Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.89692 | −0.716967 | −0.358483 | − | 0.933536i | \(-0.616706\pi\) | ||||
−0.358483 | + | 0.933536i | \(0.616706\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.38776 | 0.719935 | 0.359968 | − | 0.932965i | \(-0.382788\pi\) | ||||
0.359968 | + | 0.932965i | \(0.382788\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38776 | −1.21694 | −0.608472 | − | 0.793575i | \(-0.708217\pi\) | ||||
−0.608472 | + | 0.793575i | \(0.708217\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.761557 | 0.184705 | 0.0923524 | − | 0.995726i | \(-0.470561\pi\) | ||||
0.0923524 | + | 0.995726i | \(0.470561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.864641 | −0.198362 | −0.0991811 | − | 0.995069i | \(-0.531622\pi\) | ||||
−0.0991811 | + | 0.995069i | \(0.531622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.89692 | 0.413941 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.76156 | 1.62698 | 0.813490 | − | 0.581579i | \(-0.197565\pi\) | ||||
0.813490 | + | 0.581579i | \(0.197565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.35548 | −1.68029 | −0.840147 | − | 0.542359i | \(-0.817531\pi\) | ||||
−0.840147 | + | 0.542359i | \(0.817531\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.38776 | −0.415655 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.89692 | −0.320637 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.103084 | −0.0169469 | −0.00847343 | − | 0.999964i | \(-0.502697\pi\) | ||||
−0.00847343 | + | 0.999964i | \(0.502697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.38776 | 0.702603 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.53707 | 1.48944 | 0.744720 | − | 0.667377i | \(-0.232583\pi\) | ||||
0.744720 | + | 0.667377i | \(0.232583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.25240 | −0.495986 | −0.247993 | − | 0.968762i | \(-0.579771\pi\) | ||||
−0.247993 | + | 0.968762i | \(0.579771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.13536 | −0.457339 | −0.228670 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228670 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.40171 | −0.485958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.761557 | −0.106639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.01395 | 1.10080 | 0.550401 | − | 0.834901i | \(-0.314475\pi\) | ||||
0.550401 | + | 0.834901i | \(0.314475\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.38776 | 0.321965 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.864641 | 0.114524 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2201 | −1.33055 | −0.665273 | − | 0.746600i | \(-0.731685\pi\) | ||||
−0.665273 | + | 0.746600i | \(0.731685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64015 | 0.466074 | 0.233037 | − | 0.972468i | \(-0.425134\pi\) | ||||
0.233037 | + | 0.972468i | \(0.425134\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.89692 | −0.238989 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.38776 | −0.544234 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6079 | −1.54030 | −0.770149 | − | 0.637865i | \(-0.779818\pi\) | ||||
−0.770149 | + | 0.637865i | \(0.779818\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.55539 | 0.777982 | 0.388991 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388991 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.92919 | −0.576918 | −0.288459 | − | 0.957492i | \(-0.593143\pi\) | ||||
−0.288459 | + | 0.957492i | \(0.593143\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.52937 | −0.516170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.04623 | 0.792763 | 0.396381 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396381 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.23844 | −0.574994 | −0.287497 | − | 0.957782i | \(-0.592823\pi\) | ||||
−0.287497 | + | 0.957782i | \(0.592823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.761557 | 0.0826025 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.76156 | −0.939338 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9817 | −1.16406 | −0.582028 | − | 0.813169i | \(-0.697741\pi\) | ||||
−0.582028 | + | 0.813169i | \(0.697741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.32320 | 0.872509 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.35548 | 0.970118 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.864641 | −0.0887103 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0645508 | −0.00655414 | −0.00327707 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327707 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.38776 | 0.239978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.30299 | −0.129653 | −0.0648264 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648264 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.98168 | 0.490859 | 0.245430 | − | 0.969414i | \(-0.421071\pi\) | ||||
0.245430 | + | 0.969414i | \(0.421071\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.89692 | 0.185120 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.697006 | 0.0673821 | 0.0336911 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336911 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.92919 | −0.472131 | −0.236065 | − | 0.971737i | \(-0.575858\pi\) | ||||
−0.236065 | + | 0.971737i | \(0.575858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.103084 | 0.00978427 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.53707 | −0.897172 | −0.448586 | − | 0.893740i | \(-0.648072\pi\) | ||||
−0.448586 | + | 0.893740i | \(0.648072\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.38776 | −0.405648 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44461 | −0.132427 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.29862 | −0.481693 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.53707 | −0.859928 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.38776 | −0.211879 | −0.105940 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105940 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.25240 | 0.286358 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.953771 | −0.0833314 | −0.0416657 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416657 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.64015 | 0.142219 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.93545 | 0.336228 | 0.168114 | − | 0.985768i | \(-0.446232\pi\) | ||||
