Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(1\) |
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: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 1.23607 | 0.330353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 0.236068 | 0.0572549 | 0.0286274 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286274 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | 6.70820 | 1.53897 | 0.769484 | − | 0.638666i | \(-0.220514\pi\) | ||||
0.769484 | + | 0.638666i | \(0.220514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 1.85410 | 0.395296 | ||||||||
\(23\) | 7.61803 | 1.58847 | 0.794235 | − | 0.607611i | \(-0.207872\pi\) | ||||
0.794235 | + | 0.607611i | \(0.207872\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.618034 | 0.121206 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | −1.38197 | −0.256625 | −0.128312 | − | 0.991734i | \(-0.540956\pi\) | ||||
−0.128312 | + | 0.991734i | \(0.540956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.70820 | −0.845618 | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | −0.145898 | −0.0250213 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −4.14590 | −0.672553 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6180 | −1.81443 | −0.907216 | − | 0.420665i | \(-0.861797\pi\) | ||||
−0.907216 | + | 0.420665i | \(0.861797\pi\) | |||||||
\(42\) | 1.23607 | 0.190729 | ||||||||
\(43\) | −9.61803 | −1.46674 | −0.733368 | − | 0.679832i | \(-0.762053\pi\) | ||||
−0.733368 | + | 0.679832i | \(0.762053\pi\) | |||||||
\(44\) | 4.85410 | 0.731783 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.70820 | −0.694187 | ||||||||
\(47\) | −9.23607 | −1.34722 | −0.673609 | − | 0.739087i | \(-0.735257\pi\) | ||||
−0.673609 | + | 0.739087i | \(0.735257\pi\) | |||||||
\(48\) | 1.85410 | 0.267617 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.236068 | 0.0330561 | ||||||||
\(52\) | 1.61803 | 0.224381 | ||||||||
\(53\) | 6.76393 | 0.929098 | 0.464549 | − | 0.885548i | \(-0.346217\pi\) | ||||
0.464549 | + | 0.885548i | \(0.346217\pi\) | |||||||
\(54\) | −0.618034 | −0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.47214 | −0.597614 | ||||||||
\(57\) | 6.70820 | 0.888523 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | −13.9443 | −1.81539 | −0.907695 | − | 0.419631i | \(-0.862159\pi\) | ||||
−0.907695 | + | 0.419631i | \(0.862159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70820 | −0.602824 | −0.301412 | − | 0.953494i | \(-0.597458\pi\) | ||||
−0.301412 | + | 0.953494i | \(0.597458\pi\) | |||||||
\(62\) | 2.90983 | 0.369549 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.85410 | 0.228224 | ||||||||
\(67\) | 9.18034 | 1.12156 | 0.560779 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560779 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(68\) | −0.381966 | −0.0463202 | ||||||||
\(69\) | 7.61803 | 0.917104 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.09017 | −0.129379 | −0.0646897 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646897 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 2.29180 | 0.268234 | 0.134117 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134117 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(74\) | 1.23607 | 0.143690 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8541 | −1.24505 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0.618034 | 0.0699786 | ||||||||
\(79\) | −15.8541 | −1.78373 | −0.891863 | − | 0.452306i | \(-0.850602\pi\) | ||||
−0.891863 | + | 0.452306i | \(0.850602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.18034 | 0.792936 | ||||||||
\(83\) | 9.00000 | 0.987878 | 0.493939 | − | 0.869496i | \(-0.335557\pi\) | ||||
0.493939 | + | 0.869496i | \(0.335557\pi\) | |||||||
\(84\) | 3.23607 | 0.353084 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.94427 | 0.640987 | ||||||||
\(87\) | −1.38197 | −0.148162 | ||||||||
\(88\) | −6.70820 | −0.715097 | ||||||||
\(89\) | 11.1803 | 1.18511 | 0.592557 | − | 0.805529i | \(-0.298119\pi\) | ||||
0.592557 | + | 0.805529i | \(0.298119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −12.3262 | −1.28510 | ||||||||
\(93\) | −4.70820 | −0.488218 | ||||||||
\(94\) | 5.70820 | 0.588756 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.61803 | −0.573388 | ||||||||
\(97\) | −2.85410 | −0.289790 | −0.144895 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144895 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(98\) | 1.85410 | 0.187293 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6180 | −1.15604 | −0.578019 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578019 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(102\) | −0.145898 | −0.0144461 | ||||||||
\(103\) | 12.4164 | 1.22343 | 0.611713 | − | 0.791080i | \(-0.290481\pi\) | ||||
0.611713 | + | 0.791080i | \(0.290481\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.18034 | −0.406031 | ||||||||
\(107\) | −7.85410 | −0.759285 | −0.379642 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379642 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(108\) | −1.61803 | −0.155695 | ||||||||
\(109\) | −10.8541 | −1.03963 | −0.519817 | − | 0.854278i | \(-0.674000\pi\) | ||||
−0.519817 | + | 0.854278i | \(0.674000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −3.70820 | −0.350392 | ||||||||
\(113\) | −8.23607 | −0.774784 | −0.387392 | − | 0.921915i | \(-0.626624\pi\) | ||||
−0.387392 | + | 0.921915i | \(0.626624\pi\) | |||||||
\(114\) | −4.14590 | −0.388299 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.23607 | 0.207614 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 8.61803 | 0.793354 | ||||||||
\(119\) | −0.472136 | −0.0432806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 2.90983 | 0.263444 | ||||||||
\(123\) | −11.6180 | −1.04756 | ||||||||
\(124\) | 7.61803 | 0.684120 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.23607 | 0.110118 | ||||||||
\(127\) | −17.6525 | −1.56640 | −0.783202 | − | 0.621767i | \(-0.786415\pi\) | ||||
−0.783202 | + | 0.621767i | \(0.786415\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −9.61803 | −0.846821 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.18034 | 0.714720 | 0.357360 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357360 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(132\) | 4.85410 | 0.422495 | ||||||||
\(133\) | −13.4164 | −1.16335 | ||||||||
\(134\) | −5.67376 | −0.490138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.527864 | 0.0452640 | ||||||||
