Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607 | 1.58114 | 0.790569 | − | 0.612372i | \(-0.209785\pi\) | ||||
0.790569 | + | 0.612372i | \(0.209785\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.23607 | −0.912871 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.23607 | −0.707107 | ||||||||
\(11\) | −2.47214 | −0.745377 | −0.372689 | − | 0.927957i | \(-0.621564\pi\) | ||||
−0.372689 | + | 0.927957i | \(0.621564\pi\) | |||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 2.23607 | 0.597614 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 2.23607 | 0.527046 | ||||||||
\(19\) | 6.47214 | 1.48481 | 0.742405 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742405 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.52786 | −1.17854 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −10.0000 | −1.96116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 2.23607 | 0.408248 | ||||||||
\(31\) | 10.4721 | 1.88085 | 0.940426 | − | 0.340000i | \(-0.110427\pi\) | ||||
0.940426 | + | 0.340000i | \(0.110427\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 2.47214 | 0.430344 | ||||||||
\(34\) | −4.47214 | −0.766965 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 10.9443 | 1.79923 | 0.899614 | − | 0.436687i | \(-0.143848\pi\) | ||||
0.899614 | + | 0.436687i | \(0.143848\pi\) | |||||||
\(38\) | 14.4721 | 2.34769 | ||||||||
\(39\) | 4.47214 | 0.716115 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | −2.23607 | −0.345033 | ||||||||
\(43\) | −8.94427 | −1.36399 | −0.681994 | − | 0.731357i | \(-0.738887\pi\) | ||||
−0.681994 | + | 0.731357i | \(0.738887\pi\) | |||||||
\(44\) | −7.41641 | −1.11807 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 8.94427 | 1.31876 | ||||||||
\(47\) | −4.94427 | −0.721196 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.23607 | 0.316228 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −13.4164 | −1.86052 | ||||||||
\(53\) | −12.4721 | −1.71318 | −0.856590 | − | 0.515998i | \(-0.827421\pi\) | ||||
−0.856590 | + | 0.515998i | \(0.827421\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | 2.47214 | 0.333343 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −6.47214 | −0.857255 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 3.00000 | 0.387298 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 23.4164 | 2.97389 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 5.52786 | 0.680433 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | −2.23607 | −0.267261 | ||||||||
\(71\) | 14.4721 | 1.71753 | 0.858763 | − | 0.512373i | \(-0.171233\pi\) | ||||
0.858763 | + | 0.512373i | \(0.171233\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −3.52786 | −0.412905 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(74\) | 24.4721 | 2.84483 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 19.4164 | 2.22721 | ||||||||
\(77\) | −2.47214 | −0.281726 | ||||||||
\(78\) | 10.0000 | 1.13228 | ||||||||
\(79\) | −4.94427 | −0.556274 | −0.278137 | − | 0.960541i | \(-0.589717\pi\) | ||||
−0.278137 | + | 0.960541i | \(0.589717\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.47214 | −0.493865 | ||||||||
\(83\) | 0.944272 | 0.103647 | 0.0518237 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518237 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | −20.0000 | −2.15666 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | −5.52786 | −0.589272 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | −2.23607 | −0.235702 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | −10.4721 | −1.08591 | ||||||||
\(94\) | −11.0557 | −1.14031 | ||||||||
\(95\) | −6.47214 | −0.664027 | ||||||||
\(96\) | 6.70820 | 0.684653 | ||||||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | −2.47214 | −0.248459 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 4.47214 | 0.442807 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −10.0000 | −0.980581 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −27.8885 | −2.70877 | ||||||||
\(107\) | 4.94427 | 0.477981 | 0.238990 | − | 0.971022i | \(-0.423184\pi\) | ||||
0.238990 | + | 0.971022i | \(0.423184\pi\) | |||||||
\(108\) | −3.00000 | −0.288675 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 5.52786 | 0.527061 | ||||||||
\(111\) | −10.9443 | −1.03878 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −8.47214 | −0.796992 | −0.398496 | − | 0.917170i | \(-0.630468\pi\) | ||||
−0.398496 | + | 0.917170i | \(0.630468\pi\) | |||||||
\(114\) | −14.4721 | −1.35544 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 20.0000 | 1.84115 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 2.23607 | 0.204124 | ||||||||
\(121\) | −4.88854 | −0.444413 | ||||||||
\(122\) | −4.47214 | −0.404888 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 31.4164 | 2.82128 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.23607 | 0.199205 | ||||||||
\(127\) | 12.9443 | 1.14862 | 0.574309 | − | 0.818638i | \(-0.305271\pi\) | ||||
0.574309 | + | 0.818638i | \(0.305271\pi\) | |||||||
\(128\) | −15.6525 | −1.38350 | ||||||||
\(129\) | 8.94427 | 0.787499 | ||||||||
\(130\) | 10.0000 | 0.877058 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 7.41641 | 0.645515 | ||||||||
\(133\) | 6.47214 | 0.561205 | ||||||||
\(134\) | −8.94427 | −0.772667 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.47214 | −0.383482 | ||||||||
\(137\) | 12.4721 | 1.06557 | 0.532783 | − | 0.846252i | \(-0.321146\pi\) | ||||
0.532783 | + | 0.846252i | \(0.321146\pi\) | |||||||
\(138\) | −8.94427 | −0.761387 | ||||||||
\(139\) | −19.4164 | −1.64688 | −0.823439 | − | 0.567405i | \(-0.807948\pi\) | ||||
−0.823439 | + | 0.567405i | \(0.807948\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 4.94427 | 0.416383 | ||||||||
\(142\) | 32.3607 | 2.71565 | ||||||||
\(143\) | 11.0557 | 0.924526 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | −7.88854 | −0.652861 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 32.8328 | 2.69884 | ||||||||
\(149\) | 2.94427 | 0.241204 | 0.120602 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120602 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(150\) | −2.23607 | −0.182574 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 14.4721 | 1.17385 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −5.52786 | −0.445448 | ||||||||
\(155\) | −10.4721 | −0.841142 | ||||||||
\(156\) | 13.4164 | 1.07417 | ||||||||
\(157\) | 8.47214 | 0.676150 | 0.338075 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338075 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(158\) | −11.0557 | −0.879547 | ||||||||