0.168114 | + | 0.985768i | \(0.446232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.87859 | 0.244159 | 0.122080 | − | 0.992520i | \(-0.461044\pi\) | ||||
0.122080 | + | 0.992520i | \(0.461044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.13536 | 0.264045 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4769 | −0.876121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.76156 | 0.727608 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.40171 | 0.280568 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.4340 | 1.59209 | 0.796047 | − | 0.605235i | \(-0.206921\pi\) | ||||
0.796047 | + | 0.605235i | \(0.206921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7110 | 0.871646 | 0.435823 | − | 0.900033i | \(-0.356457\pi\) | ||||
0.435823 | + | 0.900033i | \(0.356457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.761557 | 0.0615682 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.35548 | −0.751450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3372 | −1.30385 | −0.651924 | − | 0.758285i | \(-0.726038\pi\) | ||||
−0.651924 | + | 0.758285i | \(0.726038\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.01395 | −0.635548 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89692 | −0.149498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2524 | −0.881356 | −0.440678 | − | 0.897665i | \(-0.645262\pi\) | ||||
−0.440678 | + | 0.897665i | \(0.645262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.38776 | −0.185886 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.59392 | 0.510253 | 0.255127 | − | 0.966908i | \(-0.417883\pi\) | ||||
0.255127 | + | 0.966908i | \(0.417883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.25240 | 0.480954 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.864641 | −0.0661207 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.7110 | −1.57463 | −0.787313 | − | 0.616554i | \(-0.788528\pi\) | ||||
−0.787313 | + | 0.616554i | \(0.788528\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.89692 | −0.143393 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2201 | 0.768191 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.2986 | −1.66668 | −0.833339 | − | 0.552763i | \(-0.813574\pi\) | ||||
−0.833339 | + | 0.552763i | \(0.813574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4865 | −1.59708 | −0.798538 | − | 0.601944i | \(-0.794393\pi\) | ||||
−0.798538 | + | 0.601944i | \(0.794393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.64015 | −0.269088 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.103084 | −0.00757886 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.81841 | 0.132975 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.89692 | 0.137980 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8646 | 0.930853 | 0.465426 | − | 0.885087i | \(-0.345901\pi\) | ||||
0.465426 | + | 0.885087i | \(0.345901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0279 | −1.29768 | −0.648839 | − | 0.760926i | \(-0.724745\pi\) | ||||
−0.648839 | + | 0.760926i | \(0.724745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.38776 | 0.314214 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2341 | 1.01414 | 0.507068 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507068 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5693 | −0.891017 | −0.445509 | − | 0.895278i | \(-0.646977\pi\) | ||||
−0.445509 | + | 0.895278i | \(0.646977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.6079 | 0.889291 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.6199 | −1.16649 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.53707 | 0.666098 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.06455 | −0.142808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.12141 | 0.352572 | 0.176286 | − | 0.984339i | \(-0.443592\pi\) | ||||
0.176286 | + | 0.984339i | \(0.443592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.55539 | −0.449168 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.25240 | −0.221812 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.7466 | 1.20472 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.92919 | 0.333084 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.34153 | −0.224775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.747604 | 0.0500633 | 0.0250316 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250316 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.49521 | −0.0992404 | −0.0496202 | − | 0.998768i | \(-0.515801\pi\) | ||||
−0.0496202 | + | 0.998768i | \(0.515801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.56934 | 0.169787 | 0.0848935 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848935 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.52937 | 0.298011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.25240 | 0.606145 | 0.303072 | − | 0.952968i | \(-0.401988\pi\) | ||||
0.303072 | + | 0.952968i | \(0.401988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.13536 | −0.204528 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.04623 | −0.457702 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0602 | −1.36227 | −0.681135 | − | 0.732158i | \(-0.738513\pi\) | ||||
−0.681135 | + | 0.732158i | \(0.738513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4340 | 0.994190 | 0.497095 | − | 0.867696i | \(-0.334400\pi\) | ||||
0.497095 | + | 0.867696i | \(0.334400\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.40171 | −0.217327 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.79383 | 0.241396 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.23844 | 0.331973 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.747604 | −0.0471883 | −0.0235942 | − | 0.999722i | \(-0.507511\pi\) | ||||
