Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.69963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.58836 | 1.49439 | 0.747196 | − | 0.664603i | \(-0.231399\pi\) | ||||
0.747196 | + | 0.664603i | \(0.231399\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.81089 | 1.06242 | 0.531209 | − | 0.847241i | \(-0.321738\pi\) | ||||
0.531209 | + | 0.847241i | \(0.321738\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.69963 | 1.23321 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58836 | 0.478910 | 0.239455 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239455 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.888736 | 0.246491 | 0.123245 | − | 0.992376i | \(-0.460670\pi\) | ||||
0.123245 | + | 0.992376i | \(0.460670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.98762 | −0.967140 | −0.483570 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483570 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.27561 | 1.58767 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.30037 | 0.688175 | 0.344088 | − | 0.938938i | \(-0.388188\pi\) | ||||
0.344088 | + | 0.938938i | \(0.388188\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.81089 | 0.348506 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.98762 | 1.29757 | 0.648784 | − | 0.760972i | \(-0.275278\pi\) | ||||
0.648784 | + | 0.760972i | \(0.275278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.51052 | −0.810113 | −0.405057 | − | 0.914292i | \(-0.632748\pi\) | ||||
−0.405057 | + | 0.914292i | \(0.632748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.11126 | 0.715679 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.41164 | −0.396471 | −0.198235 | − | 0.980154i | \(-0.563521\pi\) | ||||
−0.198235 | + | 0.980154i | \(0.563521\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.30037 | 0.368354 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.09888 | 0.796312 | 0.398156 | − | 0.917318i | \(-0.369650\pi\) | ||||
0.398156 | + | 0.917318i | \(0.369650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.17673 | 1.24694 | 0.623470 | − | 0.781848i | \(-0.285722\pi\) | ||||
0.623470 | + | 0.781848i | \(0.285722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.08650 | −1.32540 | −0.662701 | − | 0.748884i | \(-0.730590\pi\) | ||||
−0.662701 | + | 0.748884i | \(0.730590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.901116 | 0.128731 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.3214 | −1.44529 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.79851 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.58836 | 0.342837 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.22253 | −0.289349 | −0.144674 | − | 0.989479i | \(-0.546213\pi\) | ||||
−0.144674 | + | 0.989479i | \(0.546213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.90978 | −1.26882 | −0.634408 | − | 0.772998i | \(-0.718756\pi\) | ||||
−0.634408 | + | 0.772998i | \(0.718756\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.3993 | 1.31018 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.56360 | −0.924041 | −0.462021 | − | 0.886869i | \(-0.652875\pi\) | ||||
−0.462021 | + | 0.886869i | \(0.652875\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.54256 | 1.02840 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.777472 | −0.0922689 | −0.0461345 | − | 0.998935i | \(-0.514690\pi\) | ||||
−0.0461345 | + | 0.998935i | \(0.514690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.876356 | −0.102570 | −0.0512849 | − | 0.998684i | \(-0.516332\pi\) | ||||
−0.0512849 | + | 0.998684i | \(0.516332\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.46472 | 0.508802 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94182 | −1.00603 | −0.503017 | − | 0.864277i | \(-0.667777\pi\) | ||||
−0.503017 | + | 0.864277i | \(0.667777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.41164 | −0.712404 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6996 | 1.28420 | 0.642101 | − | 0.766620i | \(-0.278063\pi\) | ||||
0.642101 | + | 0.766620i | \(0.278063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0865 | 1.93908 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.27561 | −0.559214 | −0.279607 | − | 0.960115i | \(-0.590204\pi\) | ||||
−0.279607 | + | 0.960115i | \(0.590204\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.49814 | 0.261876 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.6749 | −1.21063 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.24219 | 0.735333 | 0.367667 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367667 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.87636 | 0.590596 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.143307 | −0.0142596 | −0.00712981 | − | 0.999975i | \(-0.502270\pi\) | ||||
−0.00712981 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8319 | −1.16584 | −0.582918 | − | 0.812531i | \(-0.698089\pi\) | ||||
−0.582918 | + | 0.812531i | \(0.698089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.9222 | 1.05588 | 0.527942 | − | 0.849280i | \(-0.322964\pi\) | ||||
0.527942 | + | 0.849280i | \(0.322964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.6749 | 1.50138 | 0.750690 | − | 0.660655i | \(-0.229721\pi\) | ||||
0.750690 | + | 0.660655i | \(0.229721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.24219 | −0.592483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.33379 | 0.595833 | 0.297917 | − | 0.954592i | \(-0.403708\pi\) | ||||