\(159\) | 12.4721 | 0.989105 | ||||||||
\(160\) | 6.70820 | 0.530330 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 2.23607 | 0.175682 | ||||||||
\(163\) | 0.944272 | 0.0739611 | 0.0369805 | − | 0.999316i | \(-0.488226\pi\) | ||||
0.0369805 | + | 0.999316i | \(0.488226\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | −2.47214 | −0.192456 | ||||||||
\(166\) | 2.11146 | 0.163881 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 4.47214 | 0.342997 | ||||||||
\(171\) | 6.47214 | 0.494937 | ||||||||
\(172\) | −26.8328 | −2.04598 | ||||||||
\(173\) | 14.9443 | 1.13619 | 0.568096 | − | 0.822962i | \(-0.307680\pi\) | ||||
0.568096 | + | 0.822962i | \(0.307680\pi\) | |||||||
\(174\) | 4.47214 | 0.339032 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 2.47214 | 0.186344 | ||||||||
\(177\) | −8.94427 | −0.672293 | ||||||||
\(178\) | −4.47214 | −0.335201 | ||||||||
\(179\) | −2.47214 | −0.184776 | −0.0923881 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923881 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(180\) | −3.00000 | −0.223607 | ||||||||
\(181\) | 18.9443 | 1.40812 | 0.704058 | − | 0.710142i | \(-0.251369\pi\) | ||||
0.704058 | + | 0.710142i | \(0.251369\pi\) | |||||||
\(182\) | −10.0000 | −0.741249 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 8.94427 | 0.659380 | ||||||||
\(185\) | −10.9443 | −0.804639 | ||||||||
\(186\) | −23.4164 | −1.71697 | ||||||||
\(187\) | 4.94427 | 0.361561 | ||||||||
\(188\) | −14.8328 | −1.08179 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −14.4721 | −1.04992 | ||||||||
\(191\) | 27.4164 | 1.98378 | 0.991891 | − | 0.127093i | \(-0.0405646\pi\) | ||||
0.991891 | + | 0.127093i | \(0.0405646\pi\) | |||||||
\(192\) | 13.0000 | 0.938194 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | −1.05573 | −0.0757969 | ||||||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 24.4721 | 1.74357 | 0.871784 | − | 0.489891i | \(-0.162963\pi\) | ||||
0.871784 | + | 0.489891i | \(0.162963\pi\) | |||||||
\(198\) | −5.52786 | −0.392848 | ||||||||
\(199\) | 0.583592 | 0.0413697 | 0.0206849 | − | 0.999786i | \(-0.493415\pi\) | ||||
0.0206849 | + | 0.999786i | \(0.493415\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | −31.3050 | −2.20261 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 4.47214 | 0.310087 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 2.23607 | 0.154303 | ||||||||
\(211\) | 0.944272 | 0.0650064 | 0.0325032 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325032 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(212\) | −37.4164 | −2.56977 | ||||||||
\(213\) | −14.4721 | −0.991614 | ||||||||
\(214\) | 11.0557 | 0.755754 | ||||||||
\(215\) | 8.94427 | 0.609994 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 10.4721 | 0.710895 | ||||||||
\(218\) | −4.47214 | −0.302891 | ||||||||
\(219\) | 3.52786 | 0.238391 | ||||||||
\(220\) | 7.41641 | 0.500014 | ||||||||
\(221\) | 8.94427 | 0.601657 | ||||||||
\(222\) | −24.4721 | −1.64246 | ||||||||
\(223\) | 4.94427 | 0.331093 | 0.165546 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165546 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(224\) | −6.70820 | −0.448211 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −18.9443 | −1.26015 | ||||||||
\(227\) | −16.9443 | −1.12463 | −0.562315 | − | 0.826923i | \(-0.690089\pi\) | ||||
−0.562315 | + | 0.826923i | \(0.690089\pi\) | |||||||
\(228\) | −19.4164 | −1.28588 | ||||||||
\(229\) | −11.8885 | −0.785617 | −0.392809 | − | 0.919620i | \(-0.628496\pi\) | ||||
−0.392809 | + | 0.919620i | \(0.628496\pi\) | |||||||
\(230\) | −8.94427 | −0.589768 | ||||||||
\(231\) | 2.47214 | 0.162655 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | 17.4164 | 1.14099 | 0.570493 | − | 0.821302i | \(-0.306752\pi\) | ||||
0.570493 | + | 0.821302i | \(0.306752\pi\) | |||||||
\(234\) | −10.0000 | −0.653720 | ||||||||
\(235\) | 4.94427 | 0.322529 | ||||||||
\(236\) | 26.8328 | 1.74667 | ||||||||
\(237\) | 4.94427 | 0.321165 | ||||||||
\(238\) | −4.47214 | −0.289886 | ||||||||
\(239\) | −1.52786 | −0.0988293 | −0.0494147 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494147 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −1.05573 | −0.0680054 | −0.0340027 | − | 0.999422i | \(-0.510825\pi\) | ||||
−0.0340027 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(242\) | −10.9311 | −0.702679 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 4.47214 | 0.285133 | ||||||||
\(247\) | −28.9443 | −1.84168 | ||||||||
\(248\) | 23.4164 | 1.48694 | ||||||||
\(249\) | −0.944272 | −0.0598408 | ||||||||
\(250\) | −2.23607 | −0.141421 | ||||||||
\(251\) | −0.944272 | −0.0596019 | −0.0298010 | − | 0.999556i | \(-0.509487\pi\) | ||||
−0.0298010 | + | 0.999556i | \(0.509487\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | −9.88854 | −0.621687 | ||||||||
\(254\) | 28.9443 | 1.81613 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 1.05573 | 0.0658545 | 0.0329273 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329273 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(258\) | 20.0000 | 1.24515 | ||||||||
\(259\) | 10.9443 | 0.680044 | ||||||||
\(260\) | 13.4164 | 0.832050 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 8.94427 | 0.552579 | ||||||||
\(263\) | 24.9443 | 1.53813 | 0.769065 | − | 0.639171i | \(-0.220722\pi\) | ||||
0.769065 | + | 0.639171i | \(0.220722\pi\) | |||||||
\(264\) | 5.52786 | 0.340217 | ||||||||
\(265\) | 12.4721 | 0.766157 | ||||||||
\(266\) | 14.4721 | 0.887344 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | −23.8885 | −1.45651 | −0.728255 | − | 0.685306i | \(-0.759668\pi\) | ||||
−0.728255 | + | 0.685306i | \(0.759668\pi\) | |||||||
\(270\) | 2.23607 | 0.136083 | ||||||||
\(271\) | −10.4721 | −0.636137 | −0.318068 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 4.47214 | 0.270666 | ||||||||
\(274\) | 27.8885 | 1.68481 | ||||||||
\(275\) | −2.47214 | −0.149075 | ||||||||
\(276\) | −12.0000 | −0.722315 | ||||||||
\(277\) | 1.05573 | 0.0634326 | 0.0317163 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317163 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(278\) | −43.4164 | −2.60394 | ||||||||
\(279\) | 10.4721 | 0.626950 | ||||||||
\(280\) | −2.23607 | −0.133631 | ||||||||
\(281\) | 6.94427 | 0.414261 | 0.207130 | − | 0.978313i | \(-0.433588\pi\) | ||||
0.207130 | + | 0.978313i | \(0.433588\pi\) | |||||||