−0.0235942 | + | 0.999722i | \(0.507511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.38776 | 0.150117 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.761557 | −0.0476906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.9388 | −1.61802 | −0.809008 | − | 0.587797i | \(-0.799995\pi\) | ||||
−0.809008 | + | 0.587797i | \(0.799995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.195541 | 0.0121503 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.76156 | 0.542327 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.8540 | 1.03926 | 0.519632 | − | 0.854390i | \(-0.326069\pi\) | ||||
0.519632 | + | 0.854390i | \(0.326069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.01395 | 0.492293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.9817 | 0.672068 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.6016 | 1.92678 | 0.963392 | − | 0.268095i | \(-0.0863943\pi\) | ||||
0.963392 | + | 0.268095i | \(0.0863943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.59829 | 0.218581 | 0.109290 | − | 0.994010i | \(-0.465142\pi\) | ||||
0.109290 | + | 0.994010i | \(0.465142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.32320 | −0.503743 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.38776 | 0.143987 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9634 | −1.19948 | −0.599741 | − | 0.800194i | \(-0.704730\pi\) | ||||
−0.599741 | + | 0.800194i | \(0.704730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.35548 | −0.560098 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4157 | −1.45652 | −0.728258 | − | 0.685303i | \(-0.759670\pi\) | ||||
−0.728258 | + | 0.685303i | \(0.759670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.9248 | −1.77885 | −0.889423 | − | 0.457085i | \(-0.848894\pi\) | ||||
−0.889423 | + | 0.457085i | \(0.848894\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.864641 | 0.0512169 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.0910 | −1.06788 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4200 | −0.965884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0645508 | 0.00378404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.1247 | −1.46780 | −0.733901 | − | 0.679256i | \(-0.762303\pi\) | ||||
−0.733901 | + | 0.679256i | \(0.762303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2201 | −0.595038 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.38776 | −0.138552 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.38776 | −0.253750 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.16952 | 0.355605 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30299 | 0.0748550 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.64015 | 0.208434 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.64015 | 0.321900 | 0.160950 | − | 0.986963i | \(-0.448544\pi\) | ||||
0.160950 | + | 0.986963i | \(0.448544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.98168 | −0.283398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0462 | −0.626374 | −0.313187 | − | 0.949691i | \(-0.601397\pi\) | ||||
−0.313187 | + | 0.949691i | \(0.601397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.30925 | −0.243573 | −0.121787 | − | 0.992556i | \(-0.538862\pi\) | ||||
−0.121787 | + | 0.992556i | \(0.538862\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.89692 | −0.106879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.62183 | 0.484250 | 0.242125 | − | 0.970245i | \(-0.422156\pi\) | ||||
0.242125 | + | 0.970245i | \(0.422156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.9205 | 1.17132 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.697006 | −0.0389031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.658473 | −0.0366384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.38776 | −0.243389 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.92919 | 0.272585 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.94751 | 0.327897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.8786 | 0.597942 | 0.298971 | − | 0.954262i | \(-0.403357\pi\) | ||||
0.298971 | + | 0.954262i | \(0.403357\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.103084 | −0.00564895 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.6079 | −0.688842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.55102 | 0.193436 | 0.0967182 | − | 0.995312i | \(-0.469165\pi\) | ||||
0.0967182 | + | 0.995312i | \(0.469165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.53707 | 0.517982 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.3386 | −1.20970 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7312 | 1.06538 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.31695 | −0.285429 | −0.142714 | − | 0.989764i | \(-0.545583\pi\) | ||||
−0.142714 | + | 0.989764i | \(0.545583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.57997 | −0.352218 | −0.176109 | − | 0.984371i | \(-0.556351\pi\) | ||||
−0.176109 | + | 0.984371i | \(0.556351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.38776 | 0.234201 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.88296 | −0.526017 | −0.263009 | − | 0.964794i | \(-0.584715\pi\) | ||||
−0.263009 | + | 0.964794i | \(0.584715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.55539 | 0.347924 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.44461 | 0.0764569 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.9109 | −0.839744 | −0.419872 | − | 0.907583i | \(-0.637925\pi\) | ||||
−0.419872 | + | 0.907583i | \(0.637925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2524 | −0.960652 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.29862 | 0.278106 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.92919 | −0.258006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5125 | 1.12294 | 0.561471 | − | 0.827496i | \(-0.310235\pi\) | ||||
0.561471 | + | 0.827496i | \(0.310235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.53707 | 0.496480 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.2018 | −0.789238 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2986 | −1.25814 | −0.629068 | − | 0.777351i | \(-0.716563\pi\) | ||||