0.297917 | + | 0.954592i | \(0.403708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.28799 | 0.303975 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.2088 | −1.02751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.47710 | −0.770645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.1978 | 1.19000 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7207 | 1.04004 | 0.520021 | − | 0.854154i | \(-0.325924\pi\) | ||||
0.520021 | + | 0.854154i | \(0.325924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.1643 | 1.86342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.45234 | −0.476373 | −0.238187 | − | 0.971219i | \(-0.576553\pi\) | ||||
−0.238187 | + | 0.971219i | \(0.576553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.81089 | 0.243735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8764 | 1.27097 | 0.635486 | − | 0.772112i | \(-0.280800\pi\) | ||||
0.635486 | + | 0.772112i | \(0.280800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.9294 | −1.86003 | −0.930015 | − | 0.367520i | \(-0.880207\pi\) | ||||
−0.930015 | + | 0.367520i | \(0.880207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.5192 | −1.98067 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.41164 | 0.118047 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.33242 | 0.192374 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1447 | 0.831085 | 0.415542 | − | 0.909574i | \(-0.363592\pi\) | ||||
0.415542 | + | 0.909574i | \(0.363592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.66621 | −0.786625 | −0.393312 | − | 0.919405i | \(-0.628671\pi\) | ||||
−0.393312 | + | 0.919405i | \(0.628671\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.7527 | −1.19269 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.25457 | −0.658787 | −0.329393 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329393 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.1854 | 1.60081 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.27699 | 0.731129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.46472 | 0.741334 | 0.370667 | − | 0.928766i | \(-0.379129\pi\) | ||||
0.370667 | + | 0.928766i | \(0.379129\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.92216 | −0.148741 | −0.0743705 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743705 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2101 | −0.939242 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.69963 | 0.282918 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3411 | −1.69856 | −0.849280 | − | 0.527942i | \(-0.822964\pi\) | ||||
−0.849280 | + | 0.527942i | \(0.822964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.75271 | −0.432400 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7738 | −1.62745 | −0.813723 | − | 0.581252i | \(-0.802563\pi\) | ||||
−0.813723 | + | 0.581252i | \(0.802563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.6501 | −1.89611 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.33379 | −0.463173 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.09022 | 0.370259 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.21015 | 0.232278 | 0.116139 | − | 0.993233i | \(-0.462948\pi\) | ||||
0.116139 | + | 0.993233i | \(0.462948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.522900 | −0.0376392 | −0.0188196 | − | 0.999823i | \(-0.505991\pi\) | ||||
−0.0188196 | + | 0.999823i | \(0.505991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.60940 | −0.185912 | −0.0929562 | − | 0.995670i | \(-0.529632\pi\) | ||||
−0.0929562 | + | 0.995670i | \(0.529632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8960 | −0.914175 | −0.457087 | − | 0.889422i | \(-0.651107\pi\) | ||||
−0.457087 | + | 0.889422i | \(0.651107\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5774 | −1.38088 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.6414 | 1.37856 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.2101 | 0.848664 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.58836 | 0.109869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3535 | 1.60772 | 0.803859 | − | 0.594820i | \(-0.202777\pi\) | ||||
0.803859 | + | 0.594820i | \(0.202777\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.01238 | −0.137886 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.6786 | −0.860679 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.26833 | −0.153279 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.54394 | −0.238391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.50914 | −0.234990 | −0.117495 | − | 0.993073i | \(-0.537486\pi\) | ||||
−0.117495 | + | 0.993073i | \(0.537486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0531 | −0.799991 | −0.399996 | − | 0.916517i | \(-0.630988\pi\) | ||||
−0.399996 | + | 0.916517i | \(0.630988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0407 | 1.39041 | 0.695204 | − | 0.718812i | \(-0.255314\pi\) | ||||
0.695204 | + | 0.718812i | \(0.255314\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.5563 | 0.760350 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4720 | 1.53770 | 0.768851 | − | 0.639428i | \(-0.220829\pi\) | ||||
0.768851 | + | 0.639428i | \(0.220829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.1447 | −1.50341 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.263233 | 0.0170271 | 0.00851355 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851355 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.8974 | −1.28170 | −0.640852 | − | 0.767664i | \(-0.721419\pi\) | ||||