\(282\) | 11.0557 | 0.658359 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 43.4164 | 2.57629 | ||||||||
\(285\) | 6.47214 | 0.383376 | ||||||||
\(286\) | 24.7214 | 1.46180 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | −6.70820 | −0.395285 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 4.47214 | 0.262613 | ||||||||
\(291\) | 0.472136 | 0.0276771 | ||||||||
\(292\) | −10.5836 | −0.619358 | ||||||||
\(293\) | 22.9443 | 1.34042 | 0.670209 | − | 0.742172i | \(-0.266204\pi\) | ||||
0.670209 | + | 0.742172i | \(0.266204\pi\) | |||||||
\(294\) | −2.23607 | −0.130410 | ||||||||
\(295\) | −8.94427 | −0.520756 | ||||||||
\(296\) | 24.4721 | 1.42241 | ||||||||
\(297\) | 2.47214 | 0.143448 | ||||||||
\(298\) | 6.58359 | 0.381377 | ||||||||
\(299\) | −17.8885 | −1.03452 | ||||||||
\(300\) | −3.00000 | −0.173205 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | −35.7771 | −2.05874 | ||||||||
\(303\) | 14.0000 | 0.804279 | ||||||||
\(304\) | −6.47214 | −0.371202 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | −4.47214 | −0.255655 | ||||||||
\(307\) | −32.9443 | −1.88023 | −0.940114 | − | 0.340859i | \(-0.889282\pi\) | ||||
−0.940114 | + | 0.340859i | \(0.889282\pi\) | |||||||
\(308\) | −7.41641 | −0.422589 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.4164 | −1.32996 | ||||||||
\(311\) | −9.88854 | −0.560728 | −0.280364 | − | 0.959894i | \(-0.590455\pi\) | ||||
−0.280364 | + | 0.959894i | \(0.590455\pi\) | |||||||
\(312\) | 10.0000 | 0.566139 | ||||||||
\(313\) | 9.41641 | 0.532247 | 0.266123 | − | 0.963939i | \(-0.414257\pi\) | ||||
0.266123 | + | 0.963939i | \(0.414257\pi\) | |||||||
\(314\) | 18.9443 | 1.06909 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −14.8328 | −0.834411 | ||||||||
\(317\) | −30.3607 | −1.70523 | −0.852613 | − | 0.522543i | \(-0.824983\pi\) | ||||
−0.852613 | + | 0.522543i | \(0.824983\pi\) | |||||||
\(318\) | 27.8885 | 1.56391 | ||||||||
\(319\) | 4.94427 | 0.276826 | ||||||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | −4.94427 | −0.275962 | ||||||||
\(322\) | 8.94427 | 0.498445 | ||||||||
\(323\) | −12.9443 | −0.720239 | ||||||||
\(324\) | 3.00000 | 0.166667 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | 2.11146 | 0.116943 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | −4.47214 | −0.246932 | ||||||||
\(329\) | −4.94427 | −0.272587 | ||||||||
\(330\) | −5.52786 | −0.304299 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | 2.83282 | 0.155471 | ||||||||
\(333\) | 10.9443 | 0.599742 | ||||||||
\(334\) | −17.8885 | −0.978818 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 11.8885 | 0.647610 | 0.323805 | − | 0.946124i | \(-0.395038\pi\) | ||||
0.323805 | + | 0.946124i | \(0.395038\pi\) | |||||||
\(338\) | 15.6525 | 0.851382 | ||||||||
\(339\) | 8.47214 | 0.460143 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | −25.8885 | −1.40194 | ||||||||
\(342\) | 14.4721 | 0.782563 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 33.4164 | 1.79648 | ||||||||
\(347\) | −8.00000 | −0.429463 | −0.214731 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214731 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(348\) | 6.00000 | 0.321634 | ||||||||
\(349\) | 23.8885 | 1.27872 | 0.639362 | − | 0.768906i | \(-0.279198\pi\) | ||||
0.639362 | + | 0.768906i | \(0.279198\pi\) | |||||||
\(350\) | 2.23607 | 0.119523 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 16.5836 | 0.883908 | ||||||||
\(353\) | −27.8885 | −1.48436 | −0.742179 | − | 0.670202i | \(-0.766207\pi\) | ||||
−0.742179 | + | 0.670202i | \(0.766207\pi\) | |||||||
\(354\) | −20.0000 | −1.06299 | ||||||||
\(355\) | −14.4721 | −0.768101 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 2.00000 | 0.105851 | ||||||||
\(358\) | −5.52786 | −0.292157 | ||||||||
\(359\) | 9.52786 | 0.502861 | 0.251431 | − | 0.967875i | \(-0.419099\pi\) | ||||
0.251431 | + | 0.967875i | \(0.419099\pi\) | |||||||
\(360\) | −2.23607 | −0.117851 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 42.3607 | 2.22643 | ||||||||
\(363\) | 4.88854 | 0.256582 | ||||||||
\(364\) | −13.4164 | −0.703211 | ||||||||
\(365\) | 3.52786 | 0.184657 | ||||||||
\(366\) | 4.47214 | 0.233762 | ||||||||
\(367\) | 20.9443 | 1.09328 | 0.546641 | − | 0.837367i | \(-0.315906\pi\) | ||||
0.546641 | + | 0.837367i | \(0.315906\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −24.4721 | −1.27225 | ||||||||
\(371\) | −12.4721 | −0.647521 | ||||||||
\(372\) | −31.4164 | −1.62886 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 11.0557 | 0.571678 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −11.0557 | −0.570156 | ||||||||
\(377\) | 8.94427 | 0.460653 | ||||||||
\(378\) | −2.23607 | −0.115011 | ||||||||
\(379\) | −2.11146 | −0.108458 | −0.0542291 | − | 0.998529i | \(-0.517270\pi\) | ||||
−0.0542291 | + | 0.998529i | \(0.517270\pi\) | |||||||
\(380\) | −19.4164 | −0.996041 | ||||||||
\(381\) | −12.9443 | −0.663155 | ||||||||
\(382\) | 61.3050 | 3.13663 | ||||||||
\(383\) | −8.00000 | −0.408781 | −0.204390 | − | 0.978889i | \(-0.565521\pi\) | ||||
−0.204390 | + | 0.978889i | \(0.565521\pi\) | |||||||
\(384\) | 15.6525 | 0.798762 | ||||||||
\(385\) | 2.47214 | 0.125992 | ||||||||
\(386\) | −31.3050 | −1.59338 | ||||||||
\(387\) | −8.94427 | −0.454663 | ||||||||
\(388\) | −1.41641 | −0.0719072 | ||||||||
\(389\) | 10.9443 | 0.554897 | 0.277448 | − | 0.960741i | \(-0.410511\pi\) | ||||
0.277448 | + | 0.960741i | \(0.410511\pi\) | |||||||
\(390\) | −10.0000 | −0.506370 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 54.7214 | 2.75682 | ||||||||
\(395\) | 4.94427 | 0.248773 | ||||||||
\(396\) | −7.41641 | −0.372689 | ||||||||
\(397\) | 13.4164 | 0.673350 | 0.336675 | − | 0.941621i | \(-0.390698\pi\) | ||||
0.336675 | + | 0.941621i | \(0.390698\pi\) | |||||||
\(398\) | 1.30495 | 0.0654113 | ||||||||
\(399\) | −6.47214 | −0.324012 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 8.94427 | 0.446100 | ||||||||
\(403\) | −46.8328 | −2.33291 | ||||||||
\(404\) | −42.0000 | −2.08958 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | −27.0557 | −1.34110 | ||||||||
\(408\) | 4.47214 | 0.221404 | ||||||||
\(409\) | −23.8885 | −1.18121 | −0.590606 | − | 0.806960i | \(-0.701111\pi\) | ||||
−0.590606 | + | 0.806960i | \(0.701111\pi\) | |||||||
\(410\) | 4.47214 | 0.220863 | ||||||||
\(411\) | −12.4721 | −0.615205 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427 | 0.440119 | ||||||||
\(414\) | 8.94427 | 0.439587 | ||||||||
\(415\) | −0.944272 | −0.0463525 | ||||||||
