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 | 1.1 | ||
Root | \(1.61803\) 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 | \(-0.790215\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | −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 | ||||||||
\(11\) | 6.47214 | 1.95142 | 0.975711 | − | 0.219061i | \(-0.0702993\pi\) | ||||
0.975711 | + | 0.219061i | \(0.0702993\pi\) | |||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | −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 | ||||||||
\(19\) | −2.47214 | −0.567147 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −14.4721 | −3.08547 | ||||||||
\(23\) | 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 | ||||||||
\(31\) | 1.52786 | 0.274412 | 0.137206 | − | 0.990543i | \(-0.456188\pi\) | ||||
0.137206 | + | 0.990543i | \(0.456188\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | −6.47214 | −1.12665 | ||||||||
\(34\) | 4.47214 | 0.766965 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −6.94427 | −1.14163 | −0.570816 | − | 0.821078i | \(-0.693373\pi\) | ||||
−0.570816 | + | 0.821078i | \(0.693373\pi\) | |||||||
\(38\) | 5.52786 | 0.896738 | ||||||||
\(39\) | −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 | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(44\) | 19.4164 | 2.92713 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.94427 | −1.31876 | ||||||||
\(47\) | 12.9443 | 1.88812 | 0.944058 | − | 0.329779i | \(-0.106974\pi\) | ||||
0.944058 | + | 0.329779i | \(0.106974\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.23607 | −0.316228 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 13.4164 | 1.86052 | ||||||||
\(53\) | −3.52786 | −0.484589 | −0.242295 | − | 0.970203i | \(-0.577900\pi\) | ||||
−0.242295 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | −6.47214 | −0.872703 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 2.47214 | 0.327442 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 3.00000 | 0.387298 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −3.41641 | −0.433884 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 14.4721 | 1.78140 | ||||||||
\(67\) | −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 | ||||||||
\(71\) | 5.52786 | 0.656037 | 0.328018 | − | 0.944671i | \(-0.393619\pi\) | ||||
0.328018 | + | 0.944671i | \(0.393619\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | −12.4721 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760422\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760422\pi\) | |||||||
\(74\) | 15.5279 | 1.80508 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −7.41641 | −0.850720 | ||||||||
\(77\) | 6.47214 | 0.737568 | ||||||||
\(78\) | 10.0000 | 1.13228 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.47214 | 0.493865 | ||||||||
\(83\) | −16.9443 | −1.85988 | −0.929938 | − | 0.367717i | \(-0.880140\pi\) | ||||
−0.929938 | + | 0.367717i | \(0.880140\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | −20.0000 | −2.15666 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | −14.4721 | −1.54273 | ||||||||
\(89\) | −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 | ||||||||
\(93\) | −1.52786 | −0.158432 | ||||||||
\(94\) | −28.9443 | −2.98537 | ||||||||
\(95\) | 2.47214 | 0.253636 | ||||||||
\(96\) | −6.70820 | −0.684653 | ||||||||
\(97\) | 8.47214 | 0.860215 | 0.430108 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430108 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(98\) | −2.23607 | −0.225877 | ||||||||
\(99\) | 6.47214 | 0.650474 | ||||||||
\(100\) | 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 | ||||||||
\(106\) | 7.88854 | 0.766203 | ||||||||
\(107\) | −12.9443 | −1.25137 | −0.625685 | − | 0.780076i | \(-0.715180\pi\) | ||||
−0.625685 | + | 0.780076i | \(0.715180\pi\) | |||||||
\(108\) | −3.00000 | −0.288675 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 14.4721 | 1.37986 | ||||||||
\(111\) | 6.94427 | 0.659121 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 0.472136 | 0.0444148 | 0.0222074 | − | 0.999753i | \(-0.492931\pi\) | ||||
0.0222074 | + | 0.999753i | \(0.492931\pi\) | |||||||
\(114\) | −5.52786 | −0.517732 | ||||||||
\(115\) | −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 | ||||||||
\(121\) | 30.8885 | 2.80805 | ||||||||
\(122\) | 4.47214 | 0.404888 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 4.58359 | 0.411619 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.23607 | −0.199205 | ||||||||
\(127\) | −4.94427 | −0.438733 | −0.219367 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219367 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(128\) | 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 | \(0.444091\pi\) | |||||||
\(132\) | −19.4164 | −1.68998 | ||||||||
\(133\) | −2.47214 | −0.214361 | ||||||||
\(134\) | 8.94427 | 0.772667 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 4.47214 | 0.383482 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | 8.94427 | 0.761387 | ||||||||
\(139\) | 7.41641 | 0.629052 | 0.314526 | − | 0.949249i | \(-0.398155\pi\) | ||||
0.314526 | + | 0.949249i | \(0.398155\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | −12.9443 | −1.09010 | ||||||||
\(142\) | −12.3607 | −1.03729 | ||||||||
\(143\) | 28.9443 | 2.42044 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 27.8885 | 2.30807 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −20.8328 | −1.71245 | ||||||||
\(149\) | −14.9443 | −1.22428 | −0.612141 | − | 0.790748i | \(-0.709692\pi\) | ||||
−0.612141 | + | 0.790748i | \(0.709692\pi\) | |||||||
\(150\) | 2.23607 | 0.182574 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 5.52786 | 0.448369 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −14.4721 | −1.16620 | ||||||||
\(155\) | −1.52786 | −0.122721 | ||||||||
\(156\) | −13.4164 | −1.07417 | ||||||||
\(157\) | −0.472136 | −0.0376806 | −0.0188403 | − | 0.999823i | \(-0.505997\pi\) | ||||
−0.0188403 | + | 0.999823i | \(0.505997\pi\) | |||||||
\(158\) | −28.9443 | −2.30268 | ||||||||
\(159\) | 3.52786 | 0.279778 | ||||||||
\(160\) | −6.70820 | −0.530330 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | −2.23607 | −0.175682 | ||||||||
\(163\) | −16.9443 | −1.32718 | −0.663589 | − | 0.748097i | \(-0.730968\pi\) | ||||
−0.663589 | + | 0.748097i | \(0.730968\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 6.47214 | 0.503855 | ||||||||