−0.629068 | + | 0.777351i | \(0.716563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.4436 | −1.97994 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5510 | −1.10700 | −0.553501 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553501 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.38776 | 0.122328 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5371 | −1.20269 | −0.601344 | − | 0.798990i | \(-0.705368\pi\) | ||||
−0.601344 | + | 0.798990i | \(0.705368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.52937 | −0.230838 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.25240 | −0.165329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6926 | −1.09986 | −0.549930 | − | 0.835211i | \(-0.685346\pi\) | ||||
−0.549930 | + | 0.835211i | \(0.685346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.761557 | 0.0385136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.953771 | 0.0481114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.04623 | 0.354534 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.8863 | −0.998064 | −0.499032 | − | 0.866583i | \(-0.666311\pi\) | ||||
−0.499032 | + | 0.866583i | \(0.666311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.64015 | −0.0821103 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.7755 | 0.538103 | 0.269052 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269052 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.0496 | 2.04482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.246139 | −0.0122006 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.3834 | −0.562872 | −0.281436 | − | 0.959580i | \(-0.590811\pi\) | ||||
−0.281436 | + | 0.959580i | \(0.590811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.93545 | −0.194121 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.3867 | 0.953958 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.23844 | −0.257145 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.87859 | −0.140965 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6218 | 0.518910 | 0.259455 | − | 0.965755i | \(-0.416457\pi\) | ||||
0.259455 | + | 0.965755i | \(0.416457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.43398 | −0.167362 | −0.0836811 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836811 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.13536 | −0.152446 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.761557 | 0.0369409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.90506 | −0.334159 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4769 | 0.505829 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.8217 | 1.14745 | 0.573726 | − | 0.819047i | \(-0.305497\pi\) | ||||
0.573726 | + | 0.819047i | \(0.305497\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.7957 | 1.14355 | 0.571775 | − | 0.820411i | \(-0.306255\pi\) | ||||
0.571775 | + | 0.820411i | \(0.306255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.76156 | −0.420085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.864641 | −0.0413614 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.6618 | −1.84523 | −0.922614 | − | 0.385726i | \(-0.873951\pi\) | ||||
−0.922614 | + | 0.385726i | \(0.873951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.40171 | −0.161986 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3232 | −1.34568 | −0.672838 | − | 0.739790i | \(-0.734925\pi\) | ||||
−0.672838 | + | 0.739790i | \(0.734925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9817 | −0.520581 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.4340 | −0.919196 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8078 | 1.12356 | 0.561779 | − | 0.827287i | \(-0.310117\pi\) | ||||
0.561779 | + | 0.827287i | \(0.310117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.7722 | 1.07230 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.7110 | −0.503245 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.32320 | 0.390198 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7003 | 1.52966 | 0.764829 | − | 0.644234i | \(-0.222824\pi\) | ||||
0.764829 | + | 0.644234i | \(0.222824\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.761557 | −0.0355464 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.7755 | −1.06076 | −0.530381 | − | 0.847760i | \(-0.677951\pi\) | ||||
−0.530381 | + | 0.847760i | \(0.677951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.4061 | 0.808929 | 0.404465 | − | 0.914554i | \(-0.367458\pi\) | ||||
0.404465 | + | 0.914554i | \(0.367458\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.35548 | 0.433850 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.8540 | −1.15011 | −0.575053 | − | 0.818116i | \(-0.695019\pi\) | ||||
−0.575053 | + | 0.818116i | \(0.695019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.9161 | 1.10434 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.3372 | 0.752776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.76593 | −0.357078 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.864641 | −0.0396724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.01395 | 0.366934 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.6402 | −0.805999 | −0.403000 | − | 0.915200i | \(-0.632032\pi\) | ||||
−0.403000 | + | 0.915200i | \(0.632032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.452306 | 0.0206234 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.89692 | 0.0863127 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0645508 | −0.00293110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7509 | 0.668428 | 0.334214 | − | 0.942497i | \(-0.391529\pi\) | ||||
0.334214 | + | 0.942497i | \(0.391529\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.2524 | 0.508851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.80779 | −0.442619 | −0.221310 | − | 0.975204i | \(-0.571033\pi\) | ||||
−0.221310 | + | 0.975204i | \(0.571033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.67243 | 0.300511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.38776 | 0.107322 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.4350 | −0.557787 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.1772 | 0.948023 | 0.474011 | − | 0.880519i | \(-0.342806\pi\) | ||||