\(137\) | 20.5623 | 1.75676 | 0.878378 | − | 0.477966i | \(-0.158626\pi\) | ||||
0.878378 | + | 0.477966i | \(0.158626\pi\) | |||||||
\(138\) | −4.70820 | −0.400789 | ||||||||
\(139\) | −13.4164 | −1.13796 | −0.568982 | − | 0.822350i | \(-0.692663\pi\) | ||||
−0.568982 | + | 0.822350i | \(0.692663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.23607 | −0.777817 | ||||||||
\(142\) | 0.673762 | 0.0565409 | ||||||||
\(143\) | 3.00000 | 0.250873 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.41641 | −0.117223 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 3.23607 | 0.266003 | ||||||||
\(149\) | −1.90983 | −0.156459 | −0.0782297 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782297 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.38197 | −0.356599 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(152\) | 15.0000 | 1.21666 | ||||||||
\(153\) | 0.236068 | 0.0190850 | ||||||||
\(154\) | −3.70820 | −0.298816 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.61803 | 0.129546 | ||||||||
\(157\) | 3.85410 | 0.307591 | 0.153795 | − | 0.988103i | \(-0.450850\pi\) | ||||
0.153795 | + | 0.988103i | \(0.450850\pi\) | |||||||
\(158\) | 9.79837 | 0.779517 | ||||||||
\(159\) | 6.76393 | 0.536415 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.2361 | −1.20077 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | −15.2705 | −1.19608 | −0.598039 | − | 0.801467i | \(-0.704053\pi\) | ||||
−0.598039 | + | 0.801467i | \(0.704053\pi\) | |||||||
\(164\) | 18.7984 | 1.46791 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.56231 | −0.431719 | ||||||||
\(167\) | −6.79837 | −0.526074 | −0.263037 | − | 0.964786i | \(-0.584724\pi\) | ||||
−0.263037 | + | 0.964786i | \(0.584724\pi\) | |||||||
\(168\) | −4.47214 | −0.345033 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.70820 | 0.512989 | ||||||||
\(172\) | 15.5623 | 1.18661 | ||||||||
\(173\) | 12.0902 | 0.919199 | 0.459599 | − | 0.888126i | \(-0.347993\pi\) | ||||
0.459599 | + | 0.888126i | \(0.347993\pi\) | |||||||
\(174\) | 0.854102 | 0.0647493 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.56231 | −0.419275 | ||||||||
\(177\) | −13.9443 | −1.04812 | ||||||||
\(178\) | −6.90983 | −0.517914 | ||||||||
\(179\) | 15.6525 | 1.16992 | 0.584960 | − | 0.811062i | \(-0.301110\pi\) | ||||
0.584960 | + | 0.811062i | \(0.301110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.52786 | −0.262224 | −0.131112 | − | 0.991368i | \(-0.541855\pi\) | ||||
−0.131112 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(182\) | −1.23607 | −0.0916235 | ||||||||
\(183\) | −4.70820 | −0.348040 | ||||||||
\(184\) | 17.0344 | 1.25580 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.90983 | 0.213359 | ||||||||
\(187\) | −0.708204 | −0.0517890 | ||||||||
\(188\) | 14.9443 | 1.08992 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.67376 | 0.121109 | 0.0605546 | − | 0.998165i | \(-0.480713\pi\) | ||||
0.0605546 | + | 0.998165i | \(0.480713\pi\) | |||||||
\(192\) | −0.236068 | −0.0170367 | ||||||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | 1.76393 | 0.126643 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | 11.0902 | 0.790142 | 0.395071 | − | 0.918651i | \(-0.370720\pi\) | ||||
0.395071 | + | 0.918651i | \(0.370720\pi\) | |||||||
\(198\) | 1.85410 | 0.131765 | ||||||||
\(199\) | −1.70820 | −0.121091 | −0.0605457 | − | 0.998165i | \(-0.519284\pi\) | ||||
−0.0605457 | + | 0.998165i | \(0.519284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.18034 | 0.647531 | ||||||||
\(202\) | 7.18034 | 0.505207 | ||||||||
\(203\) | 2.76393 | 0.193990 | ||||||||
\(204\) | −0.381966 | −0.0267430 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.67376 | −0.534656 | ||||||||
\(207\) | 7.61803 | 0.529490 | ||||||||
\(208\) | −1.85410 | −0.128559 | ||||||||
\(209\) | −20.1246 | −1.39205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | −10.9443 | −0.751656 | ||||||||
\(213\) | −1.09017 | −0.0746972 | ||||||||
\(214\) | 4.85410 | 0.331820 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 9.41641 | 0.639227 | ||||||||
\(218\) | 6.70820 | 0.454337 | ||||||||
\(219\) | 2.29180 | 0.154865 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.236068 | −0.0158797 | ||||||||
\(222\) | 1.23607 | 0.0829595 | ||||||||
\(223\) | −16.8541 | −1.12863 | −0.564317 | − | 0.825558i | \(-0.690860\pi\) | ||||
−0.564317 | + | 0.825558i | \(0.690860\pi\) | |||||||
\(224\) | 11.2361 | 0.750741 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.09017 | 0.338593 | ||||||||
\(227\) | 10.2361 | 0.679392 | 0.339696 | − | 0.940535i | \(-0.389676\pi\) | ||||
0.339696 | + | 0.940535i | \(0.389676\pi\) | |||||||
\(228\) | −10.8541 | −0.718830 | ||||||||
\(229\) | 6.18034 | 0.408408 | 0.204204 | − | 0.978928i | \(-0.434539\pi\) | ||||
0.204204 | + | 0.978928i | \(0.434539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | −3.09017 | −0.202880 | ||||||||
\(233\) | −12.1803 | −0.797961 | −0.398980 | − | 0.916959i | \(-0.630636\pi\) | ||||
−0.398980 | + | 0.916959i | \(0.630636\pi\) | |||||||
\(234\) | 0.618034 | 0.0404021 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.5623 | 1.46868 | ||||||||
\(237\) | −15.8541 | −1.02983 | ||||||||
\(238\) | 0.291796 | 0.0189143 | ||||||||
\(239\) | 23.6180 | 1.52772 | 0.763862 | − | 0.645380i | \(-0.223301\pi\) | ||||
0.763862 | + | 0.645380i | \(0.223301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.32624 | −0.536340 | −0.268170 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268170 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(242\) | 1.23607 | 0.0794575 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.61803 | 0.487695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.18034 | 0.457802 | ||||||||
\(247\) | −6.70820 | −0.426833 | ||||||||
\(248\) | −10.5279 | −0.668520 | ||||||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.9787 | 1.76600 | 0.883000 | − | 0.469372i | \(-0.155520\pi\) | ||||
0.883000 | + | 0.469372i | \(0.155520\pi\) | |||||||
\(252\) | 3.23607 | 0.203853 | ||||||||
\(253\) | −22.8541 | −1.43683 | ||||||||
\(254\) | 10.9098 | 0.684544 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −20.2148 | −1.26096 | −0.630482 | − | 0.776204i | \(-0.717143\pi\) | ||||
−0.630482 | + | 0.776204i | \(0.717143\pi\) | |||||||
\(258\) | 5.94427 | 0.370074 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.38197 | −0.0855415 | ||||||||
\(262\) | −5.05573 | −0.312344 | ||||||||
\(263\) | 25.5066 | 1.57280 | 0.786401 | − | 0.617716i | \(-0.211942\pi\) | ||||