\(416\) | 30.0000 | 1.47087 | ||||||||
\(417\) | 19.4164 | 0.950826 | ||||||||
\(418\) | −35.7771 | −1.74991 | ||||||||
\(419\) | 5.88854 | 0.287674 | 0.143837 | − | 0.989601i | \(-0.454056\pi\) | ||||
0.143837 | + | 0.989601i | \(0.454056\pi\) | |||||||
\(420\) | 3.00000 | 0.146385 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 2.11146 | 0.102784 | ||||||||
\(423\) | −4.94427 | −0.240399 | ||||||||
\(424\) | −27.8885 | −1.35439 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | −32.3607 | −1.56788 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 14.8328 | 0.716971 | ||||||||
\(429\) | −11.0557 | −0.533776 | ||||||||
\(430\) | 20.0000 | 0.964486 | ||||||||
\(431\) | −9.52786 | −0.458941 | −0.229471 | − | 0.973316i | \(-0.573699\pi\) | ||||
−0.229471 | + | 0.973316i | \(0.573699\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 7.52786 | 0.361766 | 0.180883 | − | 0.983505i | \(-0.442104\pi\) | ||||
0.180883 | + | 0.983505i | \(0.442104\pi\) | |||||||
\(434\) | 23.4164 | 1.12402 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | 25.8885 | 1.23842 | ||||||||
\(438\) | 7.88854 | 0.376929 | ||||||||
\(439\) | 10.4721 | 0.499808 | 0.249904 | − | 0.968271i | \(-0.419601\pi\) | ||||
0.249904 | + | 0.968271i | \(0.419601\pi\) | |||||||
\(440\) | 5.52786 | 0.263531 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 20.0000 | 0.951303 | ||||||||
\(443\) | −8.00000 | −0.380091 | −0.190046 | − | 0.981775i | \(-0.560864\pi\) | ||||
−0.190046 | + | 0.981775i | \(0.560864\pi\) | |||||||
\(444\) | −32.8328 | −1.55818 | ||||||||
\(445\) | 2.00000 | 0.0948091 | ||||||||
\(446\) | 11.0557 | 0.523504 | ||||||||
\(447\) | −2.94427 | −0.139259 | ||||||||
\(448\) | −13.0000 | −0.614192 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 2.23607 | 0.105409 | ||||||||
\(451\) | 4.94427 | 0.232817 | ||||||||
\(452\) | −25.4164 | −1.19549 | ||||||||
\(453\) | 16.0000 | 0.751746 | ||||||||
\(454\) | −37.8885 | −1.77820 | ||||||||
\(455\) | 4.47214 | 0.209657 | ||||||||
\(456\) | −14.4721 | −0.677720 | ||||||||
\(457\) | −10.9443 | −0.511951 | −0.255976 | − | 0.966683i | \(-0.582397\pi\) | ||||
−0.255976 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(458\) | −26.5836 | −1.24217 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | −31.8885 | −1.48520 | −0.742599 | − | 0.669737i | \(-0.766407\pi\) | ||||
−0.742599 | + | 0.669737i | \(0.766407\pi\) | |||||||
\(462\) | 5.52786 | 0.257180 | ||||||||
\(463\) | 3.05573 | 0.142012 | 0.0710059 | − | 0.997476i | \(-0.477379\pi\) | ||||
0.0710059 | + | 0.997476i | \(0.477379\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 10.4721 | 0.485634 | ||||||||
\(466\) | 38.9443 | 1.80406 | ||||||||
\(467\) | 8.94427 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(468\) | −13.4164 | −0.620174 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 11.0557 | 0.509963 | ||||||||
\(471\) | −8.47214 | −0.390375 | ||||||||
\(472\) | 20.0000 | 0.920575 | ||||||||
\(473\) | 22.1115 | 1.01669 | ||||||||
\(474\) | 11.0557 | 0.507806 | ||||||||
\(475\) | 6.47214 | 0.296962 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | −12.4721 | −0.571060 | ||||||||
\(478\) | −3.41641 | −0.156263 | ||||||||
\(479\) | 17.8885 | 0.817348 | 0.408674 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408674 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(480\) | −6.70820 | −0.306186 | ||||||||
\(481\) | −48.9443 | −2.23167 | ||||||||
\(482\) | −2.36068 | −0.107526 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | −14.6656 | −0.666620 | ||||||||
\(485\) | 0.472136 | 0.0214386 | ||||||||
\(486\) | −2.23607 | −0.101430 | ||||||||
\(487\) | −3.05573 | −0.138468 | −0.0692341 | − | 0.997600i | \(-0.522056\pi\) | ||||
−0.0692341 | + | 0.997600i | \(0.522056\pi\) | |||||||
\(488\) | −4.47214 | −0.202444 | ||||||||
\(489\) | −0.944272 | −0.0427015 | ||||||||
\(490\) | −2.23607 | −0.101015 | ||||||||
\(491\) | 41.3050 | 1.86407 | 0.932033 | − | 0.362373i | \(-0.118033\pi\) | ||||
0.932033 | + | 0.362373i | \(0.118033\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | −64.7214 | −2.91195 | ||||||||
\(495\) | 2.47214 | 0.111114 | ||||||||
\(496\) | −10.4721 | −0.470213 | ||||||||
\(497\) | 14.4721 | 0.649164 | ||||||||
\(498\) | −2.11146 | −0.0946166 | ||||||||
\(499\) | 21.8885 | 0.979866 | 0.489933 | − | 0.871760i | \(-0.337021\pi\) | ||||
0.489933 | + | 0.871760i | \(0.337021\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | −2.11146 | −0.0942389 | ||||||||
\(503\) | 32.0000 | 1.42681 | 0.713405 | − | 0.700752i | \(-0.247152\pi\) | ||||
0.713405 | + | 0.700752i | \(0.247152\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | −22.1115 | −0.982974 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 38.8328 | 1.72293 | ||||||||
\(509\) | 11.8885 | 0.526950 | 0.263475 | − | 0.964666i | \(-0.415131\pi\) | ||||
0.263475 | + | 0.964666i | \(0.415131\pi\) | |||||||
\(510\) | −4.47214 | −0.198030 | ||||||||
\(511\) | −3.52786 | −0.156064 | ||||||||
\(512\) | 11.1803 | 0.494106 | ||||||||
\(513\) | −6.47214 | −0.285752 | ||||||||
\(514\) | 2.36068 | 0.104125 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 26.8328 | 1.18125 | ||||||||
\(517\) | 12.2229 | 0.537563 | ||||||||
\(518\) | 24.4721 | 1.07524 | ||||||||
\(519\) | −14.9443 | −0.655981 | ||||||||
\(520\) | 10.0000 | 0.438529 | ||||||||
\(521\) | 15.8885 | 0.696090 | 0.348045 | − | 0.937478i | \(-0.386846\pi\) | ||||
0.348045 | + | 0.937478i | \(0.386846\pi\) | |||||||
\(522\) | −4.47214 | −0.195740 | ||||||||
\(523\) | 8.94427 | 0.391106 | 0.195553 | − | 0.980693i | \(-0.437350\pi\) | ||||
0.195553 | + | 0.980693i | \(0.437350\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 55.7771 | 2.43200 | ||||||||
\(527\) | −20.9443 | −0.912347 | ||||||||
\(528\) | −2.47214 | −0.107586 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 27.8885 | 1.21140 | ||||||||
\(531\) | 8.94427 | 0.388148 | ||||||||
\(532\) | 19.4164 | 0.841808 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 4.47214 | 0.193528 | ||||||||
\(535\) | −4.94427 | −0.213760 | ||||||||
\(536\) | −8.94427 | −0.386334 | ||||||||
\(537\) | 2.47214 | 0.106681 | ||||||||
\(538\) | −53.4164 | −2.30294 | ||||||||
\(539\) | −2.47214 | −0.106482 | ||||||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 23.8885 | 1.02705 | 0.513524 | − | 0.858075i | \(-0.328340\pi\) | ||||
0.513524 | + | 0.858075i | \(0.328340\pi\) | |||||||
\(542\) | −23.4164 | −1.00582 | ||||||||
\(543\) | −18.9443 | −0.812977 | ||||||||
