Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.23607 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.61803 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(14\) | 1.23607 | 0.330353 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.09017 | 1.23455 | 0.617274 | − | 0.786748i | \(-0.288237\pi\) | ||||
0.617274 | + | 0.786748i | \(0.288237\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.23607 | −0.742405 | −0.371202 | − | 0.928552i | \(-0.621054\pi\) | ||||
−0.371202 | + | 0.928552i | \(0.621054\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.145898 | 0.0304218 | 0.0152109 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152109 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.61803 | 1.10179 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.23607 | 0.233595 | ||||||||
\(29\) | −0.381966 | −0.0709293 | −0.0354647 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354647 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −3.61803 | −0.649818 | −0.324909 | − | 0.945745i | \(-0.605334\pi\) | ||||
−0.324909 | + | 0.945745i | \(0.605334\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.09017 | 0.872957 | ||||||||
\(35\) | −1.23607 | −0.208934 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.61803 | −1.41680 | −0.708398 | − | 0.705813i | \(-0.750582\pi\) | ||||
−0.708398 | + | 0.705813i | \(0.750582\pi\) | |||||||
\(38\) | −3.23607 | −0.524960 | ||||||||
\(39\) | −5.61803 | −0.899605 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.23607 | −0.505389 | −0.252694 | − | 0.967546i | \(-0.581317\pi\) | ||||
−0.252694 | + | 0.967546i | \(0.581317\pi\) | |||||||
\(42\) | −1.23607 | −0.190729 | ||||||||
\(43\) | 11.0902 | 1.69124 | 0.845618 | − | 0.533789i | \(-0.179232\pi\) | ||||
0.845618 | + | 0.533789i | \(0.179232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0.145898 | 0.0215115 | ||||||||
\(47\) | 11.3262 | 1.65210 | 0.826051 | − | 0.563596i | \(-0.190582\pi\) | ||||
0.826051 | + | 0.563596i | \(0.190582\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −5.09017 | −0.712766 | ||||||||
\(52\) | 5.61803 | 0.779081 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.23607 | 0.165177 | ||||||||
\(57\) | 3.23607 | 0.428628 | ||||||||
\(58\) | −0.381966 | −0.0501546 | ||||||||
\(59\) | 2.90983 | 0.378828 | 0.189414 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189414 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −3.61803 | −0.459491 | ||||||||
\(63\) | 1.23607 | 0.155730 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.61803 | −0.696831 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09017 | 0.744033 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(68\) | 5.09017 | 0.617274 | ||||||||
\(69\) | −0.145898 | −0.0175641 | ||||||||
\(70\) | −1.23607 | −0.147738 | ||||||||
\(71\) | 1.52786 | 0.181324 | 0.0906621 | − | 0.995882i | \(-0.471102\pi\) | ||||
0.0906621 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.4164 | −1.57027 | −0.785136 | − | 0.619324i | \(-0.787407\pi\) | ||||
−0.785136 | + | 0.619324i | \(0.787407\pi\) | |||||||
\(74\) | −8.61803 | −1.00183 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −3.23607 | −0.371202 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.61803 | −0.636117 | ||||||||
\(79\) | 7.09017 | 0.797706 | 0.398853 | − | 0.917015i | \(-0.369408\pi\) | ||||
0.398853 | + | 0.917015i | \(0.369408\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.23607 | −0.357364 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | −1.23607 | −0.134866 | ||||||||
\(85\) | −5.09017 | −0.552106 | ||||||||
\(86\) | 11.0902 | 1.19588 | ||||||||
\(87\) | 0.381966 | 0.0409511 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7639 | 1.35297 | 0.676487 | − | 0.736455i | \(-0.263501\pi\) | ||||
0.676487 | + | 0.736455i | \(0.263501\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 6.94427 | 0.727957 | ||||||||
\(92\) | 0.145898 | 0.0152109 | ||||||||
\(93\) | 3.61803 | 0.375173 | ||||||||
\(94\) | 11.3262 | 1.16821 | ||||||||
\(95\) | 3.23607 | 0.332014 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.6525 | −1.28466 | −0.642332 | − | 0.766426i | \(-0.722033\pi\) | ||||
−0.642332 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(98\) | −5.47214 | −0.552769 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.3820 | 1.33156 | 0.665778 | − | 0.746150i | \(-0.268100\pi\) | ||||
0.665778 | + | 0.746150i | \(0.268100\pi\) | |||||||
\(102\) | −5.09017 | −0.504002 | ||||||||
\(103\) | 11.2361 | 1.10712 | 0.553561 | − | 0.832808i | \(-0.313268\pi\) | ||||
0.553561 | + | 0.832808i | \(0.313268\pi\) | |||||||
\(104\) | 5.61803 | 0.550894 | ||||||||
\(105\) | 1.23607 | 0.120628 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | 19.7082 | 1.90526 | 0.952632 | − | 0.304125i | \(-0.0983642\pi\) | ||||
0.952632 | + | 0.304125i | \(0.0983642\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.47214 | 0.619918 | 0.309959 | − | 0.950750i | \(-0.399685\pi\) | ||||
0.309959 | + | 0.950750i | \(0.399685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.61803 | 0.817988 | ||||||||
\(112\) | 1.23607 | 0.116797 | ||||||||
\(113\) | 0.562306 | 0.0528973 | 0.0264486 | − | 0.999650i | \(-0.491580\pi\) | ||||
0.0264486 | + | 0.999650i | \(0.491580\pi\) | |||||||
\(114\) | 3.23607 | 0.303086 | ||||||||
\(115\) | −0.145898 | −0.0136051 | ||||||||
\(116\) | −0.381966 | −0.0354647 | ||||||||
\(117\) | 5.61803 | 0.519387 | ||||||||
\(118\) | 2.90983 | 0.267872 | ||||||||
\(119\) | 6.29180 | 0.576768 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.23607 | 0.291786 | ||||||||
\(124\) | −3.61803 | −0.324909 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.23607 | 0.110118 | ||||||||
\(127\) | −16.6525 | −1.47767 | −0.738834 | − | 0.673887i | \(-0.764623\pi\) | ||||
−0.738834 | + | 0.673887i | \(0.764623\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.0902 | −0.976435 | ||||||||
\(130\) | −5.61803 | −0.492734 | ||||||||
\(131\) | −5.61803 | −0.490850 | −0.245425 | − | 0.969416i | \(-0.578927\pi\) | ||||
−0.245425 | + | 0.969416i | \(0.578927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 6.09017 | 0.526111 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 5.09017 | 0.436478 | ||||||||
\(137\) | 11.7984 | 1.00800 | 0.504002 | − | 0.863703i | \(-0.331861\pi\) | ||||
0.504002 | + | 0.863703i | \(0.331861\pi\) | |||||||
\(138\) | −0.145898 | −0.0124197 | ||||||||
\(139\) | 13.2361 | 1.12267 | 0.561334 | − | 0.827589i | \(-0.310288\pi\) | ||||
0.561334 | + | 0.827589i | \(0.310288\pi\) | |||||||
\(140\) | −1.23607 | −0.104467 | ||||||||
