
\(336\) | −4.65960 | −0.254202 | ||||||||
\(337\) | 21.9345 | 1.19485 | 0.597423 | − | 0.801926i | \(-0.296191\pi\) | ||||
0.597423 | + | 0.801926i | \(0.296191\pi\) | |||||||
\(338\) | −12.9198 | −0.702747 | ||||||||
\(339\) | −2.91099 | −0.158103 | ||||||||
\(340\) | 0.266899 | 0.0144747 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.88544 | −0.318248 | ||||||||
\(343\) | 35.9345 | 1.94028 | ||||||||
\(344\) | −3.07617 | −0.165856 | ||||||||
\(345\) | −2.45167 | −0.131994 | ||||||||
\(346\) | 1.16687 | 0.0627312 | ||||||||
\(347\) | 16.6468 | 0.893645 | 0.446823 | − | 0.894623i | \(-0.352556\pi\) | ||||
0.446823 | + | 0.894623i | \(0.352556\pi\) | |||||||
\(348\) | −5.16687 | −0.276973 | ||||||||
\(349\) | 4.49442 | 0.240581 | 0.120291 | − | 0.992739i | \(-0.461617\pi\) | ||||
0.120291 | + | 0.992739i | \(0.461617\pi\) | |||||||
\(350\) | −22.4895 | −1.20211 | ||||||||
\(351\) | −0.283116 | −0.0151116 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.72523 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(354\) | −3.20962 | −0.170589 | ||||||||
\(355\) | −3.58414 | −0.190226 | ||||||||
\(356\) | 3.94103 | 0.208874 | ||||||||
\(357\) | −2.98547 | −0.158008 | ||||||||
\(358\) | 7.77088 | 0.410704 | ||||||||
\(359\) | −9.61854 | −0.507647 | −0.253824 | − | 0.967251i | \(-0.581688\pi\) | ||||
−0.253824 | + | 0.967251i | \(0.581688\pi\) | |||||||
\(360\) | 0.416566 | 0.0219549 | ||||||||
\(361\) | 15.6384 | 0.823075 | ||||||||
\(362\) | 10.2570 | 0.539094 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 1.31921 | 0.0691453 | ||||||||
\(365\) | 0.944313 | 0.0494276 | ||||||||
\(366\) | 1.16687 | 0.0609932 | ||||||||
\(367\) | 14.1523 | 0.738746 | 0.369373 | − | 0.929281i | \(-0.379572\pi\) | ||||
0.369373 | + | 0.929281i | \(0.379572\pi\) | |||||||
\(368\) | 5.88544 | 0.306800 | ||||||||
\(369\) | 12.4116 | 0.646122 | ||||||||
\(370\) | −2.84438 | −0.147872 | ||||||||
\(371\) | −25.4828 | −1.32300 | ||||||||
\(372\) | −1.22584 | −0.0635567 | ||||||||
\(373\) | −28.1149 | −1.45574 | −0.727868 | − | 0.685717i | \(-0.759489\pi\) | ||||
−0.727868 | + | 0.685717i | \(0.759489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.09337 | 0.211381 | ||||||||
\(376\) | 7.82647 | 0.403620 | ||||||||
\(377\) | 1.46282 | 0.0753392 | ||||||||
\(378\) | −4.65960 | −0.239664 | ||||||||
\(379\) | 16.5212 | 0.848636 | 0.424318 | − | 0.905513i | \(-0.360514\pi\) | ||||
0.424318 | + | 0.905513i | \(0.360514\pi\) | |||||||
\(380\) | −2.45167 | −0.125768 | ||||||||
\(381\) | 21.2636 | 1.08937 | ||||||||
\(382\) | −13.5630 | −0.693941 | ||||||||
\(383\) | −15.6907 | −0.801759 | −0.400879 | − | 0.916131i | \(-0.631295\pi\) | ||||
−0.400879 | + | 0.916131i | \(0.631295\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.56623 | −0.130618 | ||||||||
\(387\) | −3.07617 | −0.156371 | ||||||||
\(388\) | 8.99334 | 0.456568 | ||||||||
\(389\) | −21.1842 | −1.07408 | −0.537040 | − | 0.843557i | \(-0.680458\pi\) | ||||
−0.537040 | + | 0.843557i | \(0.680458\pi\) | |||||||
\(390\) | −0.117936 | −0.00597195 | ||||||||
\(391\) | 3.77088 | 0.190702 | ||||||||
\(392\) | 14.7119 | 0.743064 | ||||||||
\(393\) | 14.2030 | 0.716445 | ||||||||
\(394\) | −2.92383 | −0.147300 | ||||||||
\(395\) | −3.20465 | −0.161243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.03778 | −0.102273 | −0.0511367 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511367 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(398\) | −3.43377 | −0.172119 | ||||||||
\(399\) | 27.4238 | 1.37291 | ||||||||
\(400\) | −4.82647 | −0.241324 | ||||||||
\(401\) | −11.3971 | −0.569142 | −0.284571 | − | 0.958655i | \(-0.591851\pi\) | ||||
−0.284571 | + | 0.958655i | \(0.591851\pi\) | |||||||
\(402\) | 2.29863 | 0.114645 | ||||||||
\(403\) | 0.347054 | 0.0172880 | ||||||||
\(404\) | −12.3364 | −0.613759 | ||||||||
\(405\) | 0.416566 | 0.0206993 | ||||||||
\(406\) | 24.0756 | 1.19485 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.640714 | −0.0317201 | ||||||||
\(409\) | −18.1012 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(410\) | 5.17025 | 0.255340 | ||||||||
\(411\) | 10.5484 | 0.520315 | ||||||||
\(412\) | −12.3448 | −0.608183 | ||||||||
\(413\) | 14.9556 | 0.735915 | ||||||||
\(414\) | 5.88544 | 0.289254 | ||||||||
\(415\) | 3.86425 | 0.189689 | ||||||||
\(416\) | 0.283116 | 0.0138809 | ||||||||
\(417\) | −11.9550 | −0.585437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2047 | 0.742796 | 0.371398 | − | 0.928474i | \(-0.378879\pi\) | ||||
0.371398 | + | 0.928474i | \(0.378879\pi\) | |||||||
