Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, 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("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.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: | \(44.7960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.19985813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 23x^{3} + 28x^{2} + 40x - 24 \) |
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 | 1.3 | ||
Root | \(-4.29600\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.23070 | 0.465160 | 0.232580 | − | 0.972577i | \(-0.425283\pi\) | ||||
0.232580 | + | 0.972577i | \(0.425283\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.87255 | 1.35140 | 0.675701 | − | 0.737176i | \(-0.263841\pi\) | ||||
0.675701 | + | 0.737176i | \(0.263841\pi\) | |||||||
\(14\) | 1.23070 | 0.328918 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.872548 | −0.200176 | −0.100088 | − | 0.994979i | \(-0.531912\pi\) | ||||
−0.100088 | + | 0.994979i | \(0.531912\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.23070 | 0.268560 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 9.36130 | 1.95197 | 0.975984 | − | 0.217844i | \(-0.0699025\pi\) | ||||
0.975984 | + | 0.217844i | \(0.0699025\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.87255 | 0.955585 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.23070 | 0.232580 | ||||||||
\(29\) | 3.64185 | 0.676275 | 0.338137 | − | 0.941097i | \(-0.390203\pi\) | ||||
0.338137 | + | 0.941097i | \(0.390203\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 2.10662 | 0.378359 | 0.189180 | − | 0.981942i | \(-0.439417\pi\) | ||||
0.189180 | + | 0.981942i | \(0.439417\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 1.23070 | 0.208026 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.3405 | −1.69996 | −0.849981 | − | 0.526813i | \(-0.823387\pi\) | ||||
−0.849981 | + | 0.526813i | \(0.823387\pi\) | |||||||
\(38\) | −0.872548 | −0.141546 | ||||||||
\(39\) | 4.87255 | 0.780232 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.59200 | −1.34185 | −0.670923 | − | 0.741527i | \(-0.734102\pi\) | ||||
−0.670923 | + | 0.741527i | \(0.734102\pi\) | |||||||
\(42\) | 1.23070 | 0.189901 | ||||||||
\(43\) | −0.979164 | −0.149321 | −0.0746606 | − | 0.997209i | \(-0.523787\pi\) | ||||
−0.0746606 | + | 0.997209i | \(0.523787\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 9.36130 | 1.38025 | ||||||||
\(47\) | 8.59200 | 1.25327 | 0.626636 | − | 0.779312i | \(-0.284431\pi\) | ||||
0.626636 | + | 0.779312i | \(0.284431\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.48539 | −0.783627 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 4.87255 | 0.675701 | ||||||||
\(53\) | −7.92931 | −1.08918 | −0.544588 | − | 0.838704i | \(-0.683314\pi\) | ||||
−0.544588 | + | 0.838704i | \(0.683314\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.23070 | 0.164459 | ||||||||
\(57\) | −0.872548 | −0.115572 | ||||||||
\(58\) | 3.64185 | 0.478199 | ||||||||
\(59\) | 9.46792 | 1.23262 | 0.616309 | − | 0.787504i | \(-0.288627\pi\) | ||||
0.616309 | + | 0.787504i | \(0.288627\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 0.00337115 | 0.000431632 0 | 0.000215816 | − | 1.00000i | \(-0.499931\pi\) | ||||
0.000215816 | 1.00000i | \(0.499931\pi\) | ||||||||
\(62\) | 2.10662 | 0.267540 | ||||||||
\(63\) | 1.23070 | 0.155053 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.87255 | 0.604365 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −11.8791 | −1.45126 | −0.725630 | − | 0.688085i | \(-0.758452\pi\) | ||||
−0.725630 | + | 0.688085i | \(0.758452\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 9.36130 | 1.12697 | ||||||||
\(70\) | 1.23070 | 0.147096 | ||||||||
\(71\) | −15.2130 | −1.80545 | −0.902726 | − | 0.430215i | \(-0.858438\pi\) | ||||
−0.902726 | + | 0.430215i | \(0.858438\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.2547 | 1.31726 | 0.658631 | − | 0.752466i | \(-0.271136\pi\) | ||||
0.658631 | + | 0.752466i | \(0.271136\pi\) | |||||||
\(74\) | −10.3405 | −1.20206 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −0.872548 | −0.100088 | ||||||||
\(77\) | −1.23070 | −0.140251 | ||||||||
\(78\) | 4.87255 | 0.551707 | ||||||||
\(79\) | 8.62102 | 0.969940 | 0.484970 | − | 0.874531i | \(-0.338831\pi\) | ||||
0.484970 | + | 0.874531i | \(0.338831\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.59200 | −0.948828 | ||||||||
\(83\) | −1.99663 | −0.219158 | −0.109579 | − | 0.993978i | \(-0.534950\pi\) | ||||
−0.109579 | + | 0.993978i | \(0.534950\pi\) | |||||||
\(84\) | 1.23070 | 0.134280 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | −0.979164 | −0.105586 | ||||||||
\(87\) | 3.64185 | 0.390447 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 1.28370 | 0.136072 | 0.0680361 | − | 0.997683i | \(-0.478327\pi\) | ||||
0.0680361 | + | 0.997683i | \(0.478327\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 5.99663 | 0.628618 | ||||||||
\(92\) | 9.36130 | 0.975984 | ||||||||
\(93\) | 2.10662 | 0.218446 | ||||||||
\(94\) | 8.59200 | 0.886197 | ||||||||
\(95\) | −0.872548 | −0.0895215 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.85171 | 0.797221 | 0.398610 | − | 0.917120i | \(-0.369493\pi\) | ||||
0.398610 | + | 0.917120i | \(0.369493\pi\) | |||||||
\(98\) | −5.48539 | −0.554108 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −15.8757 | −1.57969 | −0.789846 | − | 0.613305i | \(-0.789839\pi\) | ||||
−0.789846 | + | 0.613305i | \(0.789839\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 16.4437 | 1.62025 | 0.810124 | − | 0.586259i | \(-0.199400\pi\) | ||||
0.810124 | + | 0.586259i | \(0.199400\pi\) | |||||||
\(104\) | 4.87255 | 0.477793 | ||||||||
\(105\) | 1.23070 | 0.120104 | ||||||||
\(106\) | −7.92931 | −0.770163 | ||||||||
\(107\) | 2.02736 | 0.195993 | 0.0979963 | − | 0.995187i | \(-0.468757\pi\) | ||||
0.0979963 | + | 0.995187i | \(0.468757\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −0.209861 | −0.0201010 | −0.0100505 | − | 0.999949i | \(-0.503199\pi\) | ||||
−0.0100505 | + | 0.999949i | \(0.503199\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −10.3405 | −0.981474 | ||||||||
\(112\) | 1.23070 | 0.116290 | ||||||||
\(113\) | −0.875919 | −0.0823996 | −0.0411998 | − | 0.999151i | \(-0.513118\pi\) | ||||
−0.0411998 | + | 0.999151i | \(0.513118\pi\) | |||||||
\(114\) | −0.872548 | −0.0817216 | ||||||||
\(115\) | 9.36130 | 0.872946 | ||||||||
\(116\) | 3.64185 | 0.338137 | ||||||||
\(117\) | 4.87255 | 0.450467 | ||||||||
\(118\) | 9.46792 | 0.871593 | ||||||||
\(119\) | −1.23070 | −0.112818 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.00337115 | 0.000305210 0 | ||||||||
\(123\) | −8.59200 | −0.774715 | ||||||||
\(124\) | 2.10662 | 0.189180 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.23070 | 0.109639 | ||||||||
\(127\) | 6.13061 | 0.544004 | 0.272002 | − | 0.962297i | \(-0.412314\pi\) | ||||