0.786401 | + | 0.617716i | \(0.211942\pi\) | |||||||
\(264\) | −6.70820 | −0.412861 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.29180 | 0.508403 | ||||||||
\(267\) | 11.1803 | 0.684226 | ||||||||
\(268\) | −14.8541 | −0.907359 | ||||||||
\(269\) | −29.4721 | −1.79695 | −0.898474 | − | 0.439027i | \(-0.855323\pi\) | ||||
−0.898474 | + | 0.439027i | \(0.855323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4164 | 0.936480 | 0.468240 | − | 0.883601i | \(-0.344888\pi\) | ||||
0.468240 | + | 0.883601i | \(0.344888\pi\) | |||||||
\(272\) | 0.437694 | 0.0265391 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | −12.7082 | −0.767731 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.3262 | −0.741952 | ||||||||
\(277\) | −30.9443 | −1.85926 | −0.929631 | − | 0.368493i | \(-0.879874\pi\) | ||||
−0.929631 | + | 0.368493i | \(0.879874\pi\) | |||||||
\(278\) | 8.29180 | 0.497309 | ||||||||
\(279\) | −4.70820 | −0.281873 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.18034 | 0.487998 | 0.243999 | − | 0.969775i | \(-0.421541\pi\) | ||||
0.243999 | + | 0.969775i | \(0.421541\pi\) | |||||||
\(282\) | 5.70820 | 0.339919 | ||||||||
\(283\) | 15.7082 | 0.933756 | 0.466878 | − | 0.884322i | \(-0.345379\pi\) | ||||
0.466878 | + | 0.884322i | \(0.345379\pi\) | |||||||
\(284\) | 1.76393 | 0.104670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.85410 | −0.109635 | ||||||||
\(287\) | 23.2361 | 1.37158 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | −16.9443 | −0.996722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.85410 | −0.167310 | ||||||||
\(292\) | −3.70820 | −0.217006 | ||||||||
\(293\) | 9.32624 | 0.544845 | 0.272422 | − | 0.962178i | \(-0.412175\pi\) | ||||
0.272422 | + | 0.962178i | \(0.412175\pi\) | |||||||
\(294\) | 1.85410 | 0.108133 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.47214 | −0.259938 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | 1.18034 | 0.0683753 | ||||||||
\(299\) | −7.61803 | −0.440562 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.2361 | 1.10875 | ||||||||
\(302\) | 2.70820 | 0.155840 | ||||||||
\(303\) | −11.6180 | −0.667439 | ||||||||
\(304\) | 12.4377 | 0.713351 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.145898 | −0.00834044 | ||||||||
\(307\) | 2.14590 | 0.122473 | 0.0612364 | − | 0.998123i | \(-0.480496\pi\) | ||||
0.0612364 | + | 0.998123i | \(0.480496\pi\) | |||||||
\(308\) | −9.70820 | −0.553176 | ||||||||
\(309\) | 12.4164 | 0.706345 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.4721 | −1.27428 | −0.637139 | − | 0.770749i | \(-0.719882\pi\) | ||||
−0.637139 | + | 0.770749i | \(0.719882\pi\) | |||||||
\(312\) | −2.23607 | −0.126592 | ||||||||
\(313\) | 15.7082 | 0.887880 | 0.443940 | − | 0.896056i | \(-0.353580\pi\) | ||||
0.443940 | + | 0.896056i | \(0.353580\pi\) | |||||||
\(314\) | −2.38197 | −0.134422 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.6525 | 1.44306 | ||||||||
\(317\) | 0.437694 | 0.0245833 | 0.0122917 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122917 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(318\) | −4.18034 | −0.234422 | ||||||||
\(319\) | 4.14590 | 0.232126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.85410 | −0.438373 | ||||||||
\(322\) | 9.41641 | 0.524756 | ||||||||
\(323\) | 1.58359 | 0.0881134 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.43769 | 0.522706 | ||||||||
\(327\) | −10.8541 | −0.600233 | ||||||||
\(328\) | −25.9787 | −1.43443 | ||||||||
\(329\) | 18.4721 | 1.01840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6869 | 1.63174 | 0.815870 | − | 0.578235i | \(-0.196258\pi\) | ||||
0.815870 | + | 0.578235i | \(0.196258\pi\) | |||||||
\(332\) | −14.5623 | −0.799210 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 4.20163 | 0.229903 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.70820 | −0.202299 | ||||||||
\(337\) | −10.8197 | −0.589384 | −0.294692 | − | 0.955592i | \(-0.595217\pi\) | ||||
−0.294692 | + | 0.955592i | \(0.595217\pi\) | |||||||
\(338\) | 7.41641 | 0.403399 | ||||||||
\(339\) | −8.23607 | −0.447322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1246 | 0.764891 | ||||||||
\(342\) | −4.14590 | −0.224184 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −21.5066 | −1.15956 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.47214 | −0.401705 | ||||||||
\(347\) | −21.2705 | −1.14186 | −0.570930 | − | 0.820998i | \(-0.693417\pi\) | ||||
−0.570930 | + | 0.820998i | \(0.693417\pi\) | |||||||
\(348\) | 2.23607 | 0.119866 | ||||||||
\(349\) | 2.76393 | 0.147950 | 0.0739749 | − | 0.997260i | \(-0.476432\pi\) | ||||
0.0739749 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 16.8541 | 0.898327 | ||||||||
\(353\) | −14.6180 | −0.778039 | −0.389020 | − | 0.921229i | \(-0.627186\pi\) | ||||
−0.389020 | + | 0.921229i | \(0.627186\pi\) | |||||||
\(354\) | 8.61803 | 0.458043 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.0902 | −0.958777 | ||||||||
\(357\) | −0.472136 | −0.0249881 | ||||||||
\(358\) | −9.67376 | −0.511274 | ||||||||
\(359\) | 6.05573 | 0.319609 | 0.159805 | − | 0.987149i | \(-0.448914\pi\) | ||||
0.159805 | + | 0.987149i | \(0.448914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 2.18034 | 0.114596 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | −3.23607 | −0.169616 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.90983 | 0.152099 | ||||||||
\(367\) | −21.4721 | −1.12084 | −0.560418 | − | 0.828210i | \(-0.689360\pi\) | ||||
−0.560418 | + | 0.828210i | \(0.689360\pi\) | |||||||
\(368\) | 14.1246 | 0.736296 | ||||||||
\(369\) | −11.6180 | −0.604811 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.5279 | −0.702332 | ||||||||
\(372\) | 7.61803 | 0.394977 | ||||||||
\(373\) | −9.41641 | −0.487563 | −0.243782 | − | 0.969830i | \(-0.578388\pi\) | ||||
−0.243782 | + | 0.969830i | \(0.578388\pi\) | |||||||
\(374\) | 0.437694 | 0.0226326 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.6525 | −1.06507 | ||||||||
\(377\) | 1.38197 | 0.0711749 | ||||||||
\(378\) | 1.23607 | 0.0635765 | ||||||||
\(379\) | −11.3820 | −0.584652 | −0.292326 | − | 0.956319i | \(-0.594429\pi\) | ||||
−0.292326 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6525 | −0.904364 | ||||||||
\(382\) | −1.03444 | −0.0529266 | ||||||||
\(383\) | 22.9443 | 1.17240 | 0.586199 | − | 0.810167i | \(-0.300624\pi\) | ||||
0.586199 | + | 0.810167i | \(0.300624\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.79837 | 0.346028 | ||||||||