\(420\) | −1.94103 | −0.0947127 | ||||||||
\(421\) | 16.2914 | 0.793992 | 0.396996 | − | 0.917820i | \(-0.370053\pi\) | ||||
0.396996 | + | 0.917820i | \(0.370053\pi\) | |||||||
\(422\) | −21.8854 | −1.06537 | ||||||||
\(423\) | 7.82647 | 0.380536 | ||||||||
\(424\) | −5.46888 | −0.265592 | ||||||||
\(425\) | −3.09239 | −0.150003 | ||||||||
\(426\) | 8.60401 | 0.416866 | ||||||||
\(427\) | −5.43715 | −0.263122 | ||||||||
\(428\) | −19.0867 | −0.922591 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.28143 | −0.0617959 | ||||||||
\(431\) | 9.53052 | 0.459069 | 0.229534 | − | 0.973301i | \(-0.426280\pi\) | ||||
0.229534 | + | 0.973301i | \(0.426280\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −28.5027 | −1.36975 | −0.684876 | − | 0.728660i | \(-0.740143\pi\) | ||||
−0.684876 | + | 0.728660i | \(0.740143\pi\) | |||||||
\(434\) | 5.71191 | 0.274181 | ||||||||
\(435\) | −2.15234 | −0.103197 | ||||||||
\(436\) | 17.2553 | 0.826378 | ||||||||
\(437\) | −34.6384 | −1.65698 | ||||||||
\(438\) | −2.26690 | −0.108317 | ||||||||
\(439\) | −38.0222 | −1.81470 | −0.907350 | − | 0.420377i | \(-0.861898\pi\) | ||||
−0.907350 | + | 0.420377i | \(0.861898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.7119 | 0.700567 | ||||||||
\(442\) | 0.181396 | 0.00862814 | ||||||||
\(443\) | 6.29633 | 0.299148 | 0.149574 | − | 0.988751i | \(-0.452210\pi\) | ||||
0.149574 | + | 0.988751i | \(0.452210\pi\) | |||||||
\(444\) | 6.82816 | 0.324050 | ||||||||
\(445\) | 1.64170 | 0.0778240 | ||||||||
\(446\) | −4.65960 | −0.220639 | ||||||||
\(447\) | −3.58343 | −0.169491 | ||||||||
\(448\) | 4.65960 | 0.220146 | ||||||||
\(449\) | 20.0967 | 0.948424 | 0.474212 | − | 0.880411i | \(-0.342733\pi\) | ||||
0.474212 | + | 0.880411i | \(0.342733\pi\) | |||||||
\(450\) | −4.82647 | −0.227522 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.91099 | 0.136921 | ||||||||
\(453\) | 3.74074 | 0.175756 | ||||||||
\(454\) | −22.4467 | −1.05348 | ||||||||
\(455\) | 0.549537 | 0.0257627 | ||||||||
\(456\) | 5.88544 | 0.275611 | ||||||||
\(457\) | 30.0278 | 1.40464 | 0.702322 | − | 0.711860i | \(-0.252147\pi\) | ||||
0.702322 | + | 0.711860i | \(0.252147\pi\) | |||||||
\(458\) | 12.3715 | 0.578083 | ||||||||
\(459\) | −0.640714 | −0.0299060 | ||||||||
\(460\) | 2.45167 | 0.114310 | ||||||||
\(461\) | −1.21459 | −0.0565691 | −0.0282845 | − | 0.999600i | \(-0.509004\pi\) | ||||
−0.0282845 | + | 0.999600i | \(0.509004\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.80637 | 0.316319 | 0.158159 | − | 0.987414i | \(-0.449444\pi\) | ||||
0.158159 | + | 0.987414i | \(0.449444\pi\) | |||||||
\(464\) | 5.16687 | 0.239866 | ||||||||
\(465\) | −0.510642 | −0.0236804 | ||||||||
\(466\) | 19.5940 | 0.907673 | ||||||||
\(467\) | 16.5563 | 0.766134 | 0.383067 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383067 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(468\) | 0.283116 | 0.0130870 | ||||||||
\(469\) | −10.7107 | −0.494574 | ||||||||
\(470\) | 3.26024 | 0.150384 | ||||||||
\(471\) | 13.7709 | 0.634529 | ||||||||
\(472\) | 3.20962 | 0.147735 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.69302 | 0.353352 | ||||||||
\(475\) | 28.4059 | 1.30335 | ||||||||
\(476\) | 2.98547 | 0.136839 | ||||||||
\(477\) | −5.46888 | −0.250403 | ||||||||
\(478\) | 3.43377 | 0.157057 | ||||||||
\(479\) | 36.6629 | 1.67517 | 0.837585 | − | 0.546307i | \(-0.183967\pi\) | ||||
0.837585 | + | 0.546307i | \(0.183967\pi\) | |||||||
\(480\) | −0.416566 | −0.0190135 | ||||||||
\(481\) | −1.93316 | −0.0881446 | ||||||||
\(482\) | 14.4861 | 0.659823 | ||||||||
\(483\) | −27.4238 | −1.24783 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 3.74632 | 0.170112 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 9.01223 | 0.408383 | 0.204192 | − | 0.978931i | \(-0.434543\pi\) | ||||
0.204192 | + | 0.978931i | \(0.434543\pi\) | |||||||
\(488\) | −1.16687 | −0.0528217 | ||||||||
\(489\) | −11.2398 | −0.508279 | ||||||||
\(490\) | 6.12848 | 0.276857 | ||||||||
\(491\) | −34.5430 | −1.55890 | −0.779451 | − | 0.626463i | \(-0.784502\pi\) | ||||
−0.779451 | + | 0.626463i | \(0.784502\pi\) | |||||||
\(492\) | −12.4116 | −0.559558 | ||||||||
\(493\) | 3.31048 | 0.149097 | ||||||||
\(494\) | −1.66626 | −0.0749687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.22584 | 0.0550417 | ||||||||
\(497\) | −40.0913 | −1.79834 | ||||||||
\(498\) | −9.27646 | −0.415688 | ||||||||
\(499\) | −35.3331 | −1.58173 | −0.790864 | − | 0.611992i | \(-0.790369\pi\) | ||||
−0.790864 | + | 0.611992i | \(0.790369\pi\) | |||||||