\(141\) | −11.3262 | −0.953841 | ||||||||
\(142\) | 1.52786 | 0.128216 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.381966 | 0.0317206 | ||||||||
\(146\) | −13.4164 | −1.11035 | ||||||||
\(147\) | 5.47214 | 0.451334 | ||||||||
\(148\) | −8.61803 | −0.708398 | ||||||||
\(149\) | −5.38197 | −0.440908 | −0.220454 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220454 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | −3.23607 | −0.262480 | ||||||||
\(153\) | 5.09017 | 0.411516 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.61803 | 0.290607 | ||||||||
\(156\) | −5.61803 | −0.449803 | ||||||||
\(157\) | 24.2705 | 1.93700 | 0.968499 | − | 0.249018i | \(-0.0801079\pi\) | ||||
0.968499 | + | 0.249018i | \(0.0801079\pi\) | |||||||
\(158\) | 7.09017 | 0.564064 | ||||||||
\(159\) | 0.472136 | 0.0374428 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.180340 | 0.0142128 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.85410 | −0.458529 | −0.229264 | − | 0.973364i | \(-0.573632\pi\) | ||||
−0.229264 | + | 0.973364i | \(0.573632\pi\) | |||||||
\(164\) | −3.23607 | −0.252694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 20.2705 | 1.56858 | 0.784290 | − | 0.620395i | \(-0.213028\pi\) | ||||
0.784290 | + | 0.620395i | \(0.213028\pi\) | |||||||
\(168\) | −1.23607 | −0.0953647 | ||||||||
\(169\) | 18.5623 | 1.42787 | ||||||||
\(170\) | −5.09017 | −0.390398 | ||||||||
\(171\) | −3.23607 | −0.247468 | ||||||||
\(172\) | 11.0902 | 0.845618 | ||||||||
\(173\) | −18.4721 | −1.40441 | −0.702205 | − | 0.711975i | \(-0.747801\pi\) | ||||
−0.702205 | + | 0.711975i | \(0.747801\pi\) | |||||||
\(174\) | 0.381966 | 0.0289568 | ||||||||
\(175\) | 1.23607 | 0.0934380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.90983 | −0.218716 | ||||||||
\(178\) | 12.7639 | 0.956697 | ||||||||
\(179\) | 24.8541 | 1.85768 | 0.928841 | − | 0.370478i | \(-0.120806\pi\) | ||||
0.928841 | + | 0.370478i | \(0.120806\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −13.8885 | −1.03233 | −0.516164 | − | 0.856490i | \(-0.672640\pi\) | ||||
−0.516164 | + | 0.856490i | \(0.672640\pi\) | |||||||
\(182\) | 6.94427 | 0.514744 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.145898 | 0.0107557 | ||||||||
\(185\) | 8.61803 | 0.633610 | ||||||||
\(186\) | 3.61803 | 0.265287 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.3262 | 0.826051 | ||||||||
\(189\) | −1.23607 | −0.0899107 | ||||||||
\(190\) | 3.23607 | 0.234769 | ||||||||
\(191\) | 4.76393 | 0.344706 | 0.172353 | − | 0.985035i | \(-0.444863\pi\) | ||||
0.172353 | + | 0.985035i | \(0.444863\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.05573 | −0.219956 | −0.109978 | − | 0.993934i | \(-0.535078\pi\) | ||||
−0.109978 | + | 0.993934i | \(0.535078\pi\) | |||||||
\(194\) | −12.6525 | −0.908395 | ||||||||
\(195\) | 5.61803 | 0.402316 | ||||||||
\(196\) | −5.47214 | −0.390867 | ||||||||
\(197\) | −6.94427 | −0.494759 | −0.247379 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247379 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9787 | −1.48714 | −0.743571 | − | 0.668657i | \(-0.766869\pi\) | ||||
−0.743571 | + | 0.668657i | \(0.766869\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −6.09017 | −0.429567 | ||||||||
\(202\) | 13.3820 | 0.941552 | ||||||||
\(203\) | −0.472136 | −0.0331374 | ||||||||
\(204\) | −5.09017 | −0.356383 | ||||||||
\(205\) | 3.23607 | 0.226017 | ||||||||
\(206\) | 11.2361 | 0.782854 | ||||||||
\(207\) | 0.145898 | 0.0101406 | ||||||||
\(208\) | 5.61803 | 0.389541 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.23607 | 0.0852968 | ||||||||
\(211\) | −20.7639 | −1.42945 | −0.714724 | − | 0.699407i | \(-0.753448\pi\) | ||||
−0.714724 | + | 0.699407i | \(0.753448\pi\) | |||||||
\(212\) | −0.472136 | −0.0324264 | ||||||||
\(213\) | −1.52786 | −0.104688 | ||||||||
\(214\) | 19.7082 | 1.34723 | ||||||||
\(215\) | −11.0902 | −0.756343 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.47214 | −0.303588 | ||||||||
\(218\) | 6.47214 | 0.438348 | ||||||||
\(219\) | 13.4164 | 0.906597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.5967 | 1.92363 | ||||||||
\(222\) | 8.61803 | 0.578405 | ||||||||
\(223\) | 2.76393 | 0.185087 | 0.0925433 | − | 0.995709i | \(-0.470500\pi\) | ||||
0.0925433 | + | 0.995709i | \(0.470500\pi\) | |||||||
\(224\) | 1.23607 | 0.0825883 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0.562306 | 0.0374040 | ||||||||
\(227\) | −24.3607 | −1.61688 | −0.808438 | − | 0.588582i | \(-0.799686\pi\) | ||||
−0.808438 | + | 0.588582i | \(0.799686\pi\) | |||||||
\(228\) | 3.23607 | 0.214314 | ||||||||
\(229\) | 5.23607 | 0.346009 | 0.173005 | − | 0.984921i | \(-0.444652\pi\) | ||||
0.173005 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(230\) | −0.145898 | −0.00962023 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.381966 | −0.0250773 | ||||||||
\(233\) | −24.5623 | −1.60913 | −0.804565 | − | 0.593864i | \(-0.797602\pi\) | ||||
−0.804565 | + | 0.593864i | \(0.797602\pi\) | |||||||
\(234\) | 5.61803 | 0.367262 | ||||||||
\(235\) | −11.3262 | −0.738842 | ||||||||
\(236\) | 2.90983 | 0.189414 | ||||||||
\(237\) | −7.09017 | −0.460556 | ||||||||
\(238\) | 6.29180 | 0.407837 | ||||||||
\(239\) | 1.23607 | 0.0799546 | 0.0399773 | − | 0.999201i | \(-0.487271\pi\) | ||||
0.0399773 | + | 0.999201i | \(0.487271\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 11.8885 | 0.765808 | 0.382904 | − | 0.923788i | \(-0.374924\pi\) | ||||
0.382904 | + | 0.923788i | \(0.374924\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.47214 | 0.349602 | ||||||||
\(246\) | 3.23607 | 0.206324 | ||||||||
\(247\) | −18.1803 | −1.15679 | ||||||||
\(248\) | −3.61803 | −0.229745 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 10.6180 | 0.670204 | 0.335102 | − | 0.942182i | \(-0.391229\pi\) | ||||
0.335102 | + | 0.942182i | \(0.391229\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.6525 | −1.04487 | ||||||||
\(255\) | 5.09017 | 0.318759 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.3607 | −0.895795 | −0.447897 | − | 0.894085i | \(-0.647827\pi\) | ||||
−0.447897 | + | 0.894085i | \(0.647827\pi\) | |||||||
\(258\) | −11.0902 | −0.690444 | ||||||||
\(259\) | −10.6525 | −0.661913 | ||||||||
\(260\) | −5.61803 | −0.348416 | ||||||||
\(261\) | −0.381966 | −0.0236431 | ||||||||
\(262\) | −5.61803 | −0.347083 | ||||||||
\(263\) | 0.145898 | 0.00899646 | 0.00449823 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449823 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | −12.7639 | −0.781140 | ||||||||
\(268\) | 6.09017 | 0.372016 | ||||||||