−0.640852 | + | 0.767664i | \(0.721419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0283 | −1.41312 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.888736 | 0.0565489 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.2829 | 1.91910 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.1964 | 0.959188 | 0.479594 | − | 0.877491i | \(-0.340784\pi\) | ||||
0.479594 | + | 0.877491i | \(0.340784\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.24219 | 0.329574 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8072 | 1.36029 | 0.680147 | − | 0.733076i | \(-0.261916\pi\) | ||||
0.680147 | + | 0.733076i | \(0.261916\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.77885 | −0.421217 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.8516 | 1.60017 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.8850 | 1.22616 | 0.613081 | − | 0.790020i | \(-0.289930\pi\) | ||||
0.613081 | + | 0.790020i | \(0.289930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.6552 | −0.835685 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.2880 | −1.90766 | −0.953831 | − | 0.300343i | \(-0.902899\pi\) | ||||
−0.953831 | + | 0.300343i | \(0.902899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3411 | −0.688921 | −0.344461 | − | 0.938801i | \(-0.611938\pi\) | ||||
−0.344461 | + | 0.938801i | \(0.611938\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.46610 | 0.391346 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1520 | −1.09065 | −0.545323 | − | 0.838226i | \(-0.683593\pi\) | ||||
−0.545323 | + | 0.838226i | \(0.683593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.6872 | −0.999039 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.42030 | −0.383003 | −0.191501 | − | 0.981492i | \(-0.561336\pi\) | ||||
−0.191501 | + | 0.981492i | \(0.561336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2051 | 1.14162 | 0.570811 | − | 0.821082i | \(-0.306629\pi\) | ||||
0.570811 | + | 0.821082i | \(0.306629\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3324 | 0.846016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.09888 | −0.0646403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.7454 | 1.09888 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.5192 | −1.89979 | −0.949895 | − | 0.312568i | \(-0.898811\pi\) | ||||
−0.949895 | + | 0.312568i | \(0.898811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.87636 | 0.166903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.93316 | 0.169629 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.9839 | 1.32477 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.370932 | −0.0213095 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.7810 | −1.52847 | −0.764237 | − | 0.644935i | \(-0.776884\pi\) | ||||
−0.764237 | + | 0.644935i | \(0.776884\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.6253 | −1.74222 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.2880 | 1.26384 | 0.631918 | − | 0.775035i | \(-0.282268\pi\) | ||||
0.631918 | + | 0.775035i | \(0.282268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9629 | 1.29794 | 0.648969 | − | 0.760815i | \(-0.275201\pi\) | ||||
0.648969 | + | 0.760815i | \(0.275201\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.1840 | −1.58297 | −0.791486 | − | 0.611187i | \(-0.790692\pi\) | ||||
−0.791486 | + | 0.611187i | \(0.790692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0989 | 0.621418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.2705 | 1.57791 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98762 | −0.221877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 40.5723 | 2.24365 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.5412 | −1.40813 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1716 | 1.05377 | 0.526884 | − | 0.849937i | \(-0.323360\pi\) | ||||
0.526884 | + | 0.849937i | \(0.323360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.92216 | −0.488931 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2632 | 0.776968 | 0.388484 | − | 0.921456i | \(-0.372999\pi\) | ||||
0.388484 | + | 0.921456i | \(0.372999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.3942 | 0.890409 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.16435 | −0.387971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1433 | −0.925652 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.90249 | 0.102131 | 0.0510656 | − | 0.998695i | \(-0.483738\pi\) | ||||
0.0510656 | + | 0.998695i | \(0.483738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.556321 | −0.0297792 | −0.0148896 | − | 0.999889i | \(-0.504740\pi\) | ||||
−0.0148896 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.60940 | 0.0859037 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.1075 | −0.697644 | −0.348822 | − | 0.937189i | \(-0.613418\pi\) | ||||
−0.348822 | + | 0.937189i | \(0.613418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.0124 | −1.53550 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.0197 | −1.10938 | −0.554688 | − | 0.832059i | \(-0.687162\pi\) | ||||
−0.554688 | + | 0.832059i | \(0.687162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.9418 | −1.15165 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.8021 | −1.60786 | −0.803928 | − | 0.594727i | \(-0.797260\pi\) | ||||