\(500\) | −4.09337 | −0.183061 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | −26.8576 | −1.19871 | ||||||||
\(503\) | −14.0245 | −0.625320 | −0.312660 | − | 0.949865i | \(-0.601220\pi\) | ||||
−0.312660 | + | 0.949865i | \(0.601220\pi\) | |||||||
\(504\) | 4.65960 | 0.207555 | ||||||||
\(505\) | −5.13893 | −0.228679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9198 | 0.573790 | ||||||||
\(508\) | −21.2636 | −0.943421 | ||||||||
\(509\) | −7.01453 | −0.310913 | −0.155457 | − | 0.987843i | \(-0.549685\pi\) | ||||
−0.155457 | + | 0.987843i | \(0.549685\pi\) | |||||||
\(510\) | −0.266899 | −0.0118185 | ||||||||
\(511\) | 10.5629 | 0.467273 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.88544 | 0.259849 | ||||||||
\(514\) | −3.57846 | −0.157839 | ||||||||
\(515\) | −5.14240 | −0.226601 | ||||||||
\(516\) | 3.07617 | 0.135421 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −31.8165 | −1.39794 | ||||||||
\(519\) | −1.16687 | −0.0512198 | ||||||||
\(520\) | 0.117936 | 0.00517186 | ||||||||
\(521\) | 3.70634 | 0.162378 | 0.0811889 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811889 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(522\) | 5.16687 | 0.226148 | ||||||||
\(523\) | 34.4417 | 1.50603 | 0.753016 | − | 0.658002i | \(-0.228598\pi\) | ||||
0.753016 | + | 0.658002i | \(0.228598\pi\) | |||||||
\(524\) | −14.2030 | −0.620459 | ||||||||
\(525\) | 22.4895 | 0.981520 | ||||||||
\(526\) | 5.52517 | 0.240909 | ||||||||
\(527\) | 0.785410 | 0.0342130 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.6384 | 0.506018 | ||||||||
\(530\) | −2.27815 | −0.0989564 | ||||||||
\(531\) | 3.20962 | 0.139286 | ||||||||
\(532\) | −27.4238 | −1.18897 | ||||||||
\(533\) | 3.51392 | 0.152205 | ||||||||
\(534\) | −3.94103 | −0.170545 | ||||||||
\(535\) | −7.95087 | −0.343746 | ||||||||
\(536\) | −2.29863 | −0.0992857 | ||||||||
\(537\) | −7.77088 | −0.335338 | ||||||||
\(538\) | 29.0039 | 1.25045 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.416566 | −0.0179261 | ||||||||
\(541\) | 2.07378 | 0.0891587 | 0.0445793 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445793 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(542\) | −24.0301 | −1.03218 | ||||||||
\(543\) | −10.2570 | −0.440168 | ||||||||
\(544\) | 0.640714 | 0.0274704 | ||||||||
\(545\) | 7.18796 | 0.307898 | ||||||||
\(546\) | −1.31921 | −0.0564569 | ||||||||
\(547\) | 37.0928 | 1.58597 | 0.792986 | − | 0.609240i | \(-0.208525\pi\) | ||||
0.792986 | + | 0.609240i | \(0.208525\pi\) | |||||||
\(548\) | −10.5484 | −0.450606 | ||||||||
\(549\) | −1.16687 | −0.0498007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.4093 | −1.29548 | ||||||||
\(552\) | −5.88544 | −0.250501 | ||||||||
\(553\) | −35.8464 | −1.52435 | ||||||||
\(554\) | 2.99382 | 0.127195 | ||||||||
\(555\) | 2.84438 | 0.120737 | ||||||||
\(556\) | 11.9550 | 0.507003 | ||||||||
\(557\) | 8.75635 | 0.371019 | 0.185509 | − | 0.982643i | \(-0.440607\pi\) | ||||
0.185509 | + | 0.982643i | \(0.440607\pi\) | |||||||
\(558\) | 1.22584 | 0.0518938 | ||||||||
\(559\) | −0.870913 | −0.0368357 | ||||||||
\(560\) | 1.94103 | 0.0820236 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.72523 | 0.0727745 | ||||||||
\(563\) | −2.41924 | −0.101959 | −0.0509794 | − | 0.998700i | \(-0.516234\pi\) | ||||
−0.0509794 | + | 0.998700i | \(0.516234\pi\) | |||||||
\(564\) | −7.82647 | −0.329554 | ||||||||
\(565\) | 1.21262 | 0.0510153 | ||||||||
\(566\) | 18.5372 | 0.779176 | ||||||||
\(567\) | 4.65960 | 0.195685 | ||||||||
\(568\) | −8.60401 | −0.361016 | ||||||||
\(569\) | −1.68627 | −0.0706920 | −0.0353460 | − | 0.999375i | \(-0.511253\pi\) | ||||
−0.0353460 | + | 0.999375i | \(0.511253\pi\) | |||||||
\(570\) | 2.45167 | 0.102689 | ||||||||
\(571\) | −1.66359 | −0.0696190 | −0.0348095 | − | 0.999394i | \(-0.511082\pi\) | ||||
−0.0348095 | + | 0.999394i | \(0.511082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5630 | 0.566600 | ||||||||
\(574\) | 57.8331 | 2.41391 | ||||||||
\(575\) | −28.4059 | −1.18461 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.7020 | −1.31977 | −0.659885 | − | 0.751366i | \(-0.729395\pi\) | ||||
−0.659885 | + | 0.751366i | \(0.729395\pi\) | |||||||
\(578\) | −16.5895 | −0.690032 | ||||||||
\(579\) | 2.56623 | 0.106649 | ||||||||
\(580\) | 2.15234 | 0.0893711 | ||||||||
\(581\) | 43.2246 | 1.79326 | ||||||||
\(582\) | −8.99334 | −0.372786 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.26690 | 0.0938050 | ||||||||
\(585\) | 0.117936 | 0.00487607 | ||||||||
\(586\) | 14.8331 | 0.612751 | ||||||||