\(269\) | 27.7984 | 1.69490 | 0.847448 | − | 0.530878i | \(-0.178138\pi\) | ||||
0.847448 | + | 0.530878i | \(0.178138\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −8.61803 | −0.523508 | −0.261754 | − | 0.965135i | \(-0.584301\pi\) | ||||
−0.261754 | + | 0.965135i | \(0.584301\pi\) | |||||||
\(272\) | 5.09017 | 0.308637 | ||||||||
\(273\) | −6.94427 | −0.420286 | ||||||||
\(274\) | 11.7984 | 0.712766 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.145898 | −0.00878203 | ||||||||
\(277\) | 14.5066 | 0.871616 | 0.435808 | − | 0.900040i | \(-0.356463\pi\) | ||||
0.435808 | + | 0.900040i | \(0.356463\pi\) | |||||||
\(278\) | 13.2361 | 0.793847 | ||||||||
\(279\) | −3.61803 | −0.216606 | ||||||||
\(280\) | −1.23607 | −0.0738692 | ||||||||
\(281\) | −16.4721 | −0.982645 | −0.491323 | − | 0.870978i | \(-0.663486\pi\) | ||||
−0.491323 | + | 0.870978i | \(0.663486\pi\) | |||||||
\(282\) | −11.3262 | −0.674468 | ||||||||
\(283\) | −6.67376 | −0.396714 | −0.198357 | − | 0.980130i | \(-0.563561\pi\) | ||||
−0.198357 | + | 0.980130i | \(0.563561\pi\) | |||||||
\(284\) | 1.52786 | 0.0906621 | ||||||||
\(285\) | −3.23607 | −0.191688 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.90983 | 0.524108 | ||||||||
\(290\) | 0.381966 | 0.0224298 | ||||||||
\(291\) | 12.6525 | 0.741701 | ||||||||
\(292\) | −13.4164 | −0.785136 | ||||||||
\(293\) | −20.0000 | −1.16841 | −0.584206 | − | 0.811605i | \(-0.698594\pi\) | ||||
−0.584206 | + | 0.811605i | \(0.698594\pi\) | |||||||
\(294\) | 5.47214 | 0.319141 | ||||||||
\(295\) | −2.90983 | −0.169417 | ||||||||
\(296\) | −8.61803 | −0.500913 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.38197 | −0.311769 | ||||||||
\(299\) | 0.819660 | 0.0474022 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 13.7082 | 0.790128 | ||||||||
\(302\) | 3.05573 | 0.175837 | ||||||||
\(303\) | −13.3820 | −0.768774 | ||||||||
\(304\) | −3.23607 | −0.185601 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.09017 | 0.290986 | ||||||||
\(307\) | 22.4508 | 1.28134 | 0.640669 | − | 0.767817i | \(-0.278657\pi\) | ||||
0.640669 | + | 0.767817i | \(0.278657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2361 | −0.639198 | ||||||||
\(310\) | 3.61803 | 0.205491 | ||||||||
\(311\) | 4.76393 | 0.270138 | 0.135069 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135069 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(312\) | −5.61803 | −0.318059 | ||||||||
\(313\) | −0.472136 | −0.0266867 | −0.0133434 | − | 0.999911i | \(-0.504247\pi\) | ||||
−0.0133434 | + | 0.999911i | \(0.504247\pi\) | |||||||
\(314\) | 24.2705 | 1.36966 | ||||||||
\(315\) | −1.23607 | −0.0696445 | ||||||||
\(316\) | 7.09017 | 0.398853 | ||||||||
\(317\) | −0.583592 | −0.0327778 | −0.0163889 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163889 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(318\) | 0.472136 | 0.0264761 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −19.7082 | −1.10000 | ||||||||
\(322\) | 0.180340 | 0.0100499 | ||||||||
\(323\) | −16.4721 | −0.916534 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.61803 | 0.311632 | ||||||||
\(326\) | −5.85410 | −0.324229 | ||||||||
\(327\) | −6.47214 | −0.357910 | ||||||||
\(328\) | −3.23607 | −0.178682 | ||||||||
\(329\) | 14.0000 | 0.771845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.76393 | 0.261849 | 0.130925 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130925 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | −8.61803 | −0.472265 | ||||||||
\(334\) | 20.2705 | 1.10915 | ||||||||
\(335\) | −6.09017 | −0.332742 | ||||||||
\(336\) | −1.23607 | −0.0674330 | ||||||||
\(337\) | −10.7639 | −0.586349 | −0.293174 | − | 0.956059i | \(-0.594712\pi\) | ||||
−0.293174 | + | 0.956059i | \(0.594712\pi\) | |||||||
\(338\) | 18.5623 | 1.00966 | ||||||||
\(339\) | −0.562306 | −0.0305403 | ||||||||
\(340\) | −5.09017 | −0.276053 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.23607 | −0.174987 | ||||||||
\(343\) | −15.4164 | −0.832408 | ||||||||
\(344\) | 11.0902 | 0.597942 | ||||||||
\(345\) | 0.145898 | 0.00785489 | ||||||||
\(346\) | −18.4721 | −0.993068 | ||||||||
\(347\) | 0.111456 | 0.00598328 | 0.00299164 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299164 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(348\) | 0.381966 | 0.0204755 | ||||||||
\(349\) | 15.4164 | 0.825221 | 0.412611 | − | 0.910907i | \(-0.364617\pi\) | ||||
0.412611 | + | 0.910907i | \(0.364617\pi\) | |||||||
\(350\) | 1.23607 | 0.0660706 | ||||||||
\(351\) | −5.61803 | −0.299868 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3820 | 1.13805 | 0.569024 | − | 0.822321i | \(-0.307321\pi\) | ||||
0.569024 | + | 0.822321i | \(0.307321\pi\) | |||||||
\(354\) | −2.90983 | −0.154656 | ||||||||
\(355\) | −1.52786 | −0.0810906 | ||||||||
\(356\) | 12.7639 | 0.676487 | ||||||||
\(357\) | −6.29180 | −0.332997 | ||||||||
\(358\) | 24.8541 | 1.31358 | ||||||||
\(359\) | 10.1803 | 0.537298 | 0.268649 | − | 0.963238i | \(-0.413423\pi\) | ||||
0.268649 | + | 0.963238i | \(0.413423\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | −13.8885 | −0.729966 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.94427 | 0.363979 | ||||||||
\(365\) | 13.4164 | 0.702247 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.2361 | −1.63051 | −0.815255 | − | 0.579103i | \(-0.803403\pi\) | ||||
−0.815255 | + | 0.579103i | \(0.803403\pi\) | |||||||
\(368\) | 0.145898 | 0.00760546 | ||||||||
\(369\) | −3.23607 | −0.168463 | ||||||||
\(370\) | 8.61803 | 0.448030 | ||||||||
\(371\) | −0.583592 | −0.0302986 | ||||||||
\(372\) | 3.61803 | 0.187586 | ||||||||
\(373\) | −20.4721 | −1.06001 | −0.530004 | − | 0.847995i | \(-0.677809\pi\) | ||||
−0.530004 | + | 0.847995i | \(0.677809\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 11.3262 | 0.584106 | ||||||||
\(377\) | −2.14590 | −0.110519 | ||||||||
\(378\) | −1.23607 | −0.0635765 | ||||||||
\(379\) | 32.3607 | 1.66226 | 0.831128 | − | 0.556081i | \(-0.187696\pi\) | ||||
0.831128 | + | 0.556081i | \(0.187696\pi\) | |||||||
\(380\) | 3.23607 | 0.166007 | ||||||||
\(381\) | 16.6525 | 0.853132 | ||||||||
\(382\) | 4.76393 | 0.243744 | ||||||||
\(383\) | 15.3262 | 0.783134 | 0.391567 | − | 0.920150i | \(-0.371933\pi\) | ||||
0.391567 | + | 0.920150i | \(0.371933\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.05573 | −0.155532 | ||||||||
\(387\) | 11.0902 | 0.563745 | ||||||||
\(388\) | −12.6525 | −0.642332 | ||||||||
\(389\) | 0.145898 | 0.00739732 | 0.00369866 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369866 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(390\) | 5.61803 | 0.284480 | ||||||||