\(387\) | −9.61803 | −0.488912 | ||||||||
\(388\) | 4.61803 | 0.234445 | ||||||||
\(389\) | −30.6525 | −1.55414 | −0.777071 | − | 0.629413i | \(-0.783295\pi\) | ||||
−0.777071 | + | 0.629413i | \(0.783295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.79837 | 0.0909477 | ||||||||
\(392\) | −6.70820 | −0.338815 | ||||||||
\(393\) | 8.18034 | 0.412644 | ||||||||
\(394\) | −6.85410 | −0.345305 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.85410 | 0.243928 | ||||||||
\(397\) | −11.4721 | −0.575770 | −0.287885 | − | 0.957665i | \(-0.592952\pi\) | ||||
−0.287885 | + | 0.957665i | \(0.592952\pi\) | |||||||
\(398\) | 1.05573 | 0.0529189 | ||||||||
\(399\) | −13.4164 | −0.671660 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.72949 | 0.136304 | 0.0681521 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681521 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(402\) | −5.67376 | −0.282982 | ||||||||
\(403\) | 4.70820 | 0.234532 | ||||||||
\(404\) | 18.7984 | 0.935254 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.70820 | −0.0847767 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0.527864 | 0.0261332 | ||||||||
\(409\) | 35.1246 | 1.73680 | 0.868400 | − | 0.495864i | \(-0.165149\pi\) | ||||
0.868400 | + | 0.495864i | \(0.165149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.5623 | 1.01426 | ||||||||
\(412\) | −20.0902 | −0.989772 | ||||||||
\(413\) | 27.8885 | 1.37231 | ||||||||
\(414\) | −4.70820 | −0.231396 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.61803 | 0.275447 | ||||||||
\(417\) | −13.4164 | −0.657004 | ||||||||
\(418\) | 12.4377 | 0.608348 | ||||||||
\(419\) | −15.3262 | −0.748736 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3607 | 0.699897 | 0.349948 | − | 0.936769i | \(-0.386199\pi\) | ||||
0.349948 | + | 0.936769i | \(0.386199\pi\) | |||||||
\(422\) | 1.85410 | 0.0902563 | ||||||||
\(423\) | −9.23607 | −0.449073 | ||||||||
\(424\) | 15.1246 | 0.734516 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.673762 | 0.0326439 | ||||||||
\(427\) | 9.41641 | 0.455692 | ||||||||
\(428\) | 12.7082 | 0.614274 | ||||||||
\(429\) | 3.00000 | 0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.2361 | 1.64909 | 0.824547 | − | 0.565794i | \(-0.191430\pi\) | ||||
0.824547 | + | 0.565794i | \(0.191430\pi\) | |||||||
\(432\) | 1.85410 | 0.0892055 | ||||||||
\(433\) | −5.47214 | −0.262974 | −0.131487 | − | 0.991318i | \(-0.541975\pi\) | ||||
−0.131487 | + | 0.991318i | \(0.541975\pi\) | |||||||
\(434\) | −5.81966 | −0.279353 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.5623 | 0.841082 | ||||||||
\(437\) | 51.1033 | 2.44460 | ||||||||
\(438\) | −1.41641 | −0.0676786 | ||||||||
\(439\) | −2.96556 | −0.141538 | −0.0707692 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707692 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0.145898 | 0.00693966 | ||||||||
\(443\) | 7.41641 | 0.352364 | 0.176182 | − | 0.984358i | \(-0.443625\pi\) | ||||
0.176182 | + | 0.984358i | \(0.443625\pi\) | |||||||
\(444\) | 3.23607 | 0.153577 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.4164 | 0.493231 | ||||||||
\(447\) | −1.90983 | −0.0903319 | ||||||||
\(448\) | 0.472136 | 0.0223063 | ||||||||
\(449\) | −21.5066 | −1.01496 | −0.507479 | − | 0.861664i | \(-0.669423\pi\) | ||||
−0.507479 | + | 0.861664i | \(0.669423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.8541 | 1.64122 | ||||||||
\(452\) | 13.3262 | 0.626814 | ||||||||
\(453\) | −4.38197 | −0.205883 | ||||||||
\(454\) | −6.32624 | −0.296905 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.0000 | 0.702439 | ||||||||
\(457\) | 25.8885 | 1.21102 | 0.605508 | − | 0.795840i | \(-0.292970\pi\) | ||||
0.605508 | + | 0.795840i | \(0.292970\pi\) | |||||||
\(458\) | −3.81966 | −0.178481 | ||||||||
\(459\) | 0.236068 | 0.0110187 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.18034 | 0.148123 | 0.0740616 | − | 0.997254i | \(-0.476404\pi\) | ||||
0.0740616 | + | 0.997254i | \(0.476404\pi\) | |||||||
\(462\) | −3.70820 | −0.172521 | ||||||||
\(463\) | 26.6869 | 1.24025 | 0.620123 | − | 0.784505i | \(-0.287083\pi\) | ||||
0.620123 | + | 0.784505i | \(0.287083\pi\) | |||||||
\(464\) | −2.56231 | −0.118952 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.52786 | 0.348722 | ||||||||
\(467\) | 16.4164 | 0.759661 | 0.379830 | − | 0.925056i | \(-0.375982\pi\) | ||||
0.379830 | + | 0.925056i | \(0.375982\pi\) | |||||||
\(468\) | 1.61803 | 0.0747936 | ||||||||
\(469\) | −18.3607 | −0.847817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.85410 | 0.177588 | ||||||||
\(472\) | −31.1803 | −1.43519 | ||||||||
\(473\) | 28.8541 | 1.32671 | ||||||||
\(474\) | 9.79837 | 0.450054 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.763932 | 0.0350148 | ||||||||
\(477\) | 6.76393 | 0.309699 | ||||||||
\(478\) | −14.5967 | −0.667640 | ||||||||
\(479\) | −19.7984 | −0.904611 | −0.452305 | − | 0.891863i | \(-0.649398\pi\) | ||||
−0.452305 | + | 0.891863i | \(0.649398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 5.14590 | 0.234389 | ||||||||
\(483\) | −15.2361 | −0.693265 | ||||||||
\(484\) | 3.23607 | 0.147094 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.618034 | −0.0280346 | ||||||||
\(487\) | 14.3820 | 0.651709 | 0.325855 | − | 0.945420i | \(-0.394348\pi\) | ||||
0.325855 | + | 0.945420i | \(0.394348\pi\) | |||||||
\(488\) | −10.5279 | −0.476574 | ||||||||
\(489\) | −15.2705 | −0.690556 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.67376 | 0.301183 | 0.150591 | − | 0.988596i | \(-0.451882\pi\) | ||||
0.150591 | + | 0.988596i | \(0.451882\pi\) | |||||||
\(492\) | 18.7984 | 0.847496 | ||||||||
\(493\) | −0.326238 | −0.0146930 | ||||||||
\(494\) | 4.14590 | 0.186533 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.72949 | −0.391966 | ||||||||
\(497\) | 2.18034 | 0.0978016 | ||||||||
\(498\) | −5.56231 | −0.249253 | ||||||||
\(499\) | −15.0000 | −0.671492 | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.79837 | −0.303729 | ||||||||
\(502\) | −17.2918 | −0.771771 | ||||||||
\(503\) | −33.0344 | −1.47293 | −0.736466 | − | 0.676474i | \(-0.763507\pi\) | ||||
−0.736466 | + | 0.676474i | \(0.763507\pi\) | |||||||
\(504\) | −4.47214 | −0.199205 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.1246 | 0.627916 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | 28.5623 | 1.26725 | ||||||||
\(509\) | −2.88854 | −0.128032 | −0.0640162 | − | 0.997949i | \(-0.520391\pi\) | ||||