\(166\) | 37.8885 | 2.94072 | ||||||||
\(167\) | −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 | ||||||||
\(171\) | −2.47214 | −0.189049 | ||||||||
\(172\) | 26.8328 | 2.04598 | ||||||||
\(173\) | −2.94427 | −0.223849 | −0.111924 | − | 0.993717i | \(-0.535701\pi\) | ||||
−0.111924 | + | 0.993717i | \(0.535701\pi\) | |||||||
\(174\) | −4.47214 | −0.339032 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −6.47214 | −0.487856 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 4.47214 | 0.335201 | ||||||||
\(179\) | 6.47214 | 0.483750 | 0.241875 | − | 0.970307i | \(-0.422238\pi\) | ||||
0.241875 | + | 0.970307i | \(0.422238\pi\) | |||||||
\(180\) | −3.00000 | −0.223607 | ||||||||
\(181\) | 1.05573 | 0.0784717 | 0.0392358 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392358 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(182\) | −10.0000 | −0.741249 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −8.94427 | −0.659380 | ||||||||
\(185\) | 6.94427 | 0.510553 | ||||||||
\(186\) | 3.41641 | 0.250503 | ||||||||
\(187\) | −12.9443 | −0.946579 | ||||||||
\(188\) | 38.8328 | 2.83217 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −5.52786 | −0.401033 | ||||||||
\(191\) | 0.583592 | 0.0422272 | 0.0211136 | − | 0.999777i | \(-0.493279\pi\) | ||||
0.0211136 | + | 0.999777i | \(0.493279\pi\) | |||||||
\(192\) | 13.0000 | 0.938194 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | −18.9443 | −1.36012 | ||||||||
\(195\) | 4.47214 | 0.320256 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 15.5279 | 1.10631 | 0.553157 | − | 0.833077i | \(-0.313423\pi\) | ||||
0.553157 | + | 0.833077i | \(0.313423\pi\) | |||||||
\(198\) | −14.4721 | −1.02849 | ||||||||
\(199\) | 27.4164 | 1.94350 | 0.971749 | − | 0.236017i | \(-0.0758423\pi\) | ||||
0.971749 | + | 0.236017i | \(0.0758423\pi\) | |||||||
\(200\) | −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 | ||||||||
\(211\) | −16.9443 | −1.16649 | −0.583246 | − | 0.812296i | \(-0.698218\pi\) | ||||
−0.583246 | + | 0.812296i | \(0.698218\pi\) | |||||||
\(212\) | −10.5836 | −0.726884 | ||||||||
\(213\) | −5.52786 | −0.378763 | ||||||||
\(214\) | 28.9443 | 1.97859 | ||||||||
\(215\) | −8.94427 | −0.609994 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 1.52786 | 0.103718 | ||||||||
\(218\) | 4.47214 | 0.302891 | ||||||||
\(219\) | 12.4721 | 0.842789 | ||||||||
\(220\) | −19.4164 | −1.30905 | ||||||||
\(221\) | −8.94427 | −0.601657 | ||||||||
\(222\) | −15.5279 | −1.04216 | ||||||||
\(223\) | −12.9443 | −0.866813 | −0.433406 | − | 0.901199i | \(-0.642688\pi\) | ||||
−0.433406 | + | 0.901199i | \(0.642688\pi\) | |||||||
\(224\) | 6.70820 | 0.448211 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −1.05573 | −0.0702260 | ||||||||
\(227\) | 0.944272 | 0.0626735 | 0.0313368 | − | 0.999509i | \(-0.490024\pi\) | ||||
0.0313368 | + | 0.999509i | \(0.490024\pi\) | |||||||
\(228\) | 7.41641 | 0.491164 | ||||||||
\(229\) | 23.8885 | 1.57860 | 0.789300 | − | 0.614008i | \(-0.210444\pi\) | ||||
0.789300 | + | 0.614008i | \(0.210444\pi\) | |||||||
\(230\) | 8.94427 | 0.589768 | ||||||||
\(231\) | −6.47214 | −0.425835 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | −9.41641 | −0.616889 | −0.308445 | − | 0.951242i | \(-0.599808\pi\) | ||||
−0.308445 | + | 0.951242i | \(0.599808\pi\) | |||||||
\(234\) | −10.0000 | −0.653720 | ||||||||
\(235\) | −12.9443 | −0.844391 | ||||||||
\(236\) | −26.8328 | −1.74667 | ||||||||
\(237\) | −12.9443 | −0.840821 | ||||||||
\(238\) | 4.47214 | 0.289886 | ||||||||
\(239\) | −10.4721 | −0.677386 | −0.338693 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338693 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −18.9443 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(242\) | −69.0689 | −4.43992 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −4.47214 | −0.285133 | ||||||||
\(247\) | −11.0557 | −0.703459 | ||||||||
\(248\) | −3.41641 | −0.216942 | ||||||||
\(249\) | 16.9443 | 1.07380 | ||||||||
\(250\) | 2.23607 | 0.141421 | ||||||||
\(251\) | 16.9443 | 1.06951 | 0.534756 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534756 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | 25.8885 | 1.62760 | ||||||||
\(254\) | 11.0557 | 0.693698 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 18.9443 | 1.18171 | 0.590856 | − | 0.806777i | \(-0.298790\pi\) | ||||
0.590856 | + | 0.806777i | \(0.298790\pi\) | |||||||
\(258\) | 20.0000 | 1.24515 | ||||||||
\(259\) | −6.94427 | −0.431496 | ||||||||
\(260\) | −13.4164 | −0.832050 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | −8.94427 | −0.552579 | ||||||||
\(263\) | 7.05573 | 0.435075 | 0.217537 | − | 0.976052i | \(-0.430198\pi\) | ||||
0.217537 | + | 0.976052i | \(0.430198\pi\) | |||||||
\(264\) | 14.4721 | 0.890698 | ||||||||
\(265\) | 3.52786 | 0.216715 | ||||||||
\(266\) | 5.52786 | 0.338935 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | 11.8885 | 0.724857 | 0.362429 | − | 0.932012i | \(-0.381948\pi\) | ||||
0.362429 | + | 0.932012i | \(0.381948\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | −1.52786 | −0.0928111 | −0.0464056 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464056 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | −4.47214 | −0.270666 | ||||||||
\(274\) | −7.88854 | −0.476564 | ||||||||
\(275\) | 6.47214 | 0.390284 | ||||||||
\(276\) | −12.0000 | −0.722315 | ||||||||
\(277\) | 18.9443 | 1.13825 | 0.569125 | − | 0.822251i | \(-0.307282\pi\) | ||||
0.569125 | + | 0.822251i | \(0.307282\pi\) | |||||||
\(278\) | −16.5836 | −0.994618 | ||||||||
\(279\) | 1.52786 | 0.0914708 | ||||||||
\(280\) | 2.23607 | 0.133631 | ||||||||
\(281\) | −10.9443 | −0.652881 | −0.326440 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326440 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(282\) | 28.9443 | 1.72361 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 16.5836 | 0.984055 | ||||||||
\(285\) | −2.47214 | −0.146437 | ||||||||
\(286\) | −64.7214 | −3.82705 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 6.70820 | 0.395285 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −4.47214 | −0.262613 | ||||||||
\(291\) | −8.47214 | −0.496645 | ||||||||
\(292\) | −37.4164 | −2.18963 | ||||||||
\(293\) | 5.05573 | 0.295359 | 0.147679 | − | 0.989035i | \(-0.452820\pi\) | ||||