−0.803928 | + | 0.594727i | \(0.797260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.8640 | 0.982019 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.9208 | 1.13807 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0902 | −0.522452 | −0.261226 | − | 0.965278i | \(-0.584127\pi\) | ||||
−0.261226 | + | 0.965278i | \(0.584127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.21015 | 0.319839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.1286 | 1.59897 | 0.799484 | − | 0.600687i | \(-0.205106\pi\) | ||||
0.799484 | + | 0.600687i | \(0.205106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.3374 | 1.55423 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4895 | 0.587085 | 0.293542 | − | 0.955946i | \(-0.405166\pi\) | ||||
0.293542 | + | 0.955946i | \(0.405166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.2509 | 1.53774 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.0146 | −1.77531 | −0.887655 | − | 0.460510i | \(-0.847667\pi\) | ||||
−0.887655 | + | 0.460510i | \(0.847667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.1606 | −0.665562 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1126 | −0.711889 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.88874 | −0.295547 | −0.147774 | − | 0.989021i | \(-0.547211\pi\) | ||||
−0.147774 | + | 0.989021i | \(0.547211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.27561 | 0.364236 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.23491 | 0.211481 | 0.105741 | − | 0.994394i | \(-0.466279\pi\) | ||||
0.105741 | + | 0.994394i | \(0.466279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00866 | −0.199686 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.83056 | −0.189874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.05308 | −0.348753 | −0.174376 | − | 0.984679i | \(-0.555791\pi\) | ||||
−0.174376 | + | 0.984679i | \(0.555791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.5054 | 1.89933 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.24729 | −0.307409 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.7614 | −2.77962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.7724 | 0.868237 | 0.434119 | − | 0.900856i | \(-0.357060\pi\) | ||||
0.434119 | + | 0.900856i | \(0.357060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.81818 | −0.283561 | −0.141780 | − | 0.989898i | \(-0.545283\pi\) | ||||
−0.141780 | + | 0.989898i | \(0.545283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.6167 | −1.63450 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.8553 | −1.34801 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.65383 | 0.176408 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.1854 | −1.11680 | −0.558400 | − | 0.829572i | \(-0.688585\pi\) | ||||
−0.558400 | + | 0.829572i | \(0.688585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3462 | −0.593319 | −0.296660 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296660 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.30037 | 0.157878 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8502 | 1.13831 | 0.569154 | − | 0.822231i | \(-0.307271\pi\) | ||||
0.569154 | + | 0.822231i | \(0.307271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.33379 | 0.158752 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.6291 | 1.55025 | 0.775127 | − | 0.631806i | \(-0.217686\pi\) | ||||
0.775127 | + | 0.631806i | \(0.217686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.2581 | 1.24197 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4152 | 1.38819 | 0.694095 | − | 0.719884i | \(-0.255805\pi\) | ||||
0.694095 | + | 0.719884i | \(0.255805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.09888 | 0.381362 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.0197 | −1.17553 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2880 | −1.22970 | −0.614850 | − | 0.788644i | \(-0.710784\pi\) | ||||
−0.614850 | + | 0.788644i | \(0.710784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.22115 | −0.337054 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5068 | −0.582500 | −0.291250 | − | 0.956647i | \(-0.594071\pi\) | ||||
−0.291250 | + | 0.956647i | \(0.594071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7083 | −1.10182 | −0.550909 | − | 0.834565i | \(-0.685719\pi\) | ||||
−0.550909 | + | 0.834565i | \(0.685719\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.4734 | 1.41014 | 0.705070 | − | 0.709138i | \(-0.250916\pi\) | ||||
0.705070 | + | 0.709138i | \(0.250916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.2605 | −0.981718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.3658 | −0.984486 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9876 | 0.597171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.8516 | 1.32102 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6676 | −0.578797 | −0.289398 | − | 0.957209i | \(-0.593455\pi\) | ||||
−0.289398 | + | 0.957209i | \(0.593455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.14331 | −0.0977264 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.0122 | 1.09259 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.2051 | 1.95781 | 0.978904 | − | 0.204321i | \(-0.0654987\pi\) | ||||
0.978904 | + | 0.204321i | \(0.0654987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.4981 | 1.10784 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4065 | 0.830676 | 0.415338 | − | 0.909667i | \(-0.363663\pi\) | ||||