−0.0640162 | + | 0.997949i | \(0.520391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.58359 | −0.202766 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 6.70820 | 0.296174 | ||||||||
\(514\) | 12.4934 | 0.551061 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15.5623 | 0.685092 | ||||||||
\(517\) | 27.7082 | 1.21861 | ||||||||
\(518\) | −2.47214 | −0.108619 | ||||||||
\(519\) | 12.0902 | 0.530700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9098 | 1.26656 | 0.633281 | − | 0.773922i | \(-0.281708\pi\) | ||||
0.633281 | + | 0.773922i | \(0.281708\pi\) | |||||||
\(522\) | 0.854102 | 0.0373830 | ||||||||
\(523\) | −18.5623 | −0.811673 | −0.405836 | − | 0.913946i | \(-0.633020\pi\) | ||||
−0.405836 | + | 0.913946i | \(0.633020\pi\) | |||||||
\(524\) | −13.2361 | −0.578220 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.7639 | −0.687340 | ||||||||
\(527\) | −1.11146 | −0.0484158 | ||||||||
\(528\) | −5.56231 | −0.242068 | ||||||||
\(529\) | 35.0344 | 1.52324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.9443 | −0.605130 | ||||||||
\(532\) | 21.7082 | 0.941170 | ||||||||
\(533\) | 11.6180 | 0.503233 | ||||||||
\(534\) | −6.90983 | −0.299018 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.5279 | 0.886669 | ||||||||
\(537\) | 15.6525 | 0.675454 | ||||||||
\(538\) | 18.2148 | 0.785295 | ||||||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.7082 | −1.70719 | −0.853595 | − | 0.520938i | \(-0.825582\pi\) | ||||
−0.853595 | + | 0.520938i | \(0.825582\pi\) | |||||||
\(542\) | −9.52786 | −0.409257 | ||||||||
\(543\) | −3.52786 | −0.151395 | ||||||||
\(544\) | −1.32624 | −0.0568620 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.23607 | −0.0528988 | ||||||||
\(547\) | 11.2918 | 0.482802 | 0.241401 | − | 0.970425i | \(-0.422393\pi\) | ||||
0.241401 | + | 0.970425i | \(0.422393\pi\) | |||||||
\(548\) | −33.2705 | −1.42125 | ||||||||
\(549\) | −4.70820 | −0.200941 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.27051 | −0.394937 | ||||||||
\(552\) | 17.0344 | 0.725034 | ||||||||
\(553\) | 31.7082 | 1.34837 | ||||||||
\(554\) | 19.1246 | 0.812527 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.7082 | 0.920633 | ||||||||
\(557\) | −6.34752 | −0.268953 | −0.134477 | − | 0.990917i | \(-0.542935\pi\) | ||||
−0.134477 | + | 0.990917i | \(0.542935\pi\) | |||||||
\(558\) | 2.90983 | 0.123183 | ||||||||
\(559\) | 9.61803 | 0.406799 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.708204 | −0.0299004 | ||||||||
\(562\) | −5.05573 | −0.213263 | ||||||||
\(563\) | 9.00000 | 0.379305 | 0.189652 | − | 0.981851i | \(-0.439264\pi\) | ||||
0.189652 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(564\) | 14.9443 | 0.629267 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.70820 | −0.408066 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | −2.43769 | −0.102283 | ||||||||
\(569\) | −4.14590 | −0.173805 | −0.0869025 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869025 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.12461 | 0.0889122 | 0.0444561 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444561 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(572\) | −4.85410 | −0.202960 | ||||||||
\(573\) | 1.67376 | 0.0699224 | ||||||||
\(574\) | −14.3607 | −0.599403 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | 37.2705 | 1.55159 | 0.775796 | − | 0.630984i | \(-0.217349\pi\) | ||||
0.775796 | + | 0.630984i | \(0.217349\pi\) | |||||||
\(578\) | 10.4721 | 0.435583 | ||||||||
\(579\) | −11.0000 | −0.457144 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 1.76393 | 0.0731173 | ||||||||
\(583\) | −20.2918 | −0.840400 | ||||||||
\(584\) | 5.12461 | 0.212058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.76393 | −0.238106 | ||||||||
\(587\) | −23.3050 | −0.961898 | −0.480949 | − | 0.876748i | \(-0.659708\pi\) | ||||
−0.480949 | + | 0.876748i | \(0.659708\pi\) | |||||||
\(588\) | 4.85410 | 0.200180 | ||||||||
\(589\) | −31.5836 | −1.30138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0902 | 0.456189 | ||||||||
\(592\) | −3.70820 | −0.152406 | ||||||||
\(593\) | 15.3820 | 0.631662 | 0.315831 | − | 0.948816i | \(-0.397717\pi\) | ||||
0.315831 | + | 0.948816i | \(0.397717\pi\) | |||||||
\(594\) | 1.85410 | 0.0760747 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.09017 | 0.126578 | ||||||||
\(597\) | −1.70820 | −0.0699121 | ||||||||
\(598\) | 4.70820 | 0.192533 | ||||||||
\(599\) | 5.72949 | 0.234101 | 0.117050 | − | 0.993126i | \(-0.462656\pi\) | ||||
0.117050 | + | 0.993126i | \(0.462656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2918 | −0.460602 | −0.230301 | − | 0.973119i | \(-0.573971\pi\) | ||||
−0.230301 | + | 0.973119i | \(0.573971\pi\) | |||||||
\(602\) | −11.8885 | −0.484541 | ||||||||
\(603\) | 9.18034 | 0.373852 | ||||||||
\(604\) | 7.09017 | 0.288495 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.18034 | 0.291681 | ||||||||
\(607\) | −16.1459 | −0.655342 | −0.327671 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327671 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(608\) | −37.6869 | −1.52841 | ||||||||
\(609\) | 2.76393 | 0.112000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.23607 | 0.373651 | ||||||||
\(612\) | −0.381966 | −0.0154401 | ||||||||
\(613\) | −46.1246 | −1.86296 | −0.931478 | − | 0.363798i | \(-0.881480\pi\) | ||||
−0.931478 | + | 0.363798i | \(0.881480\pi\) | |||||||
\(614\) | −1.32624 | −0.0535226 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.4164 | 0.540562 | ||||||||
\(617\) | 20.7639 | 0.835924 | 0.417962 | − | 0.908464i | \(-0.362744\pi\) | ||||
0.417962 | + | 0.908464i | \(0.362744\pi\) | |||||||
\(618\) | −7.67376 | −0.308684 | ||||||||
\(619\) | 0.729490 | 0.0293207 | 0.0146603 | − | 0.999893i | \(-0.495333\pi\) | ||||
0.0146603 | + | 0.999893i | \(0.495333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.61803 | 0.305701 | ||||||||
\(622\) | 13.8885 | 0.556880 | ||||||||
\(623\) | −22.3607 | −0.895862 | ||||||||
\(624\) | −1.85410 | −0.0742235 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.70820 | −0.388018 | ||||||||
\(627\) | −20.1246 | −0.803700 | ||||||||
\(628\) | −6.23607 | −0.248846 | ||||||||
\(629\) | −0.472136 | −0.0188253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2361 | −0.606538 | −0.303269 | − | 0.952905i | \(-0.598078\pi\) | ||||
−0.303269 | + | 0.952905i | \(0.598078\pi\) | |||||||
\(632\) | −35.4508 | −1.41016 | ||||||||
\(633\) | −3.00000 | −0.119239 | ||||||||