0.147679 | + | 0.989035i | \(0.452820\pi\) | |||||||
\(294\) | 2.23607 | 0.130410 | ||||||||
\(295\) | 8.94427 | 0.520756 | ||||||||
\(296\) | 15.5279 | 0.902539 | ||||||||
\(297\) | −6.47214 | −0.375551 | ||||||||
\(298\) | 33.4164 | 1.93576 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | −3.00000 | −0.173205 | ||||||||
\(301\) | 8.94427 | 0.515539 | ||||||||
\(302\) | 35.7771 | 2.05874 | ||||||||
\(303\) | 14.0000 | 0.804279 | ||||||||
\(304\) | 2.47214 | 0.141787 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 4.47214 | 0.255655 | ||||||||
\(307\) | −15.0557 | −0.859276 | −0.429638 | − | 0.903001i | \(-0.641359\pi\) | ||||
−0.429638 | + | 0.903001i | \(0.641359\pi\) | |||||||
\(308\) | 19.4164 | 1.10635 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.41641 | 0.194039 | ||||||||
\(311\) | 25.8885 | 1.46800 | 0.734002 | − | 0.679147i | \(-0.237650\pi\) | ||||
0.734002 | + | 0.679147i | \(0.237650\pi\) | |||||||
\(312\) | 10.0000 | 0.566139 | ||||||||
\(313\) | −17.4164 | −0.984434 | −0.492217 | − | 0.870473i | \(-0.663813\pi\) | ||||
−0.492217 | + | 0.870473i | \(0.663813\pi\) | |||||||
\(314\) | 1.05573 | 0.0595782 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 38.8328 | 2.18452 | ||||||||
\(317\) | 14.3607 | 0.806576 | 0.403288 | − | 0.915073i | \(-0.367867\pi\) | ||||
0.403288 | + | 0.915073i | \(0.367867\pi\) | |||||||
\(318\) | −7.88854 | −0.442368 | ||||||||
\(319\) | −12.9443 | −0.724740 | ||||||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | 12.9443 | 0.722479 | ||||||||
\(322\) | −8.94427 | −0.498445 | ||||||||
\(323\) | 4.94427 | 0.275107 | ||||||||
\(324\) | 3.00000 | 0.166667 | ||||||||
\(325\) | 4.47214 | 0.248069 | ||||||||
\(326\) | 37.8885 | 2.09845 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 4.47214 | 0.246932 | ||||||||
\(329\) | 12.9443 | 0.713641 | ||||||||
\(330\) | −14.4721 | −0.796665 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | −50.8328 | −2.78981 | ||||||||
\(333\) | −6.94427 | −0.380544 | ||||||||
\(334\) | 17.8885 | 0.978818 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −23.8885 | −1.30129 | −0.650646 | − | 0.759381i | \(-0.725502\pi\) | ||||
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(338\) | −15.6525 | −0.851382 | ||||||||
\(339\) | −0.472136 | −0.0256429 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 9.88854 | 0.535495 | ||||||||
\(342\) | 5.52786 | 0.298913 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 6.58359 | 0.353936 | ||||||||
\(347\) | −8.00000 | −0.429463 | −0.214731 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214731 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(348\) | 6.00000 | 0.321634 | ||||||||
\(349\) | −11.8885 | −0.636379 | −0.318190 | − | 0.948027i | \(-0.603075\pi\) | ||||
−0.318190 | + | 0.948027i | \(0.603075\pi\) | |||||||
\(350\) | −2.23607 | −0.119523 | ||||||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | 43.4164 | 2.31410 | ||||||||
\(353\) | 7.88854 | 0.419865 | 0.209932 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209932 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(354\) | −20.0000 | −1.06299 | ||||||||
\(355\) | −5.52786 | −0.293389 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 2.00000 | 0.105851 | ||||||||
\(358\) | −14.4721 | −0.764876 | ||||||||
\(359\) | 18.4721 | 0.974922 | 0.487461 | − | 0.873145i | \(-0.337923\pi\) | ||||
0.487461 | + | 0.873145i | \(0.337923\pi\) | |||||||
\(360\) | 2.23607 | 0.117851 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | −2.36068 | −0.124075 | ||||||||
\(363\) | −30.8885 | −1.62123 | ||||||||
\(364\) | 13.4164 | 0.703211 | ||||||||
\(365\) | 12.4721 | 0.652821 | ||||||||
\(366\) | −4.47214 | −0.233762 | ||||||||
\(367\) | 3.05573 | 0.159508 | 0.0797539 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797539 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −15.5279 | −0.807255 | ||||||||
\(371\) | −3.52786 | −0.183158 | ||||||||
\(372\) | −4.58359 | −0.237648 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 28.9443 | 1.49667 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −28.9443 | −1.49269 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 2.23607 | 0.115011 | ||||||||
\(379\) | −37.8885 | −1.94620 | −0.973102 | − | 0.230375i | \(-0.926005\pi\) | ||||
−0.973102 | + | 0.230375i | \(0.926005\pi\) | |||||||
\(380\) | 7.41641 | 0.380454 | ||||||||
\(381\) | 4.94427 | 0.253303 | ||||||||
\(382\) | −1.30495 | −0.0667671 | ||||||||
\(383\) | −8.00000 | −0.408781 | −0.204390 | − | 0.978889i | \(-0.565521\pi\) | ||||
−0.204390 | + | 0.978889i | \(0.565521\pi\) | |||||||
\(384\) | −15.6525 | −0.798762 | ||||||||
\(385\) | −6.47214 | −0.329851 | ||||||||
\(386\) | 31.3050 | 1.59338 | ||||||||
\(387\) | 8.94427 | 0.454663 | ||||||||
\(388\) | 25.4164 | 1.29032 | ||||||||
\(389\) | −6.94427 | −0.352089 | −0.176044 | − | 0.984382i | \(-0.556330\pi\) | ||||
−0.176044 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(390\) | −10.0000 | −0.506370 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −2.23607 | −0.112938 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −34.7214 | −1.74924 | ||||||||
\(395\) | −12.9443 | −0.651297 | ||||||||
\(396\) | 19.4164 | 0.975711 | ||||||||
\(397\) | −13.4164 | −0.673350 | −0.336675 | − | 0.941621i | \(-0.609302\pi\) | ||||
−0.336675 | + | 0.941621i | \(0.609302\pi\) | |||||||
\(398\) | −61.3050 | −3.07294 | ||||||||
\(399\) | 2.47214 | 0.123762 | ||||||||
\(400\) | −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 | ||||||||
\(403\) | 6.83282 | 0.340367 | ||||||||
\(404\) | −42.0000 | −2.08958 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 4.47214 | 0.221948 | ||||||||
\(407\) | −44.9443 | −2.22780 | ||||||||
\(408\) | −4.47214 | −0.221404 | ||||||||
\(409\) | 11.8885 | 0.587851 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(410\) | −4.47214 | −0.220863 | ||||||||
\(411\) | −3.52786 | −0.174017 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.94427 | −0.440119 | ||||||||
\(414\) | −8.94427 | −0.439587 | ||||||||
\(415\) | 16.9443 | 0.831762 | ||||||||
\(416\) | 30.0000 | 1.47087 | ||||||||
\(417\) | −7.41641 | −0.363183 | ||||||||
\(418\) | 35.7771 | 1.74991 | ||||||||
\(419\) | −29.8885 | −1.46015 | −0.730075 | − | 0.683367i | \(-0.760515\pi\) | ||||
−0.730075 | + | 0.683367i | \(0.760515\pi\) | |||||||