0.474011 | + | 0.880519i | \(0.342806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.59392 | −0.294595 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4542 | −1.00118 | −0.500592 | − | 0.865684i | \(-0.666884\pi\) | ||||
−0.500592 | + | 0.865684i | \(0.666884\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.30299 | −0.0579825 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.25240 | −0.277679 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9817 | 1.01864 | 0.509322 | − | 0.860576i | \(-0.329896\pi\) | ||||
0.509322 | + | 0.860576i | \(0.329896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.35026 | 0.413631 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.864641 | 0.0381748 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.98168 | 0.219519 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.48647 | −0.329255 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7110 | 0.909110 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.4985 | 0.941868 | 0.470934 | − | 0.882168i | \(-0.343917\pi\) | ||||
0.470934 | + | 0.882168i | \(0.343917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4586 | 0.675956 | 0.337978 | − | 0.941154i | \(-0.390257\pi\) | ||||
0.337978 | + | 0.941154i | \(0.390257\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.89692 | 0.0827882 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.12473 | −0.310358 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.2201 | −0.443515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.8463 | −1.81257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.697006 | 0.0301342 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.2986 | 0.962257 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.12245 | −0.349859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0279 | −0.603107 | −0.301553 | − | 0.953449i | \(-0.597505\pi\) | ||||
−0.301553 | + | 0.953449i | \(0.597505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.4865 | 0.922073 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.92919 | −0.211143 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.64015 | 0.155358 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.57560 | −0.322731 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3661 | −0.568385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.103084 | 0.00437566 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.9860 | −1.01632 | −0.508161 | − | 0.861262i | \(-0.669674\pi\) | ||||
−0.508161 | + | 0.861262i | \(0.669674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2707 | 0.603587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.81841 | −0.0767734 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.2297 | 1.14760 | 0.573798 | − | 0.818997i | \(-0.305470\pi\) | ||||
0.573798 | + | 0.818997i | \(0.305470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.53707 | −0.401227 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.89692 | −0.0796630 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.9046 | −0.457145 | −0.228573 | − | 0.973527i | \(-0.573406\pi\) | ||||
−0.228573 | + | 0.973527i | \(0.573406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.02458 | 0.0847260 | 0.0423630 | − | 0.999102i | \(-0.486511\pi\) | ||||
0.0423630 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.8646 | −0.537428 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.8034 | −0.949319 | −0.474659 | − | 0.880170i | \(-0.657429\pi\) | ||||
−0.474659 | + | 0.880170i | \(0.657429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.0279 | 0.749214 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.93689 | 0.412252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1354 | 0.792506 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.38776 | −0.181411 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.38150 | −0.304667 | −0.152334 | − | 0.988329i | \(-0.548679\pi\) | ||||
−0.152334 | + | 0.988329i | \(0.548679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.08913 | 0.333307 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.2341 | −0.585512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.05829 | 0.207719 | 0.103860 | − | 0.994592i | \(-0.466881\pi\) | ||||
0.103860 | + | 0.994592i | \(0.466881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.44461 | −0.0592232 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.5693 | 0.514429 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2707 | −0.583086 | −0.291543 | − | 0.956558i | \(-0.594169\pi\) | ||||
−0.291543 | + | 0.956558i | \(0.594169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4384 | 0.833698 | 0.416849 | − | 0.908976i | \(-0.363134\pi\) | ||||
0.416849 | + | 0.908976i | \(0.363134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6079 | −0.513432 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.29862 | −0.215420 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.8925 | 1.33507 | 0.667534 | − | 0.744580i | \(-0.267350\pi\) | ||||
0.667534 | + | 0.744580i | \(0.267350\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.6199 | 0.673474 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7572 | 0.556556 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.0000 | −1.53481 | −0.767403 | − | 0.641165i | \(-0.778451\pi\) | ||||
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.53707 | −0.384572 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.56497 | 0.0630035 | 0.0315017 | − | 0.999504i | \(-0.489971\pi\) | ||||
0.0315017 | + | 0.999504i | \(0.489971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0925 | −1.37029 | −0.685146 | − | 0.728406i | \(-0.740262\pi\) | ||||
−0.685146 | + | 0.728406i | \(0.740262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.8313 | 0.834589 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.06455 | 0.0824502 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.0785041 | −0.00313016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2924 | 0.927255 | 0.463627 | − | 0.886030i | \(-0.346548\pi\) | ||||