\(391\) | 0.742646 | 0.0375572 | ||||||||
\(392\) | −5.47214 | −0.276385 | ||||||||
\(393\) | 5.61803 | 0.283392 | ||||||||
\(394\) | −6.94427 | −0.349847 | ||||||||
\(395\) | −7.09017 | −0.356745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7984 | 1.34497 | 0.672486 | − | 0.740110i | \(-0.265227\pi\) | ||||
0.672486 | + | 0.740110i | \(0.265227\pi\) | |||||||
\(398\) | −20.9787 | −1.05157 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −36.0689 | −1.80119 | −0.900597 | − | 0.434655i | \(-0.856870\pi\) | ||||
−0.900597 | + | 0.434655i | \(0.856870\pi\) | |||||||
\(402\) | −6.09017 | −0.303750 | ||||||||
\(403\) | −20.3262 | −1.01252 | ||||||||
\(404\) | 13.3820 | 0.665778 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −0.472136 | −0.0234317 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.09017 | −0.252001 | ||||||||
\(409\) | −33.9787 | −1.68014 | −0.840070 | − | 0.542479i | \(-0.817486\pi\) | ||||
−0.840070 | + | 0.542479i | \(0.817486\pi\) | |||||||
\(410\) | 3.23607 | 0.159818 | ||||||||
\(411\) | −11.7984 | −0.581971 | ||||||||
\(412\) | 11.2361 | 0.553561 | ||||||||
\(413\) | 3.59675 | 0.176984 | ||||||||
\(414\) | 0.145898 | 0.00717050 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 5.61803 | 0.275447 | ||||||||
\(417\) | −13.2361 | −0.648173 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1459 | 0.788779 | 0.394389 | − | 0.918943i | \(-0.370956\pi\) | ||||
0.394389 | + | 0.918943i | \(0.370956\pi\) | |||||||
\(420\) | 1.23607 | 0.0603139 | ||||||||
\(421\) | 6.47214 | 0.315433 | 0.157716 | − | 0.987484i | \(-0.449587\pi\) | ||||
0.157716 | + | 0.987484i | \(0.449587\pi\) | |||||||
\(422\) | −20.7639 | −1.01077 | ||||||||
\(423\) | 11.3262 | 0.550701 | ||||||||
\(424\) | −0.472136 | −0.0229289 | ||||||||
\(425\) | 5.09017 | 0.246910 | ||||||||
\(426\) | −1.52786 | −0.0740253 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.7082 | 0.952632 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.0902 | −0.534815 | ||||||||
\(431\) | −22.3607 | −1.07708 | −0.538538 | − | 0.842601i | \(-0.681023\pi\) | ||||
−0.538538 | + | 0.842601i | \(0.681023\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 30.8328 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(434\) | −4.47214 | −0.214669 | ||||||||
\(435\) | −0.381966 | −0.0183139 | ||||||||
\(436\) | 6.47214 | 0.309959 | ||||||||
\(437\) | −0.472136 | −0.0225853 | ||||||||
\(438\) | 13.4164 | 0.641061 | ||||||||
\(439\) | 17.3262 | 0.826936 | 0.413468 | − | 0.910519i | \(-0.364317\pi\) | ||||
0.413468 | + | 0.910519i | \(0.364317\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | 28.5967 | 1.36021 | ||||||||
\(443\) | 12.6525 | 0.601137 | 0.300569 | − | 0.953760i | \(-0.402824\pi\) | ||||
0.300569 | + | 0.953760i | \(0.402824\pi\) | |||||||
\(444\) | 8.61803 | 0.408994 | ||||||||
\(445\) | −12.7639 | −0.605068 | ||||||||
\(446\) | 2.76393 | 0.130876 | ||||||||
\(447\) | 5.38197 | 0.254558 | ||||||||
\(448\) | 1.23607 | 0.0583987 | ||||||||
\(449\) | 29.1246 | 1.37448 | 0.687238 | − | 0.726433i | \(-0.258823\pi\) | ||||
0.687238 | + | 0.726433i | \(0.258823\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.562306 | 0.0264486 | ||||||||
\(453\) | −3.05573 | −0.143571 | ||||||||
\(454\) | −24.3607 | −1.14330 | ||||||||
\(455\) | −6.94427 | −0.325552 | ||||||||
\(456\) | 3.23607 | 0.151543 | ||||||||
\(457\) | −26.6525 | −1.24675 | −0.623375 | − | 0.781923i | \(-0.714239\pi\) | ||||
−0.623375 | + | 0.781923i | \(0.714239\pi\) | |||||||
\(458\) | 5.23607 | 0.244665 | ||||||||
\(459\) | −5.09017 | −0.237589 | ||||||||
\(460\) | −0.145898 | −0.00680253 | ||||||||
\(461\) | −28.2148 | −1.31409 | −0.657047 | − | 0.753850i | \(-0.728195\pi\) | ||||
−0.657047 | + | 0.753850i | \(0.728195\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.8885 | −1.11019 | −0.555097 | − | 0.831785i | \(-0.687319\pi\) | ||||
−0.555097 | + | 0.831785i | \(0.687319\pi\) | |||||||
\(464\) | −0.381966 | −0.0177323 | ||||||||
\(465\) | −3.61803 | −0.167782 | ||||||||
\(466\) | −24.5623 | −1.13783 | ||||||||
\(467\) | −38.5410 | −1.78347 | −0.891733 | − | 0.452562i | \(-0.850510\pi\) | ||||
−0.891733 | + | 0.452562i | \(0.850510\pi\) | |||||||
\(468\) | 5.61803 | 0.259694 | ||||||||
\(469\) | 7.52786 | 0.347604 | ||||||||
\(470\) | −11.3262 | −0.522440 | ||||||||
\(471\) | −24.2705 | −1.11833 | ||||||||
\(472\) | 2.90983 | 0.133936 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −7.09017 | −0.325662 | ||||||||
\(475\) | −3.23607 | −0.148481 | ||||||||
\(476\) | 6.29180 | 0.288384 | ||||||||
\(477\) | −0.472136 | −0.0216176 | ||||||||
\(478\) | 1.23607 | 0.0565364 | ||||||||
\(479\) | 17.2361 | 0.787536 | 0.393768 | − | 0.919210i | \(-0.371171\pi\) | ||||
0.393768 | + | 0.919210i | \(0.371171\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −48.4164 | −2.20760 | ||||||||
\(482\) | 11.8885 | 0.541508 | ||||||||
\(483\) | −0.180340 | −0.00820575 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.6525 | 0.574519 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −15.4164 | −0.698584 | −0.349292 | − | 0.937014i | \(-0.613578\pi\) | ||||
−0.349292 | + | 0.937014i | \(0.613578\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.85410 | 0.264732 | ||||||||
\(490\) | 5.47214 | 0.247206 | ||||||||
\(491\) | −1.03444 | −0.0466837 | −0.0233419 | − | 0.999728i | \(-0.507431\pi\) | ||||
−0.0233419 | + | 0.999728i | \(0.507431\pi\) | |||||||
\(492\) | 3.23607 | 0.145893 | ||||||||
\(493\) | −1.94427 | −0.0875656 | ||||||||
\(494\) | −18.1803 | −0.817972 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.61803 | −0.162455 | ||||||||
\(497\) | 1.88854 | 0.0847128 | ||||||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | −23.5279 | −1.05325 | −0.526626 | − | 0.850097i | \(-0.676543\pi\) | ||||
−0.526626 | + | 0.850097i | \(0.676543\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −20.2705 | −0.905620 | ||||||||
\(502\) | 10.6180 | 0.473906 | ||||||||
\(503\) | −8.67376 | −0.386744 | −0.193372 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193372 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(504\) | 1.23607 | 0.0550588 | ||||||||
\(505\) | −13.3820 | −0.595490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.5623 | −0.824381 | ||||||||
\(508\) | −16.6525 | −0.738834 | ||||||||
\(509\) | −15.7984 | −0.700251 | −0.350125 | − | 0.936703i | \(-0.613861\pi\) | ||||
−0.350125 | + | 0.936703i | \(0.613861\pi\) | |||||||
\(510\) | 5.09017 | 0.225397 | ||||||||