0.415338 | + | 0.909667i | \(0.363663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.8640 | −1.25493 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.18539 | −0.0980281 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.9208 | −0.623180 | −0.311590 | − | 0.950217i | \(-0.600861\pi\) | ||||
−0.311590 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.97524 | −0.222277 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.8777 | −0.841717 | −0.420858 | − | 0.907126i | \(-0.638271\pi\) | ||||
−0.420858 | + | 0.907126i | \(0.638271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.6043 | −1.40360 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.63554 | −0.338439 | −0.169220 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169220 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.46334 | −0.108972 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.81089 | 0.0799528 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4327 | −0.634748 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −57.8268 | −2.53832 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3324 | −1.02221 | −0.511106 | − | 0.859518i | \(-0.670764\pi\) | ||||
−0.511106 | + | 0.859518i | \(0.670764\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6735 | −0.597900 | −0.298950 | − | 0.954269i | \(-0.596636\pi\) | ||||
−0.298950 | + | 0.954269i | \(0.596636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.9862 | 0.783493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.1075 | −0.526415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.22253 | −0.356827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.53156 | 0.196284 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −56.3584 | −2.43204 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.43130 | 0.0616504 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.4472 | −1.52400 | −0.761998 | − | 0.647579i | \(-0.775781\pi\) | ||||
−0.761998 | + | 0.647579i | \(0.775781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.1185 | −0.777541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8392 | 0.591722 | 0.295861 | − | 0.955231i | \(-0.404393\pi\) | ||||
0.295861 | + | 0.955231i | \(0.404393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.6625 | −1.56472 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.98762 | 0.297683 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1345 | −1.06883 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.8777 | 1.30833 | 0.654166 | − | 0.756351i | \(-0.273020\pi\) | ||||
0.654166 | + | 0.756351i | \(0.273020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.26695 | 0.307359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3942 | −0.692162 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.38688 | −0.269175 | −0.134587 | − | 0.990902i | \(-0.542971\pi\) | ||||
−0.134587 | + | 0.990902i | \(0.542971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0224 | −0.756870 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.2334 | −1.81244 | −0.906219 | − | 0.422809i | \(-0.861044\pi\) | ||||
−0.906219 | + | 0.422809i | \(0.861044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.8726 | −1.41753 | −0.708763 | − | 0.705447i | \(-0.750746\pi\) | ||||
−0.708763 | + | 0.705447i | \(0.750746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.30903 | 0.347115 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0975 | 0.628517 | 0.314259 | − | 0.949337i | \(-0.398244\pi\) | ||||
0.314259 | + | 0.949337i | \(0.398244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.35346 | −0.0562477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.8864 | 1.36436 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3869 | 0.513012 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.7651 | 1.68256 | 0.841278 | − | 0.540603i | \(-0.181804\pi\) | ||||
0.841278 | + | 0.540603i | \(0.181804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.51052 | −0.185853 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.75409 | −0.277826 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.77609 | −0.237196 | −0.118598 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118598 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −33.3796 | −1.36614 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0087 | −0.572378 | −0.286189 | − | 0.958173i | \(-0.592389\pi\) | ||||
−0.286189 | + | 0.958173i | \(0.592389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.9222 | −0.975805 | −0.487903 | − | 0.872898i | \(-0.662238\pi\) | ||||
−0.487903 | + | 0.872898i | \(0.662238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.9825 | −1.13954 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1026 | −0.734762 | −0.367381 | − | 0.930071i | \(-0.619745\pi\) | ||||
−0.367381 | + | 0.930071i | \(0.619745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50.8392 | 2.06011 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.07550 | −0.326700 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.9701 | 1.69516 | 0.847579 | − | 0.530669i | \(-0.178059\pi\) | ||||
0.847579 | + | 0.530669i | \(0.178059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9112 | 0.640559 | 0.320279 | − | 0.947323i | \(-0.396223\pi\) | ||||
0.320279 | + | 0.947323i | \(0.396223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.8726 | −1.12030 | −0.560148 | − | 0.828393i | \(-0.689256\pi\) | ||||