0.463627 | + | 0.886030i | \(0.346548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.12141 | −0.203558 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.38776 | −0.0947552 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.9259 | 0.591384 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.55539 | 0.259327 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4252 | 1.63620 | 0.818099 | − | 0.575077i | \(-0.195028\pi\) | ||||
0.818099 | + | 0.575077i | \(0.195028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.6820 | 1.40716 | 0.703581 | − | 0.710615i | \(-0.251583\pi\) | ||||
0.703581 | + | 0.710615i | \(0.251583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.25240 | 0.128063 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4436 | 1.03960 | 0.519802 | − | 0.854287i | \(-0.326006\pi\) | ||||
0.519802 | + | 0.854287i | \(0.326006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4031 | −0.957907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.7466 | −0.695543 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.64015 | −0.142450 | −0.0712251 | − | 0.997460i | \(-0.522691\pi\) | ||||
−0.0712251 | + | 0.997460i | \(0.522691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.953771 | −0.0372669 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.92919 | −0.192306 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.1999 | −0.514195 | −0.257098 | − | 0.966385i | \(-0.582766\pi\) | ||||
−0.257098 | + | 0.966385i | \(0.582766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.2707 | −1.09960 | −0.549802 | − | 0.835295i | \(-0.685297\pi\) | ||||
−0.549802 | + | 0.835295i | \(0.685297\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.34153 | 0.129774 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.64015 | 0.0636023 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.76156 | 0.339249 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.747604 | −0.0289040 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.69179 | 0.335543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.22782 | −0.278612 | −0.139306 | − | 0.990249i | \(-0.544487\pi\) | ||||
−0.139306 | + | 0.990249i | \(0.544487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.1064 | −1.00335 | −0.501675 | − | 0.865056i | \(-0.667283\pi\) | ||||
−0.501675 | + | 0.865056i | \(0.667283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.122447 | 0.00469910 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.49521 | 0.0572965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.3203 | −1.35149 | −0.675746 | − | 0.737134i | \(-0.736179\pi\) | ||||
−0.675746 | + | 0.737134i | \(0.736179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.93545 | 0.150366 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.56934 | −0.0980266 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.1633 | −1.33961 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.8496 | −1.51595 | −0.757976 | − | 0.652282i | \(-0.773812\pi\) | ||||
−0.757976 | + | 0.652282i | \(0.773812\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.52937 | −0.172057 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.87859 | 0.109191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.26302 | 0.275107 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.25240 | −0.349958 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.1170 | 1.89289 | 0.946447 | − | 0.322859i | \(-0.104644\pi\) | ||||
0.946447 | + | 0.322859i | \(0.104644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0891304 | 0.00336162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.13536 | 0.118084 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.47167 | 0.0929567 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.8742 | −1.19706 | −0.598531 | − | 0.801100i | \(-0.704249\pi\) | ||||
−0.598531 | + | 0.801100i | \(0.704249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.04623 | 0.264254 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.35548 | −0.350365 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.4769 | −0.391813 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0602 | 0.786507 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.1526 | 0.714273 | 0.357136 | − | 0.934052i | \(-0.383753\pi\) | ||||
0.357136 | + | 0.934052i | \(0.383753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.44983 | −0.351930 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.4340 | −0.573996 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.76156 | 0.325396 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7553 | 0.881035 | 0.440518 | − | 0.897744i | \(-0.354795\pi\) | ||||
0.440518 | + | 0.897744i | \(0.354795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.47689 | −0.0916109 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9152 | −0.698650 | −0.349325 | − | 0.937002i | \(-0.613589\pi\) | ||||
−0.349325 | + | 0.937002i | \(0.613589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.40171 | 0.125474 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.1045 | −1.10891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1310 | −1.54981 | −0.774907 | − | 0.632076i | \(-0.782203\pi\) | ||||
−0.774907 | + | 0.632076i | \(0.782203\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.79383 | −0.139370 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.41233 | 0.308619 | 0.154309 | − | 0.988023i | \(-0.450685\pi\) | ||||
0.154309 | + | 0.988023i | \(0.450685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.4340 | 0.712006 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.23844 | −0.191665 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.32216 | −0.0483108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5110 | 0.930911 | 0.465456 | − | 0.885071i | \(-0.345890\pi\) | ||||
0.465456 | + | 0.885071i | \(0.345890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.747604 | 0.0272442 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.7110 | 0.389812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.0452 | 1.67354 | 0.836770 | − | 0.547554i | \(-0.184441\pi\) | ||||