\(587\) | 23.0817 | 0.952686 | 0.476343 | − | 0.879260i | \(-0.341962\pi\) | ||||
0.476343 | + | 0.879260i | \(0.341962\pi\) | |||||||
\(588\) | −14.7119 | −0.606709 | ||||||||
\(589\) | −7.21459 | −0.297272 | ||||||||
\(590\) | 1.33702 | 0.0550442 | ||||||||
\(591\) | 2.92383 | 0.120270 | ||||||||
\(592\) | −6.82816 | −0.280636 | ||||||||
\(593\) | 21.0156 | 0.863008 | 0.431504 | − | 0.902111i | \(-0.357983\pi\) | ||||
0.431504 | + | 0.902111i | \(0.357983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.24365 | 0.0509845 | ||||||||
\(596\) | 3.58343 | 0.146783 | ||||||||
\(597\) | 3.43377 | 0.140535 | ||||||||
\(598\) | 1.66626 | 0.0681386 | ||||||||
\(599\) | −0.274769 | −0.0112267 | −0.00561337 | − | 0.999984i | \(-0.501787\pi\) | ||||
−0.00561337 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(600\) | 4.82647 | 0.197040 | ||||||||
\(601\) | −42.1590 | −1.71970 | −0.859851 | − | 0.510546i | \(-0.829443\pi\) | ||||
−0.859851 | + | 0.510546i | \(0.829443\pi\) | |||||||
\(602\) | −14.3337 | −0.584200 | ||||||||
\(603\) | −2.29863 | −0.0936074 | ||||||||
\(604\) | −3.74074 | −0.152209 | ||||||||
\(605\) | −4.58222 | −0.186294 | ||||||||
\(606\) | 12.3364 | 0.501132 | ||||||||
\(607\) | 36.3658 | 1.47604 | 0.738022 | − | 0.674777i | \(-0.235760\pi\) | ||||
0.738022 | + | 0.674777i | \(0.235760\pi\) | |||||||
\(608\) | −5.88544 | −0.238686 | ||||||||
\(609\) | −24.0756 | −0.975591 | ||||||||
\(610\) | −0.486077 | −0.0196807 | ||||||||
\(611\) | 2.21580 | 0.0896417 | ||||||||
\(612\) | 0.640714 | 0.0258993 | ||||||||
\(613\) | −28.3291 | −1.14420 | −0.572102 | − | 0.820183i | \(-0.693872\pi\) | ||||
−0.572102 | + | 0.820183i | \(0.693872\pi\) | |||||||
\(614\) | −31.9927 | −1.29112 | ||||||||
\(615\) | −5.17025 | −0.208484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.7941 | 1.80334 | 0.901672 | − | 0.432421i | \(-0.142340\pi\) | ||||
0.901672 | + | 0.432421i | \(0.142340\pi\) | |||||||
\(618\) | 12.3448 | 0.496579 | ||||||||
\(619\) | 43.9682 | 1.76723 | 0.883615 | − | 0.468214i | \(-0.155102\pi\) | ||||
0.883615 | + | 0.468214i | \(0.155102\pi\) | |||||||
\(620\) | 0.510642 | 0.0205079 | ||||||||
\(621\) | −5.88544 | −0.236175 | ||||||||
\(622\) | −7.07884 | −0.283836 | ||||||||
\(623\) | 18.3636 | 0.735724 | ||||||||
\(624\) | −0.283116 | −0.0113337 | ||||||||
\(625\) | 22.4272 | 0.897088 | ||||||||
\(626\) | 23.6496 | 0.945227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.7709 | −0.549518 | ||||||||
\(629\) | −4.37490 | −0.174439 | ||||||||
\(630\) | 1.94103 | 0.0773326 | ||||||||
\(631\) | 15.8265 | 0.630042 | 0.315021 | − | 0.949085i | \(-0.397988\pi\) | ||||
0.315021 | + | 0.949085i | \(0.397988\pi\) | |||||||
\(632\) | −7.69302 | −0.306012 | ||||||||
\(633\) | 21.8854 | 0.869868 | ||||||||
\(634\) | −13.7007 | −0.544123 | ||||||||
\(635\) | −8.85770 | −0.351507 | ||||||||
\(636\) | 5.46888 | 0.216855 | ||||||||
\(637\) | 4.16518 | 0.165030 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.60401 | −0.340370 | ||||||||
\(640\) | 0.416566 | 0.0164662 | ||||||||
\(641\) | −25.4792 | −1.00637 | −0.503184 | − | 0.864179i | \(-0.667838\pi\) | ||||
−0.503184 | + | 0.864179i | \(0.667838\pi\) | |||||||
\(642\) | 19.0867 | 0.753293 | ||||||||
\(643\) | 20.6623 | 0.814841 | 0.407420 | − | 0.913241i | \(-0.366428\pi\) | ||||
0.407420 | + | 0.913241i | \(0.366428\pi\) | |||||||
\(644\) | 27.4238 | 1.08065 | ||||||||
\(645\) | 1.28143 | 0.0504561 | ||||||||
\(646\) | −3.77088 | −0.148363 | ||||||||
\(647\) | 1.24899 | 0.0491030 | 0.0245515 | − | 0.999699i | \(-0.492184\pi\) | ||||
0.0245515 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.36645 | −0.0535967 | ||||||||
\(651\) | −5.71191 | −0.223868 | ||||||||
\(652\) | 11.2398 | 0.440183 | ||||||||
\(653\) | 3.27149 | 0.128023 | 0.0640116 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640116 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(654\) | −17.2553 | −0.674734 | ||||||||
\(655\) | −5.91647 | −0.231176 | ||||||||
\(656\) | 12.4116 | 0.484591 | ||||||||
\(657\) | 2.26690 | 0.0884402 | ||||||||
\(658\) | 36.4683 | 1.42168 | ||||||||
\(659\) | −20.0805 | −0.782227 | −0.391113 | − | 0.920343i | \(-0.627910\pi\) | ||||
−0.391113 | + | 0.920343i | \(0.627910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.6738 | −0.959698 | −0.479849 | − | 0.877351i | \(-0.659309\pi\) | ||||
−0.479849 | + | 0.877351i | \(0.659309\pi\) | |||||||
\(662\) | −9.40991 | −0.365726 | ||||||||
\(663\) | −0.181396 | −0.00704485 | ||||||||
\(664\) | 9.27646 | 0.359996 | ||||||||
\(665\) | −11.4238 | −0.442997 | ||||||||
\(666\) | −6.82816 | −0.264586 | ||||||||