\(544\) | 13.4164 | 0.575224 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 10.0000 | 0.427960 | ||||||||
\(547\) | −29.8885 | −1.27794 | −0.638971 | − | 0.769231i | \(-0.720640\pi\) | ||||
−0.638971 | + | 0.769231i | \(0.720640\pi\) | |||||||
\(548\) | 37.4164 | 1.59835 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | −5.52786 | −0.235709 | ||||||||
\(551\) | −12.9443 | −0.551445 | ||||||||
\(552\) | −8.94427 | −0.380693 | ||||||||
\(553\) | −4.94427 | −0.210252 | ||||||||
\(554\) | 2.36068 | 0.100296 | ||||||||
\(555\) | 10.9443 | 0.464558 | ||||||||
\(556\) | −58.2492 | −2.47032 | ||||||||
\(557\) | 11.5279 | 0.488451 | 0.244226 | − | 0.969718i | \(-0.421466\pi\) | ||||
0.244226 | + | 0.969718i | \(0.421466\pi\) | |||||||
\(558\) | 23.4164 | 0.991296 | ||||||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −4.94427 | −0.208747 | ||||||||
\(562\) | 15.5279 | 0.655003 | ||||||||
\(563\) | −21.8885 | −0.922492 | −0.461246 | − | 0.887272i | \(-0.652597\pi\) | ||||
−0.461246 | + | 0.887272i | \(0.652597\pi\) | |||||||
\(564\) | 14.8328 | 0.624574 | ||||||||
\(565\) | 8.47214 | 0.356425 | ||||||||
\(566\) | 26.8328 | 1.12787 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 32.3607 | 1.35782 | ||||||||
\(569\) | −4.11146 | −0.172361 | −0.0861806 | − | 0.996280i | \(-0.527466\pi\) | ||||
−0.0861806 | + | 0.996280i | \(0.527466\pi\) | |||||||
\(570\) | 14.4721 | 0.606171 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 33.1672 | 1.38679 | ||||||||
\(573\) | −27.4164 | −1.14534 | ||||||||
\(574\) | −4.47214 | −0.186663 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −13.0000 | −0.541667 | ||||||||
\(577\) | −34.3607 | −1.43045 | −0.715227 | − | 0.698892i | \(-0.753677\pi\) | ||||
−0.715227 | + | 0.698892i | \(0.753677\pi\) | |||||||
\(578\) | −29.0689 | −1.20911 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 0.944272 | 0.0391750 | ||||||||
\(582\) | 1.05573 | 0.0437613 | ||||||||
\(583\) | 30.8328 | 1.27696 | ||||||||
\(584\) | −7.88854 | −0.326430 | ||||||||
\(585\) | 4.47214 | 0.184900 | ||||||||
\(586\) | 51.3050 | 2.11939 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | 67.7771 | 2.79271 | ||||||||
\(590\) | −20.0000 | −0.823387 | ||||||||
\(591\) | −24.4721 | −1.00665 | ||||||||
\(592\) | −10.9443 | −0.449807 | ||||||||
\(593\) | −11.8885 | −0.488204 | −0.244102 | − | 0.969750i | \(-0.578493\pi\) | ||||
−0.244102 | + | 0.969750i | \(0.578493\pi\) | |||||||
\(594\) | 5.52786 | 0.226811 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | 8.83282 | 0.361806 | ||||||||
\(597\) | −0.583592 | −0.0238848 | ||||||||
\(598\) | −40.0000 | −1.63572 | ||||||||
\(599\) | −32.3607 | −1.32222 | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||||
−0.661111 | + | 0.750288i | \(0.729915\pi\) | |||||||
\(600\) | −2.23607 | −0.0912871 | ||||||||
\(601\) | 21.0557 | 0.858881 | 0.429441 | − | 0.903095i | \(-0.358711\pi\) | ||||
0.429441 | + | 0.903095i | \(0.358711\pi\) | |||||||
\(602\) | −20.0000 | −0.815139 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −48.0000 | −1.95309 | ||||||||
\(605\) | 4.88854 | 0.198748 | ||||||||
\(606\) | 31.3050 | 1.27168 | ||||||||
\(607\) | −14.8328 | −0.602045 | −0.301023 | − | 0.953617i | \(-0.597328\pi\) | ||||
−0.301023 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(608\) | −43.4164 | −1.76077 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 4.47214 | 0.181071 | ||||||||
\(611\) | 22.1115 | 0.894534 | ||||||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | 10.9443 | 0.442035 | 0.221017 | − | 0.975270i | \(-0.429062\pi\) | ||||
0.221017 | + | 0.975270i | \(0.429062\pi\) | |||||||
\(614\) | −73.6656 | −2.97290 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | −5.52786 | −0.222724 | ||||||||
\(617\) | 7.52786 | 0.303060 | 0.151530 | − | 0.988453i | \(-0.451580\pi\) | ||||
0.151530 | + | 0.988453i | \(0.451580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5836 | 0.505777 | 0.252889 | − | 0.967495i | \(-0.418619\pi\) | ||||
0.252889 | + | 0.967495i | \(0.418619\pi\) | |||||||
\(620\) | −31.4164 | −1.26171 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −22.1115 | −0.886589 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | −4.47214 | −0.179029 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.0557 | 0.841556 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | 25.4164 | 1.01423 | ||||||||
\(629\) | −21.8885 | −0.872753 | ||||||||
\(630\) | −2.23607 | −0.0890871 | ||||||||
\(631\) | −22.8328 | −0.908960 | −0.454480 | − | 0.890757i | \(-0.650175\pi\) | ||||
−0.454480 | + | 0.890757i | \(0.650175\pi\) | |||||||
\(632\) | −11.0557 | −0.439773 | ||||||||
\(633\) | −0.944272 | −0.0375314 | ||||||||
\(634\) | −67.8885 | −2.69620 | ||||||||
\(635\) | −12.9443 | −0.513678 | ||||||||
\(636\) | 37.4164 | 1.48366 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 11.0557 | 0.437700 | ||||||||
\(639\) | 14.4721 | 0.572509 | ||||||||
\(640\) | 15.6525 | 0.618718 | ||||||||
\(641\) | −36.8328 | −1.45481 | −0.727404 | − | 0.686209i | \(-0.759274\pi\) | ||||
−0.727404 | + | 0.686209i | \(0.759274\pi\) | |||||||
\(642\) | −11.0557 | −0.436335 | ||||||||
\(643\) | −32.9443 | −1.29920 | −0.649598 | − | 0.760278i | \(-0.725063\pi\) | ||||
−0.649598 | + | 0.760278i | \(0.725063\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | −8.94427 | −0.352180 | ||||||||
\(646\) | −28.9443 | −1.13880 | ||||||||
\(647\) | 33.8885 | 1.33230 | 0.666148 | − | 0.745820i | \(-0.267942\pi\) | ||||
0.666148 | + | 0.745820i | \(0.267942\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −22.1115 | −0.867951 | ||||||||
\(650\) | −10.0000 | −0.392232 | ||||||||
\(651\) | −10.4721 | −0.410435 | ||||||||
\(652\) | 2.83282 | 0.110942 | ||||||||
\(653\) | −49.4164 | −1.93381 | −0.966907 | − | 0.255130i | \(-0.917882\pi\) | ||||
−0.966907 | + | 0.255130i | \(0.917882\pi\) | |||||||
\(654\) | 4.47214 | 0.174874 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | −3.52786 | −0.137635 | ||||||||
\(658\) | −11.0557 | −0.430997 | ||||||||
\(659\) | −41.3050 | −1.60901 | −0.804506 | − | 0.593944i | \(-0.797570\pi\) | ||||
−0.804506 | + | 0.593944i | \(0.797570\pi\) | |||||||
\(660\) | −7.41641 | −0.288683 | ||||||||
\(661\) | −0.111456 | −0.00433514 | −0.00216757 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216757 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(662\) | −37.8885 | −1.47258 | ||||||||
\(663\) | −8.94427 | −0.347367 | ||||||||
\(664\) | 2.11146 | 0.0819404 | ||||||||