0.836770 | + | 0.547554i | \(0.184441\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.38776 | −0.0866700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.5929 | −1.36274 | −0.681370 | − | 0.731939i | \(-0.738616\pi\) | ||||
−0.681370 | + | 0.731939i | \(0.738616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.35026 | 0.338502 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.761557 | 0.0275342 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44.8434 | 1.61920 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.230747 | −0.00832095 | −0.00416047 | − | 0.999991i | \(-0.501324\pi\) | ||||
−0.00416047 | + | 0.999991i | \(0.501324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.9388 | 0.934162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3998 | −0.445991 | −0.222995 | − | 0.974820i | \(-0.571583\pi\) | ||||
−0.222995 | + | 0.974820i | \(0.571583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.35548 | −0.336059 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.195541 | −0.00701500 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.24614 | −0.295449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.6527 | 0.560096 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.76156 | −0.313113 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.3372 | −0.583098 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0943 | 1.00146 | 0.500728 | − | 0.865605i | \(-0.333066\pi\) | ||||
0.500728 | + | 0.865605i | \(0.333066\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.8540 | −0.600019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0910 | 0.643243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9721 | −0.567186 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.01395 | −0.284226 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5187 | −0.372593 | −0.186297 | − | 0.982494i | \(-0.559649\pi\) | ||||
−0.186297 | + | 0.982494i | \(0.559649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.38776 | −0.0844727 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.9817 | −0.388019 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.7697 | −0.415344 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.89692 | −0.0668575 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.6016 | −1.11243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.527483 | −0.0185453 | −0.00927266 | − | 0.999957i | \(-0.502952\pi\) | ||||
−0.00927266 | + | 0.999957i | \(0.502952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.4200 | −1.10331 | −0.551653 | − | 0.834074i | \(-0.686003\pi\) | ||||
−0.551653 | + | 0.834074i | \(0.686003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.59829 | −0.126198 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.2524 | −0.394154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.81215 | 0.0983848 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.32320 | 0.290836 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6060 | −0.858755 | −0.429377 | − | 0.903125i | \(-0.641267\pi\) | ||||
−0.429377 | + | 0.903125i | \(0.641267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0925 | 0.770095 | 0.385047 | − | 0.922897i | \(-0.374185\pi\) | ||||
0.385047 | + | 0.922897i | \(0.374185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.38776 | −0.0831310 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0419 | 1.04466 | 0.522329 | − | 0.852744i | \(-0.325063\pi\) | ||||
0.522329 | + | 0.852744i | \(0.325063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6358 | −1.06402 | −0.532012 | − | 0.846737i | \(-0.678564\pi\) | ||||
−0.532012 | + | 0.846737i | \(0.678564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.9634 | 0.692521 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.59060 | −0.0897588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.59392 | 0.228192 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.35548 | 0.323373 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.3449 | 1.28929 | 0.644644 | − | 0.764483i | \(-0.277006\pi\) | ||||
0.644644 | + | 0.764483i | \(0.277006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.7649 | 1.64706 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.4157 | 0.840920 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.25240 | 0.215089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0510 | 0.345358 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.9248 | 1.02702 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.103084 | −0.00353366 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.78510 | 0.266557 | 0.133278 | − | 0.991079i | \(-0.457450\pi\) | ||||
0.133278 | + | 0.991079i | \(0.457450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.864641 | −0.0295701 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.1483 | 1.91799 | 0.958994 | − | 0.283426i | \(-0.0914709\pi\) | ||||
0.958994 | + | 0.283426i | \(0.0914709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.25051 | 0.0426668 | 0.0213334 | − | 0.999772i | \(-0.493209\pi\) | ||||
0.0213334 | + | 0.999772i | \(0.493209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0910 | 0.616540 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.4865 | −0.527166 | −0.263583 | − | 0.964637i | \(-0.584904\pi\) | ||||
−0.263583 | + | 0.964637i | \(0.584904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.7110 | −0.704194 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4200 | 0.557653 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8247 | 0.570738 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.3203 | 1.87446 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0645508 | −0.00218471 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.89692 | −0.0641275 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7755 | 0.904145 | 0.452072 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452072 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.1247 | 0.847436 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.75386 | 0.193853 | 0.0969263 | − | 0.995292i | \(-0.469099\pi\) | ||||