\(511\) | −16.5836 | −0.733615 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.23607 | 0.142876 | ||||||||
\(514\) | −14.3607 | −0.633422 | ||||||||
\(515\) | −11.2361 | −0.495120 | ||||||||
\(516\) | −11.0902 | −0.488218 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.6525 | −0.468043 | ||||||||
\(519\) | 18.4721 | 0.810837 | ||||||||
\(520\) | −5.61803 | −0.246367 | ||||||||
\(521\) | 42.3607 | 1.85586 | 0.927928 | − | 0.372761i | \(-0.121589\pi\) | ||||
0.927928 | + | 0.372761i | \(0.121589\pi\) | |||||||
\(522\) | −0.381966 | −0.0167182 | ||||||||
\(523\) | −14.8328 | −0.648594 | −0.324297 | − | 0.945955i | \(-0.605128\pi\) | ||||
−0.324297 | + | 0.945955i | \(0.605128\pi\) | |||||||
\(524\) | −5.61803 | −0.245425 | ||||||||
\(525\) | −1.23607 | −0.0539464 | ||||||||
\(526\) | 0.145898 | 0.00636146 | ||||||||
\(527\) | −18.4164 | −0.802231 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9787 | −0.999075 | ||||||||
\(530\) | 0.472136 | 0.0205083 | ||||||||
\(531\) | 2.90983 | 0.126276 | ||||||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | −18.1803 | −0.787478 | ||||||||
\(534\) | −12.7639 | −0.552349 | ||||||||
\(535\) | −19.7082 | −0.852060 | ||||||||
\(536\) | 6.09017 | 0.263055 | ||||||||
\(537\) | −24.8541 | −1.07253 | ||||||||
\(538\) | 27.7984 | 1.19847 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −32.0689 | −1.37875 | −0.689374 | − | 0.724405i | \(-0.742115\pi\) | ||||
−0.689374 | + | 0.724405i | \(0.742115\pi\) | |||||||
\(542\) | −8.61803 | −0.370176 | ||||||||
\(543\) | 13.8885 | 0.596014 | ||||||||
\(544\) | 5.09017 | 0.218239 | ||||||||
\(545\) | −6.47214 | −0.277236 | ||||||||
\(546\) | −6.94427 | −0.297187 | ||||||||
\(547\) | 18.6738 | 0.798432 | 0.399216 | − | 0.916857i | \(-0.369282\pi\) | ||||
0.399216 | + | 0.916857i | \(0.369282\pi\) | |||||||
\(548\) | 11.7984 | 0.504002 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.23607 | 0.0526583 | ||||||||
\(552\) | −0.145898 | −0.00620983 | ||||||||
\(553\) | 8.76393 | 0.372680 | ||||||||
\(554\) | 14.5066 | 0.616325 | ||||||||
\(555\) | −8.61803 | −0.365815 | ||||||||
\(556\) | 13.2361 | 0.561334 | ||||||||
\(557\) | 5.12461 | 0.217137 | 0.108568 | − | 0.994089i | \(-0.465373\pi\) | ||||
0.108568 | + | 0.994089i | \(0.465373\pi\) | |||||||
\(558\) | −3.61803 | −0.153164 | ||||||||
\(559\) | 62.3050 | 2.63522 | ||||||||
\(560\) | −1.23607 | −0.0522334 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.4721 | −0.694835 | ||||||||
\(563\) | 34.9443 | 1.47273 | 0.736363 | − | 0.676587i | \(-0.236542\pi\) | ||||
0.736363 | + | 0.676587i | \(0.236542\pi\) | |||||||
\(564\) | −11.3262 | −0.476921 | ||||||||
\(565\) | −0.562306 | −0.0236564 | ||||||||
\(566\) | −6.67376 | −0.280519 | ||||||||
\(567\) | 1.23607 | 0.0519100 | ||||||||
\(568\) | 1.52786 | 0.0641078 | ||||||||
\(569\) | 1.41641 | 0.0593789 | 0.0296895 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296895 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(570\) | −3.23607 | −0.135544 | ||||||||
\(571\) | 16.3607 | 0.684673 | 0.342337 | − | 0.939577i | \(-0.388782\pi\) | ||||
0.342337 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.76393 | −0.199016 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 0.145898 | 0.00608437 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.9443 | 1.45475 | 0.727375 | − | 0.686241i | \(-0.240740\pi\) | ||||
0.727375 | + | 0.686241i | \(0.240740\pi\) | |||||||
\(578\) | 8.90983 | 0.370600 | ||||||||
\(579\) | 3.05573 | 0.126992 | ||||||||
\(580\) | 0.381966 | 0.0158603 | ||||||||
\(581\) | 4.94427 | 0.205123 | ||||||||
\(582\) | 12.6525 | 0.524462 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | −5.61803 | −0.232277 | ||||||||
\(586\) | −20.0000 | −0.826192 | ||||||||
\(587\) | −39.7082 | −1.63893 | −0.819466 | − | 0.573127i | \(-0.805730\pi\) | ||||
−0.819466 | + | 0.573127i | \(0.805730\pi\) | |||||||
\(588\) | 5.47214 | 0.225667 | ||||||||
\(589\) | 11.7082 | 0.482428 | ||||||||
\(590\) | −2.90983 | −0.119796 | ||||||||
\(591\) | 6.94427 | 0.285649 | ||||||||
\(592\) | −8.61803 | −0.354199 | ||||||||
\(593\) | −33.3262 | −1.36854 | −0.684272 | − | 0.729227i | \(-0.739880\pi\) | ||||
−0.684272 | + | 0.729227i | \(0.739880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.29180 | −0.257938 | ||||||||
\(596\) | −5.38197 | −0.220454 | ||||||||
\(597\) | 20.9787 | 0.858602 | ||||||||
\(598\) | 0.819660 | 0.0335184 | ||||||||
\(599\) | −4.18034 | −0.170804 | −0.0854020 | − | 0.996347i | \(-0.527217\pi\) | ||||
−0.0854020 | + | 0.996347i | \(0.527217\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −1.05573 | −0.0430640 | −0.0215320 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215320 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(602\) | 13.7082 | 0.558705 | ||||||||
\(603\) | 6.09017 | 0.248011 | ||||||||
\(604\) | 3.05573 | 0.124336 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.3820 | −0.543605 | ||||||||
\(607\) | 4.47214 | 0.181518 | 0.0907592 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907592 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(608\) | −3.23607 | −0.131240 | ||||||||
\(609\) | 0.472136 | 0.0191319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.6312 | 2.57424 | ||||||||
\(612\) | 5.09017 | 0.205758 | ||||||||
\(613\) | 6.00000 | 0.242338 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(614\) | 22.4508 | 0.906043 | ||||||||
\(615\) | −3.23607 | −0.130491 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.3607 | −0.739173 | −0.369587 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369587 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(618\) | −11.2361 | −0.451981 | ||||||||
\(619\) | 18.4721 | 0.742458 | 0.371229 | − | 0.928541i | \(-0.378937\pi\) | ||||
0.371229 | + | 0.928541i | \(0.378937\pi\) | |||||||
\(620\) | 3.61803 | 0.145304 | ||||||||
\(621\) | −0.145898 | −0.00585469 | ||||||||
\(622\) | 4.76393 | 0.191016 | ||||||||
\(623\) | 15.7771 | 0.632096 | ||||||||
\(624\) | −5.61803 | −0.224901 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.472136 | −0.0188703 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.2705 | 0.968499 | ||||||||
\(629\) | −43.8673 | −1.74910 | ||||||||
\(630\) | −1.23607 | −0.0492461 | ||||||||
\(631\) | −21.3262 | −0.848984 | −0.424492 | − | 0.905432i | \(-0.639547\pi\) | ||||
−0.424492 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(632\) | 7.09017 | 0.282032 | ||||||||
\(633\) | 20.7639 | 0.825292 | ||||||||
\(634\) | −0.583592 | −0.0231774 | ||||||||
\(635\) | 16.6525 | 0.660833 | ||||||||
\(636\) | 0.472136 | 0.0187214 | ||||||||