\(634\) | −0.270510 | −0.0107433 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10.9443 | −0.433969 | ||||||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | −2.56231 | −0.101443 | ||||||||
\(639\) | −1.09017 | −0.0431265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.67376 | −0.303095 | −0.151548 | − | 0.988450i | \(-0.548426\pi\) | ||||
−0.151548 | + | 0.988450i | \(0.548426\pi\) | |||||||
\(642\) | 4.85410 | 0.191576 | ||||||||
\(643\) | 17.0902 | 0.673971 | 0.336985 | − | 0.941510i | \(-0.390593\pi\) | ||||
0.336985 | + | 0.941510i | \(0.390593\pi\) | |||||||
\(644\) | 24.6525 | 0.971444 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.978714 | −0.0385070 | ||||||||
\(647\) | 10.0344 | 0.394495 | 0.197247 | − | 0.980354i | \(-0.436800\pi\) | ||||
0.197247 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 41.8328 | 1.64208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.41641 | 0.369058 | ||||||||
\(652\) | 24.7082 | 0.967648 | ||||||||
\(653\) | −1.65248 | −0.0646664 | −0.0323332 | − | 0.999477i | \(-0.510294\pi\) | ||||
−0.0323332 | + | 0.999477i | \(0.510294\pi\) | |||||||
\(654\) | 6.70820 | 0.262312 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.5410 | −0.841036 | ||||||||
\(657\) | 2.29180 | 0.0894115 | ||||||||
\(658\) | −11.4164 | −0.445058 | ||||||||
\(659\) | 2.23607 | 0.0871048 | 0.0435524 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435524 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8885 | −1.20143 | −0.600713 | − | 0.799465i | \(-0.705116\pi\) | ||||
−0.600713 | + | 0.799465i | \(0.705116\pi\) | |||||||
\(662\) | −18.3475 | −0.713097 | ||||||||
\(663\) | −0.236068 | −0.00916812 | ||||||||
\(664\) | 20.1246 | 0.780986 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.23607 | 0.0478967 | ||||||||
\(667\) | −10.5279 | −0.407641 | ||||||||
\(668\) | 11.0000 | 0.425603 | ||||||||
\(669\) | −16.8541 | −0.651617 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.1246 | 0.545275 | ||||||||
\(672\) | 11.2361 | 0.433441 | ||||||||
\(673\) | 24.7771 | 0.955087 | 0.477543 | − | 0.878608i | \(-0.341527\pi\) | ||||
0.477543 | + | 0.878608i | \(0.341527\pi\) | |||||||
\(674\) | 6.68692 | 0.257570 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.4164 | 0.746785 | ||||||||
\(677\) | −9.11146 | −0.350182 | −0.175091 | − | 0.984552i | \(-0.556022\pi\) | ||||
−0.175091 | + | 0.984552i | \(0.556022\pi\) | |||||||
\(678\) | 5.09017 | 0.195487 | ||||||||
\(679\) | 5.70820 | 0.219061 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.2361 | 0.392247 | ||||||||
\(682\) | −8.72949 | −0.334269 | ||||||||
\(683\) | 48.5967 | 1.85950 | 0.929751 | − | 0.368188i | \(-0.120022\pi\) | ||||
0.929751 | + | 0.368188i | \(0.120022\pi\) | |||||||
\(684\) | −10.8541 | −0.415017 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.3607 | −0.471933 | ||||||||
\(687\) | 6.18034 | 0.235795 | ||||||||
\(688\) | −17.8328 | −0.679870 | ||||||||
\(689\) | −6.76393 | −0.257685 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.90983 | 0.148737 | 0.0743685 | − | 0.997231i | \(-0.476306\pi\) | ||||
0.0743685 | + | 0.997231i | \(0.476306\pi\) | |||||||
\(692\) | −19.5623 | −0.743647 | ||||||||
\(693\) | 6.00000 | 0.227921 | ||||||||
\(694\) | 13.1459 | 0.499011 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.09017 | −0.117133 | ||||||||
\(697\) | −2.74265 | −0.103885 | ||||||||
\(698\) | −1.70820 | −0.0646565 | ||||||||
\(699\) | −12.1803 | −0.460703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.3475 | −0.655207 | −0.327603 | − | 0.944815i | \(-0.606241\pi\) | ||||
−0.327603 | + | 0.944815i | \(0.606241\pi\) | |||||||
\(702\) | 0.618034 | 0.0233262 | ||||||||
\(703\) | −13.4164 | −0.506009 | ||||||||
\(704\) | 0.708204 | 0.0266914 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.03444 | 0.340016 | ||||||||
\(707\) | 23.2361 | 0.873882 | ||||||||
\(708\) | 22.5623 | 0.847943 | ||||||||
\(709\) | −29.7984 | −1.11910 | −0.559551 | − | 0.828796i | \(-0.689026\pi\) | ||||
−0.559551 | + | 0.828796i | \(0.689026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.8541 | −0.594575 | ||||||||
\(712\) | 25.0000 | 0.936915 | ||||||||
\(713\) | −35.8673 | −1.34324 | ||||||||
\(714\) | 0.291796 | 0.0109202 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.3262 | −0.946486 | ||||||||
\(717\) | 23.6180 | 0.882032 | ||||||||
\(718\) | −3.74265 | −0.139674 | ||||||||
\(719\) | 5.12461 | 0.191116 | 0.0955579 | − | 0.995424i | \(-0.469536\pi\) | ||||
0.0955579 | + | 0.995424i | \(0.469536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.8328 | −0.924822 | ||||||||
\(722\) | −16.0689 | −0.598022 | ||||||||
\(723\) | −8.32624 | −0.309656 | ||||||||
\(724\) | 5.70820 | 0.212144 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.23607 | 0.0458748 | ||||||||
\(727\) | −34.5623 | −1.28184 | −0.640922 | − | 0.767606i | \(-0.721448\pi\) | ||||
−0.640922 | + | 0.767606i | \(0.721448\pi\) | |||||||
\(728\) | 4.47214 | 0.165748 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.27051 | −0.0839778 | ||||||||
\(732\) | 7.61803 | 0.281571 | ||||||||
\(733\) | −16.8541 | −0.622520 | −0.311260 | − | 0.950325i | \(-0.600751\pi\) | ||||
−0.311260 | + | 0.950325i | \(0.600751\pi\) | |||||||
\(734\) | 13.2705 | 0.489823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.7984 | −1.57757 | ||||||||
\(737\) | −27.5410 | −1.01449 | ||||||||
\(738\) | 7.18034 | 0.264312 | ||||||||
\(739\) | 11.7082 | 0.430693 | 0.215347 | − | 0.976538i | \(-0.430912\pi\) | ||||
0.215347 | + | 0.976538i | \(0.430912\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.70820 | −0.246432 | ||||||||
\(742\) | 8.36068 | 0.306930 | ||||||||
\(743\) | −25.4721 | −0.934482 | −0.467241 | − | 0.884130i | \(-0.654752\pi\) | ||||
−0.467241 | + | 0.884130i | \(0.654752\pi\) | |||||||
\(744\) | −10.5279 | −0.385970 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.81966 | 0.213073 | ||||||||
\(747\) | 9.00000 | 0.329293 | ||||||||
\(748\) | 1.14590 | 0.0418982 | ||||||||
\(749\) | 15.7082 | 0.573965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.7082 | 1.04758 | 0.523789 | − | 0.851848i | \(-0.324518\pi\) | ||||
0.523789 | + | 0.851848i | \(0.324518\pi\) | |||||||
\(752\) | −17.1246 | −0.624470 | ||||||||
\(753\) | 27.9787 | 1.01960 | ||||||||
\(754\) | −0.854102 | −0.0311046 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.23607 | 0.117695 | ||||||||
\(757\) | −1.27051 | −0.0461775 | −0.0230887 | − | 0.999733i | \(-0.507350\pi\) | ||||
−0.0230887 | + | 0.999733i | \(0.507350\pi\) | |||||||
\(758\) | 7.03444 | 0.255502 | ||||||||
\(759\) | −22.8541 | −0.829551 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1803 | −0.695287 | −0.347643 | − | 0.937627i | \(-0.613018\pi\) | ||||
−0.347643 | + | 0.937627i | \(0.613018\pi\) | |||||||
\(762\) | 10.9098 | 0.395221 | ||||||||
\(763\) | 21.7082 | 0.785890 | ||||||||
\(764\) | −2.70820 | −0.0979794 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.1803 | −0.512357 | ||||||||
\(767\) | 13.9443 | 0.503498 | ||||||||
\(768\) | −6.56231 | −0.236797 | ||||||||
\(769\) | 26.3050 | 0.948581 | 0.474290 | − | 0.880368i | \(-0.342705\pi\) | ||||
0.474290 | + | 0.880368i | \(0.342705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.2148 | −0.728018 | ||||||||
\(772\) | 17.7984 | 0.640577 | ||||||||
\(773\) | 29.7771 | 1.07101 | 0.535504 | − | 0.844533i | \(-0.320122\pi\) | ||||
0.535504 | + | 0.844533i | \(0.320122\pi\) | |||||||
\(774\) | 5.94427 | 0.213662 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.38197 | −0.229099 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 18.9443 | 0.679185 | ||||||||
\(779\) | −77.9361 | −2.79235 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.27051 | 0.117028 | ||||||||
\(782\) | −1.11146 | −0.0397456 | ||||||||
\(783\) | −1.38197 | −0.0493874 | ||||||||
\(784\) | −5.56231 | −0.198654 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.05573 | −0.180332 | ||||||||
\(787\) | 23.8541 | 0.850307 | 0.425153 | − | 0.905121i | \(-0.360220\pi\) | ||||
0.425153 | + | 0.905121i | \(0.360220\pi\) | |||||||
\(788\) | −17.9443 | −0.639238 | ||||||||
\(789\) | 25.5066 | 0.908058 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4721 | 0.585682 | ||||||||
\(792\) | −6.70820 | −0.238366 | ||||||||
\(793\) | 4.70820 | 0.167193 | ||||||||
\(794\) | 7.09017 | 0.251621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.76393 | 0.0979650 | ||||||||
\(797\) | 46.0132 | 1.62987 | 0.814935 | − | 0.579553i | \(-0.196773\pi\) | ||||
0.814935 | + | 0.579553i | \(0.196773\pi\) | |||||||
\(798\) | 8.29180 | 0.293526 | ||||||||
\(799\) | −2.18034 | −0.0771349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.1803 | 0.395038 | ||||||||
\(802\) | −1.68692 | −0.0595671 | ||||||||
\(803\) | −6.87539 | −0.242627 | ||||||||
\(804\) | −14.8541 | −0.523864 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.90983 | −0.102494 | ||||||||
\(807\) | −29.4721 | −1.03747 | ||||||||
\(808\) | −25.9787 | −0.913928 | ||||||||
\(809\) | 24.9230 | 0.876246 | 0.438123 | − | 0.898915i | \(-0.355644\pi\) | ||||
0.438123 | + | 0.898915i | \(0.355644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.7771 | 1.32653 | 0.663266 | − | 0.748383i | \(-0.269170\pi\) | ||||
0.663266 | + | 0.748383i | \(0.269170\pi\) | |||||||
\(812\) | −4.47214 | −0.156941 | ||||||||
\(813\) | 15.4164 | 0.540677 | ||||||||
\(814\) | −3.70820 | −0.129972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.437694 | 0.0153224 | ||||||||
\(817\) | −64.5197 | −2.25726 | ||||||||
\(818\) | −21.7082 | −0.759010 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.9443 | −0.416858 | −0.208429 | − | 0.978038i | \(-0.566835\pi\) | ||||
−0.208429 | + | 0.978038i | \(0.566835\pi\) | |||||||
\(822\) | −12.7082 | −0.443250 | ||||||||
\(823\) | −8.43769 | −0.294120 | −0.147060 | − | 0.989128i | \(-0.546981\pi\) | ||||
−0.147060 | + | 0.989128i | \(0.546981\pi\) | |||||||
\(824\) | 27.7639 | 0.967202 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.2361 | −0.599720 | ||||||||
\(827\) | 2.02129 | 0.0702870 | 0.0351435 | − | 0.999382i | \(-0.488811\pi\) | ||||
0.0351435 | + | 0.999382i | \(0.488811\pi\) | |||||||
\(828\) | −12.3262 | −0.428366 | ||||||||
\(829\) | −9.87539 | −0.342986 | −0.171493 | − | 0.985185i | \(-0.554859\pi\) | ||||
−0.171493 | + | 0.985185i | \(0.554859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.9443 | −1.07344 | ||||||||
\(832\) | 0.236068 | 0.00818418 | ||||||||
\(833\) | −0.708204 | −0.0245378 | ||||||||
\(834\) | 8.29180 | 0.287121 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.5623 | 1.12619 | ||||||||
\(837\) | −4.70820 | −0.162739 | ||||||||
\(838\) | 9.47214 | 0.327210 | ||||||||
\(839\) | 48.2148 | 1.66456 | 0.832280 | − | 0.554356i | \(-0.187035\pi\) | ||||
0.832280 | + | 0.554356i | \(0.187035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0902 | −0.934144 | ||||||||
\(842\) | −8.87539 | −0.305866 | ||||||||
\(843\) | 8.18034 | 0.281746 | ||||||||
\(844\) | 4.85410 | 0.167085 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.70820 | 0.196252 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | 12.5410 | 0.430660 | ||||||||
\(849\) | 15.7082 | 0.539104 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.2361 | −0.522286 | ||||||||
\(852\) | 1.76393 | 0.0604313 | ||||||||
\(853\) | 53.3951 | 1.82821 | 0.914107 | − | 0.405473i | \(-0.132893\pi\) | ||||
0.914107 | + | 0.405473i | \(0.132893\pi\) | |||||||
\(854\) | −5.81966 | −0.199145 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.5623 | −0.600267 | ||||||||
\(857\) | 26.9443 | 0.920399 | 0.460199 | − | 0.887816i | \(-0.347778\pi\) | ||||
0.460199 | + | 0.887816i | \(0.347778\pi\) | |||||||
\(858\) | −1.85410 | −0.0632980 | ||||||||
\(859\) | −25.1246 | −0.857241 | −0.428620 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428620 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.2361 | 0.791883 | ||||||||
\(862\) | −21.1591 | −0.720680 | ||||||||
\(863\) | −45.0689 | −1.53416 | −0.767081 | − | 0.641550i | \(-0.778292\pi\) | ||||
−0.767081 | + | 0.641550i | \(0.778292\pi\) | |||||||
\(864\) | −5.61803 | −0.191129 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.38197 | 0.114924 | ||||||||
\(867\) | −16.9443 | −0.575458 | ||||||||
\(868\) | −15.2361 | −0.517146 | ||||||||
\(869\) | 47.5623 | 1.61344 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.18034 | −0.311064 | ||||||||
\(872\) | −24.2705 | −0.821903 | ||||||||
\(873\) | −2.85410 | −0.0965967 | ||||||||
\(874\) | −31.5836 | −1.06833 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.70820 | −0.125289 | ||||||||
\(877\) | 2.87539 | 0.0970950 | 0.0485475 | − | 0.998821i | \(-0.484541\pi\) | ||||
0.0485475 | + | 0.998821i | \(0.484541\pi\) | |||||||
\(878\) | 1.83282 | 0.0618545 | ||||||||
\(879\) | 9.32624 | 0.314566 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.90983 | 0.131726 | 0.0658628 | − | 0.997829i | \(-0.479020\pi\) | ||||
0.0658628 | + | 0.997829i | \(0.479020\pi\) | |||||||
\(882\) | 1.85410 | 0.0624309 | ||||||||
\(883\) | 53.7984 | 1.81046 | 0.905230 | − | 0.424923i | \(-0.139699\pi\) | ||||
0.905230 | + | 0.424923i | \(0.139699\pi\) | |||||||
\(884\) | 0.381966 | 0.0128469 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.58359 | −0.153989 | ||||||||
\(887\) | −21.9230 | −0.736102 | −0.368051 | − | 0.929806i | \(-0.619975\pi\) | ||||
−0.368051 | + | 0.929806i | \(0.619975\pi\) | |||||||
\(888\) | −4.47214 | −0.150075 | ||||||||
\(889\) | 35.3050 | 1.18409 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | 27.2705 | 0.913084 | ||||||||
\(893\) | −61.9574 | −2.07333 | ||||||||
\(894\) | 1.18034 | 0.0394765 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.7639 | −0.760490 | ||||||||
\(897\) | −7.61803 | −0.254359 | ||||||||
\(898\) | 13.2918 | 0.443553 | ||||||||
\(899\) | 6.50658 | 0.217007 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.59675 | 0.0531954 | ||||||||
\(902\) | −21.5410 | −0.717238 | ||||||||
\(903\) | 19.2361 | 0.640136 | ||||||||
\(904\) | −18.4164 | −0.612521 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.70820 | 0.0899740 | ||||||||
\(907\) | −17.0000 | −0.564476 | −0.282238 | − | 0.959344i | \(-0.591077\pi\) | ||||
−0.282238 | + | 0.959344i | \(0.591077\pi\) | |||||||
\(908\) | −16.5623 | −0.549639 | ||||||||
\(909\) | −11.6180 | −0.385346 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.8885 | −0.692068 | −0.346034 | − | 0.938222i | \(-0.612472\pi\) | ||||
−0.346034 | + | 0.938222i | \(0.612472\pi\) | |||||||
\(912\) | 12.4377 | 0.411853 | ||||||||
\(913\) | −27.0000 | −0.893570 | ||||||||
\(914\) | −16.0000 | −0.529233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | −16.3607 | −0.540277 | ||||||||
\(918\) | −0.145898 | −0.00481535 | ||||||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.14590 | 0.0707097 | ||||||||
\(922\) | −1.96556 | −0.0647322 | ||||||||
\(923\) | 1.09017 | 0.0358834 | ||||||||
\(924\) | −9.70820 | −0.319376 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.4934 | −0.542007 | ||||||||
\(927\) | 12.4164 | 0.407808 | ||||||||
\(928\) | 7.76393 | 0.254864 | ||||||||
\(929\) | 19.5967 | 0.642948 | 0.321474 | − | 0.946918i | \(-0.395822\pi\) | ||||
0.321474 | + | 0.946918i | \(0.395822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.1246 | −0.659558 | ||||||||
\(932\) | 19.7082 | 0.645564 | ||||||||
\(933\) | −22.4721 | −0.735705 | ||||||||
\(934\) | −10.1459 | −0.331984 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.23607 | −0.0730882 | ||||||||
\(937\) | 16.4164 | 0.536301 | 0.268150 | − | 0.963377i | \(-0.413588\pi\) | ||||
0.268150 | + | 0.963377i | \(0.413588\pi\) | |||||||
\(938\) | 11.3475 | 0.370510 | ||||||||
\(939\) | 15.7082 | 0.512618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0213 | 0.359284 | 0.179642 | − | 0.983732i | \(-0.442506\pi\) | ||||
0.179642 | + | 0.983732i | \(0.442506\pi\) | |||||||
\(942\) | −2.38197 | −0.0776086 | ||||||||
\(943\) | −88.5066 | −2.88217 | ||||||||
\(944\) | −25.8541 | −0.841479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8328 | −0.579795 | ||||||||
\(947\) | 29.8328 | 0.969436 | 0.484718 | − | 0.874670i | \(-0.338922\pi\) | ||||
0.484718 | + | 0.874670i | \(0.338922\pi\) | |||||||
\(948\) | 25.6525 | 0.833154 | ||||||||
\(949\) | −2.29180 | −0.0743948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.437694 | 0.0141932 | ||||||||
\(952\) | −1.05573 | −0.0342163 | ||||||||
\(953\) | −59.9443 | −1.94179 | −0.970893 | − | 0.239515i | \(-0.923012\pi\) | ||||
−0.970893 | + | 0.239515i | \(0.923012\pi\) | |||||||
\(954\) | −4.18034 | −0.135344 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −38.2148 | −1.23595 | ||||||||
\(957\) | 4.14590 | 0.134018 | ||||||||
\(958\) | 12.2361 | 0.395329 | ||||||||
\(959\) | −41.1246 | −1.32798 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.83282 | −0.284930 | ||||||||
\(962\) | −1.23607 | −0.0398524 | ||||||||
\(963\) | −7.85410 | −0.253095 | ||||||||
\(964\) | 13.4721 | 0.433908 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.41641 | 0.302968 | ||||||||
\(967\) | −8.58359 | −0.276030 | −0.138015 | − | 0.990430i | \(-0.544072\pi\) | ||||
−0.138015 | + | 0.990430i | \(0.544072\pi\) | |||||||
\(968\) | −4.47214 | −0.143740 | ||||||||
\(969\) | 1.58359 | 0.0508723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.88854 | −0.188972 | −0.0944862 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944862 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(972\) | −1.61803 | −0.0518985 | ||||||||
\(973\) | 26.8328 | 0.860221 | ||||||||
\(974\) | −8.88854 | −0.284807 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72949 | −0.279424 | ||||||||
\(977\) | −6.34752 | −0.203075 | −0.101538 | − | 0.994832i | \(-0.532376\pi\) | ||||
−0.101538 | + | 0.994832i | \(0.532376\pi\) | |||||||
\(978\) | 9.43769 | 0.301784 | ||||||||
\(979\) | −33.5410 | −1.07198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8541 | −0.346545 | ||||||||
\(982\) | −4.12461 | −0.131622 | ||||||||
\(983\) | −22.3820 | −0.713874 | −0.356937 | − | 0.934128i | \(-0.616179\pi\) | ||||
−0.356937 | + | 0.934128i | \(0.616179\pi\) | |||||||
\(984\) | −25.9787 | −0.828171 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.201626 | 0.00642108 | ||||||||
\(987\) | 18.4721 | 0.587975 | ||||||||
\(988\) | 10.8541 | 0.345315 | ||||||||
\(989\) | −73.2705 | −2.32987 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 26.4508 | 0.839815 | ||||||||
\(993\) | 29.6869 | 0.942086 | ||||||||
\(994\) | −1.34752 | −0.0427409 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.5623 | −0.461424 | ||||||||
\(997\) | −61.0689 | −1.93407 | −0.967035 | − | 0.254642i | \(-0.918042\pi\) | ||||
−0.967035 | + | 0.254642i | \(0.918042\pi\) | |||||||
\(998\) | 9.27051 | 0.293453 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 1875.2.a.c.1.1 | yes | 2 | |
3.2 | odd | 2 | 5625.2.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 1875.2.b.a.1249.2 | 4 | |||
5.3 | odd | 4 | 1875.2.b.a.1249.3 | 4 | |||
5.4 | even | 2 | 1875.2.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 5625.2.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.b.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1875.2.a.c.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1875.2.b.a.1249.2 | 4 | 5.2 | odd | 4 | |||
1875.2.b.a.1249.3 | 4 | 5.3 | odd | 4 | |||
5625.2.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
5625.2.a.g.1.1 | 2 | 15.14 | odd | 2 |