0.0969263 | + | 0.995292i | \(0.469099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.8559 | −0.769162 | −0.384581 | − | 0.923091i | \(-0.625654\pi\) | ||||
−0.384581 | + | 0.923091i | \(0.625654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2201 | 0.343546 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.0741 | 1.31198 | 0.655991 | − | 0.754769i | \(-0.272251\pi\) | ||||
0.655991 | + | 0.754769i | \(0.272251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.52937 | 0.151910 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.38776 | 0.0799928 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.71096 | 0.0907188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.2986 | −0.745361 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.38776 | 0.146503 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −81.9686 | −2.73380 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.10308 | 0.203323 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.16952 | −0.205309 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.4865 | −0.714234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.2784 | −0.972174 | −0.486087 | − | 0.873910i | \(-0.661576\pi\) | ||||
−0.486087 | + | 0.873910i | \(0.661576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.30299 | −0.0432176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9634 | 0.860204 | 0.430102 | − | 0.902780i | \(-0.358478\pi\) | ||||
0.430102 | + | 0.902780i | \(0.358478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5081 | −0.413958 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.64015 | −0.120340 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.80922 | 0.0597458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.9171 | 0.887914 | 0.443957 | − | 0.896048i | \(-0.353574\pi\) | ||||
0.443957 | + | 0.896048i | \(0.353574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.64015 | −0.185849 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.7634 | −0.946760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.103084 | −0.00338937 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.98168 | 0.163620 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.9494 | 1.37632 | 0.688158 | − | 0.725561i | \(-0.258420\pi\) | ||||
0.688158 | + | 0.725561i | \(0.258420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.94126 | 0.0963958 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0462 | 0.361637 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.81841 | 0.0594684 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9817 | 1.14280 | 0.571401 | − | 0.820671i | \(-0.306400\pi\) | ||||
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.30925 | 0.140627 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.38776 | −0.143037 | −0.0715184 | − | 0.997439i | \(-0.522784\pi\) | ||||
−0.0715184 | + | 0.997439i | \(0.522784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.53707 | 0.310570 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.89692 | 0.0617067 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3265 | −0.335567 | −0.167784 | − | 0.985824i | \(-0.553661\pi\) | ||||
−0.167784 | + | 0.985824i | \(0.553661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.6281 | 0.702077 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.62183 | −0.279582 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.5048 | −1.57122 | −0.785612 | − | 0.618719i | \(-0.787652\pi\) | ||||
−0.785612 | + | 0.618719i | \(0.787652\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.8646 | 0.416290 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.9205 | −0.676262 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.46522 | −0.241064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.5250 | 1.82339 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.697006 | 0.0224607 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.0279 | −0.580339 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.9021 | −0.961588 | −0.480794 | − | 0.876834i | \(-0.659651\pi\) | ||||
−0.480794 | + | 0.876834i | \(0.659651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.658473 | 0.0211532 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.15120 | 0.229493 | 0.114746 | − | 0.993395i | \(-0.463394\pi\) | ||||
0.114746 | + | 0.993395i | \(0.463394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.46045 | −0.175054 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.38776 | 0.140521 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.7249 | −0.982977 | −0.491489 | − | 0.870884i | \(-0.663547\pi\) | ||||
−0.491489 | + | 0.870884i | \(0.663547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.2216 | −0.838045 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.92919 | −0.157377 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.3588 | 1.00019 | 0.500095 | − | 0.865970i | \(-0.333298\pi\) | ||||
0.500095 | + | 0.865970i | \(0.333298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2341 | 0.453535 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.94751 | −0.189311 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.25240 | −0.103420 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.1868 | 1.72130 | 0.860650 | − | 0.509197i | \(-0.170057\pi\) | ||||
0.860650 | + | 0.509197i | \(0.170057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.8786 | −0.345222 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.5693 | −0.398475 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.9354 | 0.884725 | 0.442362 | − | 0.896836i | \(-0.354141\pi\) | ||||
0.442362 | + | 0.896836i | \(0.354141\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.103084 | 0.00326142 |
(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 | 5520.2.a.bz.1.2 | 3 | ||
4.3 | odd | 2 | 2760.2.a.u.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 8280.2.a.bi.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.u.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
5520.2.a.bz.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8280.2.a.bi.1.2 | 3 | 12.11 | even | 2 |