0.272002 | + | 0.962297i | \(0.412314\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.979164 | −0.0862106 | ||||||||
\(130\) | 4.87255 | 0.427351 | ||||||||
\(131\) | 15.1874 | 1.32693 | 0.663464 | − | 0.748209i | \(-0.269086\pi\) | ||||
0.663464 | + | 0.748209i | \(0.269086\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −1.07384 | −0.0931139 | ||||||||
\(134\) | −11.8791 | −1.02620 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 14.4437 | 1.23401 | 0.617005 | − | 0.786959i | \(-0.288346\pi\) | ||||
0.617005 | + | 0.786959i | \(0.288346\pi\) | |||||||
\(138\) | 9.36130 | 0.796887 | ||||||||
\(139\) | 2.74366 | 0.232714 | 0.116357 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116357 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(140\) | 1.23070 | 0.104013 | ||||||||
\(141\) | 8.59200 | 0.723577 | ||||||||
\(142\) | −15.2130 | −1.27665 | ||||||||
\(143\) | −4.87255 | −0.407463 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.64185 | 0.302439 | ||||||||
\(146\) | 11.2547 | 0.931445 | ||||||||
\(147\) | −5.48539 | −0.452427 | ||||||||
\(148\) | −10.3405 | −0.849981 | ||||||||
\(149\) | −12.3405 | −1.01097 | −0.505485 | − | 0.862835i | \(-0.668687\pi\) | ||||
−0.505485 | + | 0.862835i | \(0.668687\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 2.59537 | 0.211208 | 0.105604 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105604 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(152\) | −0.872548 | −0.0707730 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.23070 | −0.0991724 | ||||||||
\(155\) | 2.10662 | 0.169207 | ||||||||
\(156\) | 4.87255 | 0.390116 | ||||||||
\(157\) | 17.6208 | 1.40629 | 0.703146 | − | 0.711045i | \(-0.251778\pi\) | ||||
0.703146 | + | 0.711045i | \(0.251778\pi\) | |||||||
\(158\) | 8.62102 | 0.685851 | ||||||||
\(159\) | −7.92931 | −0.628836 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.5209 | 0.907976 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.79495 | 0.218917 | 0.109459 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109459 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(164\) | −8.59200 | −0.670923 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −1.99663 | −0.154968 | ||||||||
\(167\) | −10.1306 | −0.783930 | −0.391965 | − | 0.919980i | \(-0.628205\pi\) | ||||
−0.391965 | + | 0.919980i | \(0.628205\pi\) | |||||||
\(168\) | 1.23070 | 0.0949503 | ||||||||
\(169\) | 10.7417 | 0.826287 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | −0.872548 | −0.0667254 | ||||||||
\(172\) | −0.979164 | −0.0746606 | ||||||||
\(173\) | 3.67259 | 0.279222 | 0.139611 | − | 0.990206i | \(-0.455415\pi\) | ||||
0.139611 | + | 0.990206i | \(0.455415\pi\) | |||||||
\(174\) | 3.64185 | 0.276088 | ||||||||
\(175\) | 1.23070 | 0.0930319 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 9.46792 | 0.711653 | ||||||||
\(178\) | 1.28370 | 0.0962176 | ||||||||
\(179\) | −11.4645 | −0.856901 | −0.428450 | − | 0.903565i | \(-0.640940\pi\) | ||||
−0.428450 | + | 0.903565i | \(0.640940\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −7.85508 | −0.583864 | −0.291932 | − | 0.956439i | \(-0.594298\pi\) | ||||
−0.291932 | + | 0.956439i | \(0.594298\pi\) | |||||||
\(182\) | 5.99663 | 0.444500 | ||||||||
\(183\) | 0.00337115 | 0.000249203 0 | ||||||||
\(184\) | 9.36130 | 0.690125 | ||||||||
\(185\) | −10.3405 | −0.760246 | ||||||||
\(186\) | 2.10662 | 0.154465 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 8.59200 | 0.626636 | ||||||||
\(189\) | 1.23070 | 0.0895200 | ||||||||
\(190\) | −0.872548 | −0.0633013 | ||||||||
\(191\) | −9.64185 | −0.697660 | −0.348830 | − | 0.937186i | \(-0.613421\pi\) | ||||
−0.348830 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 24.4967 | 1.76331 | 0.881656 | − | 0.471892i | \(-0.156429\pi\) | ||||
0.881656 | + | 0.471892i | \(0.156429\pi\) | |||||||
\(194\) | 7.85171 | 0.563720 | ||||||||
\(195\) | 4.87255 | 0.348930 | ||||||||
\(196\) | −5.48539 | −0.391813 | ||||||||
\(197\) | −13.6242 | −0.970682 | −0.485341 | − | 0.874325i | \(-0.661305\pi\) | ||||
−0.485341 | + | 0.874325i | \(0.661305\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −27.8307 | −1.97286 | −0.986432 | − | 0.164173i | \(-0.947505\pi\) | ||||
−0.986432 | + | 0.164173i | \(0.947505\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −11.8791 | −0.837885 | ||||||||
\(202\) | −15.8757 | −1.11701 | ||||||||
\(203\) | 4.48201 | 0.314576 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −8.59200 | −0.600091 | ||||||||
\(206\) | 16.4437 | 1.14569 | ||||||||
\(207\) | 9.36130 | 0.650656 | ||||||||
\(208\) | 4.87255 | 0.337850 | ||||||||
\(209\) | 0.872548 | 0.0603554 | ||||||||
\(210\) | 1.23070 | 0.0849261 | ||||||||
\(211\) | −11.9857 | −0.825129 | −0.412565 | − | 0.910928i | \(-0.635367\pi\) | ||||
−0.412565 | + | 0.910928i | \(0.635367\pi\) | |||||||
\(212\) | −7.92931 | −0.544588 | ||||||||
\(213\) | −15.2130 | −1.04238 | ||||||||
\(214\) | 2.02736 | 0.138588 | ||||||||
\(215\) | −0.979164 | −0.0667784 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.59261 | 0.175998 | ||||||||
\(218\) | −0.209861 | −0.0142136 | ||||||||
\(219\) | 11.2547 | 0.760521 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −4.87255 | −0.327763 | ||||||||
\(222\) | −10.3405 | −0.694007 | ||||||||
\(223\) | −26.7466 | −1.79108 | −0.895542 | − | 0.444976i | \(-0.853212\pi\) | ||||
−0.895542 | + | 0.444976i | \(0.853212\pi\) | |||||||
\(224\) | 1.23070 | 0.0822294 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −0.875919 | −0.0582653 | ||||||||
\(227\) | −11.9277 | −0.791667 | −0.395833 | − | 0.918322i | \(-0.629544\pi\) | ||||
−0.395833 | + | 0.918322i | \(0.629544\pi\) | |||||||
\(228\) | −0.872548 | −0.0577859 | ||||||||
\(229\) | −0.770954 | −0.0509461 | −0.0254730 | − | 0.999676i | \(-0.508109\pi\) | ||||
−0.0254730 | + | 0.999676i | \(0.508109\pi\) | |||||||
\(230\) | 9.36130 | 0.617266 | ||||||||
\(231\) | −1.23070 | −0.0809739 | ||||||||
\(232\) | 3.64185 | 0.239099 | ||||||||
\(233\) | 5.00144 | 0.327655 | 0.163827 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163827 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(234\) | 4.87255 | 0.318528 | ||||||||
\(235\) | 8.59200 | 0.560480 | ||||||||
\(236\) | 9.46792 | 0.616309 | ||||||||
\(237\) | 8.62102 | 0.559995 | ||||||||
\(238\) | −1.23070 | −0.0797742 | ||||||||
\(239\) | −7.38418 | −0.477643 | −0.238821 | − | 0.971063i | \(-0.576761\pi\) | ||||
−0.238821 | + | 0.971063i | \(0.576761\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 24.6033 | 1.58484 | 0.792420 | − | 0.609976i | \(-0.208821\pi\) | ||||
0.792420 | + | 0.609976i | \(0.208821\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.00337115 | 0.000215816 0 | ||||||||
\(245\) | −5.48539 | −0.350448 | ||||||||
\(246\) | −8.59200 | −0.547806 | ||||||||
\(247\) | −4.25153 | −0.270519 | ||||||||
\(248\) | 2.10662 | 0.133770 | ||||||||