\(420\) | 3.00000 | 0.146385 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 37.8885 | 1.84439 | ||||||||
\(423\) | 12.9443 | 0.629372 | ||||||||
\(424\) | 7.88854 | 0.383102 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 12.3607 | 0.598877 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | −38.8328 | −1.87705 | ||||||||
\(429\) | −28.9443 | −1.39744 | ||||||||
\(430\) | 20.0000 | 0.964486 | ||||||||
\(431\) | −18.4721 | −0.889771 | −0.444886 | − | 0.895587i | \(-0.646756\pi\) | ||||
−0.444886 | + | 0.895587i | \(0.646756\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 16.4721 | 0.791600 | 0.395800 | − | 0.918337i | \(-0.370467\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(434\) | −3.41641 | −0.163993 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | −9.88854 | −0.473033 | ||||||||
\(438\) | −27.8885 | −1.33257 | ||||||||
\(439\) | 1.52786 | 0.0729210 | 0.0364605 | − | 0.999335i | \(-0.488392\pi\) | ||||
0.0364605 | + | 0.999335i | \(0.488392\pi\) | |||||||
\(440\) | 14.4721 | 0.689932 | ||||||||
\(441\) | 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 | \(0.560864\pi\) | |||||||
\(444\) | 20.8328 | 0.988682 | ||||||||
\(445\) | 2.00000 | 0.0948091 | ||||||||
\(446\) | 28.9443 | 1.37055 | ||||||||
\(447\) | 14.9443 | 0.706840 | ||||||||
\(448\) | −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 | ||||||||
\(451\) | −12.9443 | −0.609522 | ||||||||
\(452\) | 1.41641 | 0.0666222 | ||||||||
\(453\) | 16.0000 | 0.751746 | ||||||||
\(454\) | −2.11146 | −0.0990955 | ||||||||
\(455\) | −4.47214 | −0.209657 | ||||||||
\(456\) | −5.52786 | −0.258866 | ||||||||
\(457\) | 6.94427 | 0.324839 | 0.162420 | − | 0.986722i | \(-0.448070\pi\) | ||||
0.162420 | + | 0.986722i | \(0.448070\pi\) | |||||||
\(458\) | −53.4164 | −2.49598 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | 3.88854 | 0.181108 | 0.0905538 | − | 0.995892i | \(-0.471136\pi\) | ||||
0.0905538 | + | 0.995892i | \(0.471136\pi\) | |||||||
\(462\) | 14.4721 | 0.673305 | ||||||||
\(463\) | 20.9443 | 0.973363 | 0.486681 | − | 0.873580i | \(-0.338207\pi\) | ||||
0.486681 | + | 0.873580i | \(0.338207\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 1.52786 | 0.0708530 | ||||||||
\(466\) | 21.0557 | 0.975388 | ||||||||
\(467\) | −8.94427 | −0.413892 | −0.206946 | − | 0.978352i | \(-0.566352\pi\) | ||||
−0.206946 | + | 0.978352i | \(0.566352\pi\) | |||||||
\(468\) | 13.4164 | 0.620174 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 28.9443 | 1.33510 | ||||||||
\(471\) | 0.472136 | 0.0217549 | ||||||||
\(472\) | 20.0000 | 0.920575 | ||||||||
\(473\) | 57.8885 | 2.66172 | ||||||||
\(474\) | 28.9443 | 1.32945 | ||||||||
\(475\) | −2.47214 | −0.113429 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | −3.52786 | −0.161530 | ||||||||
\(478\) | 23.4164 | 1.07104 | ||||||||
\(479\) | −17.8885 | −0.817348 | −0.408674 | − | 0.912680i | \(-0.634009\pi\) | ||||
−0.408674 | + | 0.912680i | \(0.634009\pi\) | |||||||
\(480\) | 6.70820 | 0.306186 | ||||||||
\(481\) | −31.0557 | −1.41602 | ||||||||
\(482\) | 42.3607 | 1.92948 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 92.6656 | 4.21207 | ||||||||
\(485\) | −8.47214 | −0.384700 | ||||||||
\(486\) | 2.23607 | 0.101430 | ||||||||
\(487\) | −20.9443 | −0.949076 | −0.474538 | − | 0.880235i | \(-0.657385\pi\) | ||||
−0.474538 | + | 0.880235i | \(0.657385\pi\) | |||||||
\(488\) | 4.47214 | 0.202444 | ||||||||
\(489\) | 16.9443 | 0.766246 | ||||||||
\(490\) | 2.23607 | 0.101015 | ||||||||
\(491\) | −21.3050 | −0.961479 | −0.480740 | − | 0.876863i | \(-0.659632\pi\) | ||||
−0.480740 | + | 0.876863i | \(0.659632\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 24.7214 | 1.11227 | ||||||||
\(495\) | −6.47214 | −0.290901 | ||||||||
\(496\) | −1.52786 | −0.0686031 | ||||||||
\(497\) | 5.52786 | 0.247959 | ||||||||
\(498\) | −37.8885 | −1.69783 | ||||||||
\(499\) | −13.8885 | −0.621737 | −0.310868 | − | 0.950453i | \(-0.600620\pi\) | ||||
−0.310868 | + | 0.950453i | \(0.600620\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | −37.8885 | −1.69105 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | −57.8885 | −2.57346 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | −14.8328 | −0.658100 | ||||||||
\(509\) | −23.8885 | −1.05884 | −0.529421 | − | 0.848360i | \(-0.677591\pi\) | ||||
−0.529421 | + | 0.848360i | \(0.677591\pi\) | |||||||
\(510\) | 4.47214 | 0.198030 | ||||||||
\(511\) | −12.4721 | −0.551735 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | 2.47214 | 0.109147 | ||||||||
\(514\) | −42.3607 | −1.86845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −26.8328 | −1.18125 | ||||||||
\(517\) | 83.7771 | 3.68451 | ||||||||
\(518\) | 15.5279 | 0.682255 | ||||||||
\(519\) | 2.94427 | 0.129239 | ||||||||
\(520\) | 10.0000 | 0.438529 | ||||||||
\(521\) | −19.8885 | −0.871333 | −0.435666 | − | 0.900108i | \(-0.643487\pi\) | ||||
−0.435666 | + | 0.900108i | \(0.643487\pi\) | |||||||
\(522\) | 4.47214 | 0.195740 | ||||||||
\(523\) | −8.94427 | −0.391106 | −0.195553 | − | 0.980693i | \(-0.562650\pi\) | ||||
−0.195553 | + | 0.980693i | \(0.562650\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −15.7771 | −0.687914 | ||||||||
\(527\) | −3.05573 | −0.133110 | ||||||||
\(528\) | 6.47214 | 0.281664 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −7.88854 | −0.342656 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | −7.41641 | −0.321542 | ||||||||
\(533\) | −8.94427 | −0.387419 | ||||||||
\(534\) | −4.47214 | −0.193528 | ||||||||
\(535\) | 12.9443 | 0.559630 | ||||||||
\(536\) | 8.94427 | 0.386334 | ||||||||
\(537\) | −6.47214 | −0.279293 | ||||||||
\(538\) | −26.5836 | −1.14610 | ||||||||
\(539\) | 6.47214 | 0.278775 | ||||||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | −11.8885 | −0.511128 | −0.255564 | − | 0.966792i | \(-0.582261\pi\) | ||||
−0.255564 | + | 0.966792i | \(0.582261\pi\) | |||||||
\(542\) | 3.41641 | 0.146747 | ||||||||
\(543\) | −1.05573 | −0.0453056 | ||||||||
\(544\) | −13.4164 | −0.575224 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 10.0000 | 0.427960 | ||||||||
\(547\) | 5.88854 | 0.251776 | 0.125888 | − | 0.992044i | \(-0.459822\pi\) | ||||
0.125888 | + | 0.992044i | \(0.459822\pi\) | |||||||
\(548\) | 10.5836 | 0.452109 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | −14.4721 | −0.617094 | ||||||||