\(667\) | 30.4093 | 1.17745 | ||||||||
\(668\) | −1.00000 | −0.0386912 | ||||||||
\(669\) | 4.65960 | 0.180151 | ||||||||
\(670\) | −0.957530 | −0.0369926 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.65960 | −0.179748 | ||||||||
\(673\) | 40.9688 | 1.57923 | 0.789615 | − | 0.613602i | \(-0.210280\pi\) | ||||
0.789615 | + | 0.613602i | \(0.210280\pi\) | |||||||
\(674\) | 21.9345 | 0.844884 | ||||||||
\(675\) | 4.82647 | 0.185771 | ||||||||
\(676\) | −12.9198 | −0.496917 | ||||||||
\(677\) | −0.194714 | −0.00748345 | −0.00374172 | − | 0.999993i | \(-0.501191\pi\) | ||||
−0.00374172 | + | 0.999993i | \(0.501191\pi\) | |||||||
\(678\) | −2.91099 | −0.111796 | ||||||||
\(679\) | 41.9054 | 1.60818 | ||||||||
\(680\) | 0.266899 | 0.0102351 | ||||||||
\(681\) | 22.4467 | 0.860160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.5156 | −1.58855 | −0.794275 | − | 0.607558i | \(-0.792149\pi\) | ||||
−0.794275 | + | 0.607558i | \(0.792149\pi\) | |||||||
\(684\) | −5.88544 | −0.225035 | ||||||||
\(685\) | −4.39411 | −0.167890 | ||||||||
\(686\) | 35.9345 | 1.37198 | ||||||||
\(687\) | −12.3715 | −0.472003 | ||||||||
\(688\) | −3.07617 | −0.117278 | ||||||||
\(689\) | −1.54833 | −0.0589865 | ||||||||
\(690\) | −2.45167 | −0.0933336 | ||||||||
\(691\) | 30.0517 | 1.14322 | 0.571610 | − | 0.820525i | \(-0.306319\pi\) | ||||
0.571610 | + | 0.820525i | \(0.306319\pi\) | |||||||
\(692\) | 1.16687 | 0.0443577 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.6468 | 0.631903 | ||||||||
\(695\) | 4.98002 | 0.188903 | ||||||||
\(696\) | −5.16687 | −0.195850 | ||||||||
\(697\) | 7.95228 | 0.301214 | ||||||||
\(698\) | 4.49442 | 0.170116 | ||||||||
\(699\) | −19.5940 | −0.741112 | ||||||||
\(700\) | −22.4895 | −0.850022 | ||||||||
\(701\) | 47.9934 | 1.81269 | 0.906344 | − | 0.422542i | \(-0.138862\pi\) | ||||
0.906344 | + | 0.422542i | \(0.138862\pi\) | |||||||
\(702\) | −0.283116 | −0.0106855 | ||||||||
\(703\) | 40.1867 | 1.51567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.26024 | −0.122788 | ||||||||
\(706\) | 9.72523 | 0.366014 | ||||||||
\(707\) | −57.4828 | −2.16186 | ||||||||
\(708\) | −3.20962 | −0.120625 | ||||||||
\(709\) | 26.5976 | 0.998895 | 0.499448 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499448 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(710\) | −3.58414 | −0.134510 | ||||||||
\(711\) | −7.69302 | −0.288511 | ||||||||
\(712\) | 3.94103 | 0.147696 | ||||||||
\(713\) | 7.21459 | 0.270189 | ||||||||
\(714\) | −2.98547 | −0.111728 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.77088 | 0.290412 | ||||||||
\(717\) | −3.43377 | −0.128236 | ||||||||
\(718\) | −9.61854 | −0.358961 | ||||||||
\(719\) | 0.951068 | 0.0354689 | 0.0177344 | − | 0.999843i | \(-0.494355\pi\) | ||||
0.0177344 | + | 0.999843i | \(0.494355\pi\) | |||||||
\(720\) | 0.416566 | 0.0155245 | ||||||||
\(721\) | −57.5217 | −2.14222 | ||||||||
\(722\) | 15.6384 | 0.582002 | ||||||||
\(723\) | −14.4861 | −0.538743 | ||||||||
\(724\) | 10.2570 | 0.381197 | ||||||||
\(725\) | −24.9378 | −0.926165 | ||||||||
\(726\) | 11.0000 | 0.408248 | ||||||||
\(727\) | −5.91558 | −0.219397 | −0.109698 | − | 0.993965i | \(-0.534988\pi\) | ||||
−0.109698 | + | 0.993965i | \(0.534988\pi\) | |||||||
\(728\) | 1.31921 | 0.0488931 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.944313 | 0.0349506 | ||||||||
\(731\) | −1.97094 | −0.0728980 | ||||||||
\(732\) | 1.16687 | 0.0431287 | ||||||||
\(733\) | −5.27487 | −0.194832 | −0.0974158 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974158 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(734\) | 14.1523 | 0.522372 | ||||||||
\(735\) | −6.12848 | −0.226052 | ||||||||
\(736\) | 5.88544 | 0.216940 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 12.4116 | 0.456877 | ||||||||
\(739\) | 7.61925 | 0.280278 | 0.140139 | − | 0.990132i | \(-0.455245\pi\) | ||||
0.140139 | + | 0.990132i | \(0.455245\pi\) | |||||||
\(740\) | −2.84438 | −0.104561 | ||||||||
\(741\) | 1.66626 | 0.0612117 | ||||||||
\(742\) | −25.4828 | −0.935503 | ||||||||
\(743\) | 35.4470 | 1.30042 | 0.650212 | − | 0.759753i | \(-0.274680\pi\) | ||||
0.650212 | + | 0.759753i | \(0.274680\pi\) | |||||||
\(744\) | −1.22584 | −0.0449414 | ||||||||
\(745\) | 1.49274 | 0.0546896 | ||||||||
\(746\) | −28.1149 | −1.02936 | ||||||||
\(747\) | 9.27646 | 0.339408 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −88.9365 | −3.24967 | ||||||||
\(750\) | 4.09337 | 0.149469 | ||||||||
\(751\) | −22.2680 | −0.812570 | −0.406285 | − | 0.913746i | \(-0.633176\pi\) | ||||