−0.560148 | + | 0.828393i | \(0.689256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.97662 | 0.239833 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.8292 | −0.594118 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.11126 | 0.164188 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.61669 | 0.383442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3214 | 1.32650 | 0.663252 | − | 0.748396i | \(-0.269176\pi\) | ||||
0.663252 | + | 0.748396i | \(0.269176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 60.4472 | 2.40256 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.800854 | 0.0317310 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.87636 | −0.113787 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7985 | 0.781994 | 0.390997 | − | 0.920392i | \(-0.372130\pi\) | ||||
0.390997 | + | 0.920392i | \(0.372130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3818 | 1.15512 | 0.577558 | − | 0.816349i | \(-0.304006\pi\) | ||||
0.577558 | + | 0.816349i | \(0.304006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.53018 | −0.138572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.8168 | −1.28619 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.8306 | −0.736897 | −0.368448 | − | 0.929648i | \(-0.620111\pi\) | ||||
−0.368448 | + | 0.929648i | \(0.620111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.24219 | −0.126490 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.7293 | −1.74241 | −0.871204 | − | 0.490922i | \(-0.836660\pi\) | ||||
−0.871204 | + | 0.490922i | \(0.836660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.28799 | 0.127888 | 0.0639440 | − | 0.997953i | \(-0.479632\pi\) | ||||
0.0639440 | + | 0.997953i | \(0.479632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.17301 | −0.356250 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.0617 | 0.892954 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.08294 | −0.351167 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7403 | −0.607649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.83703 | 0.0708123 | 0.0354061 | − | 0.999373i | \(-0.488728\pi\) | ||||
0.0354061 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.2953 | 1.01061 | 0.505305 | − | 0.862941i | \(-0.331380\pi\) | ||||
0.505305 | + | 0.862941i | \(0.331380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.3570 | 0.781231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.1978 | −1.19550 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.29899 | 0.317552 | 0.158776 | − | 0.987315i | \(-0.449245\pi\) | ||||
0.158776 | + | 0.987315i | \(0.449245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.4610 | 2.07782 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.93082 | 0.264043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.2123 | 1.45367 | 0.726833 | − | 0.686814i | \(-0.240991\pi\) | ||||
0.726833 | + | 0.686814i | \(0.240991\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.5178 | 0.627459 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3324 | −0.770145 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 60.7541 | 2.29793 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2212 | 0.499356 | 0.249678 | − | 0.968329i | \(-0.419675\pi\) | ||||
0.249678 | + | 0.968329i | \(0.419675\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.41164 | −0.0909566 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.402822 | −0.0151497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.7266 | −1.64219 | −0.821093 | − | 0.570794i | \(-0.806635\pi\) | ||||
−0.821093 | + | 0.570794i | \(0.806635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.0814 | −1.24065 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.8864 | −0.557500 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.681342 | 0.0254452 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.1716 | 1.19980 | 0.599900 | − | 0.800075i | \(-0.295207\pi\) | ||||
0.599900 | + | 0.800075i | \(0.295207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.2583 | −1.23860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.5017 | −1.91537 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.25967 | −0.232158 | −0.116079 | − | 0.993240i | \(-0.537033\pi\) | ||||
−0.116079 | + | 0.993240i | \(0.537033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.7824 | −1.39935 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.6057 | −1.20596 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.81955 | 0.178014 | 0.0890071 | − | 0.996031i | \(-0.471631\pi\) | ||||
0.0890071 | + | 0.996031i | \(0.471631\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0138 | −0.442532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3969 | 1.08138 | 0.540692 | − | 0.841221i | \(-0.318163\pi\) | ||||
0.540692 | + | 0.841221i | \(0.318163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.30037 | 0.0845063 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9890 | 0.623266 | 0.311633 | − | 0.950203i | \(-0.399124\pi\) | ||||
0.311633 | + | 0.950203i | \(0.399124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43.2843 | 1.58369 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.7010 | 1.12179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.98252 | 0.291286 | 0.145643 | − | 0.989337i | \(-0.453475\pi\) | ||||
0.145643 | + | 0.989337i | \(0.453475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.3338 | 1.43340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6749 | −0.533367 | −0.266684 | − | 0.963784i | \(-0.585928\pi\) | ||||
−0.266684 | + | 0.963784i | \(0.585928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.5687 | 0.492513 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.85807 | −0.357355 | −0.178677 | − | 0.983908i | \(-0.557182\pi\) | ||||
−0.178677 | + | 0.983908i | \(0.557182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.0604 | 1.59509 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.97524 | −0.0713218 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.7948 | −0.641697 | −0.320848 | − | 0.947131i | \(-0.603968\pi\) | ||||
−0.320848 | + | 0.947131i | \(0.603968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.4449 | 2.03281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34617 | −0.0843859 | −0.0421930 | − | 0.999109i | \(-0.513434\pi\) | ||||
−0.0421930 | + | 0.999109i | \(0.513434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.5461 | −0.629464 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.09888 | 0.182686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.23491 | −0.0441885 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.6538 | 0.452211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.2422 | −0.971079 | −0.485540 | − | 0.874215i | \(-0.661377\pi\) | ||||
−0.485540 | + | 0.874215i | \(0.661377\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.4697 | 1.83237 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.8036 | 0.633023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.80717 | −0.312752 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.2261 | 0.433070 | 0.216535 | − | 0.976275i | \(-0.430524\pi\) | ||||
0.216535 | + | 0.976275i | \(0.430524\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.2335 | 1.28185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.5178 | −0.689628 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.39197 | −0.0491216 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −80.9847 | −2.85080 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.40063 | 0.330509 | 0.165254 | − | 0.986251i | \(-0.447156\pi\) | ||||
0.165254 | + | 0.986251i | \(0.447156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.9729 | 1.33341 | 0.666704 | − | 0.745322i | \(-0.267704\pi\) | ||||
0.666704 | + | 0.745322i | \(0.267704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3548 | −1.02952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.17673 | 0.286068 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.24219 | 0.322948 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.0283 | −0.489592 | −0.244796 | − | 0.969575i | \(-0.578721\pi\) | ||||
−0.244796 | + | 0.969575i | \(0.578721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.66621 | 0.267227 | 0.133614 | − | 0.991034i | \(-0.457342\pi\) | ||||
0.133614 | + | 0.991034i | \(0.457342\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0122 | −0.834987 | −0.417493 | − | 0.908680i | \(-0.637091\pi\) | ||||
−0.417493 | + | 0.908680i | \(0.637091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.7527 | 0.686040 | 0.343020 | − | 0.939328i | \(-0.388550\pi\) | ||||
0.343020 | + | 0.939328i | \(0.388550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.9839 | −1.62985 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.59331 | −0.124501 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.16807 | −0.282330 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.5736 | −0.951948 | −0.475974 | − | 0.879459i | \(-0.657904\pi\) | ||||
−0.475974 | + | 0.879459i | \(0.657904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.8268 | 0.683684 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6181 | −0.572357 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.8282 | −0.818747 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.7097 | 1.70603 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.95930 | −0.272841 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.5599 | 1.52570 | 0.762851 | − | 0.646575i | \(-0.223799\pi\) | ||||
0.762851 | + | 0.646575i | \(0.223799\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.4400 | 1.44972 | 0.724861 | − | 0.688895i | \(-0.241904\pi\) | ||||
0.724861 | + | 0.688895i | \(0.241904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.9998 | 1.94481 | 0.972405 | − | 0.233300i | \(-0.0749524\pi\) | ||||
0.972405 | + | 0.233300i | \(0.0749524\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.0975 | 1.26428 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.0210 | 1.56657 | 0.783287 | − | 0.621660i | \(-0.213541\pi\) | ||||
0.783287 | + | 0.621660i | \(0.213541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.84431 | −0.0965979 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.2029 | −0.481799 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.72205 | −0.227768 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.7934 | 0.906820 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.5475 | 1.53803 | 0.769015 | − | 0.639231i | \(-0.220747\pi\) | ||||
0.769015 | + | 0.639231i | \(0.220747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −84.1715 | −2.83903 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0283 | 1.38228 | 0.691140 | − | 0.722721i | \(-0.257109\pi\) | ||||
0.691140 | + | 0.722721i | \(0.257109\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.67625 | −0.123716 | −0.0618578 | − | 0.998085i | \(-0.519703\pi\) | ||||
−0.0618578 | + | 0.998085i | \(0.519703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.00591 | 0.302389 | 0.151194 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151194 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.9455 | 1.10496 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.1840 | −0.341177 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.08650 | −0.304068 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.59208 | 0.253492 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.5178 | −1.05118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.0975 | −1.03601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 59.4907 | 1.97973 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.5687 | −0.483746 | −0.241873 | − | 0.970308i | \(-0.577762\pi\) | ||||
−0.241873 | + | 0.970308i | \(0.577762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.530184 | −0.0175851 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3694 | 0.608605 | 0.304303 | − | 0.952575i | \(-0.401577\pi\) | ||||
0.304303 | + | 0.952575i | \(0.401577\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.5833 | 0.615016 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.3259 | −0.506107 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.6130 | 0.877881 | 0.438940 | − | 0.898516i | \(-0.355354\pi\) | ||||
0.438940 | + | 0.898516i | \(0.355354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −69.3191 | −2.28414 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.690967 | −0.0227435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −43.7738 | −1.43772 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.2939 | 0.436159 | 0.218079 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218079 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.901116 | 0.0295329 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57.6894 | 1.88867 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.2980 | 1.47982 | 0.739911 | − | 0.672705i | \(-0.234868\pi\) | ||||
0.739911 | + | 0.672705i | \(0.234868\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.4362 | 1.93963 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.5192 | 1.35349 | 0.676743 | − | 0.736219i | \(-0.263391\pi\) | ||||
0.676743 | + | 0.736219i | \(0.263391\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.8282 | 0.548002 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.65658 | 0.183814 | 0.0919071 | − | 0.995768i | \(-0.470704\pi\) | ||||
0.0919071 | + | 0.995768i | \(0.470704\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.778849 | −0.0252825 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.9505 | −2.36558 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.2967 | 1.07858 | 0.539292 | − | 0.842119i | \(-0.318692\pi\) | ||||
0.539292 | + | 0.842119i | \(0.318692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.7280 | 0.928643 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.8158 | 1.35030 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.6552 | −0.343716 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.4079 | 1.30213 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4647 | 1.17263 | 0.586313 | − | 0.810084i | \(-0.300579\pi\) | ||||
0.586313 | + | 0.810084i | \(0.300579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3214 | −0.331572 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9047 | 0.735046 | 0.367523 | − | 0.930014i | \(-0.380206\pi\) | ||||
0.367523 | + | 0.930014i | \(0.380206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.6413 | −1.97613 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.57736 | −0.210428 | −0.105214 | − | 0.994450i | \(-0.533553\pi\) | ||||
−0.105214 | + | 0.994450i | \(0.533553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.37959 | −0.267813 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.9912 | 1.85152 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.4451 | 0.811571 | 0.405786 | − | 0.913968i | \(-0.366998\pi\) | ||||
0.405786 | + | 0.913968i | \(0.366998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −66.1099 | −2.10430 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.9862 | 0.858113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.5090 | 1.31858 | 0.659288 | − | 0.751890i | \(-0.270858\pi\) | ||||
0.659288 | + | 0.751890i | \(0.270858\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.6232 | 1.57474 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4486 | −0.489263 | −0.244631 | − | 0.969616i | \(-0.578667\pi\) | ||||
−0.244631 | + | 0.969616i | \(0.578667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.36721 | −0.138173 |
(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 | 1900.2.a.i.1.3 | yes | 3 | |
4.3 | odd | 2 | 7600.2.a.bl.1.1 | 3 | |||
5.2 | odd | 4 | 1900.2.c.f.1749.1 | 6 | |||
5.3 | odd | 4 | 1900.2.c.f.1749.6 | 6 | |||
5.4 | even | 2 | 1900.2.a.g.1.1 | ✓ | 3 | ||
20.19 | odd | 2 | 7600.2.a.ca.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.g.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
1900.2.a.i.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
1900.2.c.f.1749.1 | 6 | 5.2 | odd | 4 | |||
1900.2.c.f.1749.6 | 6 | 5.3 | odd | 4 | |||
7600.2.a.bl.1.1 | 3 | 4.3 | odd | 2 | |||
7600.2.a.ca.1.3 | 3 | 20.19 | odd | 2 |