\(249\) | −1.99663 | −0.126531 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 4.23213 | 0.267130 | 0.133565 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133565 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(252\) | 1.23070 | 0.0775266 | ||||||||
\(253\) | −9.36130 | −0.588540 | ||||||||
\(254\) | 6.13061 | 0.384669 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.4115 | 0.961346 | 0.480673 | − | 0.876900i | \(-0.340392\pi\) | ||||
0.480673 | + | 0.876900i | \(0.340392\pi\) | |||||||
\(258\) | −0.979164 | −0.0609601 | ||||||||
\(259\) | −12.7260 | −0.790754 | ||||||||
\(260\) | 4.87255 | 0.302183 | ||||||||
\(261\) | 3.64185 | 0.225425 | ||||||||
\(262\) | 15.1874 | 0.938279 | ||||||||
\(263\) | −13.1600 | −0.811481 | −0.405741 | − | 0.913988i | \(-0.632986\pi\) | ||||
−0.405741 | + | 0.913988i | \(0.632986\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −7.92931 | −0.487094 | ||||||||
\(266\) | −1.07384 | −0.0658415 | ||||||||
\(267\) | 1.28370 | 0.0785613 | ||||||||
\(268\) | −11.8791 | −0.725630 | ||||||||
\(269\) | −19.4355 | −1.18501 | −0.592503 | − | 0.805568i | \(-0.701860\pi\) | ||||
−0.592503 | + | 0.805568i | \(0.701860\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 4.31648 | 0.262207 | 0.131104 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131104 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 5.99663 | 0.362932 | ||||||||
\(274\) | 14.4437 | 0.872577 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 9.36130 | 0.563484 | ||||||||
\(277\) | 5.99326 | 0.360100 | 0.180050 | − | 0.983657i | \(-0.442374\pi\) | ||||
0.180050 | + | 0.983657i | \(0.442374\pi\) | |||||||
\(278\) | 2.74366 | 0.164554 | ||||||||
\(279\) | 2.10662 | 0.126120 | ||||||||
\(280\) | 1.23070 | 0.0735482 | ||||||||
\(281\) | −8.07865 | −0.481932 | −0.240966 | − | 0.970534i | \(-0.577464\pi\) | ||||
−0.240966 | + | 0.970534i | \(0.577464\pi\) | |||||||
\(282\) | 8.59200 | 0.511646 | ||||||||
\(283\) | −18.7294 | −1.11334 | −0.556672 | − | 0.830732i | \(-0.687922\pi\) | ||||
−0.556672 | + | 0.830732i | \(0.687922\pi\) | |||||||
\(284\) | −15.2130 | −0.902726 | ||||||||
\(285\) | −0.872548 | −0.0516853 | ||||||||
\(286\) | −4.87255 | −0.288120 | ||||||||
\(287\) | −10.5741 | −0.624172 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.64185 | 0.213857 | ||||||||
\(291\) | 7.85171 | 0.460276 | ||||||||
\(292\) | 11.2547 | 0.658631 | ||||||||
\(293\) | −0.895423 | −0.0523112 | −0.0261556 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261556 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(294\) | −5.48539 | −0.319914 | ||||||||
\(295\) | 9.46792 | 0.551244 | ||||||||
\(296\) | −10.3405 | −0.601028 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −12.3405 | −0.714864 | ||||||||
\(299\) | 45.6134 | 2.63789 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −1.20505 | −0.0694582 | ||||||||
\(302\) | 2.59537 | 0.149347 | ||||||||
\(303\) | −15.8757 | −0.912035 | ||||||||
\(304\) | −0.872548 | −0.0500441 | ||||||||
\(305\) | 0.00337115 | 0.000193032 0 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 20.3490 | 1.16138 | 0.580690 | − | 0.814124i | \(-0.302783\pi\) | ||||
0.580690 | + | 0.814124i | \(0.302783\pi\) | |||||||
\(308\) | −1.23070 | −0.0701255 | ||||||||
\(309\) | 16.4437 | 0.935450 | ||||||||
\(310\) | 2.10662 | 0.119648 | ||||||||
\(311\) | 21.1713 | 1.20052 | 0.600258 | − | 0.799806i | \(-0.295064\pi\) | ||||
0.600258 | + | 0.799806i | \(0.295064\pi\) | |||||||
\(312\) | 4.87255 | 0.275854 | ||||||||
\(313\) | 16.3262 | 0.922809 | 0.461405 | − | 0.887190i | \(-0.347346\pi\) | ||||
0.461405 | + | 0.887190i | \(0.347346\pi\) | |||||||
\(314\) | 17.6208 | 0.994399 | ||||||||
\(315\) | 1.23070 | 0.0693419 | ||||||||
\(316\) | 8.62102 | 0.484970 | ||||||||
\(317\) | 28.6536 | 1.60935 | 0.804673 | − | 0.593719i | \(-0.202341\pi\) | ||||
0.804673 | + | 0.593719i | \(0.202341\pi\) | |||||||
\(318\) | −7.92931 | −0.444654 | ||||||||
\(319\) | −3.64185 | −0.203905 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.02736 | 0.113156 | ||||||||
\(322\) | 11.5209 | 0.642036 | ||||||||
\(323\) | 0.872548 | 0.0485499 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.87255 | 0.270280 | ||||||||
\(326\) | 2.79495 | 0.154798 | ||||||||
\(327\) | −0.209861 | −0.0116053 | ||||||||
\(328\) | −8.59200 | −0.474414 | ||||||||
\(329\) | 10.5741 | 0.582972 | ||||||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | −26.6536 | −1.46501 | −0.732506 | − | 0.680760i | \(-0.761650\pi\) | ||||
−0.732506 | + | 0.680760i | \(0.761650\pi\) | |||||||
\(332\) | −1.99663 | −0.109579 | ||||||||
\(333\) | −10.3405 | −0.566654 | ||||||||
\(334\) | −10.1306 | −0.554322 | ||||||||
\(335\) | −11.8791 | −0.649023 | ||||||||
\(336\) | 1.23070 | 0.0671400 | ||||||||
\(337\) | 28.4387 | 1.54915 | 0.774577 | − | 0.632479i | \(-0.217963\pi\) | ||||
0.774577 | + | 0.632479i | \(0.217963\pi\) | |||||||
\(338\) | 10.7417 | 0.584273 | ||||||||
\(339\) | −0.875919 | −0.0475734 | ||||||||
\(340\) | −1.00000 | −0.0542326 | ||||||||
\(341\) | −2.10662 | −0.114080 | ||||||||
\(342\) | −0.872548 | −0.0471820 | ||||||||
\(343\) | −15.3657 | −0.829671 | ||||||||
\(344\) | −0.979164 | −0.0527930 | ||||||||
\(345\) | 9.36130 | 0.503996 | ||||||||
\(346\) | 3.67259 | 0.197439 | ||||||||
\(347\) | −10.1135 | −0.542923 | −0.271461 | − | 0.962449i | \(-0.587507\pi\) | ||||
−0.271461 | + | 0.962449i | \(0.587507\pi\) | |||||||
\(348\) | 3.64185 | 0.195224 | ||||||||
\(349\) | 31.4742 | 1.68478 | 0.842389 | − | 0.538871i | \(-0.181149\pi\) | ||||
0.842389 | + | 0.538871i | \(0.181149\pi\) | |||||||
\(350\) | 1.23070 | 0.0657835 | ||||||||
\(351\) | 4.87255 | 0.260077 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −5.86879 | −0.312364 | −0.156182 | − | 0.987728i | \(-0.549919\pi\) | ||||
−0.156182 | + | 0.987728i | \(0.549919\pi\) | |||||||
\(354\) | 9.46792 | 0.503214 | ||||||||
\(355\) | −15.2130 | −0.807423 | ||||||||
\(356\) | 1.28370 | 0.0680361 | ||||||||
\(357\) | −1.23070 | −0.0651354 | ||||||||
\(358\) | −11.4645 | −0.605920 | ||||||||
\(359\) | −1.96507 | −0.103712 | −0.0518562 | − | 0.998655i | \(-0.516514\pi\) | ||||
−0.0518562 | + | 0.998655i | \(0.516514\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.2387 | −0.959929 | ||||||||
\(362\) | −7.85508 | −0.412854 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 5.99663 | 0.314309 | ||||||||
\(365\) | 11.2547 | 0.589097 | ||||||||
\(366\) | 0.00337115 | 0.000176213 0 | ||||||||
\(367\) | −20.9291 | −1.09249 | −0.546245 | − | 0.837625i | \(-0.683943\pi\) | ||||
−0.546245 | + | 0.837625i | \(0.683943\pi\) | |||||||
\(368\) | 9.36130 | 0.487992 | ||||||||
\(369\) | −8.59200 | −0.447282 | ||||||||
\(370\) | −10.3405 | −0.537575 | ||||||||
\(371\) | −9.75858 | −0.506640 | ||||||||
\(372\) | 2.10662 | 0.109223 | ||||||||
\(373\) | −32.1659 | −1.66549 | −0.832744 | − | 0.553657i | \(-0.813232\pi\) | ||||
−0.832744 | + | 0.553657i | \(0.813232\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 8.59200 | 0.443099 | ||||||||