−0.406285 | + | 0.913746i | \(0.633176\pi\) | |||||||
\(752\) | 7.82647 | 0.285402 | ||||||||
\(753\) | 26.8576 | 0.978745 | ||||||||
\(754\) | 1.46282 | 0.0532729 | ||||||||
\(755\) | −1.55827 | −0.0567111 | ||||||||
\(756\) | −4.65960 | −0.169468 | ||||||||
\(757\) | 25.1259 | 0.913216 | 0.456608 | − | 0.889668i | \(-0.349064\pi\) | ||||
0.456608 | + | 0.889668i | \(0.349064\pi\) | |||||||
\(758\) | 16.5212 | 0.600076 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.45167 | −0.0889315 | ||||||||
\(761\) | 19.0755 | 0.691485 | 0.345743 | − | 0.938329i | \(-0.387627\pi\) | ||||
0.345743 | + | 0.938329i | \(0.387627\pi\) | |||||||
\(762\) | 21.2636 | 0.770300 | ||||||||
\(763\) | 80.4027 | 2.91077 | ||||||||
\(764\) | −13.5630 | −0.490690 | ||||||||
\(765\) | 0.266899 | 0.00964977 | ||||||||
\(766\) | −15.6907 | −0.566929 | ||||||||
\(767\) | 0.908695 | 0.0328111 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 7.11577 | 0.256601 | 0.128301 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128301 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.57846 | 0.128875 | ||||||||
\(772\) | −2.56623 | −0.0923607 | ||||||||
\(773\) | 38.4478 | 1.38287 | 0.691435 | − | 0.722438i | \(-0.256979\pi\) | ||||
0.691435 | + | 0.722438i | \(0.256979\pi\) | |||||||
\(774\) | −3.07617 | −0.110571 | ||||||||
\(775\) | −5.91647 | −0.212526 | ||||||||
\(776\) | 8.99334 | 0.322842 | ||||||||
\(777\) | 31.8165 | 1.14141 | ||||||||
\(778\) | −21.1842 | −0.759489 | ||||||||
\(779\) | −73.0477 | −2.61721 | ||||||||
\(780\) | −0.117936 | −0.00422280 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.77088 | 0.134846 | ||||||||
\(783\) | −5.16687 | −0.184649 | ||||||||
\(784\) | 14.7119 | 0.525426 | ||||||||
\(785\) | −5.73648 | −0.204744 | ||||||||
\(786\) | 14.2030 | 0.506603 | ||||||||
\(787\) | 37.5332 | 1.33791 | 0.668957 | − | 0.743301i | \(-0.266741\pi\) | ||||
0.668957 | + | 0.743301i | \(0.266741\pi\) | |||||||
\(788\) | −2.92383 | −0.104157 | ||||||||
\(789\) | −5.52517 | −0.196701 | ||||||||
\(790\) | −3.20465 | −0.114016 | ||||||||
\(791\) | 13.5641 | 0.482283 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.330359 | −0.0117314 | ||||||||
\(794\) | −2.03778 | −0.0723182 | ||||||||
\(795\) | 2.27815 | 0.0807975 | ||||||||
\(796\) | −3.43377 | −0.121707 | ||||||||
\(797\) | 36.2808 | 1.28513 | 0.642566 | − | 0.766230i | \(-0.277870\pi\) | ||||
0.642566 | + | 0.766230i | \(0.277870\pi\) | |||||||
\(798\) | 27.4238 | 0.970793 | ||||||||
\(799\) | 5.01453 | 0.177401 | ||||||||
\(800\) | −4.82647 | −0.170642 | ||||||||
\(801\) | 3.94103 | 0.139250 | ||||||||
\(802\) | −11.3971 | −0.402444 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.29863 | 0.0810664 | ||||||||
\(805\) | 11.4238 | 0.402637 | ||||||||
\(806\) | 0.347054 | 0.0122245 | ||||||||
\(807\) | −29.0039 | −1.02099 | ||||||||
\(808\) | −12.3364 | −0.433993 | ||||||||
\(809\) | 10.4305 | 0.366716 | 0.183358 | − | 0.983046i | \(-0.441303\pi\) | ||||
0.183358 | + | 0.983046i | \(0.441303\pi\) | |||||||
\(810\) | 0.416566 | 0.0146366 | ||||||||
\(811\) | 1.68468 | 0.0591570 | 0.0295785 | − | 0.999562i | \(-0.490584\pi\) | ||||
0.0295785 | + | 0.999562i | \(0.490584\pi\) | |||||||
\(812\) | 24.0756 | 0.844887 | ||||||||
\(813\) | 24.0301 | 0.842774 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.68210 | 0.164007 | ||||||||
\(816\) | −0.640714 | −0.0224295 | ||||||||
\(817\) | 18.1046 | 0.633400 | ||||||||
\(818\) | −18.1012 | −0.632895 | ||||||||
\(819\) | 1.31921 | 0.0460969 | ||||||||
\(820\) | 5.17025 | 0.180553 | ||||||||
\(821\) | 1.38085 | 0.0481920 | 0.0240960 | − | 0.999710i | \(-0.492329\pi\) | ||||
0.0240960 | + | 0.999710i | \(0.492329\pi\) | |||||||
\(822\) | 10.5484 | 0.367919 | ||||||||
\(823\) | −12.9488 | −0.451366 | −0.225683 | − | 0.974201i | \(-0.572461\pi\) | ||||
−0.225683 | + | 0.974201i | \(0.572461\pi\) | |||||||
\(824\) | −12.3448 | −0.430050 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9556 | 0.520370 | ||||||||
\(827\) | −25.7924 | −0.896891 | −0.448446 | − | 0.893810i | \(-0.648022\pi\) | ||||
−0.448446 | + | 0.893810i | \(0.648022\pi\) | |||||||
\(828\) | 5.88544 | 0.204533 | ||||||||
\(829\) | −23.6347 | −0.820866 | −0.410433 | − | 0.911891i | \(-0.634622\pi\) | ||||
−0.410433 | + | 0.911891i | \(0.634622\pi\) | |||||||
\(830\) | 3.86425 | 0.134130 | ||||||||
\(831\) | −2.99382 | −0.103854 | ||||||||
\(832\) | 0.283116 | 0.00981528 | ||||||||
\(833\) | 9.42612 | 0.326596 | ||||||||
\(834\) | −11.9550 | −0.413966 | ||||||||
\(835\) | −0.416566 | −0.0144159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.22584 | −0.0423711 | ||||||||