\(551\) | 4.94427 | 0.210633 | ||||||||
\(552\) | 8.94427 | 0.380693 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | −42.3607 | −1.79973 | ||||||||
\(555\) | −6.94427 | −0.294768 | ||||||||
\(556\) | 22.2492 | 0.943577 | ||||||||
\(557\) | 20.4721 | 0.867432 | 0.433716 | − | 0.901050i | \(-0.357202\pi\) | ||||
0.433716 | + | 0.901050i | \(0.357202\pi\) | |||||||
\(558\) | −3.41641 | −0.144628 | ||||||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | 24.4721 | 1.03229 | ||||||||
\(563\) | 13.8885 | 0.585332 | 0.292666 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292666 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(564\) | −38.8328 | −1.63516 | ||||||||
\(565\) | −0.472136 | −0.0198629 | ||||||||
\(566\) | −26.8328 | −1.12787 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −12.3607 | −0.518643 | ||||||||
\(569\) | −39.8885 | −1.67221 | −0.836107 | − | 0.548566i | \(-0.815174\pi\) | ||||
−0.836107 | + | 0.548566i | \(0.815174\pi\) | |||||||
\(570\) | 5.52786 | 0.231537 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 86.8328 | 3.63066 | ||||||||
\(573\) | −0.583592 | −0.0243799 | ||||||||
\(574\) | 4.47214 | 0.186663 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −13.0000 | −0.541667 | ||||||||
\(577\) | 10.3607 | 0.431321 | 0.215660 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215660 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(578\) | 29.0689 | 1.20911 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | −16.9443 | −0.702967 | ||||||||
\(582\) | 18.9443 | 0.785265 | ||||||||
\(583\) | −22.8328 | −0.945639 | ||||||||
\(584\) | 27.8885 | 1.15404 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | −11.3050 | −0.467003 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | −3.77709 | −0.155632 | ||||||||
\(590\) | −20.0000 | −0.823387 | ||||||||
\(591\) | −15.5279 | −0.638731 | ||||||||
\(592\) | 6.94427 | 0.285408 | ||||||||
\(593\) | 23.8885 | 0.980985 | 0.490492 | − | 0.871445i | \(-0.336817\pi\) | ||||
0.490492 | + | 0.871445i | \(0.336817\pi\) | |||||||
\(594\) | 14.4721 | 0.593799 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | −44.8328 | −1.83642 | ||||||||
\(597\) | −27.4164 | −1.12208 | ||||||||
\(598\) | −40.0000 | −1.63572 | ||||||||
\(599\) | 12.3607 | 0.505044 | 0.252522 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252522 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(600\) | 2.23607 | 0.0912871 | ||||||||
\(601\) | 38.9443 | 1.58857 | 0.794285 | − | 0.607545i | \(-0.207846\pi\) | ||||
0.794285 | + | 0.607545i | \(0.207846\pi\) | |||||||
\(602\) | −20.0000 | −0.815139 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −48.0000 | −1.95309 | ||||||||
\(605\) | −30.8885 | −1.25580 | ||||||||
\(606\) | −31.3050 | −1.27168 | ||||||||
\(607\) | 38.8328 | 1.57618 | 0.788088 | − | 0.615563i | \(-0.211071\pi\) | ||||
0.788088 | + | 0.615563i | \(0.211071\pi\) | |||||||
\(608\) | −16.5836 | −0.672553 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | −4.47214 | −0.181071 | ||||||||
\(611\) | 57.8885 | 2.34192 | ||||||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | −6.94427 | −0.280477 | −0.140238 | − | 0.990118i | \(-0.544787\pi\) | ||||
−0.140238 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(614\) | 33.6656 | 1.35863 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | −14.4721 | −0.583099 | ||||||||
\(617\) | 16.4721 | 0.663143 | 0.331572 | − | 0.943430i | \(-0.392421\pi\) | ||||
0.331572 | + | 0.943430i | \(0.392421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4164 | 1.58428 | 0.792140 | − | 0.610340i | \(-0.208967\pi\) | ||||
0.792140 | + | 0.610340i | \(0.208967\pi\) | |||||||
\(620\) | −4.58359 | −0.184081 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −57.8885 | −2.32112 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 4.47214 | 0.179029 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 38.9443 | 1.55653 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | −1.41641 | −0.0565208 | ||||||||
\(629\) | 13.8885 | 0.553773 | ||||||||
\(630\) | 2.23607 | 0.0890871 | ||||||||
\(631\) | 30.8328 | 1.22744 | 0.613718 | − | 0.789526i | \(-0.289673\pi\) | ||||
0.613718 | + | 0.789526i | \(0.289673\pi\) | |||||||
\(632\) | −28.9443 | −1.15134 | ||||||||
\(633\) | 16.9443 | 0.673474 | ||||||||
\(634\) | −32.1115 | −1.27531 | ||||||||
\(635\) | 4.94427 | 0.196207 | ||||||||
\(636\) | 10.5836 | 0.419667 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 28.9443 | 1.14591 | ||||||||
\(639\) | 5.52786 | 0.218679 | ||||||||
\(640\) | −15.6525 | −0.618718 | ||||||||
\(641\) | 16.8328 | 0.664856 | 0.332428 | − | 0.943129i | \(-0.392132\pi\) | ||||
0.332428 | + | 0.943129i | \(0.392132\pi\) | |||||||
\(642\) | −28.9443 | −1.14234 | ||||||||
\(643\) | −15.0557 | −0.593740 | −0.296870 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296870 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | 8.94427 | 0.352180 | ||||||||
\(646\) | −11.0557 | −0.434982 | ||||||||
\(647\) | −1.88854 | −0.0742463 | −0.0371232 | − | 0.999311i | \(-0.511819\pi\) | ||||
−0.0371232 | + | 0.999311i | \(0.511819\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | −57.8885 | −2.27232 | ||||||||
\(650\) | −10.0000 | −0.392232 | ||||||||
\(651\) | −1.52786 | −0.0598817 | ||||||||
\(652\) | −50.8328 | −1.99077 | ||||||||
\(653\) | −22.5836 | −0.883764 | −0.441882 | − | 0.897073i | \(-0.645689\pi\) | ||||
−0.441882 | + | 0.897073i | \(0.645689\pi\) | |||||||
\(654\) | −4.47214 | −0.174874 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | −12.4721 | −0.486584 | ||||||||
\(658\) | −28.9443 | −1.12837 | ||||||||
\(659\) | 21.3050 | 0.829923 | 0.414962 | − | 0.909839i | \(-0.363795\pi\) | ||||
0.414962 | + | 0.909839i | \(0.363795\pi\) | |||||||
\(660\) | 19.4164 | 0.755783 | ||||||||
\(661\) | −35.8885 | −1.39590 | −0.697951 | − | 0.716145i | \(-0.745905\pi\) | ||||
−0.697951 | + | 0.716145i | \(0.745905\pi\) | |||||||
\(662\) | −2.11146 | −0.0820641 | ||||||||
\(663\) | 8.94427 | 0.347367 | ||||||||
\(664\) | 37.8885 | 1.47036 | ||||||||
\(665\) | 2.47214 | 0.0958653 | ||||||||
\(666\) | 15.5279 | 0.601693 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −24.0000 | −0.928588 | ||||||||
\(669\) | 12.9443 | 0.500454 | ||||||||
\(670\) | −8.94427 | −0.345547 | ||||||||