\(377\) | 17.7451 | 0.913919 | ||||||||
\(378\) | 1.23070 | 0.0633002 | ||||||||
\(379\) | −27.6004 | −1.41773 | −0.708867 | − | 0.705342i | \(-0.750794\pi\) | ||||
−0.708867 | + | 0.705342i | \(0.750794\pi\) | |||||||
\(380\) | −0.872548 | −0.0447608 | ||||||||
\(381\) | 6.13061 | 0.314081 | ||||||||
\(382\) | −9.64185 | −0.493320 | ||||||||
\(383\) | −11.6692 | −0.596269 | −0.298135 | − | 0.954524i | \(-0.596364\pi\) | ||||
−0.298135 | + | 0.954524i | \(0.596364\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.23070 | −0.0627221 | ||||||||
\(386\) | 24.4967 | 1.24685 | ||||||||
\(387\) | −0.979164 | −0.0497737 | ||||||||
\(388\) | 7.85171 | 0.398610 | ||||||||
\(389\) | 9.33057 | 0.473079 | 0.236539 | − | 0.971622i | \(-0.423987\pi\) | ||||
0.236539 | + | 0.971622i | \(0.423987\pi\) | |||||||
\(390\) | 4.87255 | 0.246731 | ||||||||
\(391\) | −9.36130 | −0.473422 | ||||||||
\(392\) | −5.48539 | −0.277054 | ||||||||
\(393\) | 15.1874 | 0.766102 | ||||||||
\(394\) | −13.6242 | −0.686376 | ||||||||
\(395\) | 8.62102 | 0.433770 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −20.5983 | −1.03380 | −0.516900 | − | 0.856046i | \(-0.672914\pi\) | ||||
−0.516900 | + | 0.856046i | \(0.672914\pi\) | |||||||
\(398\) | −27.8307 | −1.39503 | ||||||||
\(399\) | −1.07384 | −0.0537593 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.53359 | 0.0765836 | 0.0382918 | − | 0.999267i | \(-0.487808\pi\) | ||||
0.0382918 | + | 0.999267i | \(0.487808\pi\) | |||||||
\(402\) | −11.8791 | −0.592474 | ||||||||
\(403\) | 10.2646 | 0.511316 | ||||||||
\(404\) | −15.8757 | −0.789846 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 4.48201 | 0.222439 | ||||||||
\(407\) | 10.3405 | 0.512558 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −10.9775 | −0.542803 | −0.271402 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271402 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(410\) | −8.59200 | −0.424329 | ||||||||
\(411\) | 14.4437 | 0.712456 | ||||||||
\(412\) | 16.4437 | 0.810124 | ||||||||
\(413\) | 11.6521 | 0.573364 | ||||||||
\(414\) | 9.36130 | 0.460083 | ||||||||
\(415\) | −1.99663 | −0.0980107 | ||||||||
\(416\) | 4.87255 | 0.238896 | ||||||||
\(417\) | 2.74366 | 0.134358 | ||||||||
\(418\) | 0.872548 | 0.0426777 | ||||||||
\(419\) | −27.0562 | −1.32178 | −0.660890 | − | 0.750483i | \(-0.729821\pi\) | ||||
−0.660890 | + | 0.750483i | \(0.729821\pi\) | |||||||
\(420\) | 1.23070 | 0.0600518 | ||||||||
\(421\) | 27.5483 | 1.34262 | 0.671311 | − | 0.741176i | \(-0.265732\pi\) | ||||
0.671311 | + | 0.741176i | \(0.265732\pi\) | |||||||
\(422\) | −11.9857 | −0.583454 | ||||||||
\(423\) | 8.59200 | 0.417757 | ||||||||
\(424\) | −7.92931 | −0.385082 | ||||||||
\(425\) | −1.00000 | −0.0485071 | ||||||||
\(426\) | −15.2130 | −0.737073 | ||||||||
\(427\) | 0.00414887 | 0.000200778 0 | ||||||||
\(428\) | 2.02736 | 0.0979963 | ||||||||
\(429\) | −4.87255 | −0.235249 | ||||||||
\(430\) | −0.979164 | −0.0472195 | ||||||||
\(431\) | 3.62478 | 0.174599 | 0.0872996 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0872996 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −14.2065 | −0.682720 | −0.341360 | − | 0.939933i | \(-0.610888\pi\) | ||||
−0.341360 | + | 0.939933i | \(0.610888\pi\) | |||||||
\(434\) | 2.59261 | 0.124449 | ||||||||
\(435\) | 3.64185 | 0.174613 | ||||||||
\(436\) | −0.209861 | −0.0100505 | ||||||||
\(437\) | −8.16819 | −0.390737 | ||||||||
\(438\) | 11.2547 | 0.537770 | ||||||||
\(439\) | 10.2601 | 0.489688 | 0.244844 | − | 0.969563i | \(-0.421263\pi\) | ||||
0.244844 | + | 0.969563i | \(0.421263\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −5.48539 | −0.261209 | ||||||||
\(442\) | −4.87255 | −0.231763 | ||||||||
\(443\) | −10.2287 | −0.485978 | −0.242989 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242989 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(444\) | −10.3405 | −0.490737 | ||||||||
\(445\) | 1.28370 | 0.0608534 | ||||||||
\(446\) | −26.7466 | −1.26649 | ||||||||
\(447\) | −12.3405 | −0.583684 | ||||||||
\(448\) | 1.23070 | 0.0581450 | ||||||||
\(449\) | −16.7626 | −0.791074 | −0.395537 | − | 0.918450i | \(-0.629442\pi\) | ||||
−0.395537 | + | 0.918450i | \(0.629442\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 8.59200 | 0.404582 | ||||||||
\(452\) | −0.875919 | −0.0411998 | ||||||||
\(453\) | 2.59537 | 0.121941 | ||||||||
\(454\) | −11.9277 | −0.559793 | ||||||||
\(455\) | 5.99663 | 0.281126 | ||||||||
\(456\) | −0.872548 | −0.0408608 | ||||||||
\(457\) | −4.41635 | −0.206588 | −0.103294 | − | 0.994651i | \(-0.532938\pi\) | ||||
−0.103294 | + | 0.994651i | \(0.532938\pi\) | |||||||
\(458\) | −0.770954 | −0.0360243 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 9.36130 | 0.436473 | ||||||||
\(461\) | −6.13735 | −0.285845 | −0.142922 | − | 0.989734i | \(-0.545650\pi\) | ||||
−0.142922 | + | 0.989734i | \(0.545650\pi\) | |||||||
\(462\) | −1.23070 | −0.0572572 | ||||||||
\(463\) | 21.3522 | 0.992321 | 0.496160 | − | 0.868231i | \(-0.334743\pi\) | ||||
0.496160 | + | 0.868231i | \(0.334743\pi\) | |||||||
\(464\) | 3.64185 | 0.169069 | ||||||||
\(465\) | 2.10662 | 0.0976920 | ||||||||
\(466\) | 5.00144 | 0.231687 | ||||||||
\(467\) | −16.6143 | −0.768817 | −0.384408 | − | 0.923163i | \(-0.625595\pi\) | ||||
−0.384408 | + | 0.923163i | \(0.625595\pi\) | |||||||
\(468\) | 4.87255 | 0.225234 | ||||||||
\(469\) | −14.6195 | −0.675068 | ||||||||
\(470\) | 8.59200 | 0.396319 | ||||||||
\(471\) | 17.6208 | 0.811924 | ||||||||
\(472\) | 9.46792 | 0.435796 | ||||||||
\(473\) | 0.979164 | 0.0450220 | ||||||||
\(474\) | 8.62102 | 0.395976 | ||||||||
\(475\) | −0.872548 | −0.0400353 | ||||||||
\(476\) | −1.23070 | −0.0564089 | ||||||||
\(477\) | −7.92931 | −0.363058 | ||||||||
\(478\) | −7.38418 | −0.337745 | ||||||||
\(479\) | 14.7403 | 0.673501 | 0.336751 | − | 0.941594i | \(-0.390672\pi\) | ||||
0.336751 | + | 0.941594i | \(0.390672\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −50.3844 | −2.29733 | ||||||||
\(482\) | 24.6033 | 1.12065 | ||||||||
\(483\) | 11.5209 | 0.524220 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.85171 | 0.356528 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 4.51612 | 0.204645 | 0.102322 | − | 0.994751i | \(-0.467373\pi\) | ||||
0.102322 | + | 0.994751i | \(0.467373\pi\) | |||||||
\(488\) | 0.00337115 | 0.000152605 0 | ||||||||
\(489\) | 2.79495 | 0.126392 | ||||||||
\(490\) | −5.48539 | −0.247804 | ||||||||
\(491\) | −34.6400 | −1.56328 | −0.781640 | − | 0.623729i | \(-0.785617\pi\) | ||||
−0.781640 | + | 0.623729i | \(0.785617\pi\) | |||||||
\(492\) | −8.59200 | −0.387357 | ||||||||
\(493\) | −3.64185 | −0.164021 | ||||||||
\(494\) | −4.25153 | −0.191285 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 2.10662 | 0.0945898 | ||||||||
\(497\) | −18.7226 | −0.839824 | ||||||||
\(498\) | −1.99663 | −0.0894711 | ||||||||
\(499\) | 30.8778 | 1.38228 | 0.691140 | − | 0.722721i | \(-0.257109\pi\) | ||||