\(637\) | −30.7426 | −1.21807 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.52786 | 0.0604414 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −10.1803 | −0.402099 | −0.201050 | − | 0.979581i | \(-0.564435\pi\) | ||||
−0.201050 | + | 0.979581i | \(0.564435\pi\) | |||||||
\(642\) | −19.7082 | −0.777821 | ||||||||
\(643\) | 19.7984 | 0.780772 | 0.390386 | − | 0.920651i | \(-0.372342\pi\) | ||||
0.390386 | + | 0.920651i | \(0.372342\pi\) | |||||||
\(644\) | 0.180340 | 0.00710639 | ||||||||
\(645\) | 11.0902 | 0.436675 | ||||||||
\(646\) | −16.4721 | −0.648088 | ||||||||
\(647\) | −14.6180 | −0.574694 | −0.287347 | − | 0.957827i | \(-0.592773\pi\) | ||||
−0.287347 | + | 0.957827i | \(0.592773\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.61803 | 0.220357 | ||||||||
\(651\) | 4.47214 | 0.175277 | ||||||||
\(652\) | −5.85410 | −0.229264 | ||||||||
\(653\) | −42.5410 | −1.66476 | −0.832379 | − | 0.554206i | \(-0.813022\pi\) | ||||
−0.832379 | + | 0.554206i | \(0.813022\pi\) | |||||||
\(654\) | −6.47214 | −0.253081 | ||||||||
\(655\) | 5.61803 | 0.219515 | ||||||||
\(656\) | −3.23607 | −0.126347 | ||||||||
\(657\) | −13.4164 | −0.523424 | ||||||||
\(658\) | 14.0000 | 0.545777 | ||||||||
\(659\) | 11.4164 | 0.444720 | 0.222360 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222360 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.3607 | −1.41427 | −0.707133 | − | 0.707080i | \(-0.750012\pi\) | ||||
−0.707133 | + | 0.707080i | \(0.750012\pi\) | |||||||
\(662\) | 4.76393 | 0.185155 | ||||||||
\(663\) | −28.5967 | −1.11061 | ||||||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 4.00000 | 0.155113 | ||||||||
\(666\) | −8.61803 | −0.333942 | ||||||||
\(667\) | −0.0557281 | −0.00215780 | ||||||||
\(668\) | 20.2705 | 0.784290 | ||||||||
\(669\) | −2.76393 | −0.106860 | ||||||||
\(670\) | −6.09017 | −0.235284 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.23607 | −0.0476824 | ||||||||
\(673\) | −2.29180 | −0.0883422 | −0.0441711 | − | 0.999024i | \(-0.514065\pi\) | ||||
−0.0441711 | + | 0.999024i | \(0.514065\pi\) | |||||||
\(674\) | −10.7639 | −0.414611 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 18.5623 | 0.713935 | ||||||||
\(677\) | 22.7639 | 0.874889 | 0.437444 | − | 0.899245i | \(-0.355884\pi\) | ||||
0.437444 | + | 0.899245i | \(0.355884\pi\) | |||||||
\(678\) | −0.562306 | −0.0215952 | ||||||||
\(679\) | −15.6393 | −0.600182 | ||||||||
\(680\) | −5.09017 | −0.195199 | ||||||||
\(681\) | 24.3607 | 0.933503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.1246 | −0.731783 | −0.365891 | − | 0.930658i | \(-0.619236\pi\) | ||||
−0.365891 | + | 0.930658i | \(0.619236\pi\) | |||||||
\(684\) | −3.23607 | −0.123734 | ||||||||
\(685\) | −11.7984 | −0.450793 | ||||||||
\(686\) | −15.4164 | −0.588601 | ||||||||
\(687\) | −5.23607 | −0.199768 | ||||||||
\(688\) | 11.0902 | 0.422809 | ||||||||
\(689\) | −2.65248 | −0.101051 | ||||||||
\(690\) | 0.145898 | 0.00555424 | ||||||||
\(691\) | 10.6525 | 0.405239 | 0.202620 | − | 0.979258i | \(-0.435054\pi\) | ||||
0.202620 | + | 0.979258i | \(0.435054\pi\) | |||||||
\(692\) | −18.4721 | −0.702205 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.111456 | 0.00423082 | ||||||||
\(695\) | −13.2361 | −0.502073 | ||||||||
\(696\) | 0.381966 | 0.0144784 | ||||||||
\(697\) | −16.4721 | −0.623927 | ||||||||
\(698\) | 15.4164 | 0.583520 | ||||||||
\(699\) | 24.5623 | 0.929032 | ||||||||
\(700\) | 1.23607 | 0.0467190 | ||||||||
\(701\) | −12.4721 | −0.471066 | −0.235533 | − | 0.971866i | \(-0.575684\pi\) | ||||
−0.235533 | + | 0.971866i | \(0.575684\pi\) | |||||||
\(702\) | −5.61803 | −0.212039 | ||||||||
\(703\) | 27.8885 | 1.05184 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.3262 | 0.426571 | ||||||||
\(706\) | 21.3820 | 0.804721 | ||||||||
\(707\) | 16.5410 | 0.622089 | ||||||||
\(708\) | −2.90983 | −0.109358 | ||||||||
\(709\) | −37.4164 | −1.40520 | −0.702601 | − | 0.711584i | \(-0.747978\pi\) | ||||
−0.702601 | + | 0.711584i | \(0.747978\pi\) | |||||||
\(710\) | −1.52786 | −0.0573397 | ||||||||
\(711\) | 7.09017 | 0.265902 | ||||||||
\(712\) | 12.7639 | 0.478349 | ||||||||
\(713\) | −0.527864 | −0.0197687 | ||||||||
\(714\) | −6.29180 | −0.235465 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.8541 | 0.928841 | ||||||||
\(717\) | −1.23607 | −0.0461618 | ||||||||
\(718\) | 10.1803 | 0.379927 | ||||||||
\(719\) | 9.34752 | 0.348604 | 0.174302 | − | 0.984692i | \(-0.444233\pi\) | ||||
0.174302 | + | 0.984692i | \(0.444233\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 13.8885 | 0.517236 | ||||||||
\(722\) | −8.52786 | −0.317374 | ||||||||
\(723\) | −11.8885 | −0.442140 | ||||||||
\(724\) | −13.8885 | −0.516164 | ||||||||
\(725\) | −0.381966 | −0.0141859 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.8197 | −1.03177 | −0.515887 | − | 0.856657i | \(-0.672538\pi\) | ||||
−0.515887 | + | 0.856657i | \(0.672538\pi\) | |||||||
\(728\) | 6.94427 | 0.257372 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.4164 | 0.496564 | ||||||||
\(731\) | 56.4508 | 2.08791 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.6738 | 1.31764 | 0.658820 | − | 0.752300i | \(-0.271056\pi\) | ||||
0.658820 | + | 0.752300i | \(0.271056\pi\) | |||||||
\(734\) | −31.2361 | −1.15294 | ||||||||
\(735\) | −5.47214 | −0.201843 | ||||||||
\(736\) | 0.145898 | 0.00537787 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.23607 | −0.119121 | ||||||||
\(739\) | −49.0132 | −1.80298 | −0.901489 | − | 0.432802i | \(-0.857525\pi\) | ||||
−0.901489 | + | 0.432802i | \(0.857525\pi\) | |||||||
\(740\) | 8.61803 | 0.316805 | ||||||||
\(741\) | 18.1803 | 0.667871 | ||||||||
\(742\) | −0.583592 | −0.0214243 | ||||||||
\(743\) | −13.7984 | −0.506213 | −0.253107 | − | 0.967438i | \(-0.581452\pi\) | ||||
−0.253107 | + | 0.967438i | \(0.581452\pi\) | |||||||
\(744\) | 3.61803 | 0.132644 | ||||||||
\(745\) | 5.38197 | 0.197180 | ||||||||
\(746\) | −20.4721 | −0.749538 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.3607 | 0.890120 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 0.0344419 | 0.00125680 | 0.000628401 | − | 1.00000i | \(-0.499800\pi\) | ||||
0.000628401 | 1.00000i | \(0.499800\pi\) | ||||||||
\(752\) | 11.3262 | 0.413025 | ||||||||
\(753\) | −10.6180 | −0.386943 | ||||||||
\(754\) | −2.14590 | −0.0781490 | ||||||||
\(755\) | −3.05573 | −0.111209 | ||||||||
\(756\) | −1.23607 | −0.0449554 | ||||||||
\(757\) | −47.1459 | −1.71355 | −0.856773 | − | 0.515693i | \(-0.827534\pi\) | ||||
−0.856773 | + | 0.515693i | \(0.827534\pi\) | |||||||