\(671\) | −12.9443 | −0.499708 | ||||||||
\(672\) | −6.70820 | −0.258775 | ||||||||
\(673\) | 8.83282 | 0.340480 | 0.170240 | − | 0.985403i | \(-0.445546\pi\) | ||||
0.170240 | + | 0.985403i | \(0.445546\pi\) | |||||||
\(674\) | 53.4164 | 2.05752 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | 21.0557 | 0.809237 | 0.404619 | − | 0.914485i | \(-0.367404\pi\) | ||||
0.404619 | + | 0.914485i | \(0.367404\pi\) | |||||||
\(678\) | 1.05573 | 0.0405450 | ||||||||
\(679\) | 8.47214 | 0.325131 | ||||||||
\(680\) | −4.47214 | −0.171499 | ||||||||
\(681\) | −0.944272 | −0.0361846 | ||||||||
\(682\) | −22.1115 | −0.846691 | ||||||||
\(683\) | −1.88854 | −0.0722631 | −0.0361316 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361316 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(684\) | −7.41641 | −0.283573 | ||||||||
\(685\) | −3.52786 | −0.134793 | ||||||||
\(686\) | −2.23607 | −0.0853735 | ||||||||
\(687\) | −23.8885 | −0.911405 | ||||||||
\(688\) | −8.94427 | −0.340997 | ||||||||
\(689\) | −15.7771 | −0.601059 | ||||||||
\(690\) | −8.94427 | −0.340503 | ||||||||
\(691\) | 44.3607 | 1.68756 | 0.843780 | − | 0.536689i | \(-0.180325\pi\) | ||||
0.843780 | + | 0.536689i | \(0.180325\pi\) | |||||||
\(692\) | −8.83282 | −0.335773 | ||||||||
\(693\) | 6.47214 | 0.245856 | ||||||||
\(694\) | 17.8885 | 0.679040 | ||||||||
\(695\) | −7.41641 | −0.281320 | ||||||||
\(696\) | −4.47214 | −0.169516 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 26.5836 | 1.00620 | ||||||||
\(699\) | 9.41641 | 0.356161 | ||||||||
\(700\) | 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 | ||||||||
\(703\) | 17.1672 | 0.647473 | ||||||||
\(704\) | −84.1378 | −3.17106 | ||||||||
\(705\) | 12.9443 | 0.487509 | ||||||||
\(706\) | −17.6393 | −0.663865 | ||||||||
\(707\) | −14.0000 | −0.526524 | ||||||||
\(708\) | 26.8328 | 1.00844 | ||||||||
\(709\) | 25.7771 | 0.968079 | 0.484039 | − | 0.875046i | \(-0.339169\pi\) | ||||
0.484039 | + | 0.875046i | \(0.339169\pi\) | |||||||
\(710\) | 12.3607 | 0.463888 | ||||||||
\(711\) | 12.9443 | 0.485448 | ||||||||
\(712\) | 4.47214 | 0.167600 | ||||||||
\(713\) | 6.11146 | 0.228876 | ||||||||
\(714\) | −4.47214 | −0.167365 | ||||||||
\(715\) | −28.9443 | −1.08245 | ||||||||
\(716\) | 19.4164 | 0.725625 | ||||||||
\(717\) | 10.4721 | 0.391089 | ||||||||
\(718\) | −41.3050 | −1.54149 | ||||||||
\(719\) | −6.83282 | −0.254821 | −0.127411 | − | 0.991850i | \(-0.540667\pi\) | ||||
−0.127411 | + | 0.991850i | \(0.540667\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 28.8197 | 1.07256 | ||||||||
\(723\) | 18.9443 | 0.704545 | ||||||||
\(724\) | 3.16718 | 0.117707 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 69.0689 | 2.56339 | ||||||||
\(727\) | −38.8328 | −1.44023 | −0.720115 | − | 0.693855i | \(-0.755911\pi\) | ||||
−0.720115 | + | 0.693855i | \(0.755911\pi\) | |||||||
\(728\) | −10.0000 | −0.370625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.8885 | −1.03220 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | 10.5836 | 0.390914 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(734\) | −6.83282 | −0.252204 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 26.8328 | 0.989071 | ||||||||
\(737\) | −25.8885 | −0.953617 | ||||||||
\(738\) | 4.47214 | 0.164622 | ||||||||
\(739\) | −5.88854 | −0.216614 | −0.108307 | − | 0.994118i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994118i | \(0.534543\pi\) | |||||||
\(740\) | 20.8328 | 0.765830 | ||||||||
\(741\) | 11.0557 | 0.406142 | ||||||||
\(742\) | 7.88854 | 0.289598 | ||||||||
\(743\) | 34.8328 | 1.27789 | 0.638946 | − | 0.769252i | \(-0.279371\pi\) | ||||
0.638946 | + | 0.769252i | \(0.279371\pi\) | |||||||
\(744\) | 3.41641 | 0.125252 | ||||||||
\(745\) | 14.9443 | 0.547516 | ||||||||
\(746\) | −13.4164 | −0.491210 | ||||||||
\(747\) | −16.9443 | −0.619958 | ||||||||
\(748\) | −38.8328 | −1.41987 | ||||||||
\(749\) | −12.9443 | −0.472973 | ||||||||
\(750\) | −2.23607 | −0.0816497 | ||||||||
\(751\) | −20.9443 | −0.764267 | −0.382134 | − | 0.924107i | \(-0.624811\pi\) | ||||
−0.382134 | + | 0.924107i | \(0.624811\pi\) | |||||||
\(752\) | −12.9443 | −0.472029 | ||||||||
\(753\) | −16.9443 | −0.617484 | ||||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | −3.00000 | −0.109109 | ||||||||
\(757\) | 31.8885 | 1.15901 | 0.579504 | − | 0.814969i | \(-0.303246\pi\) | ||||
0.579504 | + | 0.814969i | \(0.303246\pi\) | |||||||
\(758\) | 84.7214 | 3.07722 | ||||||||
\(759\) | −25.8885 | −0.939695 | ||||||||
\(760\) | −5.52786 | −0.200517 | ||||||||
\(761\) | −27.8885 | −1.01096 | −0.505479 | − | 0.862839i | \(-0.668684\pi\) | ||||
−0.505479 | + | 0.862839i | \(0.668684\pi\) | |||||||
\(762\) | −11.0557 | −0.400507 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 1.75078 | 0.0633409 | ||||||||
\(765\) | 2.00000 | 0.0723102 | ||||||||
\(766\) | 17.8885 | 0.646339 | ||||||||
\(767\) | −40.0000 | −1.44432 | ||||||||
\(768\) | 9.00000 | 0.324760 | ||||||||
\(769\) | −52.8328 | −1.90520 | −0.952600 | − | 0.304226i | \(-0.901602\pi\) | ||||
−0.952600 | + | 0.304226i | \(0.901602\pi\) | |||||||
\(770\) | 14.4721 | 0.521540 | ||||||||
\(771\) | −18.9443 | −0.682261 | ||||||||
\(772\) | −42.0000 | −1.51161 | ||||||||
\(773\) | −42.9443 | −1.54460 | −0.772299 | − | 0.635259i | \(-0.780893\pi\) | ||||
−0.772299 | + | 0.635259i | \(0.780893\pi\) | |||||||
\(774\) | −20.0000 | −0.718885 | ||||||||
\(775\) | 1.52786 | 0.0548825 | ||||||||
\(776\) | −18.9443 | −0.680060 | ||||||||
\(777\) | 6.94427 | 0.249124 | ||||||||
\(778\) | 15.5279 | 0.556701 | ||||||||
\(779\) | 4.94427 | 0.177147 | ||||||||
\(780\) | 13.4164 | 0.480384 | ||||||||
\(781\) | 35.7771 | 1.28020 | ||||||||
\(782\) | 17.8885 | 0.639693 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0.472136 | 0.0168513 | ||||||||
\(786\) | 8.94427 | 0.319032 | ||||||||
\(787\) | 31.0557 | 1.10702 | 0.553509 | − | 0.832843i | \(-0.313289\pi\) | ||||
0.553509 | + | 0.832843i | \(0.313289\pi\) | |||||||
\(788\) | 46.5836 | 1.65947 | ||||||||
\(789\) | −7.05573 | −0.251191 | ||||||||
\(790\) | 28.9443 | 1.02979 | ||||||||
\(791\) | 0.472136 | 0.0167872 | ||||||||
\(792\) | −14.4721 | −0.514245 | ||||||||
\(793\) | −8.94427 | −0.317620 | ||||||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | −3.52786 | −0.125120 | ||||||||
\(796\) | 82.2492 | 2.91525 | ||||||||