0.691140 | + | 0.722721i | \(0.257109\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −10.1306 | −0.452602 | ||||||||
\(502\) | 4.23213 | 0.188889 | ||||||||
\(503\) | −27.6625 | −1.23341 | −0.616704 | − | 0.787195i | \(-0.711533\pi\) | ||||
−0.616704 | + | 0.787195i | \(0.711533\pi\) | |||||||
\(504\) | 1.23070 | 0.0548196 | ||||||||
\(505\) | −15.8757 | −0.706460 | ||||||||
\(506\) | −9.36130 | −0.416161 | ||||||||
\(507\) | 10.7417 | 0.477057 | ||||||||
\(508\) | 6.13061 | 0.272002 | ||||||||
\(509\) | −6.15288 | −0.272722 | −0.136361 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136361 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(510\) | −1.00000 | −0.0442807 | ||||||||
\(511\) | 13.8511 | 0.612737 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.872548 | −0.0385239 | ||||||||
\(514\) | 15.4115 | 0.679774 | ||||||||
\(515\) | 16.4437 | 0.724597 | ||||||||
\(516\) | −0.979164 | −0.0431053 | ||||||||
\(517\) | −8.59200 | −0.377876 | ||||||||
\(518\) | −12.7260 | −0.559148 | ||||||||
\(519\) | 3.67259 | 0.161209 | ||||||||
\(520\) | 4.87255 | 0.213675 | ||||||||
\(521\) | −16.4870 | −0.722310 | −0.361155 | − | 0.932506i | \(-0.617618\pi\) | ||||
−0.361155 | + | 0.932506i | \(0.617618\pi\) | |||||||
\(522\) | 3.64185 | 0.159400 | ||||||||
\(523\) | 0.346211 | 0.0151387 | 0.00756937 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756937 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(524\) | 15.1874 | 0.663464 | ||||||||
\(525\) | 1.23070 | 0.0537120 | ||||||||
\(526\) | −13.1600 | −0.573804 | ||||||||
\(527\) | −2.10662 | −0.0917656 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 64.6340 | 2.81018 | ||||||||
\(530\) | −7.92931 | −0.344427 | ||||||||
\(531\) | 9.46792 | 0.410873 | ||||||||
\(532\) | −1.07384 | −0.0465570 | ||||||||
\(533\) | −41.8649 | −1.81337 | ||||||||
\(534\) | 1.28370 | 0.0555513 | ||||||||
\(535\) | 2.02736 | 0.0876506 | ||||||||
\(536\) | −11.8791 | −0.513098 | ||||||||
\(537\) | −11.4645 | −0.494732 | ||||||||
\(538\) | −19.4355 | −0.837925 | ||||||||
\(539\) | 5.48539 | 0.236272 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 9.13194 | 0.392613 | 0.196306 | − | 0.980543i | \(-0.437105\pi\) | ||||
0.196306 | + | 0.980543i | \(0.437105\pi\) | |||||||
\(542\) | 4.31648 | 0.185409 | ||||||||
\(543\) | −7.85508 | −0.337094 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −0.209861 | −0.00898945 | ||||||||
\(546\) | 5.99663 | 0.256632 | ||||||||
\(547\) | −30.4130 | −1.30037 | −0.650184 | − | 0.759777i | \(-0.725308\pi\) | ||||
−0.650184 | + | 0.759777i | \(0.725308\pi\) | |||||||
\(548\) | 14.4437 | 0.617005 | ||||||||
\(549\) | 0.00337115 | 0.000143877 0 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −3.17769 | −0.135374 | ||||||||
\(552\) | 9.36130 | 0.398444 | ||||||||
\(553\) | 10.6099 | 0.451177 | ||||||||
\(554\) | 5.99326 | 0.254629 | ||||||||
\(555\) | −10.3405 | −0.438928 | ||||||||
\(556\) | 2.74366 | 0.116357 | ||||||||
\(557\) | 7.04985 | 0.298712 | 0.149356 | − | 0.988784i | \(-0.452280\pi\) | ||||
0.149356 | + | 0.988784i | \(0.452280\pi\) | |||||||
\(558\) | 2.10662 | 0.0891802 | ||||||||
\(559\) | −4.77102 | −0.201793 | ||||||||
\(560\) | 1.23070 | 0.0520064 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −8.07865 | −0.340777 | ||||||||
\(563\) | −1.08058 | −0.0455412 | −0.0227706 | − | 0.999741i | \(-0.507249\pi\) | ||||
−0.0227706 | + | 0.999741i | \(0.507249\pi\) | |||||||
\(564\) | 8.59200 | 0.361789 | ||||||||
\(565\) | −0.875919 | −0.0368502 | ||||||||
\(566\) | −18.7294 | −0.787253 | ||||||||
\(567\) | 1.23070 | 0.0516844 | ||||||||
\(568\) | −15.2130 | −0.638324 | ||||||||
\(569\) | −25.0802 | −1.05141 | −0.525707 | − | 0.850665i | \(-0.676199\pi\) | ||||
−0.525707 | + | 0.850665i | \(0.676199\pi\) | |||||||
\(570\) | −0.872548 | −0.0365470 | ||||||||
\(571\) | 43.7447 | 1.83066 | 0.915329 | − | 0.402708i | \(-0.131931\pi\) | ||||
0.915329 | + | 0.402708i | \(0.131931\pi\) | |||||||
\(572\) | −4.87255 | −0.203731 | ||||||||
\(573\) | −9.64185 | −0.402794 | ||||||||
\(574\) | −10.5741 | −0.441356 | ||||||||
\(575\) | 9.36130 | 0.390393 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −3.69381 | −0.153775 | −0.0768877 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768877 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 24.4967 | 1.01805 | ||||||||
\(580\) | 3.64185 | 0.151220 | ||||||||
\(581\) | −2.45724 | −0.101944 | ||||||||
\(582\) | 7.85171 | 0.325464 | ||||||||
\(583\) | 7.92931 | 0.328399 | ||||||||
\(584\) | 11.2547 | 0.465722 | ||||||||
\(585\) | 4.87255 | 0.201455 | ||||||||
\(586\) | −0.895423 | −0.0369896 | ||||||||
\(587\) | 11.4707 | 0.473446 | 0.236723 | − | 0.971577i | \(-0.423927\pi\) | ||||
0.236723 | + | 0.971577i | \(0.423927\pi\) | |||||||
\(588\) | −5.48539 | −0.226213 | ||||||||
\(589\) | −1.83812 | −0.0757386 | ||||||||
\(590\) | 9.46792 | 0.389788 | ||||||||
\(591\) | −13.6242 | −0.560424 | ||||||||
\(592\) | −10.3405 | −0.424991 | ||||||||
\(593\) | 9.85863 | 0.404845 | 0.202423 | − | 0.979298i | \(-0.435119\pi\) | ||||
0.202423 | + | 0.979298i | \(0.435119\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −1.23070 | −0.0504536 | ||||||||
\(596\) | −12.3405 | −0.505485 | ||||||||
\(597\) | −27.8307 | −1.13903 | ||||||||
\(598\) | 45.6134 | 1.86527 | ||||||||
\(599\) | −9.28431 | −0.379346 | −0.189673 | − | 0.981847i | \(-0.560743\pi\) | ||||
−0.189673 | + | 0.981847i | \(0.560743\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −4.98608 | −0.203386 | −0.101693 | − | 0.994816i | \(-0.532426\pi\) | ||||
−0.101693 | + | 0.994816i | \(0.532426\pi\) | |||||||
\(602\) | −1.20505 | −0.0491143 | ||||||||
\(603\) | −11.8791 | −0.483753 | ||||||||
\(604\) | 2.59537 | 0.105604 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −15.8757 | −0.644906 | ||||||||
\(607\) | 13.3224 | 0.540740 | 0.270370 | − | 0.962757i | \(-0.412854\pi\) | ||||
0.270370 | + | 0.962757i | \(0.412854\pi\) | |||||||
\(608\) | −0.872548 | −0.0353865 | ||||||||
\(609\) | 4.48201 | 0.181620 | ||||||||
\(610\) | 0.00337115 | 0.000136494 0 | ||||||||
\(611\) | 41.8649 | 1.69367 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −6.10834 | −0.246713 | −0.123357 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123357 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(614\) | 20.3490 | 0.821220 | ||||||||
\(615\) | −8.59200 | −0.346463 | ||||||||
\(616\) | −1.23070 | −0.0495862 | ||||||||
\(617\) | 6.21169 | 0.250073 | 0.125037 | − | 0.992152i | \(-0.460095\pi\) | ||||
0.125037 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(618\) | 16.4437 | 0.661463 | ||||||||
\(619\) | 21.7834 | 0.875549 | 0.437774 | − | 0.899085i | \(-0.355767\pi\) | ||||
0.437774 | + | 0.899085i | \(0.355767\pi\) | |||||||
\(620\) | 2.10662 | 0.0846037 | ||||||||
\(621\) | 9.36130 | 0.375656 | ||||||||
\(622\) | 21.1713 | 0.848894 | ||||||||
\(623\) | 1.57985 | 0.0632953 | ||||||||