\(838\) | 15.2047 | 0.525236 | ||||||||
\(839\) | −37.1047 | −1.28100 | −0.640499 | − | 0.767959i | \(-0.721272\pi\) | ||||
−0.640499 | + | 0.767959i | \(0.721272\pi\) | |||||||
\(840\) | −1.94103 | −0.0669720 | ||||||||
\(841\) | −2.30347 | −0.0794300 | ||||||||
\(842\) | 16.2914 | 0.561437 | ||||||||
\(843\) | −1.72523 | −0.0594201 | ||||||||
\(844\) | −21.8854 | −0.753328 | ||||||||
\(845\) | −5.38197 | −0.185145 | ||||||||
\(846\) | 7.82647 | 0.269080 | ||||||||
\(847\) | −51.2556 | −1.76116 | ||||||||
\(848\) | −5.46888 | −0.187802 | ||||||||
\(849\) | −18.5372 | −0.636194 | ||||||||
\(850\) | −3.09239 | −0.106068 | ||||||||
\(851\) | −40.1867 | −1.37758 | ||||||||
\(852\) | 8.60401 | 0.294769 | ||||||||
\(853\) | 3.93316 | 0.134669 | 0.0673345 | − | 0.997730i | \(-0.478551\pi\) | ||||
0.0673345 | + | 0.997730i | \(0.478551\pi\) | |||||||
\(854\) | −5.43715 | −0.186055 | ||||||||
\(855\) | −2.45167 | −0.0838455 | ||||||||
\(856\) | −19.0867 | −0.652370 | ||||||||
\(857\) | −57.5073 | −1.96441 | −0.982205 | − | 0.187810i | \(-0.939861\pi\) | ||||
−0.982205 | + | 0.187810i | \(0.939861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.51851 | −0.290648 | −0.145324 | − | 0.989384i | \(-0.546422\pi\) | ||||
−0.145324 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(860\) | −1.28143 | −0.0436963 | ||||||||
\(861\) | −57.8331 | −1.97095 | ||||||||
\(862\) | 9.53052 | 0.324611 | ||||||||
\(863\) | −27.1894 | −0.925537 | −0.462768 | − | 0.886479i | \(-0.653144\pi\) | ||||
−0.462768 | + | 0.886479i | \(0.653144\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.486077 | 0.0165271 | ||||||||
\(866\) | −28.5027 | −0.968560 | ||||||||
\(867\) | 16.5895 | 0.563408 | ||||||||
\(868\) | 5.71191 | 0.193875 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.15234 | −0.0729712 | ||||||||
\(871\) | −0.650779 | −0.0220508 | ||||||||
\(872\) | 17.2553 | 0.584337 | ||||||||
\(873\) | 8.99334 | 0.304378 | ||||||||
\(874\) | −34.6384 | −1.17166 | ||||||||
\(875\) | −19.0735 | −0.644802 | ||||||||
\(876\) | −2.26690 | −0.0765914 | ||||||||
\(877\) | −40.8576 | −1.37966 | −0.689831 | − | 0.723970i | \(-0.742315\pi\) | ||||
−0.689831 | + | 0.723970i | \(0.742315\pi\) | |||||||
\(878\) | −38.0222 | −1.28319 | ||||||||
\(879\) | −14.8331 | −0.500309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9645 | −0.369404 | −0.184702 | − | 0.982795i | \(-0.559132\pi\) | ||||
−0.184702 | + | 0.982795i | \(0.559132\pi\) | |||||||
\(882\) | 14.7119 | 0.495376 | ||||||||
\(883\) | −38.3081 | −1.28917 | −0.644584 | − | 0.764533i | \(-0.722970\pi\) | ||||
−0.644584 | + | 0.764533i | \(0.722970\pi\) | |||||||
\(884\) | 0.181396 | 0.00610102 | ||||||||
\(885\) | −1.33702 | −0.0449434 | ||||||||
\(886\) | 6.29633 | 0.211529 | ||||||||
\(887\) | −54.4403 | −1.82793 | −0.913964 | − | 0.405796i | \(-0.866994\pi\) | ||||
−0.913964 | + | 0.405796i | \(0.866994\pi\) | |||||||
\(888\) | 6.82816 | 0.229138 | ||||||||
\(889\) | −99.0801 | −3.32304 | ||||||||
\(890\) | 1.64170 | 0.0550299 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.65960 | −0.156015 | ||||||||
\(893\) | −46.0622 | −1.54141 | ||||||||
\(894\) | −3.58343 | −0.119848 | ||||||||
\(895\) | 3.23708 | 0.108204 | ||||||||
\(896\) | 4.65960 | 0.155666 | ||||||||
\(897\) | −1.66626 | −0.0556349 | ||||||||
\(898\) | 20.0967 | 0.670637 | ||||||||
\(899\) | 6.33374 | 0.211242 | ||||||||
\(900\) | −4.82647 | −0.160882 | ||||||||
\(901\) | −3.50398 | −0.116735 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.3337 | 0.476997 | ||||||||
\(904\) | 2.91099 | 0.0968181 | ||||||||
\(905\) | 4.27270 | 0.142029 | ||||||||
\(906\) | 3.74074 | 0.124278 | ||||||||
\(907\) | −1.05231 | −0.0349414 | −0.0174707 | − | 0.999847i | \(-0.505561\pi\) | ||||
−0.0174707 | + | 0.999847i | \(0.505561\pi\) | |||||||
\(908\) | −22.4467 | −0.744920 | ||||||||
\(909\) | −12.3364 | −0.409173 | ||||||||
\(910\) | 0.549537 | 0.0182170 | ||||||||
\(911\) | 59.5240 | 1.97212 | 0.986058 | − | 0.166400i | \(-0.0532143\pi\) | ||||
0.986058 | + | 0.166400i | \(0.0532143\pi\) | |||||||
\(912\) | 5.88544 | 0.194886 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 30.0278 | 0.993233 | ||||||||
\(915\) | 0.486077 | 0.0160692 | ||||||||
\(916\) | 12.3715 | 0.408766 | ||||||||
\(917\) | −66.1802 | −2.18546 | ||||||||
\(918\) | −0.640714 | −0.0211467 | ||||||||
\(919\) | 13.2091 | 0.435729 | 0.217865 | − | 0.975979i | \(-0.430091\pi\) | ||||
0.217865 | + | 0.975979i | \(0.430091\pi\) | |||||||
\(920\) | 2.45167 | 0.0808293 | ||||||||
\(921\) | 31.9927 | 1.05420 | ||||||||
\(922\) | −1.21459 | −0.0400004 | ||||||||
\(923\) | −2.43593 | −0.0801798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.9559 | 1.08358 | ||||||||
\(926\) | 6.80637 | 0.223671 | ||||||||
\(927\) | −12.3448 | −0.405455 | ||||||||
\(928\) | 5.16687 | 0.169611 | ||||||||
\(929\) | 34.0834 | 1.11824 | 0.559121 | − | 0.829086i | \(-0.311139\pi\) | ||||
0.559121 | + | 0.829086i | \(0.311139\pi\) | |||||||
\(930\) | −0.510642 | −0.0167446 | ||||||||
\(931\) | −86.5861 | −2.83774 | ||||||||
\(932\) | 19.5940 | 0.641822 | ||||||||
\(933\) | 7.07884 | 0.231751 | ||||||||
\(934\) | 16.5563 | 0.541738 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.283116 | 0.00925394 | ||||||||
\(937\) | 20.5272 | 0.670596 | 0.335298 | − | 0.942112i | \(-0.391163\pi\) | ||||
0.335298 | + | 0.942112i | \(0.391163\pi\) | |||||||
\(938\) | −10.7107 | −0.349717 | ||||||||
\(939\) | −23.6496 | −0.771774 | ||||||||
\(940\) | 3.26024 | 0.106337 | ||||||||
\(941\) | −32.9415 | −1.07386 | −0.536932 | − | 0.843626i | \(-0.680417\pi\) | ||||
−0.536932 | + | 0.843626i | \(0.680417\pi\) | |||||||
\(942\) | 13.7709 | 0.448680 | ||||||||
\(943\) | 73.0477 | 2.37876 | ||||||||
\(944\) | 3.20962 | 0.104464 | ||||||||
\(945\) | −1.94103 | −0.0631418 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.9867 | −1.75433 | −0.877166 | − | 0.480188i | \(-0.840569\pi\) | ||||
−0.877166 | + | 0.480188i | \(0.840569\pi\) | |||||||
\(948\) | 7.69302 | 0.249858 | ||||||||
\(949\) | 0.641796 | 0.0208336 | ||||||||
\(950\) | 28.4059 | 0.921610 | ||||||||
\(951\) | 13.7007 | 0.444275 | ||||||||
\(952\) | 2.98547 | 0.0967597 | ||||||||
\(953\) | −21.7843 | −0.705664 | −0.352832 | − | 0.935687i | \(-0.614781\pi\) | ||||
−0.352832 | + | 0.935687i | \(0.614781\pi\) | |||||||
\(954\) | −5.46888 | −0.177061 | ||||||||
\(955\) | −5.64986 | −0.182825 | ||||||||
\(956\) | 3.43377 | 0.111056 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.6629 | 1.18452 | ||||||||
\(959\) | −49.1515 | −1.58718 | ||||||||
\(960\) | −0.416566 | −0.0134446 | ||||||||
\(961\) | −29.4973 | −0.951527 | ||||||||
\(962\) | −1.93316 | −0.0623277 | ||||||||
\(963\) | −19.0867 | −0.615061 | ||||||||
\(964\) | 14.4861 | 0.466565 | ||||||||
\(965\) | −1.06900 | −0.0344125 | ||||||||
\(966\) | −27.4238 | −0.882347 | ||||||||
\(967\) | 25.9385 | 0.834126 | 0.417063 | − | 0.908878i | \(-0.363059\pi\) | ||||
0.417063 | + | 0.908878i | \(0.363059\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 3.77088 | 0.121138 | ||||||||
\(970\) | 3.74632 | 0.120287 | ||||||||
\(971\) | 27.4566 | 0.881126 | 0.440563 | − | 0.897722i | \(-0.354779\pi\) | ||||
0.440563 | + | 0.897722i | \(0.354779\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 55.7054 | 1.78583 | ||||||||
\(974\) | 9.01223 | 0.288771 | ||||||||
\(975\) | 1.36645 | 0.0437615 | ||||||||
\(976\) | −1.16687 | −0.0373505 | ||||||||
\(977\) | 45.3036 | 1.44939 | 0.724695 | − | 0.689070i | \(-0.241981\pi\) | ||||
0.724695 | + | 0.689070i | \(0.241981\pi\) | |||||||
\(978\) | −11.2398 | −0.359408 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.12848 | 0.195767 | ||||||||
\(981\) | 17.2553 | 0.550918 | ||||||||
\(982\) | −34.5430 | −1.10231 | ||||||||
\(983\) | 34.6987 | 1.10672 | 0.553358 | − | 0.832943i | \(-0.313346\pi\) | ||||
0.553358 | + | 0.832943i | \(0.313346\pi\) | |||||||
\(984\) | −12.4116 | −0.395667 | ||||||||
\(985\) | −1.21797 | −0.0388077 | ||||||||
\(986\) | 3.31048 | 0.105427 | ||||||||
\(987\) | −36.4683 | −1.16080 | ||||||||
\(988\) | −1.66626 | −0.0530109 | ||||||||
\(989\) | −18.1046 | −0.575693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.6320 | 1.06836 | 0.534178 | − | 0.845372i | \(-0.320621\pi\) | ||||
0.534178 | + | 0.845372i | \(0.320621\pi\) | |||||||
\(992\) | 1.22584 | 0.0389204 | ||||||||
\(993\) | 9.40991 | 0.298614 | ||||||||
\(994\) | −40.0913 | −1.27162 | ||||||||
\(995\) | −1.43039 | −0.0453464 | ||||||||
\(996\) | −9.27646 | −0.293936 | ||||||||
\(997\) | 36.8954 | 1.16849 | 0.584244 | − | 0.811578i | \(-0.301391\pi\) | ||||
0.584244 | + | 0.811578i | \(0.301391\pi\) | |||||||
\(998\) | −35.3331 | −1.11845 | ||||||||
\(999\) | 6.82816 | 0.216033 |
(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 | 1002.2.a.i.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 3006.2.a.s.1.3 | 4 | |||
4.3 | odd | 2 | 8016.2.a.o.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1002.2.a.i.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3006.2.a.s.1.3 | 4 | 3.2 | odd | 2 | |||
8016.2.a.o.1.2 | 4 | 4.3 | odd | 2 |