\(665\) | −6.47214 | −0.250979 | ||||||||
\(666\) | 24.4721 | 0.948276 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −24.0000 | −0.928588 | ||||||||
\(669\) | −4.94427 | −0.191157 | ||||||||
\(670\) | 8.94427 | 0.345547 | ||||||||
\(671\) | 4.94427 | 0.190872 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | −44.8328 | −1.72818 | −0.864089 | − | 0.503339i | \(-0.832105\pi\) | ||||
−0.864089 | + | 0.503339i | \(0.832105\pi\) | |||||||
\(674\) | 26.5836 | 1.02396 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | 38.9443 | 1.49675 | 0.748375 | − | 0.663276i | \(-0.230834\pi\) | ||||
0.748375 | + | 0.663276i | \(0.230834\pi\) | |||||||
\(678\) | 18.9443 | 0.727550 | ||||||||
\(679\) | −0.472136 | −0.0181189 | ||||||||
\(680\) | 4.47214 | 0.171499 | ||||||||
\(681\) | 16.9443 | 0.649306 | ||||||||
\(682\) | −57.8885 | −2.21667 | ||||||||
\(683\) | 33.8885 | 1.29671 | 0.648355 | − | 0.761339i | \(-0.275457\pi\) | ||||
0.648355 | + | 0.761339i | \(0.275457\pi\) | |||||||
\(684\) | 19.4164 | 0.742405 | ||||||||
\(685\) | −12.4721 | −0.476536 | ||||||||
\(686\) | 2.23607 | 0.0853735 | ||||||||
\(687\) | 11.8885 | 0.453576 | ||||||||
\(688\) | 8.94427 | 0.340997 | ||||||||
\(689\) | 55.7771 | 2.12494 | ||||||||
\(690\) | 8.94427 | 0.340503 | ||||||||
\(691\) | −0.360680 | −0.0137209 | −0.00686045 | − | 0.999976i | \(-0.502184\pi\) | ||||
−0.00686045 | + | 0.999976i | \(0.502184\pi\) | |||||||
\(692\) | 44.8328 | 1.70429 | ||||||||
\(693\) | −2.47214 | −0.0939087 | ||||||||
\(694\) | −17.8885 | −0.679040 | ||||||||
\(695\) | 19.4164 | 0.736506 | ||||||||
\(696\) | 4.47214 | 0.169516 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 53.4164 | 2.02184 | ||||||||
\(699\) | −17.4164 | −0.658749 | ||||||||
\(700\) | 3.00000 | 0.113389 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 10.0000 | 0.377426 | ||||||||
\(703\) | 70.8328 | 2.67151 | ||||||||
\(704\) | 32.1378 | 1.21124 | ||||||||
\(705\) | −4.94427 | −0.186212 | ||||||||
\(706\) | −62.3607 | −2.34698 | ||||||||
\(707\) | −14.0000 | −0.526524 | ||||||||
\(708\) | −26.8328 | −1.00844 | ||||||||
\(709\) | −45.7771 | −1.71919 | −0.859597 | − | 0.510972i | \(-0.829286\pi\) | ||||
−0.859597 | + | 0.510972i | \(0.829286\pi\) | |||||||
\(710\) | −32.3607 | −1.21447 | ||||||||
\(711\) | −4.94427 | −0.185425 | ||||||||
\(712\) | −4.47214 | −0.167600 | ||||||||
\(713\) | 41.8885 | 1.56874 | ||||||||
\(714\) | 4.47214 | 0.167365 | ||||||||
\(715\) | −11.0557 | −0.413461 | ||||||||
\(716\) | −7.41641 | −0.277164 | ||||||||
\(717\) | 1.52786 | 0.0570591 | ||||||||
\(718\) | 21.3050 | 0.795094 | ||||||||
\(719\) | 46.8328 | 1.74657 | 0.873285 | − | 0.487210i | \(-0.161985\pi\) | ||||
0.873285 | + | 0.487210i | \(0.161985\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 51.1803 | 1.90474 | ||||||||
\(723\) | 1.05573 | 0.0392630 | ||||||||
\(724\) | 56.8328 | 2.11217 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 10.9311 | 0.405692 | ||||||||
\(727\) | 14.8328 | 0.550119 | 0.275059 | − | 0.961427i | \(-0.411302\pi\) | ||||
0.275059 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(728\) | −10.0000 | −0.370625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.88854 | 0.291968 | ||||||||
\(731\) | 17.8885 | 0.661632 | ||||||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | 37.4164 | 1.38201 | 0.691003 | − | 0.722852i | \(-0.257169\pi\) | ||||
0.691003 | + | 0.722852i | \(0.257169\pi\) | |||||||
\(734\) | 46.8328 | 1.72863 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −26.8328 | −0.989071 | ||||||||
\(737\) | 9.88854 | 0.364249 | ||||||||
\(738\) | −4.47214 | −0.164622 | ||||||||
\(739\) | 29.8885 | 1.09947 | 0.549734 | − | 0.835340i | \(-0.314729\pi\) | ||||
0.549734 | + | 0.835340i | \(0.314729\pi\) | |||||||
\(740\) | −32.8328 | −1.20696 | ||||||||
\(741\) | 28.9443 | 1.06329 | ||||||||
\(742\) | −27.8885 | −1.02382 | ||||||||
\(743\) | −18.8328 | −0.690909 | −0.345455 | − | 0.938436i | \(-0.612275\pi\) | ||||
−0.345455 | + | 0.938436i | \(0.612275\pi\) | |||||||
\(744\) | −23.4164 | −0.858487 | ||||||||
\(745\) | −2.94427 | −0.107870 | ||||||||
\(746\) | 13.4164 | 0.491210 | ||||||||
\(747\) | 0.944272 | 0.0345491 | ||||||||
\(748\) | 14.8328 | 0.542341 | ||||||||
\(749\) | 4.94427 | 0.180660 | ||||||||
\(750\) | 2.23607 | 0.0816497 | ||||||||
\(751\) | −3.05573 | −0.111505 | −0.0557526 | − | 0.998445i | \(-0.517756\pi\) | ||||
−0.0557526 | + | 0.998445i | \(0.517756\pi\) | |||||||
\(752\) | 4.94427 | 0.180299 | ||||||||
\(753\) | 0.944272 | 0.0344112 | ||||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | −3.00000 | −0.109109 | ||||||||
\(757\) | −3.88854 | −0.141332 | −0.0706658 | − | 0.997500i | \(-0.522512\pi\) | ||||
−0.0706658 | + | 0.997500i | \(0.522512\pi\) | |||||||
\(758\) | −4.72136 | −0.171488 | ||||||||
\(759\) | 9.88854 | 0.358931 | ||||||||
\(760\) | −14.4721 | −0.524960 | ||||||||
\(761\) | 7.88854 | 0.285959 | 0.142980 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142980 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(762\) | −28.9443 | −1.04854 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 82.2492 | 2.97567 | ||||||||
\(765\) | 2.00000 | 0.0723102 | ||||||||
\(766\) | −17.8885 | −0.646339 | ||||||||
\(767\) | −40.0000 | −1.44432 | ||||||||
\(768\) | 9.00000 | 0.324760 | ||||||||
\(769\) | 0.832816 | 0.0300321 | 0.0150161 | − | 0.999887i | \(-0.495220\pi\) | ||||
0.0150161 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(770\) | 5.52786 | 0.199210 | ||||||||
\(771\) | −1.05573 | −0.0380211 | ||||||||
\(772\) | −42.0000 | −1.51161 | ||||||||
\(773\) | −25.0557 | −0.901192 | −0.450596 | − | 0.892728i | \(-0.648788\pi\) | ||||
−0.450596 | + | 0.892728i | \(0.648788\pi\) | |||||||
\(774\) | −20.0000 | −0.718885 | ||||||||
\(775\) | 10.4721 | 0.376170 | ||||||||
\(776\) | −1.05573 | −0.0378984 | ||||||||
\(777\) | −10.9443 | −0.392624 | ||||||||
\(778\) | 24.4721 | 0.877369 | ||||||||
\(779\) | −12.9443 | −0.463777 | ||||||||
\(780\) | −13.4164 | −0.480384 | ||||||||
\(781\) | −35.7771 | −1.28020 | ||||||||
\(782\) | −17.8885 | −0.639693 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −8.47214 | −0.302383 | ||||||||
\(786\) | −8.94427 | −0.319032 | ||||||||
\(787\) | 48.9443 | 1.74467 | 0.872337 | − | 0.488904i | \(-0.162603\pi\) | ||||
0.872337 | + | 0.488904i | \(0.162603\pi\) | |||||||
\(788\) | 73.4164 | 2.61535 | ||||||||
\(789\) | −24.9443 | −0.888040 | ||||||||
\(790\) | 11.0557 | 0.393345 | ||||||||
\(791\) | −8.47214 | −0.301234 | ||||||||