\(758\) | 32.3607 | 1.17539 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.23607 | 0.117385 | ||||||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 16.6525 | 0.603256 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | 4.76393 | 0.172353 | ||||||||
\(765\) | −5.09017 | −0.184035 | ||||||||
\(766\) | 15.3262 | 0.553759 | ||||||||
\(767\) | 16.3475 | 0.590275 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 31.4508 | 1.13415 | 0.567073 | − | 0.823667i | \(-0.308076\pi\) | ||||
0.567073 | + | 0.823667i | \(0.308076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3607 | 0.517187 | ||||||||
\(772\) | −3.05573 | −0.109978 | ||||||||
\(773\) | −29.5967 | −1.06452 | −0.532261 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532261 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(774\) | 11.0902 | 0.398628 | ||||||||
\(775\) | −3.61803 | −0.129964 | ||||||||
\(776\) | −12.6525 | −0.454197 | ||||||||
\(777\) | 10.6525 | 0.382155 | ||||||||
\(778\) | 0.145898 | 0.00523070 | ||||||||
\(779\) | 10.4721 | 0.375203 | ||||||||
\(780\) | 5.61803 | 0.201158 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.742646 | 0.0265570 | ||||||||
\(783\) | 0.381966 | 0.0136504 | ||||||||
\(784\) | −5.47214 | −0.195433 | ||||||||
\(785\) | −24.2705 | −0.866252 | ||||||||
\(786\) | 5.61803 | 0.200389 | ||||||||
\(787\) | −8.03444 | −0.286397 | −0.143198 | − | 0.989694i | \(-0.545739\pi\) | ||||
−0.143198 | + | 0.989694i | \(0.545739\pi\) | |||||||
\(788\) | −6.94427 | −0.247379 | ||||||||
\(789\) | −0.145898 | −0.00519411 | ||||||||
\(790\) | −7.09017 | −0.252257 | ||||||||
\(791\) | 0.695048 | 0.0247131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 26.7984 | 0.951039 | ||||||||
\(795\) | −0.472136 | −0.0167449 | ||||||||
\(796\) | −20.9787 | −0.743571 | ||||||||
\(797\) | −8.29180 | −0.293710 | −0.146855 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146855 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(798\) | 4.00000 | 0.141598 | ||||||||
\(799\) | 57.6525 | 2.03960 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 12.7639 | 0.450991 | ||||||||
\(802\) | −36.0689 | −1.27364 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.09017 | −0.214784 | ||||||||
\(805\) | −0.180340 | −0.00635615 | ||||||||
\(806\) | −20.3262 | −0.715961 | ||||||||
\(807\) | −27.7984 | −0.978549 | ||||||||
\(808\) | 13.3820 | 0.470776 | ||||||||
\(809\) | 28.6525 | 1.00737 | 0.503684 | − | 0.863888i | \(-0.331978\pi\) | ||||
0.503684 | + | 0.863888i | \(0.331978\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −31.4164 | −1.10318 | −0.551590 | − | 0.834116i | \(-0.685979\pi\) | ||||
−0.551590 | + | 0.834116i | \(0.685979\pi\) | |||||||
\(812\) | −0.472136 | −0.0165687 | ||||||||
\(813\) | 8.61803 | 0.302248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.85410 | 0.205060 | ||||||||
\(816\) | −5.09017 | −0.178192 | ||||||||
\(817\) | −35.8885 | −1.25558 | ||||||||
\(818\) | −33.9787 | −1.18804 | ||||||||
\(819\) | 6.94427 | 0.242652 | ||||||||
\(820\) | 3.23607 | 0.113008 | ||||||||
\(821\) | 19.3050 | 0.673747 | 0.336874 | − | 0.941550i | \(-0.390630\pi\) | ||||
0.336874 | + | 0.941550i | \(0.390630\pi\) | |||||||
\(822\) | −11.7984 | −0.411516 | ||||||||
\(823\) | −17.2361 | −0.600812 | −0.300406 | − | 0.953811i | \(-0.597122\pi\) | ||||
−0.300406 | + | 0.953811i | \(0.597122\pi\) | |||||||
\(824\) | 11.2361 | 0.391427 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.59675 | 0.125147 | ||||||||
\(827\) | 43.7082 | 1.51988 | 0.759942 | − | 0.649991i | \(-0.225228\pi\) | ||||
0.759942 | + | 0.649991i | \(0.225228\pi\) | |||||||
\(828\) | 0.145898 | 0.00507031 | ||||||||
\(829\) | −13.5967 | −0.472235 | −0.236117 | − | 0.971725i | \(-0.575875\pi\) | ||||
−0.236117 | + | 0.971725i | \(0.575875\pi\) | |||||||
\(830\) | −4.00000 | −0.138842 | ||||||||
\(831\) | −14.5066 | −0.503228 | ||||||||
\(832\) | 5.61803 | 0.194770 | ||||||||
\(833\) | −27.8541 | −0.965087 | ||||||||
\(834\) | −13.2361 | −0.458328 | ||||||||
\(835\) | −20.2705 | −0.701490 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.61803 | 0.125058 | ||||||||
\(838\) | 16.1459 | 0.557751 | ||||||||
\(839\) | −54.6525 | −1.88681 | −0.943407 | − | 0.331639i | \(-0.892399\pi\) | ||||
−0.943407 | + | 0.331639i | \(0.892399\pi\) | |||||||
\(840\) | 1.23607 | 0.0426484 | ||||||||
\(841\) | −28.8541 | −0.994969 | ||||||||
\(842\) | 6.47214 | 0.223045 | ||||||||
\(843\) | 16.4721 | 0.567330 | ||||||||
\(844\) | −20.7639 | −0.714724 | ||||||||
\(845\) | −18.5623 | −0.638563 | ||||||||
\(846\) | 11.3262 | 0.389404 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | 6.67376 | 0.229043 | ||||||||
\(850\) | 5.09017 | 0.174591 | ||||||||
\(851\) | −1.25735 | −0.0431015 | ||||||||
\(852\) | −1.52786 | −0.0523438 | ||||||||
\(853\) | −36.4721 | −1.24878 | −0.624391 | − | 0.781112i | \(-0.714653\pi\) | ||||
−0.624391 | + | 0.781112i | \(0.714653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.23607 | 0.110671 | ||||||||
\(856\) | 19.7082 | 0.673613 | ||||||||
\(857\) | −45.1591 | −1.54260 | −0.771302 | − | 0.636469i | \(-0.780394\pi\) | ||||
−0.771302 | + | 0.636469i | \(0.780394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.1246 | 0.720762 | 0.360381 | − | 0.932805i | \(-0.382647\pi\) | ||||
0.360381 | + | 0.932805i | \(0.382647\pi\) | |||||||
\(860\) | −11.0902 | −0.378172 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | −22.3607 | −0.761608 | ||||||||
\(863\) | 47.3394 | 1.61145 | 0.805726 | − | 0.592289i | \(-0.201775\pi\) | ||||
0.805726 | + | 0.592289i | \(0.201775\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 18.4721 | 0.628071 | ||||||||
\(866\) | 30.8328 | 1.04774 | ||||||||
\(867\) | −8.90983 | −0.302594 | ||||||||
\(868\) | −4.47214 | −0.151794 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.381966 | −0.0129499 | ||||||||
\(871\) | 34.2148 | 1.15932 | ||||||||
\(872\) | 6.47214 | 0.219174 | ||||||||
\(873\) | −12.6525 | −0.428221 | ||||||||
\(874\) | −0.472136 | −0.0159702 | ||||||||
\(875\) | −1.23607 | −0.0417867 | ||||||||
\(876\) | 13.4164 | 0.453298 | ||||||||
\(877\) | 48.0344 | 1.62201 | 0.811004 | − | 0.585041i | \(-0.198921\pi\) | ||||
0.811004 | + | 0.585041i | \(0.198921\pi\) | |||||||
\(878\) | 17.3262 | 0.584732 | ||||||||
\(879\) | 20.0000 | 0.674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.00000 | 0.269527 | 0.134763 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134763 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(882\) | −5.47214 | −0.184256 | ||||||||
\(883\) | −20.3262 | −0.684032 | −0.342016 | − | 0.939694i | \(-0.611110\pi\) | ||||
−0.342016 | + | 0.939694i | \(0.611110\pi\) | |||||||