\(624\) | 4.87255 | 0.195058 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.3262 | 0.652525 | ||||||||
\(627\) | 0.872548 | 0.0348462 | ||||||||
\(628\) | 17.6208 | 0.703146 | ||||||||
\(629\) | 10.3405 | 0.412301 | ||||||||
\(630\) | 1.23070 | 0.0490321 | ||||||||
\(631\) | 2.51942 | 0.100297 | 0.0501483 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501483 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(632\) | 8.62102 | 0.342926 | ||||||||
\(633\) | −11.9857 | −0.476388 | ||||||||
\(634\) | 28.6536 | 1.13798 | ||||||||
\(635\) | 6.13061 | 0.243286 | ||||||||
\(636\) | −7.92931 | −0.314418 | ||||||||
\(637\) | −26.7278 | −1.05899 | ||||||||
\(638\) | −3.64185 | −0.144182 | ||||||||
\(639\) | −15.2130 | −0.601818 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −20.0012 | −0.790001 | −0.395000 | − | 0.918681i | \(-0.629256\pi\) | ||||
−0.395000 | + | 0.918681i | \(0.629256\pi\) | |||||||
\(642\) | 2.02736 | 0.0800137 | ||||||||
\(643\) | −9.46957 | −0.373443 | −0.186722 | − | 0.982413i | \(-0.559786\pi\) | ||||
−0.186722 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(644\) | 11.5209 | 0.453988 | ||||||||
\(645\) | −0.979164 | −0.0385545 | ||||||||
\(646\) | 0.872548 | 0.0343299 | ||||||||
\(647\) | −31.7343 | −1.24761 | −0.623803 | − | 0.781582i | \(-0.714413\pi\) | ||||
−0.623803 | + | 0.781582i | \(0.714413\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −9.46792 | −0.371648 | ||||||||
\(650\) | 4.87255 | 0.191117 | ||||||||
\(651\) | 2.59261 | 0.101612 | ||||||||
\(652\) | 2.79495 | 0.109459 | ||||||||
\(653\) | −11.7661 | −0.460445 | −0.230222 | − | 0.973138i | \(-0.573945\pi\) | ||||
−0.230222 | + | 0.973138i | \(0.573945\pi\) | |||||||
\(654\) | −0.209861 | −0.00820620 | ||||||||
\(655\) | 15.1874 | 0.593420 | ||||||||
\(656\) | −8.59200 | −0.335461 | ||||||||
\(657\) | 11.2547 | 0.439087 | ||||||||
\(658\) | 10.5741 | 0.412223 | ||||||||
\(659\) | 31.3385 | 1.22078 | 0.610388 | − | 0.792103i | \(-0.291014\pi\) | ||||
0.610388 | + | 0.792103i | \(0.291014\pi\) | |||||||
\(660\) | −1.00000 | −0.0389249 | ||||||||
\(661\) | 0.880407 | 0.0342439 | 0.0171219 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171219 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(662\) | −26.6536 | −1.03592 | ||||||||
\(663\) | −4.87255 | −0.189234 | ||||||||
\(664\) | −1.99663 | −0.0774842 | ||||||||
\(665\) | −1.07384 | −0.0416418 | ||||||||
\(666\) | −10.3405 | −0.400685 | ||||||||
\(667\) | 34.0925 | 1.32007 | ||||||||
\(668\) | −10.1306 | −0.391965 | ||||||||
\(669\) | −26.7466 | −1.03408 | ||||||||
\(670\) | −11.8791 | −0.458929 | ||||||||
\(671\) | −0.00337115 | −0.000130142 0 | ||||||||
\(672\) | 1.23070 | 0.0474752 | ||||||||
\(673\) | 40.0416 | 1.54349 | 0.771746 | − | 0.635931i | \(-0.219384\pi\) | ||||
0.771746 | + | 0.635931i | \(0.219384\pi\) | |||||||
\(674\) | 28.4387 | 1.09542 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 10.7417 | 0.413143 | ||||||||
\(677\) | 12.0759 | 0.464114 | 0.232057 | − | 0.972702i | \(-0.425454\pi\) | ||||
0.232057 | + | 0.972702i | \(0.425454\pi\) | |||||||
\(678\) | −0.875919 | −0.0336395 | ||||||||
\(679\) | 9.66308 | 0.370835 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | −11.9277 | −0.457069 | ||||||||
\(682\) | −2.10662 | −0.0806665 | ||||||||
\(683\) | −50.0652 | −1.91569 | −0.957846 | − | 0.287284i | \(-0.907248\pi\) | ||||
−0.957846 | + | 0.287284i | \(0.907248\pi\) | |||||||
\(684\) | −0.872548 | −0.0333627 | ||||||||
\(685\) | 14.4437 | 0.551866 | ||||||||
\(686\) | −15.3657 | −0.586666 | ||||||||
\(687\) | −0.770954 | −0.0294137 | ||||||||
\(688\) | −0.979164 | −0.0373303 | ||||||||
\(689\) | −38.6360 | −1.47191 | ||||||||
\(690\) | 9.36130 | 0.356379 | ||||||||
\(691\) | −0.302818 | −0.0115197 | −0.00575987 | − | 0.999983i | \(-0.501833\pi\) | ||||
−0.00575987 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(692\) | 3.67259 | 0.139611 | ||||||||
\(693\) | −1.23070 | −0.0467503 | ||||||||
\(694\) | −10.1135 | −0.383904 | ||||||||
\(695\) | 2.74366 | 0.104073 | ||||||||
\(696\) | 3.64185 | 0.138044 | ||||||||
\(697\) | 8.59200 | 0.325445 | ||||||||
\(698\) | 31.4742 | 1.19132 | ||||||||
\(699\) | 5.00144 | 0.189172 | ||||||||
\(700\) | 1.23070 | 0.0465160 | ||||||||
\(701\) | −35.0467 | −1.32369 | −0.661847 | − | 0.749639i | \(-0.730227\pi\) | ||||
−0.661847 | + | 0.749639i | \(0.730227\pi\) | |||||||
\(702\) | 4.87255 | 0.183902 | ||||||||
\(703\) | 9.02256 | 0.340292 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 8.59200 | 0.323594 | ||||||||
\(706\) | −5.86879 | −0.220875 | ||||||||
\(707\) | −19.5382 | −0.734809 | ||||||||
\(708\) | 9.46792 | 0.355826 | ||||||||
\(709\) | 16.1853 | 0.607853 | 0.303927 | − | 0.952695i | \(-0.401702\pi\) | ||||
0.303927 | + | 0.952695i | \(0.401702\pi\) | |||||||
\(710\) | −15.2130 | −0.570934 | ||||||||
\(711\) | 8.62102 | 0.323313 | ||||||||
\(712\) | 1.28370 | 0.0481088 | ||||||||
\(713\) | 19.7207 | 0.738545 | ||||||||
\(714\) | −1.23070 | −0.0460577 | ||||||||
\(715\) | −4.87255 | −0.182223 | ||||||||
\(716\) | −11.4645 | −0.428450 | ||||||||
\(717\) | −7.38418 | −0.275767 | ||||||||
\(718\) | −1.96507 | −0.0733358 | ||||||||
\(719\) | −37.3778 | −1.39396 | −0.696979 | − | 0.717092i | \(-0.745473\pi\) | ||||
−0.696979 | + | 0.717092i | \(0.745473\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 20.2372 | 0.753674 | ||||||||
\(722\) | −18.2387 | −0.678773 | ||||||||
\(723\) | 24.6033 | 0.915008 | ||||||||
\(724\) | −7.85508 | −0.291932 | ||||||||
\(725\) | 3.64185 | 0.135255 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 25.5108 | 0.946144 | 0.473072 | − | 0.881024i | \(-0.343145\pi\) | ||||
0.473072 | + | 0.881024i | \(0.343145\pi\) | |||||||
\(728\) | 5.99663 | 0.222250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.2547 | 0.416555 | ||||||||
\(731\) | 0.979164 | 0.0362157 | ||||||||
\(732\) | 0.00337115 | 0.000124601 0 | ||||||||
\(733\) | −51.7116 | −1.91001 | −0.955005 | − | 0.296590i | \(-0.904151\pi\) | ||||
−0.955005 | + | 0.296590i | \(0.904151\pi\) | |||||||
\(734\) | −20.9291 | −0.772507 | ||||||||
\(735\) | −5.48539 | −0.202331 | ||||||||
\(736\) | 9.36130 | 0.345062 | ||||||||
\(737\) | 11.8791 | 0.437571 | ||||||||
\(738\) | −8.59200 | −0.316276 | ||||||||
\(739\) | −9.43034 | −0.346901 | −0.173450 | − | 0.984843i | \(-0.555492\pi\) | ||||
−0.173450 | + | 0.984843i | \(0.555492\pi\) | |||||||
\(740\) | −10.3405 | −0.380123 | ||||||||
\(741\) | −4.25153 | −0.156184 | ||||||||
\(742\) | −9.75858 | −0.358249 | ||||||||
\(743\) | 5.02521 | 0.184357 | 0.0921785 | − | 0.995742i | \(-0.470617\pi\) | ||||
0.0921785 | + | 0.995742i | \(0.470617\pi\) | |||||||
\(744\) | 2.10662 | 0.0772323 | ||||||||
\(745\) | −12.3405 | −0.452120 | ||||||||
\(746\) | −32.1659 | −1.17768 | ||||||||
\(747\) | −1.99663 | −0.0730528 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 2.49507 | 0.0911679 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −22.8806 | −0.834924 | −0.417462 | − | 0.908694i | \(-0.637080\pi\) | ||||