\(792\) | −5.52786 | −0.196424 | ||||||||
\(793\) | 8.94427 | 0.317620 | ||||||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | −12.4721 | −0.442341 | ||||||||
\(796\) | 1.75078 | 0.0620546 | ||||||||
\(797\) | −1.05573 | −0.0373958 | −0.0186979 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186979 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(798\) | −14.4721 | −0.512308 | ||||||||
\(799\) | 9.88854 | 0.349832 | ||||||||
\(800\) | −6.70820 | −0.237171 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 22.3607 | 0.789583 | ||||||||
\(803\) | 8.72136 | 0.307770 | ||||||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | −104.721 | −3.68865 | ||||||||
\(807\) | 23.8885 | 0.840917 | ||||||||
\(808\) | −31.3050 | −1.10130 | ||||||||
\(809\) | 21.0557 | 0.740280 | 0.370140 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370140 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(810\) | −2.23607 | −0.0785674 | ||||||||
\(811\) | 28.5836 | 1.00371 | 0.501853 | − | 0.864953i | \(-0.332652\pi\) | ||||
0.501853 | + | 0.864953i | \(0.332652\pi\) | |||||||
\(812\) | −6.00000 | −0.210559 | ||||||||
\(813\) | 10.4721 | 0.367274 | ||||||||
\(814\) | −60.4984 | −2.12047 | ||||||||
\(815\) | −0.944272 | −0.0330764 | ||||||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | −57.8885 | −2.02526 | ||||||||
\(818\) | −53.4164 | −1.86766 | ||||||||
\(819\) | −4.47214 | −0.156269 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −37.7771 | −1.31843 | −0.659215 | − | 0.751955i | \(-0.729111\pi\) | ||||
−0.659215 | + | 0.751955i | \(0.729111\pi\) | |||||||
\(822\) | −27.8885 | −0.972725 | ||||||||
\(823\) | 27.0557 | 0.943103 | 0.471552 | − | 0.881838i | \(-0.343694\pi\) | ||||
0.471552 | + | 0.881838i | \(0.343694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.47214 | 0.0860687 | ||||||||
\(826\) | 20.0000 | 0.695889 | ||||||||
\(827\) | −4.94427 | −0.171929 | −0.0859646 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859646 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(828\) | 12.0000 | 0.417029 | ||||||||
\(829\) | −30.9443 | −1.07474 | −0.537369 | − | 0.843347i | \(-0.680582\pi\) | ||||
−0.537369 | + | 0.843347i | \(0.680582\pi\) | |||||||
\(830\) | −2.11146 | −0.0732897 | ||||||||
\(831\) | −1.05573 | −0.0366228 | ||||||||
\(832\) | 58.1378 | 2.01556 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 43.4164 | 1.50339 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | −48.0000 | −1.66011 | ||||||||
\(837\) | −10.4721 | −0.361970 | ||||||||
\(838\) | 13.1672 | 0.454853 | ||||||||
\(839\) | 1.16718 | 0.0402957 | 0.0201478 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201478 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(840\) | 2.23607 | 0.0771517 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 49.1935 | 1.69532 | ||||||||
\(843\) | −6.94427 | −0.239173 | ||||||||
\(844\) | 2.83282 | 0.0975095 | ||||||||
\(845\) | −7.00000 | −0.240807 | ||||||||
\(846\) | −11.0557 | −0.380104 | ||||||||
\(847\) | −4.88854 | −0.167972 | ||||||||
\(848\) | 12.4721 | 0.428295 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | −4.47214 | −0.153393 | ||||||||
\(851\) | 43.7771 | 1.50066 | ||||||||
\(852\) | −43.4164 | −1.48742 | ||||||||
\(853\) | 31.3050 | 1.07186 | 0.535931 | − | 0.844262i | \(-0.319961\pi\) | ||||
0.535931 | + | 0.844262i | \(0.319961\pi\) | |||||||
\(854\) | −4.47214 | −0.153033 | ||||||||
\(855\) | −6.47214 | −0.221342 | ||||||||
\(856\) | 11.0557 | 0.377877 | ||||||||
\(857\) | −16.8328 | −0.574998 | −0.287499 | − | 0.957781i | \(-0.592824\pi\) | ||||
−0.287499 | + | 0.957781i | \(0.592824\pi\) | |||||||
\(858\) | −24.7214 | −0.843973 | ||||||||
\(859\) | 41.5279 | 1.41691 | 0.708456 | − | 0.705755i | \(-0.249392\pi\) | ||||
0.708456 | + | 0.705755i | \(0.249392\pi\) | |||||||
\(860\) | 26.8328 | 0.914991 | ||||||||
\(861\) | 2.00000 | 0.0681598 | ||||||||
\(862\) | −21.3050 | −0.725650 | ||||||||
\(863\) | −13.8885 | −0.472772 | −0.236386 | − | 0.971659i | \(-0.575963\pi\) | ||||
−0.236386 | + | 0.971659i | \(0.575963\pi\) | |||||||
\(864\) | 6.70820 | 0.228218 | ||||||||
\(865\) | −14.9443 | −0.508120 | ||||||||
\(866\) | 16.8328 | 0.572002 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 31.4164 | 1.06634 | ||||||||
\(869\) | 12.2229 | 0.414634 | ||||||||
\(870\) | −4.47214 | −0.151620 | ||||||||
\(871\) | 17.8885 | 0.606130 | ||||||||
\(872\) | −4.47214 | −0.151446 | ||||||||
\(873\) | −0.472136 | −0.0159794 | ||||||||
\(874\) | 57.8885 | 1.95811 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 10.5836 | 0.357586 | ||||||||
\(877\) | −3.16718 | −0.106948 | −0.0534741 | − | 0.998569i | \(-0.517029\pi\) | ||||
−0.0534741 | + | 0.998569i | \(0.517029\pi\) | |||||||
\(878\) | 23.4164 | 0.790265 | ||||||||
\(879\) | −22.9443 | −0.773891 | ||||||||
\(880\) | −2.47214 | −0.0833357 | ||||||||
\(881\) | 7.88854 | 0.265772 | 0.132886 | − | 0.991131i | \(-0.457576\pi\) | ||||
0.132886 | + | 0.991131i | \(0.457576\pi\) | |||||||
\(882\) | 2.23607 | 0.0752923 | ||||||||
\(883\) | −2.11146 | −0.0710562 | −0.0355281 | − | 0.999369i | \(-0.511311\pi\) | ||||
−0.0355281 | + | 0.999369i | \(0.511311\pi\) | |||||||
\(884\) | 26.8328 | 0.902485 | ||||||||
\(885\) | 8.94427 | 0.300658 | ||||||||
\(886\) | −17.8885 | −0.600977 | ||||||||
\(887\) | 22.8328 | 0.766651 | 0.383325 | − | 0.923613i | \(-0.374779\pi\) | ||||
0.383325 | + | 0.923613i | \(0.374779\pi\) | |||||||
\(888\) | −24.4721 | −0.821231 | ||||||||
\(889\) | 12.9443 | 0.434137 | ||||||||
\(890\) | 4.47214 | 0.149906 | ||||||||
\(891\) | −2.47214 | −0.0828197 | ||||||||
\(892\) | 14.8328 | 0.496639 | ||||||||
\(893\) | −32.0000 | −1.07084 | ||||||||
\(894\) | −6.58359 | −0.220188 | ||||||||
\(895\) | 2.47214 | 0.0826344 | ||||||||
\(896\) | −15.6525 | −0.522913 | ||||||||
\(897\) | 17.8885 | 0.597281 | ||||||||
\(898\) | −31.3050 | −1.04466 | ||||||||
\(899\) | −20.9443 | −0.698531 | ||||||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 24.9443 | 0.831014 | ||||||||
\(902\) | 11.0557 | 0.368115 | ||||||||
\(903\) | 8.94427 | 0.297647 | ||||||||
\(904\) | −18.9443 | −0.630077 | ||||||||
\(905\) | −18.9443 | −0.629729 | ||||||||
\(906\) | 35.7771 | 1.18861 | ||||||||
\(907\) | 18.1115 | 0.601381 | 0.300691 | − | 0.953722i | \(-0.402783\pi\) | ||||
0.300691 | + | 0.953722i | \(0.402783\pi\) | |||||||
\(908\) | −50.8328 | −1.68695 | ||||||||
\(909\) | −14.0000 | −0.464351 | ||||||||
\(910\) | 10.0000 | 0.331497 | ||||||||
\(911\) | −34.2492 | −1.13473 | −0.567364 | − | 0.823467i | \(-0.692037\pi\) | ||||
−0.567364 | + | 0.823467i | \(0.692037\pi\) | |||||||
\(912\) | 6.47214 | 0.214314 | ||||||||
\(913\) | −2.33437 | −0.0772563 | ||||||||
\(914\) | −24.4721 | −0.809466 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | −35.6656 | −1.17843 | ||||||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | 4.47214 | 0.147602 | ||||||||
\(919\) | −52.9443 | −1.74647 | −0.873235 | − | 0.487299i | \(-0.837982\pi\) | ||||
−0.873235 | + | 0.487299i | \(0.837982\pi\) | |||||||
\(920\) | −8.94427 | −0.294884 | ||||||||
\(921\) | 32.9443 | 1.08555 | ||||||||
\(922\) | −71.3050 | −2.34830 | ||||||||
\(923\) | −64.7214 | −2.13033 | ||||||||
\(924\) | 7.41641 | 0.243982 | ||||||||
\(925\) | 10.9443 | 0.359845 | ||||||||
\(926\) | 6.83282 | 0.224540 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.4164 | 0.440415 | ||||||||
\(929\) | −51.8885 | −1.70241 | −0.851204 | − | 0.524835i | \(-0.824127\pi\) | ||||
−0.851204 | + | 0.524835i | \(0.824127\pi\) | |||||||
\(930\) | 23.4164 | 0.767854 | ||||||||
\(931\) | 6.47214 | 0.212116 | ||||||||
\(932\) | 52.2492 | 1.71148 | ||||||||
\(933\) | 9.88854 | 0.323736 | ||||||||
\(934\) | 20.0000 | 0.654420 | ||||||||
\(935\) | −4.94427 | −0.161695 | ||||||||
\(936\) | −10.0000 | −0.326860 | ||||||||
\(937\) | −43.5279 | −1.42199 | −0.710997 | − | 0.703195i | \(-0.751756\pi\) | ||||
−0.710997 | + | 0.703195i | \(0.751756\pi\) | |||||||
\(938\) | −8.94427 | −0.292041 | ||||||||
\(939\) | −9.41641 | −0.307293 | ||||||||
\(940\) | 14.8328 | 0.483793 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | −18.9443 | −0.617238 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | −8.94427 | −0.291111 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 49.4427 | 1.60752 | ||||||||
\(947\) | 17.8885 | 0.581300 | 0.290650 | − | 0.956830i | \(-0.406129\pi\) | ||||
0.290650 | + | 0.956830i | \(0.406129\pi\) | |||||||
\(948\) | 14.8328 | 0.481747 | ||||||||
\(949\) | 15.7771 | 0.512146 | ||||||||
\(950\) | 14.4721 | 0.469538 | ||||||||
\(951\) | 30.3607 | 0.984512 | ||||||||
\(952\) | −4.47214 | −0.144943 | ||||||||
\(953\) | −6.58359 | −0.213263 | −0.106632 | − | 0.994299i | \(-0.534007\pi\) | ||||
−0.106632 | + | 0.994299i | \(0.534007\pi\) | |||||||
\(954\) | −27.8885 | −0.902925 | ||||||||
\(955\) | −27.4164 | −0.887174 | ||||||||
\(956\) | −4.58359 | −0.148244 | ||||||||
\(957\) | −4.94427 | −0.159826 | ||||||||
\(958\) | 40.0000 | 1.29234 | ||||||||
\(959\) | 12.4721 | 0.402746 | ||||||||
\(960\) | −13.0000 | −0.419573 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | −109.443 | −3.52857 | ||||||||
\(963\) | 4.94427 | 0.159327 | ||||||||
\(964\) | −3.16718 | −0.102008 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | −8.94427 | −0.287777 | ||||||||
\(967\) | −9.88854 | −0.317994 | −0.158997 | − | 0.987279i | \(-0.550826\pi\) | ||||
−0.158997 | + | 0.987279i | \(0.550826\pi\) | |||||||
\(968\) | −10.9311 | −0.351339 | ||||||||
\(969\) | 12.9443 | 0.415830 | ||||||||
\(970\) | 1.05573 | 0.0338974 | ||||||||
\(971\) | 23.0557 | 0.739894 | 0.369947 | − | 0.929053i | \(-0.379376\pi\) | ||||
0.369947 | + | 0.929053i | \(0.379376\pi\) | |||||||
\(972\) | −3.00000 | −0.0962250 | ||||||||
\(973\) | −19.4164 | −0.622461 | ||||||||
\(974\) | −6.83282 | −0.218938 | ||||||||
\(975\) | 4.47214 | 0.143223 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 57.4164 | 1.83691 | 0.918457 | − | 0.395521i | \(-0.129436\pi\) | ||||
0.918457 | + | 0.395521i | \(0.129436\pi\) | |||||||
\(978\) | −2.11146 | −0.0675169 | ||||||||
\(979\) | 4.94427 | 0.158020 | ||||||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 92.3607 | 2.94735 | ||||||||
\(983\) | 30.8328 | 0.983414 | 0.491707 | − | 0.870761i | \(-0.336373\pi\) | ||||
0.491707 | + | 0.870761i | \(0.336373\pi\) | |||||||
\(984\) | 4.47214 | 0.142566 | ||||||||
\(985\) | −24.4721 | −0.779747 | ||||||||
\(986\) | 8.94427 | 0.284844 | ||||||||
\(987\) | 4.94427 | 0.157378 | ||||||||
\(988\) | −86.8328 | −2.76252 | ||||||||
\(989\) | −35.7771 | −1.13765 | ||||||||
\(990\) | 5.52786 | 0.175687 | ||||||||
\(991\) | −12.9443 | −0.411188 | −0.205594 | − | 0.978637i | \(-0.565913\pi\) | ||||
−0.205594 | + | 0.978637i | \(0.565913\pi\) | |||||||
\(992\) | −70.2492 | −2.23042 | ||||||||
\(993\) | 16.9443 | 0.537710 | ||||||||
\(994\) | 32.3607 | 1.02642 | ||||||||
\(995\) | −0.583592 | −0.0185011 | ||||||||
\(996\) | −2.83282 | −0.0897612 | ||||||||
\(997\) | 21.4164 | 0.678264 | 0.339132 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339132 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(998\) | 48.9443 | 1.54930 | ||||||||
\(999\) | −10.9443 | −0.346261 |
(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 | 105.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 315.2.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 1680.2.a.v.1.2 | 2 | |||
5.2 | odd | 4 | 525.2.d.c.274.4 | 4 | |||
5.3 | odd | 4 | 525.2.d.c.274.1 | 4 | |||
5.4 | even | 2 | 525.2.a.g.1.1 | 2 | |||
7.2 | even | 3 | 735.2.i.k.361.1 | 4 | |||
7.3 | odd | 6 | 735.2.i.i.226.1 | 4 | |||
7.4 | even | 3 | 735.2.i.k.226.1 | 4 | |||
7.5 | odd | 6 | 735.2.i.i.361.1 | 4 | |||
7.6 | odd | 2 | 735.2.a.k.1.2 | 2 | |||
8.3 | odd | 2 | 6720.2.a.cs.1.1 | 2 | |||
8.5 | even | 2 | 6720.2.a.cx.1.2 | 2 | |||
12.11 | even | 2 | 5040.2.a.bw.1.1 | 2 | |||
15.2 | even | 4 | 1575.2.d.d.1324.2 | 4 | |||
15.8 | even | 4 | 1575.2.d.d.1324.3 | 4 | |||
15.14 | odd | 2 | 1575.2.a.r.1.2 | 2 | |||
20.19 | odd | 2 | 8400.2.a.cx.1.2 | 2 | |||
21.20 | even | 2 | 2205.2.a.w.1.1 | 2 | |||
35.34 | odd | 2 | 3675.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.2.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
525.2.a.g.1.1 | 2 | 5.4 | even | 2 | |||
525.2.d.c.274.1 | 4 | 5.3 | odd | 4 | |||
525.2.d.c.274.4 | 4 | 5.2 | odd | 4 | |||
735.2.a.k.1.2 | 2 | 7.6 | odd | 2 | |||
735.2.i.i.226.1 | 4 | 7.3 | odd | 6 | |||
735.2.i.i.361.1 | 4 | 7.5 | odd | 6 | |||
735.2.i.k.226.1 | 4 | 7.4 | even | 3 | |||
735.2.i.k.361.1 | 4 | 7.2 | even | 3 | |||
1575.2.a.r.1.2 | 2 | 15.14 | odd | 2 | |||
1575.2.d.d.1324.2 | 4 | 15.2 | even | 4 | |||
1575.2.d.d.1324.3 | 4 | 15.8 | even | 4 | |||
1680.2.a.v.1.2 | 2 | 4.3 | odd | 2 | |||
2205.2.a.w.1.1 | 2 | 21.20 | even | 2 | |||
3675.2.a.y.1.1 | 2 | 35.34 | odd | 2 | |||
5040.2.a.bw.1.1 | 2 | 12.11 | even | 2 | |||
6720.2.a.cs.1.1 | 2 | 8.3 | odd | 2 | |||
6720.2.a.cx.1.2 | 2 | 8.5 | even | 2 | |||
8400.2.a.cx.1.2 | 2 | 20.19 | odd | 2 |