\(884\) | 28.5967 | 0.961813 | ||||||||
\(885\) | 2.90983 | 0.0978129 | ||||||||
\(886\) | 12.6525 | 0.425068 | ||||||||
\(887\) | 13.4508 | 0.451635 | 0.225818 | − | 0.974170i | \(-0.427495\pi\) | ||||
0.225818 | + | 0.974170i | \(0.427495\pi\) | |||||||
\(888\) | 8.61803 | 0.289202 | ||||||||
\(889\) | −20.5836 | −0.690352 | ||||||||
\(890\) | −12.7639 | −0.427848 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.76393 | 0.0925433 | ||||||||
\(893\) | −36.6525 | −1.22653 | ||||||||
\(894\) | 5.38197 | 0.180000 | ||||||||
\(895\) | −24.8541 | −0.830781 | ||||||||
\(896\) | 1.23607 | 0.0412941 | ||||||||
\(897\) | −0.819660 | −0.0273677 | ||||||||
\(898\) | 29.1246 | 0.971901 | ||||||||
\(899\) | 1.38197 | 0.0460911 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −2.40325 | −0.0800639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.7082 | −0.456180 | ||||||||
\(904\) | 0.562306 | 0.0187020 | ||||||||
\(905\) | 13.8885 | 0.461671 | ||||||||
\(906\) | −3.05573 | −0.101520 | ||||||||
\(907\) | 14.5066 | 0.481683 | 0.240842 | − | 0.970564i | \(-0.422577\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422577\pi\) | |||||||
\(908\) | −24.3607 | −0.808438 | ||||||||
\(909\) | 13.3820 | 0.443852 | ||||||||
\(910\) | −6.94427 | −0.230200 | ||||||||
\(911\) | 12.4721 | 0.413220 | 0.206610 | − | 0.978423i | \(-0.433757\pi\) | ||||
0.206610 | + | 0.978423i | \(0.433757\pi\) | |||||||
\(912\) | 3.23607 | 0.107157 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.6525 | −0.881586 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.23607 | 0.173005 | ||||||||
\(917\) | −6.94427 | −0.229320 | ||||||||
\(918\) | −5.09017 | −0.168001 | ||||||||
\(919\) | −45.3394 | −1.49561 | −0.747804 | − | 0.663919i | \(-0.768892\pi\) | ||||
−0.747804 | + | 0.663919i | \(0.768892\pi\) | |||||||
\(920\) | −0.145898 | −0.00481012 | ||||||||
\(921\) | −22.4508 | −0.739781 | ||||||||
\(922\) | −28.2148 | −0.929204 | ||||||||
\(923\) | 8.58359 | 0.282532 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.61803 | −0.283359 | ||||||||
\(926\) | −23.8885 | −0.785026 | ||||||||
\(927\) | 11.2361 | 0.369041 | ||||||||
\(928\) | −0.381966 | −0.0125386 | ||||||||
\(929\) | −21.5279 | −0.706306 | −0.353153 | − | 0.935566i | \(-0.614891\pi\) | ||||
−0.353153 | + | 0.935566i | \(0.614891\pi\) | |||||||
\(930\) | −3.61803 | −0.118640 | ||||||||
\(931\) | 17.7082 | 0.580363 | ||||||||
\(932\) | −24.5623 | −0.804565 | ||||||||
\(933\) | −4.76393 | −0.155964 | ||||||||
\(934\) | −38.5410 | −1.26110 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.61803 | 0.183631 | ||||||||
\(937\) | −11.3475 | −0.370707 | −0.185354 | − | 0.982672i | \(-0.559343\pi\) | ||||
−0.185354 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(938\) | 7.52786 | 0.245793 | ||||||||
\(939\) | 0.472136 | 0.0154076 | ||||||||
\(940\) | −11.3262 | −0.369421 | ||||||||
\(941\) | 47.9787 | 1.56406 | 0.782031 | − | 0.623240i | \(-0.214184\pi\) | ||||
0.782031 | + | 0.623240i | \(0.214184\pi\) | |||||||
\(942\) | −24.2705 | −0.790776 | ||||||||
\(943\) | −0.472136 | −0.0153749 | ||||||||
\(944\) | 2.90983 | 0.0947069 | ||||||||
\(945\) | 1.23607 | 0.0402093 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −7.09017 | −0.230278 | ||||||||
\(949\) | −75.3738 | −2.44674 | ||||||||
\(950\) | −3.23607 | −0.104992 | ||||||||
\(951\) | 0.583592 | 0.0189243 | ||||||||
\(952\) | 6.29180 | 0.203918 | ||||||||
\(953\) | −7.78522 | −0.252188 | −0.126094 | − | 0.992018i | \(-0.540244\pi\) | ||||
−0.126094 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(954\) | −0.472136 | −0.0152860 | ||||||||
\(955\) | −4.76393 | −0.154157 | ||||||||
\(956\) | 1.23607 | 0.0399773 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.2361 | 0.556872 | ||||||||
\(959\) | 14.5836 | 0.470929 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −17.9098 | −0.577736 | ||||||||
\(962\) | −48.4164 | −1.56101 | ||||||||
\(963\) | 19.7082 | 0.635088 | ||||||||
\(964\) | 11.8885 | 0.382904 | ||||||||
\(965\) | 3.05573 | 0.0983674 | ||||||||
\(966\) | −0.180340 | −0.00580234 | ||||||||
\(967\) | −9.30495 | −0.299227 | −0.149614 | − | 0.988745i | \(-0.547803\pi\) | ||||
−0.149614 | + | 0.988745i | \(0.547803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.4721 | 0.529161 | ||||||||
\(970\) | 12.6525 | 0.406247 | ||||||||
\(971\) | −36.3607 | −1.16687 | −0.583435 | − | 0.812160i | \(-0.698292\pi\) | ||||
−0.583435 | + | 0.812160i | \(0.698292\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 16.3607 | 0.524499 | ||||||||
\(974\) | −15.4164 | −0.493974 | ||||||||
\(975\) | −5.61803 | −0.179921 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.8328 | −0.794472 | −0.397236 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397236 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(978\) | 5.85410 | 0.187194 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.47214 | 0.174801 | ||||||||
\(981\) | 6.47214 | 0.206639 | ||||||||
\(982\) | −1.03444 | −0.0330104 | ||||||||
\(983\) | 47.1935 | 1.50524 | 0.752619 | − | 0.658456i | \(-0.228790\pi\) | ||||
0.752619 | + | 0.658456i | \(0.228790\pi\) | |||||||
\(984\) | 3.23607 | 0.103162 | ||||||||
\(985\) | 6.94427 | 0.221263 | ||||||||
\(986\) | −1.94427 | −0.0619182 | ||||||||
\(987\) | −14.0000 | −0.445625 | ||||||||
\(988\) | −18.1803 | −0.578394 | ||||||||
\(989\) | 1.61803 | 0.0514505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.5197 | −1.89071 | −0.945353 | − | 0.326048i | \(-0.894283\pi\) | ||||
−0.945353 | + | 0.326048i | \(0.894283\pi\) | |||||||
\(992\) | −3.61803 | −0.114873 | ||||||||
\(993\) | −4.76393 | −0.151179 | ||||||||
\(994\) | 1.88854 | 0.0599010 | ||||||||
\(995\) | 20.9787 | 0.665070 | ||||||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | 4.03444 | 0.127772 | 0.0638860 | − | 0.997957i | \(-0.479651\pi\) | ||||
0.0638860 | + | 0.997957i | \(0.479651\pi\) | |||||||
\(998\) | −23.5279 | −0.744762 | ||||||||
\(999\) | 8.61803 | 0.272663 |
(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 | 3630.2.a.bj.1.2 | 2 | ||
11.3 | even | 5 | 330.2.m.b.31.1 | ✓ | 4 | ||
11.4 | even | 5 | 330.2.m.b.181.1 | yes | 4 | ||
11.10 | odd | 2 | 3630.2.a.bb.1.1 | 2 | |||
33.14 | odd | 10 | 990.2.n.e.361.1 | 4 | |||
33.26 | odd | 10 | 990.2.n.e.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.b.31.1 | ✓ | 4 | 11.3 | even | 5 | ||
330.2.m.b.181.1 | yes | 4 | 11.4 | even | 5 | ||
990.2.n.e.181.1 | 4 | 33.26 | odd | 10 | |||
990.2.n.e.361.1 | 4 | 33.14 | odd | 10 | |||
3630.2.a.bb.1.1 | 2 | 11.10 | odd | 2 | |||
3630.2.a.bj.1.2 | 2 | 1.1 | even | 1 | trivial |