−0.417462 | + | 0.908694i | \(0.637080\pi\) | |||||||
\(752\) | 8.59200 | 0.313318 | ||||||||
\(753\) | 4.23213 | 0.154227 | ||||||||
\(754\) | 17.7451 | 0.646238 | ||||||||
\(755\) | 2.59537 | 0.0944553 | ||||||||
\(756\) | 1.23070 | 0.0447600 | ||||||||
\(757\) | −26.3228 | −0.956718 | −0.478359 | − | 0.878164i | \(-0.658768\pi\) | ||||
−0.478359 | + | 0.878164i | \(0.658768\pi\) | |||||||
\(758\) | −27.6004 | −1.00249 | ||||||||
\(759\) | −9.36130 | −0.339794 | ||||||||
\(760\) | −0.872548 | −0.0316506 | ||||||||
\(761\) | −48.1602 | −1.74581 | −0.872903 | − | 0.487894i | \(-0.837765\pi\) | ||||
−0.872903 | + | 0.487894i | \(0.837765\pi\) | |||||||
\(762\) | 6.13061 | 0.222089 | ||||||||
\(763\) | −0.258275 | −0.00935018 | ||||||||
\(764\) | −9.64185 | −0.348830 | ||||||||
\(765\) | −1.00000 | −0.0361551 | ||||||||
\(766\) | −11.6692 | −0.421626 | ||||||||
\(767\) | 46.1329 | 1.66576 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −18.3125 | −0.660366 | −0.330183 | − | 0.943917i | \(-0.607110\pi\) | ||||
−0.330183 | + | 0.943917i | \(0.607110\pi\) | |||||||
\(770\) | −1.23070 | −0.0443512 | ||||||||
\(771\) | 15.4115 | 0.555033 | ||||||||
\(772\) | 24.4967 | 0.881656 | ||||||||
\(773\) | −6.03316 | −0.216998 | −0.108499 | − | 0.994097i | \(-0.534604\pi\) | ||||
−0.108499 | + | 0.994097i | \(0.534604\pi\) | |||||||
\(774\) | −0.979164 | −0.0351953 | ||||||||
\(775\) | 2.10662 | 0.0756719 | ||||||||
\(776\) | 7.85171 | 0.281860 | ||||||||
\(777\) | −12.7260 | −0.456542 | ||||||||
\(778\) | 9.33057 | 0.334517 | ||||||||
\(779\) | 7.49693 | 0.268606 | ||||||||
\(780\) | 4.87255 | 0.174465 | ||||||||
\(781\) | 15.2130 | 0.544365 | ||||||||
\(782\) | −9.36130 | −0.334760 | ||||||||
\(783\) | 3.64185 | 0.130149 | ||||||||
\(784\) | −5.48539 | −0.195907 | ||||||||
\(785\) | 17.6208 | 0.628913 | ||||||||
\(786\) | 15.1874 | 0.541716 | ||||||||
\(787\) | −40.8744 | −1.45702 | −0.728508 | − | 0.685037i | \(-0.759786\pi\) | ||||
−0.728508 | + | 0.685037i | \(0.759786\pi\) | |||||||
\(788\) | −13.6242 | −0.485341 | ||||||||
\(789\) | −13.1600 | −0.468509 | ||||||||
\(790\) | 8.62102 | 0.306722 | ||||||||
\(791\) | −1.07799 | −0.0383289 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0.0164261 | 0.000583308 0 | ||||||||
\(794\) | −20.5983 | −0.731007 | ||||||||
\(795\) | −7.92931 | −0.281224 | ||||||||
\(796\) | −27.8307 | −0.986432 | ||||||||
\(797\) | 28.3520 | 1.00428 | 0.502139 | − | 0.864787i | \(-0.332546\pi\) | ||||
0.502139 | + | 0.864787i | \(0.332546\pi\) | |||||||
\(798\) | −1.07384 | −0.0380136 | ||||||||
\(799\) | −8.59200 | −0.303963 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 1.28370 | 0.0453574 | ||||||||
\(802\) | 1.53359 | 0.0541528 | ||||||||
\(803\) | −11.2547 | −0.397169 | ||||||||
\(804\) | −11.8791 | −0.418943 | ||||||||
\(805\) | 11.5209 | 0.406059 | ||||||||
\(806\) | 10.2646 | 0.361555 | ||||||||
\(807\) | −19.4355 | −0.684163 | ||||||||
\(808\) | −15.8757 | −0.558505 | ||||||||
\(809\) | −11.9337 | −0.419568 | −0.209784 | − | 0.977748i | \(-0.567276\pi\) | ||||
−0.209784 | + | 0.977748i | \(0.567276\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 10.9426 | 0.384246 | 0.192123 | − | 0.981371i | \(-0.438463\pi\) | ||||
0.192123 | + | 0.981371i | \(0.438463\pi\) | |||||||
\(812\) | 4.48201 | 0.157288 | ||||||||
\(813\) | 4.31648 | 0.151385 | ||||||||
\(814\) | 10.3405 | 0.362433 | ||||||||
\(815\) | 2.79495 | 0.0979027 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 0.854368 | 0.0298905 | ||||||||
\(818\) | −10.9775 | −0.383820 | ||||||||
\(819\) | 5.99663 | 0.209539 | ||||||||
\(820\) | −8.59200 | −0.300046 | ||||||||
\(821\) | 24.8806 | 0.868338 | 0.434169 | − | 0.900831i | \(-0.357042\pi\) | ||||
0.434169 | + | 0.900831i | \(0.357042\pi\) | |||||||
\(822\) | 14.4437 | 0.503782 | ||||||||
\(823\) | −27.1840 | −0.947575 | −0.473787 | − | 0.880639i | \(-0.657113\pi\) | ||||
−0.473787 | + | 0.880639i | \(0.657113\pi\) | |||||||
\(824\) | 16.4437 | 0.572844 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 11.6521 | 0.405430 | ||||||||
\(827\) | −2.68893 | −0.0935034 | −0.0467517 | − | 0.998907i | \(-0.514887\pi\) | ||||
−0.0467517 | + | 0.998907i | \(0.514887\pi\) | |||||||
\(828\) | 9.36130 | 0.325328 | ||||||||
\(829\) | 20.9262 | 0.726796 | 0.363398 | − | 0.931634i | \(-0.381617\pi\) | ||||
0.363398 | + | 0.931634i | \(0.381617\pi\) | |||||||
\(830\) | −1.99663 | −0.0693040 | ||||||||
\(831\) | 5.99326 | 0.207904 | ||||||||
\(832\) | 4.87255 | 0.168925 | ||||||||
\(833\) | 5.48539 | 0.190057 | ||||||||
\(834\) | 2.74366 | 0.0950052 | ||||||||
\(835\) | −10.1306 | −0.350584 | ||||||||
\(836\) | 0.872548 | 0.0301777 | ||||||||
\(837\) | 2.10662 | 0.0728153 | ||||||||
\(838\) | −27.0562 | −0.934640 | ||||||||
\(839\) | 0.780241 | 0.0269369 | 0.0134684 | − | 0.999909i | \(-0.495713\pi\) | ||||
0.0134684 | + | 0.999909i | \(0.495713\pi\) | |||||||
\(840\) | 1.23070 | 0.0424631 | ||||||||
\(841\) | −15.7369 | −0.542652 | ||||||||
\(842\) | 27.5483 | 0.949377 | ||||||||
\(843\) | −8.07865 | −0.278243 | ||||||||
\(844\) | −11.9857 | −0.412565 | ||||||||
\(845\) | 10.7417 | 0.369527 | ||||||||
\(846\) | 8.59200 | 0.295399 | ||||||||
\(847\) | 1.23070 | 0.0422872 | ||||||||
\(848\) | −7.92931 | −0.272294 | ||||||||
\(849\) | −18.7294 | −0.642790 | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | −96.8003 | −3.31827 | ||||||||
\(852\) | −15.2130 | −0.521189 | ||||||||
\(853\) | 5.35274 | 0.183274 | 0.0916371 | − | 0.995792i | \(-0.470790\pi\) | ||||
0.0916371 | + | 0.995792i | \(0.470790\pi\) | |||||||
\(854\) | 0.00414887 | 0.000141971 0 | ||||||||
\(855\) | −0.872548 | −0.0298405 | ||||||||
\(856\) | 2.02736 | 0.0692939 | ||||||||
\(857\) | −16.2468 | −0.554981 | −0.277491 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277491 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(858\) | −4.87255 | −0.166346 | ||||||||
\(859\) | −4.22424 | −0.144129 | −0.0720646 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720646 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(860\) | −0.979164 | −0.0333892 | ||||||||
\(861\) | −10.5741 | −0.360366 | ||||||||
\(862\) | 3.62478 | 0.123460 | ||||||||
\(863\) | 23.0248 | 0.783773 | 0.391886 | − | 0.920014i | \(-0.371823\pi\) | ||||
0.391886 | + | 0.920014i | \(0.371823\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 3.67259 | 0.124872 | ||||||||
\(866\) | −14.2065 | −0.482756 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 2.59261 | 0.0879988 | ||||||||
\(869\) | −8.62102 | −0.292448 | ||||||||
\(870\) | 3.64185 | 0.123470 | ||||||||
\(871\) | −57.8814 | −1.96124 | ||||||||
\(872\) | −0.209861 | −0.00710678 | ||||||||
\(873\) | 7.85171 | 0.265740 | ||||||||
\(874\) | −8.16819 | −0.276293 | ||||||||
\(875\) | 1.23070 | 0.0416051 | ||||||||
\(876\) | 11.2547 | 0.380261 | ||||||||