\(797\) | −18.9443 | −0.671041 | −0.335520 | − | 0.942033i | \(-0.608912\pi\) | ||||
−0.335520 | + | 0.942033i | \(0.608912\pi\) | |||||||
\(798\) | −5.52786 | −0.195684 | ||||||||
\(799\) | −25.8885 | −0.915871 | ||||||||
\(800\) | 6.70820 | 0.237171 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | −22.3607 | −0.789583 | ||||||||
\(803\) | −80.7214 | −2.84859 | ||||||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | −15.2786 | −0.538167 | ||||||||
\(807\) | −11.8885 | −0.418497 | ||||||||
\(808\) | 31.3050 | 1.10130 | ||||||||
\(809\) | 38.9443 | 1.36921 | 0.684604 | − | 0.728915i | \(-0.259975\pi\) | ||||
0.684604 | + | 0.728915i | \(0.259975\pi\) | |||||||
\(810\) | 2.23607 | 0.0785674 | ||||||||
\(811\) | 55.4164 | 1.94593 | 0.972967 | − | 0.230946i | \(-0.0741820\pi\) | ||||
0.972967 | + | 0.230946i | \(0.0741820\pi\) | |||||||
\(812\) | −6.00000 | −0.210559 | ||||||||
\(813\) | 1.52786 | 0.0535845 | ||||||||
\(814\) | 100.498 | 3.52247 | ||||||||
\(815\) | 16.9443 | 0.593532 | ||||||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | −22.1115 | −0.773582 | ||||||||
\(818\) | −26.5836 | −0.929474 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 33.7771 | 1.17883 | 0.589414 | − | 0.807831i | \(-0.299359\pi\) | ||||
0.589414 | + | 0.807831i | \(0.299359\pi\) | |||||||
\(822\) | 7.88854 | 0.275145 | ||||||||
\(823\) | 44.9443 | 1.56666 | 0.783329 | − | 0.621607i | \(-0.213520\pi\) | ||||
0.783329 | + | 0.621607i | \(0.213520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.47214 | −0.225331 | ||||||||
\(826\) | 20.0000 | 0.695889 | ||||||||
\(827\) | 12.9443 | 0.450116 | 0.225058 | − | 0.974345i | \(-0.427743\pi\) | ||||
0.225058 | + | 0.974345i | \(0.427743\pi\) | |||||||
\(828\) | 12.0000 | 0.417029 | ||||||||
\(829\) | −13.0557 | −0.453444 | −0.226722 | − | 0.973959i | \(-0.572801\pi\) | ||||
−0.226722 | + | 0.973959i | \(0.572801\pi\) | |||||||
\(830\) | −37.8885 | −1.31513 | ||||||||
\(831\) | −18.9443 | −0.657170 | ||||||||
\(832\) | −58.1378 | −2.01556 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 16.5836 | 0.574243 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | −48.0000 | −1.66011 | ||||||||
\(837\) | −1.52786 | −0.0528107 | ||||||||
\(838\) | 66.8328 | 2.30870 | ||||||||
\(839\) | 54.8328 | 1.89304 | 0.946520 | − | 0.322647i | \(-0.104573\pi\) | ||||
0.946520 | + | 0.322647i | \(0.104573\pi\) | |||||||
\(840\) | −2.23607 | −0.0771517 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −49.1935 | −1.69532 | ||||||||
\(843\) | 10.9443 | 0.376941 | ||||||||
\(844\) | −50.8328 | −1.74974 | ||||||||
\(845\) | −7.00000 | −0.240807 | ||||||||
\(846\) | −28.9443 | −0.995125 | ||||||||
\(847\) | 30.8885 | 1.06134 | ||||||||
\(848\) | 3.52786 | 0.121147 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 4.47214 | 0.153393 | ||||||||
\(851\) | −27.7771 | −0.952186 | ||||||||
\(852\) | −16.5836 | −0.568145 | ||||||||
\(853\) | −31.3050 | −1.07186 | −0.535931 | − | 0.844262i | \(-0.680039\pi\) | ||||
−0.535931 | + | 0.844262i | \(0.680039\pi\) | |||||||
\(854\) | 4.47214 | 0.153033 | ||||||||
\(855\) | 2.47214 | 0.0845453 | ||||||||
\(856\) | 28.9443 | 0.989295 | ||||||||
\(857\) | 36.8328 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283427\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283427\pi\) | |||||||
\(858\) | 64.7214 | 2.20955 | ||||||||
\(859\) | 50.4721 | 1.72209 | 0.861044 | − | 0.508531i | \(-0.169811\pi\) | ||||
0.861044 | + | 0.508531i | \(0.169811\pi\) | |||||||
\(860\) | −26.8328 | −0.914991 | ||||||||
\(861\) | 2.00000 | 0.0681598 | ||||||||
\(862\) | 41.3050 | 1.40685 | ||||||||
\(863\) | 21.8885 | 0.745095 | 0.372547 | − | 0.928013i | \(-0.378484\pi\) | ||||
0.372547 | + | 0.928013i | \(0.378484\pi\) | |||||||
\(864\) | −6.70820 | −0.228218 | ||||||||
\(865\) | 2.94427 | 0.100108 | ||||||||
\(866\) | −36.8328 | −1.25163 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 4.58359 | 0.155577 | ||||||||
\(869\) | 83.7771 | 2.84194 | ||||||||
\(870\) | 4.47214 | 0.151620 | ||||||||
\(871\) | −17.8885 | −0.606130 | ||||||||
\(872\) | 4.47214 | 0.151446 | ||||||||
\(873\) | 8.47214 | 0.286738 | ||||||||
\(874\) | 22.1115 | 0.747931 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 37.4164 | 1.26418 | ||||||||
\(877\) | −56.8328 | −1.91911 | −0.959554 | − | 0.281525i | \(-0.909160\pi\) | ||||
−0.959554 | + | 0.281525i | \(0.909160\pi\) | |||||||
\(878\) | −3.41641 | −0.115298 | ||||||||
\(879\) | −5.05573 | −0.170525 | ||||||||
\(880\) | 6.47214 | 0.218176 | ||||||||
\(881\) | −27.8885 | −0.939589 | −0.469794 | − | 0.882776i | \(-0.655672\pi\) | ||||
−0.469794 | + | 0.882776i | \(0.655672\pi\) | |||||||
\(882\) | −2.23607 | −0.0752923 | ||||||||
\(883\) | −37.8885 | −1.27505 | −0.637526 | − | 0.770429i | \(-0.720042\pi\) | ||||
−0.637526 | + | 0.770429i | \(0.720042\pi\) | |||||||
\(884\) | −26.8328 | −0.902485 | ||||||||
\(885\) | −8.94427 | −0.300658 | ||||||||
\(886\) | 17.8885 | 0.600977 | ||||||||
\(887\) | −30.8328 | −1.03526 | −0.517632 | − | 0.855603i | \(-0.673186\pi\) | ||||
−0.517632 | + | 0.855603i | \(0.673186\pi\) | |||||||
\(888\) | −15.5279 | −0.521081 | ||||||||
\(889\) | −4.94427 | −0.165826 | ||||||||
\(890\) | −4.47214 | −0.149906 | ||||||||
\(891\) | 6.47214 | 0.216825 | ||||||||
\(892\) | −38.8328 | −1.30022 | ||||||||
\(893\) | −32.0000 | −1.07084 | ||||||||
\(894\) | −33.4164 | −1.11761 | ||||||||
\(895\) | −6.47214 | −0.216340 | ||||||||
\(896\) | 15.6525 | 0.522913 | ||||||||
\(897\) | −17.8885 | −0.597281 | ||||||||
\(898\) | 31.3050 | 1.04466 | ||||||||
\(899\) | −3.05573 | −0.101914 | ||||||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 7.05573 | 0.235060 | ||||||||
\(902\) | 28.9443 | 0.963739 | ||||||||
\(903\) | −8.94427 | −0.297647 | ||||||||
\(904\) | −1.05573 | −0.0351130 | ||||||||
\(905\) | −1.05573 | −0.0350936 | ||||||||
\(906\) | −35.7771 | −1.18861 | ||||||||
\(907\) | 53.8885 | 1.78934 | 0.894670 | − | 0.446728i | \(-0.147411\pi\) | ||||
0.894670 | + | 0.446728i | \(0.147411\pi\) | |||||||
\(908\) | 2.83282 | 0.0940103 | ||||||||
\(909\) | −14.0000 | −0.464351 | ||||||||
\(910\) | 10.0000 | 0.331497 | ||||||||
\(911\) | 46.2492 | 1.53231 | 0.766153 | − | 0.642659i | \(-0.222169\pi\) | ||||
0.766153 | + | 0.642659i | \(0.222169\pi\) | |||||||
\(912\) | −2.47214 | −0.0818606 | ||||||||
\(913\) | −109.666 | −3.62940 | ||||||||
\(914\) | −15.5279 | −0.513616 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | 71.6656 | 2.36790 | ||||||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | −4.47214 | −0.147602 | ||||||||
\(919\) | −35.0557 | −1.15638 | −0.578191 | − | 0.815902i | \(-0.696241\pi\) | ||||
−0.578191 | + | 0.815902i | \(0.696241\pi\) | |||||||
\(920\) | 8.94427 | 0.294884 | ||||||||
\(921\) | 15.0557 | 0.496103 | ||||||||
\(922\) | −8.69505 | −0.286356 | ||||||||
\(923\) | 24.7214 | 0.813713 | ||||||||
\(924\) | −19.4164 | −0.638753 | ||||||||
\(925\) | −6.94427 | −0.228326 | ||||||||
\(926\) | −46.8328 | −1.53902 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.4164 | −0.440415 | ||||||||
\(929\) | −16.1115 | −0.528600 | −0.264300 | − | 0.964441i | \(-0.585141\pi\) | ||||
−0.264300 | + | 0.964441i | \(0.585141\pi\) | |||||||
\(930\) | −3.41641 | −0.112028 | ||||||||
\(931\) | −2.47214 | −0.0810210 | ||||||||
\(932\) | −28.2492 | −0.925334 | ||||||||
\(933\) | −25.8885 | −0.847553 | ||||||||
\(934\) | 20.0000 | 0.654420 | ||||||||
\(935\) | 12.9443 | 0.423323 | ||||||||
\(936\) | −10.0000 | −0.326860 | ||||||||
\(937\) | −52.4721 | −1.71419 | −0.857095 | − | 0.515158i | \(-0.827733\pi\) | ||||
−0.857095 | + | 0.515158i | \(0.827733\pi\) | |||||||
\(938\) | 8.94427 | 0.292041 | ||||||||
\(939\) | 17.4164 | 0.568363 | ||||||||
\(940\) | −38.8328 | −1.26659 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | −1.05573 | −0.0343975 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 8.94427 | 0.291111 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −129.443 | −4.20855 | ||||||||
\(947\) | −17.8885 | −0.581300 | −0.290650 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290650 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(948\) | −38.8328 | −1.26123 | ||||||||
\(949\) | −55.7771 | −1.81060 | ||||||||
\(950\) | 5.52786 | 0.179348 | ||||||||
\(951\) | −14.3607 | −0.465677 | ||||||||
\(952\) | 4.47214 | 0.144943 | ||||||||
\(953\) | −33.4164 | −1.08246 | −0.541232 | − | 0.840873i | \(-0.682042\pi\) | ||||
−0.541232 | + | 0.840873i | \(0.682042\pi\) | |||||||
\(954\) | 7.88854 | 0.255401 | ||||||||
\(955\) | −0.583592 | −0.0188846 | ||||||||
\(956\) | −31.4164 | −1.01608 | ||||||||
\(957\) | 12.9443 | 0.418429 | ||||||||
\(958\) | 40.0000 | 1.29234 | ||||||||
\(959\) | 3.52786 | 0.113921 | ||||||||
\(960\) | −13.0000 | −0.419573 | ||||||||
\(961\) | −28.6656 | −0.924698 | ||||||||
\(962\) | 69.4427 | 2.23892 | ||||||||
\(963\) | −12.9443 | −0.417123 | ||||||||
\(964\) | −56.8328 | −1.83046 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 8.94427 | 0.287777 | ||||||||
\(967\) | 25.8885 | 0.832519 | 0.416260 | − | 0.909246i | \(-0.363341\pi\) | ||||
0.416260 | + | 0.909246i | \(0.363341\pi\) | |||||||
\(968\) | −69.0689 | −2.21996 | ||||||||
\(969\) | −4.94427 | −0.158833 | ||||||||
\(970\) | 18.9443 | 0.608264 | ||||||||
\(971\) | 40.9443 | 1.31396 | 0.656982 | − | 0.753906i | \(-0.271833\pi\) | ||||
0.656982 | + | 0.753906i | \(0.271833\pi\) | |||||||
\(972\) | −3.00000 | −0.0962250 | ||||||||
\(973\) | 7.41641 | 0.237759 | ||||||||
\(974\) | 46.8328 | 1.50062 | ||||||||
\(975\) | −4.47214 | −0.143223 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 30.5836 | 0.978456 | 0.489228 | − | 0.872156i | \(-0.337279\pi\) | ||||
0.489228 | + | 0.872156i | \(0.337279\pi\) | |||||||
\(978\) | −37.8885 | −1.21154 | ||||||||
\(979\) | −12.9443 | −0.413701 | ||||||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 47.6393 | 1.52023 | ||||||||
\(983\) | −22.8328 | −0.728254 | −0.364127 | − | 0.931349i | \(-0.618633\pi\) | ||||
−0.364127 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(984\) | −4.47214 | −0.142566 | ||||||||
\(985\) | −15.5279 | −0.494759 | ||||||||
\(986\) | −8.94427 | −0.284844 | ||||||||
\(987\) | −12.9443 | −0.412021 | ||||||||
\(988\) | −33.1672 | −1.05519 | ||||||||
\(989\) | 35.7771 | 1.13765 | ||||||||
\(990\) | 14.4721 | 0.459955 | ||||||||
\(991\) | 4.94427 | 0.157060 | 0.0785300 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785300 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(992\) | 10.2492 | 0.325413 | ||||||||
\(993\) | −0.944272 | −0.0299656 | ||||||||
\(994\) | −12.3607 | −0.392057 | ||||||||
\(995\) | −27.4164 | −0.869159 | ||||||||
\(996\) | 50.8328 | 1.61070 | ||||||||
\(997\) | −5.41641 | −0.171539 | −0.0857697 | − | 0.996315i | \(-0.527335\pi\) | ||||
−0.0857697 | + | 0.996315i | \(0.527335\pi\) | |||||||
\(998\) | 31.0557 | 0.983052 | ||||||||
\(999\) | 6.94427 | 0.219707 |
(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.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.2.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 1680.2.a.v.1.1 | 2 | |||
5.2 | odd | 4 | 525.2.d.c.274.2 | 4 | |||
5.3 | odd | 4 | 525.2.d.c.274.3 | 4 | |||
5.4 | even | 2 | 525.2.a.g.1.2 | 2 | |||
7.2 | even | 3 | 735.2.i.k.361.2 | 4 | |||
7.3 | odd | 6 | 735.2.i.i.226.2 | 4 | |||
7.4 | even | 3 | 735.2.i.k.226.2 | 4 | |||
7.5 | odd | 6 | 735.2.i.i.361.2 | 4 | |||
7.6 | odd | 2 | 735.2.a.k.1.1 | 2 | |||
8.3 | odd | 2 | 6720.2.a.cs.1.2 | 2 | |||
8.5 | even | 2 | 6720.2.a.cx.1.1 | 2 | |||
12.11 | even | 2 | 5040.2.a.bw.1.2 | 2 | |||
15.2 | even | 4 | 1575.2.d.d.1324.4 | 4 | |||
15.8 | even | 4 | 1575.2.d.d.1324.1 | 4 | |||
15.14 | odd | 2 | 1575.2.a.r.1.1 | 2 | |||
20.19 | odd | 2 | 8400.2.a.cx.1.1 | 2 | |||
21.20 | even | 2 | 2205.2.a.w.1.2 | 2 | |||
35.34 | odd | 2 | 3675.2.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.2.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
525.2.a.g.1.2 | 2 | 5.4 | even | 2 | |||
525.2.d.c.274.2 | 4 | 5.2 | odd | 4 | |||
525.2.d.c.274.3 | 4 | 5.3 | odd | 4 | |||
735.2.a.k.1.1 | 2 | 7.6 | odd | 2 | |||
735.2.i.i.226.2 | 4 | 7.3 | odd | 6 | |||
735.2.i.i.361.2 | 4 | 7.5 | odd | 6 | |||
735.2.i.k.226.2 | 4 | 7.4 | even | 3 | |||
735.2.i.k.361.2 | 4 | 7.2 | even | 3 | |||
1575.2.a.r.1.1 | 2 | 15.14 | odd | 2 | |||
1575.2.d.d.1324.1 | 4 | 15.8 | even | 4 | |||
1575.2.d.d.1324.4 | 4 | 15.2 | even | 4 | |||
1680.2.a.v.1.1 | 2 | 4.3 | odd | 2 | |||
2205.2.a.w.1.2 | 2 | 21.20 | even | 2 | |||
3675.2.a.y.1.2 | 2 | 35.34 | odd | 2 | |||
5040.2.a.bw.1.2 | 2 | 12.11 | even | 2 | |||
6720.2.a.cs.1.2 | 2 | 8.3 | odd | 2 | |||
6720.2.a.cx.1.1 | 2 | 8.5 | even | 2 | |||
8400.2.a.cx.1.1 | 2 | 20.19 | odd | 2 |