\(877\) | 49.0208 | 1.65531 | 0.827657 | − | 0.561234i | \(-0.189673\pi\) | ||||
0.827657 | + | 0.561234i | \(0.189673\pi\) | |||||||
\(878\) | 10.2601 | 0.346262 | ||||||||
\(879\) | −0.895423 | −0.0302019 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −3.99878 | −0.134722 | −0.0673611 | − | 0.997729i | \(-0.521458\pi\) | ||||
−0.0673611 | + | 0.997729i | \(0.521458\pi\) | |||||||
\(882\) | −5.48539 | −0.184703 | ||||||||
\(883\) | −9.04665 | −0.304444 | −0.152222 | − | 0.988346i | \(-0.548643\pi\) | ||||
−0.152222 | + | 0.988346i | \(0.548643\pi\) | |||||||
\(884\) | −4.87255 | −0.163882 | ||||||||
\(885\) | 9.46792 | 0.318261 | ||||||||
\(886\) | −10.2287 | −0.343638 | ||||||||
\(887\) | −2.48886 | −0.0835678 | −0.0417839 | − | 0.999127i | \(-0.513304\pi\) | ||||
−0.0417839 | + | 0.999127i | \(0.513304\pi\) | |||||||
\(888\) | −10.3405 | −0.347003 | ||||||||
\(889\) | 7.54492 | 0.253048 | ||||||||
\(890\) | 1.28370 | 0.0430298 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −26.7466 | −0.895542 | ||||||||
\(893\) | −7.49693 | −0.250875 | ||||||||
\(894\) | −12.3405 | −0.412727 | ||||||||
\(895\) | −11.4645 | −0.383218 | ||||||||
\(896\) | 1.23070 | 0.0411147 | ||||||||
\(897\) | 45.6134 | 1.52299 | ||||||||
\(898\) | −16.7626 | −0.559374 | ||||||||
\(899\) | 7.67198 | 0.255875 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 7.92931 | 0.264164 | ||||||||
\(902\) | 8.59200 | 0.286082 | ||||||||
\(903\) | −1.20505 | −0.0401017 | ||||||||
\(904\) | −0.875919 | −0.0291326 | ||||||||
\(905\) | −7.85508 | −0.261112 | ||||||||
\(906\) | 2.59537 | 0.0862255 | ||||||||
\(907\) | 25.3591 | 0.842033 | 0.421017 | − | 0.907053i | \(-0.361673\pi\) | ||||
0.421017 | + | 0.907053i | \(0.361673\pi\) | |||||||
\(908\) | −11.9277 | −0.395833 | ||||||||
\(909\) | −15.8757 | −0.526564 | ||||||||
\(910\) | 5.99663 | 0.198786 | ||||||||
\(911\) | −21.7324 | −0.720028 | −0.360014 | − | 0.932947i | \(-0.617228\pi\) | ||||
−0.360014 | + | 0.932947i | \(0.617228\pi\) | |||||||
\(912\) | −0.872548 | −0.0288930 | ||||||||
\(913\) | 1.99663 | 0.0660788 | ||||||||
\(914\) | −4.41635 | −0.146080 | ||||||||
\(915\) | 0.00337115 | 0.000111447 0 | ||||||||
\(916\) | −0.770954 | −0.0254730 | ||||||||
\(917\) | 18.6911 | 0.617233 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 29.3870 | 0.969388 | 0.484694 | − | 0.874684i | \(-0.338931\pi\) | ||||
0.484694 | + | 0.874684i | \(0.338931\pi\) | |||||||
\(920\) | 9.36130 | 0.308633 | ||||||||
\(921\) | 20.3490 | 0.670524 | ||||||||
\(922\) | −6.13735 | −0.202123 | ||||||||
\(923\) | −74.1262 | −2.43989 | ||||||||
\(924\) | −1.23070 | −0.0404869 | ||||||||
\(925\) | −10.3405 | −0.339993 | ||||||||
\(926\) | 21.3522 | 0.701677 | ||||||||
\(927\) | 16.4437 | 0.540082 | ||||||||
\(928\) | 3.64185 | 0.119550 | ||||||||
\(929\) | 38.0184 | 1.24734 | 0.623672 | − | 0.781686i | \(-0.285640\pi\) | ||||
0.623672 | + | 0.781686i | \(0.285640\pi\) | |||||||
\(930\) | 2.10662 | 0.0690787 | ||||||||
\(931\) | 4.78626 | 0.156863 | ||||||||
\(932\) | 5.00144 | 0.163827 | ||||||||
\(933\) | 21.1713 | 0.693119 | ||||||||
\(934\) | −16.6143 | −0.543636 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 4.87255 | 0.159264 | ||||||||
\(937\) | −49.4931 | −1.61687 | −0.808435 | − | 0.588585i | \(-0.799685\pi\) | ||||
−0.808435 | + | 0.588585i | \(0.799685\pi\) | |||||||
\(938\) | −14.6195 | −0.477345 | ||||||||
\(939\) | 16.3262 | 0.532784 | ||||||||
\(940\) | 8.59200 | 0.280240 | ||||||||
\(941\) | 51.6792 | 1.68469 | 0.842347 | − | 0.538936i | \(-0.181174\pi\) | ||||
0.842347 | + | 0.538936i | \(0.181174\pi\) | |||||||
\(942\) | 17.6208 | 0.574117 | ||||||||
\(943\) | −80.4323 | −2.61924 | ||||||||
\(944\) | 9.46792 | 0.308155 | ||||||||
\(945\) | 1.23070 | 0.0400346 | ||||||||
\(946\) | 0.979164 | 0.0318354 | ||||||||
\(947\) | −4.56453 | −0.148327 | −0.0741637 | − | 0.997246i | \(-0.523629\pi\) | ||||
−0.0741637 | + | 0.997246i | \(0.523629\pi\) | |||||||
\(948\) | 8.62102 | 0.279998 | ||||||||
\(949\) | 54.8390 | 1.78015 | ||||||||
\(950\) | −0.872548 | −0.0283092 | ||||||||
\(951\) | 28.6536 | 0.929156 | ||||||||
\(952\) | −1.23070 | −0.0398871 | ||||||||
\(953\) | −12.2549 | −0.396975 | −0.198488 | − | 0.980103i | \(-0.563603\pi\) | ||||
−0.198488 | + | 0.980103i | \(0.563603\pi\) | |||||||
\(954\) | −7.92931 | −0.256721 | ||||||||
\(955\) | −9.64185 | −0.312003 | ||||||||
\(956\) | −7.38418 | −0.238821 | ||||||||
\(957\) | −3.64185 | −0.117724 | ||||||||
\(958\) | 14.7403 | 0.476237 | ||||||||
\(959\) | 17.7758 | 0.574012 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −26.5622 | −0.856844 | ||||||||
\(962\) | −50.3844 | −1.62446 | ||||||||
\(963\) | 2.02736 | 0.0653309 | ||||||||
\(964\) | 24.6033 | 0.792420 | ||||||||
\(965\) | 24.4967 | 0.788577 | ||||||||
\(966\) | 11.5209 | 0.370680 | ||||||||
\(967\) | −37.0597 | −1.19176 | −0.595880 | − | 0.803074i | \(-0.703197\pi\) | ||||
−0.595880 | + | 0.803074i | \(0.703197\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0.872548 | 0.0280303 | ||||||||
\(970\) | 7.85171 | 0.252103 | ||||||||
\(971\) | −24.4933 | −0.786029 | −0.393014 | − | 0.919532i | \(-0.628568\pi\) | ||||
−0.393014 | + | 0.919532i | \(0.628568\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 3.37661 | 0.108249 | ||||||||
\(974\) | 4.51612 | 0.144706 | ||||||||
\(975\) | 4.87255 | 0.156046 | ||||||||
\(976\) | 0.00337115 | 0.000107908 0 | ||||||||
\(977\) | 34.5127 | 1.10416 | 0.552080 | − | 0.833791i | \(-0.313834\pi\) | ||||
0.552080 | + | 0.833791i | \(0.313834\pi\) | |||||||
\(978\) | 2.79495 | 0.0893725 | ||||||||
\(979\) | −1.28370 | −0.0410273 | ||||||||
\(980\) | −5.48539 | −0.175224 | ||||||||
\(981\) | −0.209861 | −0.00670034 | ||||||||
\(982\) | −34.6400 | −1.10541 | ||||||||
\(983\) | −21.8193 | −0.695928 | −0.347964 | − | 0.937508i | \(-0.613127\pi\) | ||||
−0.347964 | + | 0.937508i | \(0.613127\pi\) | |||||||
\(984\) | −8.59200 | −0.273903 | ||||||||
\(985\) | −13.6242 | −0.434102 | ||||||||
\(986\) | −3.64185 | −0.115980 | ||||||||
\(987\) | 10.5741 | 0.336579 | ||||||||
\(988\) | −4.25153 | −0.135259 | ||||||||
\(989\) | −9.16625 | −0.291470 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | 37.5868 | 1.19398 | 0.596991 | − | 0.802248i | \(-0.296363\pi\) | ||||
0.596991 | + | 0.802248i | \(0.296363\pi\) | |||||||
\(992\) | 2.10662 | 0.0668851 | ||||||||
\(993\) | −26.6536 | −0.845826 | ||||||||
\(994\) | −18.7226 | −0.593845 | ||||||||
\(995\) | −27.8307 | −0.882291 | ||||||||
\(996\) | −1.99663 | −0.0632656 | ||||||||
\(997\) | −10.9565 | −0.346995 | −0.173497 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173497 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(998\) | 30.8778 | 0.977420 | ||||||||
\(999\) | −10.3405 | −0.327158 |
(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 | 5610.2.a.ck.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.ck.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial |