Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
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([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
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.be (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Root | \(3.68710 - 3.68710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.a.1471.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.58474 | −0.598974 | −0.299487 | − | 0.954100i | \(-0.596816\pi\) | ||||
−0.299487 | + | 0.954100i | \(0.596816\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.94482 | 0.887898 | 0.443949 | − | 0.896052i | \(-0.353577\pi\) | ||||
0.443949 | + | 0.896052i | \(0.353577\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23011 | −0.341172 | −0.170586 | − | 0.985343i | \(-0.554566\pi\) | ||||
−0.170586 | + | 0.985343i | \(0.554566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.25392i | 0.304120i | 0.988371 | + | 0.152060i | \(0.0485906\pi\) | ||||
−0.988371 | + | 0.152060i | \(0.951409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.26714 | −1.20836 | −0.604182 | − | 0.796846i | \(-0.706500\pi\) | ||||
−0.604182 | + | 0.796846i | \(0.706500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58474i | 0.345818i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.83865 | − | 4.42937i | −0.383386 | − | 0.923588i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.54806 | 1.40164 | 0.700820 | − | 0.713338i | \(-0.252818\pi\) | ||||
0.700820 | + | 0.713338i | \(0.252818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.690205i | − | 0.123965i | −0.998077 | − | 0.0619823i | \(-0.980258\pi\) | ||
0.998077 | − | 0.0619823i | \(-0.0197422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.94482i | − | 0.512628i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.58474i | − | 0.267869i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.83340i | − | 0.794606i | −0.917688 | − | 0.397303i | \(-0.869946\pi\) | ||
0.917688 | − | 0.397303i | \(-0.130054\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.23011i | 0.196976i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.98783 | 1.09132 | 0.545658 | − | 0.838008i | \(-0.316280\pi\) | ||||
0.545658 | + | 0.838008i | \(0.316280\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.06681 | −0.620183 | −0.310091 | − | 0.950707i | \(-0.600360\pi\) | ||||
−0.310091 | + | 0.950707i | \(0.600360\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.95368i | 1.30603i | 0.757346 | + | 0.653014i | \(0.226496\pi\) | ||||
−0.757346 | + | 0.653014i | \(0.773504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.48861 | −0.641230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25392 | 0.175583 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8852i | 1.49520i | 0.664148 | + | 0.747601i | \(0.268794\pi\) | ||||
−0.664148 | + | 0.747601i | \(0.731206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.94482i | 0.397080i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.26714i | 0.697649i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.33680i | 0.304226i | 0.988363 | + | 0.152113i | \(0.0486077\pi\) | ||||
−0.988363 | + | 0.152113i | \(0.951392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.28658i | 0.676877i | 0.940989 | + | 0.338438i | \(0.109899\pi\) | ||||
−0.940989 | + | 0.338438i | \(0.890101\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.58474 | 0.199658 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.23011i | − | 0.152577i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.49359 | 1.15983 | 0.579913 | − | 0.814678i | \(-0.303087\pi\) | ||||
0.579913 | + | 0.814678i | \(0.303087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.42937 | + | 1.83865i | −0.533234 | + | 0.221348i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.5262i | − | 1.60527i | −0.596473 | − | 0.802633i | \(-0.703432\pi\) | ||
0.596473 | − | 0.802633i | \(-0.296568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.51828 | −1.11403 | −0.557015 | − | 0.830502i | \(-0.688054\pi\) | ||||
−0.557015 | + | 0.830502i | \(0.688054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.66677 | −0.531828 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.71307 | 0.417753 | 0.208876 | − | 0.977942i | \(-0.433019\pi\) | ||||
0.208876 | + | 0.977942i | \(0.433019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.5130 | −1.81253 | −0.906267 | − | 0.422705i | \(-0.861081\pi\) | ||||
−0.906267 | + | 0.422705i | \(0.861081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.25392 | −0.136006 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.54806i | − | 0.809237i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2406i | 1.29750i | 0.761003 | + | 0.648748i | \(0.224707\pi\) | ||||
−0.761003 | + | 0.648748i | \(0.775293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94940 | 0.204353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.690205 | −0.0715710 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.26714i | − | 0.540397i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.70591i | 0.782417i | 0.920302 | + | 0.391208i | \(0.127943\pi\) | ||||
−0.920302 | + | 0.391208i | \(0.872057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.94482 | −0.295966 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.43609 | −0.938926 | −0.469463 | − | 0.882952i | \(-0.655552\pi\) | ||||
−0.469463 | + | 0.882952i | \(0.655552\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.07692 | −0.697310 | −0.348655 | − | 0.937251i | \(-0.613361\pi\) | ||||
−0.348655 | + | 0.937251i | \(0.613361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.58474 | −0.154654 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.20879 | −0.600227 | −0.300113 | − | 0.953904i | \(-0.597024\pi\) | ||||
−0.300113 | + | 0.953904i | \(0.597024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.46182i | 0.523147i | 0.965184 | + | 0.261574i | \(0.0842414\pi\) | ||||
−0.965184 | + | 0.261574i | \(0.915759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.83340 | −0.458766 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.98548i | 0.186778i | 0.995630 | + | 0.0933891i | \(0.0297700\pi\) | ||||
−0.995630 | + | 0.0933891i | \(0.970230\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.42937 | − | 1.83865i | 0.413041 | − | 0.171455i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.23011 | 0.113724 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.98713i | − | 0.182160i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.32801 | −0.211638 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 6.98783i | − | 0.630071i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.35495i | 0.386439i | 0.981156 | + | 0.193220i | \(0.0618929\pi\) | ||||
−0.981156 | + | 0.193220i | \(0.938107\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.06681i | 0.358063i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.92541i | 0.168224i | 0.996456 | + | 0.0841118i | \(0.0268053\pi\) | ||||
−0.996456 | + | 0.0841118i | \(0.973195\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.34702 | 0.723779 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9282i | 1.01910i | 0.860442 | + | 0.509548i | \(0.170187\pi\) | ||||
−0.860442 | + | 0.509548i | \(0.829813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.31703i | − | 0.111709i | −0.998439 | − | 0.0558545i | \(-0.982212\pi\) | ||
0.998439 | − | 0.0558545i | \(-0.0177883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.95368 | 0.754036 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.62246 | −0.302925 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.54806i | 0.626832i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.48861i | 0.370214i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.50615i | − | 0.614928i | −0.951560 | − | 0.307464i | \(-0.900520\pi\) | ||
0.951560 | − | 0.307464i | \(-0.0994804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.78698i | − | 0.389559i | −0.980847 | − | 0.194780i | \(-0.937601\pi\) | ||
0.980847 | − | 0.194780i | \(-0.0623992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.25392i | − | 0.101373i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.690205 | 0.0554386 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.01182i | 0.479795i | 0.970798 | + | 0.239898i | \(0.0771139\pi\) | ||||
−0.970798 | + | 0.239898i | \(0.922886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8852 | 0.863255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.91378 | + | 7.01939i | 0.229638 | + | 0.553206i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.41003i | 0.737051i | 0.929618 | + | 0.368525i | \(0.120137\pi\) | ||||
−0.929618 | + | 0.368525i | \(0.879863\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.94482 | 0.229254 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.39043i | − | 0.184977i | −0.995714 | − | 0.0924884i | \(-0.970518\pi\) | ||
0.995714 | − | 0.0924884i | \(-0.0294821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4868 | −0.883602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.26714 | 0.402788 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.24943 | 0.551164 | 0.275582 | − | 0.961278i | \(-0.411129\pi\) | ||||
0.275582 | + | 0.961278i | \(0.411129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.58474 | 0.119795 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.33680 | 0.175645 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.2088i | − | 0.912532i | −0.889843 | − | 0.456266i | \(-0.849187\pi\) | ||
0.889843 | − | 0.456266i | \(-0.150813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9328i | 1.25860i | 0.777161 | + | 0.629302i | \(0.216659\pi\) | ||||
−0.777161 | + | 0.629302i | \(0.783341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.28658 | 0.390795 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.83340 | 0.355359 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.69256i | 0.270027i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.58474i | − | 0.115273i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.46417 | 0.467731 | 0.233865 | − | 0.972269i | \(-0.424862\pi\) | ||||
0.233865 | + | 0.972269i | \(0.424862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5952 | −1.55445 | −0.777227 | − | 0.629220i | \(-0.783375\pi\) | ||||
−0.777227 | + | 0.629220i | \(0.783375\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.23011 | −0.0880901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.11055 | −0.292865 | −0.146432 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146432 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.25603 | 0.230814 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.49359i | − | 0.669626i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.9617 | −0.839546 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.98783i | 0.488051i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.83865 | + | 4.42937i | 0.127795 | + | 0.307863i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.5108 | −1.07290 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1011i | 1.24613i | 0.782169 | + | 0.623066i | \(0.214113\pi\) | ||||
−0.782169 | + | 0.623066i | \(0.785887\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5262 | −0.926801 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.06681i | − | 0.277354i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.09379i | 0.0742516i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.51828i | 0.643186i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.54246i | − | 0.103757i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.72334i | − | 0.182368i | −0.995834 | − | 0.0911842i | \(-0.970935\pi\) | ||
0.995834 | − | 0.0911842i | \(-0.0290652\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.7426 | −1.44311 | −0.721554 | − | 0.692358i | \(-0.756572\pi\) | ||||
−0.721554 | + | 0.692358i | \(0.756572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.81560i | − | 0.119978i | −0.998199 | − | 0.0599891i | \(-0.980893\pi\) | ||
0.998199 | − | 0.0599891i | \(-0.0191066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.66677i | 0.307051i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.1093 | −1.64496 | −0.822482 | − | 0.568792i | \(-0.807411\pi\) | ||||
−0.822482 | + | 0.568792i | \(0.807411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.95368 | −0.584074 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.71307i | − | 0.241190i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.5463i | 1.65245i | 0.563338 | + | 0.826226i | \(0.309517\pi\) | ||||
−0.563338 | + | 0.826226i | \(0.690483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7500i | 1.14338i | 0.820471 | + | 0.571689i | \(0.193711\pi\) | ||||
−0.820471 | + | 0.571689i | \(0.806289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.48861i | − | 0.286767i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.47916 | 0.412259 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.5130i | 1.04647i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.8514 | −1.18989 | −0.594946 | − | 0.803766i | \(-0.702826\pi\) | ||||
−0.594946 | + | 0.803766i | \(0.702826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.41451 | − | 13.0437i | −0.340407 | − | 0.820052i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.25392i | 0.0785233i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1245 | 1.13058 | 0.565289 | − | 0.824893i | \(-0.308765\pi\) | ||||
0.565289 | + | 0.824893i | \(0.308765\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.65967i | 0.475948i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.54806 | −0.467213 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.0810 | 1.79321 | 0.896606 | − | 0.442829i | \(-0.146025\pi\) | ||||
0.896606 | + | 0.442829i | \(0.146025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.8852 | −0.668675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2406 | 0.749110 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.2290 | −1.29435 | −0.647176 | − | 0.762340i | \(-0.724050\pi\) | ||||
−0.647176 | + | 0.762340i | \(0.724050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.18826i | 0.558147i | 0.960270 | + | 0.279073i | \(0.0900273\pi\) | ||||
−0.960270 | + | 0.279073i | \(0.909973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.94940i | − | 0.117983i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.94482 | −0.177580 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.9814 | 1.44090 | 0.720451 | − | 0.693505i | \(-0.243935\pi\) | ||||
0.720451 | + | 0.693505i | \(0.243935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.690205i | 0.0413215i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5638i | 1.10742i | 0.832709 | + | 0.553711i | \(0.186789\pi\) | ||||
−0.832709 | + | 0.553711i | \(0.813211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8548 | −0.764138 | −0.382069 | − | 0.924134i | \(-0.624788\pi\) | ||||
−0.382069 | + | 0.924134i | \(0.624788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.26714 | −0.311998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0739 | −0.653670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4277 | 0.907511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.70591 | 0.451728 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3576i | 1.48141i | 0.671831 | + | 0.740705i | \(0.265508\pi\) | ||||
−0.671831 | + | 0.740705i | \(0.734492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.33680 | −0.136054 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.94482i | 0.170876i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.26175 | + | 5.44862i | 0.130800 | + | 0.315102i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.44483 | 0.371474 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.43609i | 0.542089i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.28658 | −0.302709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7630i | 0.728422i | 0.931316 | + | 0.364211i | \(0.118661\pi\) | ||||
−0.931316 | + | 0.364211i | \(0.881339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.07692i | 0.402592i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.7842i | − | 0.838333i | −0.907909 | − | 0.419166i | \(-0.862322\pi\) | ||
0.907909 | − | 0.419166i | \(-0.137678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.48723i | − | 0.0840632i | −0.999116 | − | 0.0420316i | \(-0.986617\pi\) | ||
0.999116 | − | 0.0420316i | \(-0.0133830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.58474i | 0.0892898i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.771575 | 0.0433360 | 0.0216680 | − | 0.999765i | \(-0.493102\pi\) | ||||
0.0216680 | + | 0.999765i | \(0.493102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.2277 | 1.24451 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.20879i | 0.346541i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.60455i | − | 0.367487i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23011 | 0.0682343 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.46182 | 0.302039 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 14.1892i | − | 0.782277i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 33.8360i | − | 1.85980i | −0.367817 | − | 0.929898i | \(-0.619895\pi\) | ||
0.367817 | − | 0.929898i | \(-0.380105\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.83340i | 0.264869i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.49359i | 0.518690i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.3943i | 1.38331i | 0.722226 | + | 0.691657i | \(0.243119\pi\) | ||||
−0.722226 | + | 0.691657i | \(0.756881\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.98548 | 0.107836 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.03253i | − | 0.110068i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2064 | 0.983054 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.83865 | − | 4.42937i | −0.0989898 | − | 0.238469i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.66039i | − | 0.411231i | −0.978633 | − | 0.205616i | \(-0.934080\pi\) | ||
0.978633 | − | 0.205616i | \(-0.0659197\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8624 | 0.849093 | 0.424546 | − | 0.905406i | \(-0.360434\pi\) | ||||
0.424546 | + | 0.905406i | \(0.360434\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.23011i | − | 0.0656585i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.7036 | −1.42129 | −0.710643 | − | 0.703552i | \(-0.751596\pi\) | ||||
−0.710643 | + | 0.703552i | \(0.751596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5262 | 0.717897 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.98713 | −0.105170 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3015 | −0.913137 | −0.456569 | − | 0.889688i | \(-0.650922\pi\) | ||||
−0.456569 | + | 0.889688i | \(0.650922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.74271 | 0.460143 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.32801i | 0.122189i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.51828i | − | 0.498210i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1050 | −0.997271 | −0.498635 | − | 0.866812i | \(-0.666165\pi\) | ||||
−0.498635 | + | 0.866812i | \(0.666165\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.98783 | −0.363772 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 17.2502i | − | 0.895587i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.5261i | − | 1.52880i | −0.644740 | − | 0.764402i | \(-0.723034\pi\) | ||
0.644740 | − | 0.764402i | \(-0.276966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.28496 | −0.478200 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9649 | 1.53920 | 0.769598 | − | 0.638529i | \(-0.220457\pi\) | ||||
0.769598 | + | 0.638529i | \(0.220457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.35495 | 0.223111 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.78342 | −0.346616 | −0.173308 | − | 0.984868i | \(-0.555446\pi\) | ||||
−0.173308 | + | 0.984868i | \(0.555446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 4.66677i | − | 0.237841i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.06681 | 0.206728 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.20216i | 0.415866i | 0.978143 | + | 0.207933i | \(0.0666736\pi\) | ||||
−0.978143 | + | 0.207933i | \(0.933326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.55407 | − | 2.30552i | 0.280881 | − | 0.116595i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.92541 | 0.0971240 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.71307i | 0.186825i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.2572 | −1.41819 | −0.709095 | − | 0.705113i | \(-0.750896\pi\) | ||||
−0.709095 | + | 0.705113i | \(0.750896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 8.34702i | − | 0.417874i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1193i | 0.854899i | 0.904039 | + | 0.427449i | \(0.140588\pi\) | ||||
−0.904039 | + | 0.427449i | \(0.859412\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.849030i | 0.0422932i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.2335i | − | 0.705529i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.8130 | 1.12803 | 0.564016 | − | 0.825764i | \(-0.309256\pi\) | ||||
0.564016 | + | 0.825764i | \(0.309256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9282 | 0.588375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.70322i | − | 0.182223i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 16.5130i | − | 0.810590i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.31703 | −0.0644952 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.54342 | −0.221960 | −0.110980 | − | 0.993823i | \(-0.535399\pi\) | ||||
−0.110980 | + | 0.993823i | \(0.535399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.02280i | 0.0985853i | 0.998784 | + | 0.0492926i | \(0.0156967\pi\) | ||||
−0.998784 | + | 0.0492926i | \(0.984303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.95368i | − | 0.435343i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.25392i | − | 0.0608239i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.37783i | − | 0.405432i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.62246i | 0.174894i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5534 | −0.508339 | −0.254169 | − | 0.967160i | \(-0.581802\pi\) | ||||
−0.254169 | + | 0.967160i | \(0.581802\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.9550i | 1.63177i | 0.578211 | + | 0.815887i | \(0.303751\pi\) | ||||
−0.578211 | + | 0.815887i | \(0.696249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.54806 | 0.361902 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.68444 | + | 23.3301i | 0.463270 | + | 1.11603i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.99231i | 0.142815i | 0.997447 | + | 0.0714076i | \(0.0227491\pi\) | ||||
−0.997447 | + | 0.0714076i | \(0.977251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.48861 | 0.213743 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.9670i | − | 0.996174i | −0.867127 | − | 0.498087i | \(-0.834036\pi\) | ||
0.867127 | − | 0.498087i | \(-0.165964\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2406 | −0.580258 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.50615 | −0.355029 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.8249 | 0.558053 | 0.279026 | − | 0.960283i | \(-0.409988\pi\) | ||||
0.279026 | + | 0.960283i | \(0.409988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.5779 | 0.968977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.78698 | −0.224912 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.94940i | 0.0913894i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.8771i | − | 0.508810i | −0.967098 | − | 0.254405i | \(-0.918120\pi\) | ||
0.967098 | − | 0.254405i | \(-0.0818796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.25392 | −0.0585278 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2626 | 0.710849 | 0.355425 | − | 0.934705i | \(-0.384336\pi\) | ||||
0.355425 | + | 0.934705i | \(0.384336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.1730i | 1.77405i | 0.461721 | + | 0.887025i | \(0.347232\pi\) | ||||
−0.461721 | + | 0.887025i | \(0.652768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.690205i | − | 0.0320075i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.21856 | −0.195212 | −0.0976059 | − | 0.995225i | \(-0.531118\pi\) | ||||
−0.0976059 | + | 0.995225i | \(0.531118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0448 | −0.694706 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.01182 | 0.277010 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.9760 | −0.550659 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.26714 | 0.241673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.8852i | − | 0.498401i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.347762 | 0.0158897 | 0.00794483 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794483 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.94562i | 0.271097i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.01939 | − | 2.91378i | 0.319393 | − | 0.132582i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.70591 | −0.349907 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.4417i | − | 0.563789i | −0.959445 | − | 0.281894i | \(-0.909037\pi\) | ||
0.959445 | − | 0.281894i | \(-0.0909628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.41003 | 0.425536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.12588i | 0.186198i | 0.995657 | + | 0.0930991i | \(0.0296774\pi\) | ||||
−0.995657 | + | 0.0930991i | \(0.970323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.46464i | 0.426266i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 2.94482i | − | 0.132360i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.4355i | 0.961514i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.3075i | − | 1.08815i | −0.839035 | − | 0.544077i | \(-0.816880\pi\) | ||
0.839035 | − | 0.544077i | \(-0.183120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.39043 | −0.106796 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.9762 | 0.533991 | 0.266995 | − | 0.963698i | \(-0.413969\pi\) | ||||
0.266995 | + | 0.963698i | \(0.413969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.43609i | − | 0.419900i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4868i | 0.510148i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.4081 | 1.92403 | 0.962015 | − | 0.272997i | \(-0.0880150\pi\) | ||||
0.962015 | + | 0.272997i | \(0.0880150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0840 | 0.667276 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.26714i | − | 0.232550i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.07692i | − | 0.311846i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.3670i | 1.15962i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.24943i | − | 0.318215i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.1561i | − | 1.32116i | −0.750754 | − | 0.660582i | \(-0.770310\pi\) | ||
0.750754 | − | 0.660582i | \(-0.229690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0503 | 1.09537 | 0.547686 | − | 0.836684i | \(-0.315509\pi\) | ||||
0.547686 | + | 0.836684i | \(0.315509\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.58474i | − | 0.0691636i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.865460 | 0.0377000 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2387 | + | 16.2882i | −0.706031 | + | 0.708181i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.33680i | − | 0.101409i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.59581 | −0.372326 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.20879i | − | 0.268430i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2088 | −0.526851 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2182 | −0.569346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9949 | 1.67652 | 0.838260 | − | 0.545271i | \(-0.183573\pi\) | ||||
0.838260 | + | 0.545271i | \(0.183573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.9328 | 0.726656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46182 | −0.233959 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9994i | 1.53922i | 0.638512 | + | 0.769612i | \(0.279550\pi\) | ||||
−0.638512 | + | 0.769612i | \(0.720450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5.28658i | − | 0.225626i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.7567 | −1.69369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.88424 | −0.250223 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 4.83340i | − | 0.205166i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 22.1601i | − | 0.938954i | −0.882945 | − | 0.469477i | \(-0.844442\pi\) | ||
0.882945 | − | 0.469477i | \(-0.155558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00263 | 0.211589 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.69256 | 0.155900 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.91544 | 0.122871 | 0.0614356 | − | 0.998111i | \(-0.480432\pi\) | ||||
0.0614356 | + | 0.998111i | \(0.480432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.98548 | −0.0835297 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.58474 | −0.0665527 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.9836i | 0.628144i | 0.949399 | + | 0.314072i | \(0.101693\pi\) | ||||
−0.949399 | + | 0.314072i | \(0.898307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.15642 | 0.132092 | 0.0660461 | − | 0.997817i | \(-0.478962\pi\) | ||||
0.0660461 | + | 0.997817i | \(0.478962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.46417i | − | 0.270044i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.83865 | + | 4.42937i | 0.0766772 | + | 0.184718i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.25189 | −0.260270 | −0.130135 | − | 0.991496i | \(-0.541541\pi\) | ||||
−0.130135 | + | 0.991496i | \(0.541541\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.5952i | 0.897465i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.1687 | 1.08566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.0551i | 1.32759i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.23011i | 0.0508589i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.22099i | − | 0.132945i | −0.997788 | − | 0.0664723i | \(-0.978826\pi\) | ||
0.997788 | − | 0.0664723i | \(-0.0211744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.63541i | 0.149794i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.11055i | 0.169085i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.3093 | −0.751873 | −0.375937 | − | 0.926645i | \(-0.622679\pi\) | ||||
−0.375937 | + | 0.926645i | \(0.622679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.98713 | 0.0814643 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3.25603i | − | 0.133261i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.79992i | − | 0.236978i | −0.992955 | − | 0.118489i | \(-0.962195\pi\) | ||
0.992955 | − | 0.118489i | \(-0.0378051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1653 | −0.496233 | −0.248116 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248116 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.49359 | −0.386609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.32801i | − | 0.0946472i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5799i | 1.36296i | 0.731834 | + | 0.681482i | \(0.238664\pi\) | ||||
−0.731834 | + | 0.681482i | \(0.761336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.9617i | 0.484712i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.0140i | − | 0.445580i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.5388i | − | 0.991113i | −0.868576 | − | 0.495556i | \(-0.834964\pi\) | ||
0.868576 | − | 0.495556i | \(-0.165036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.98783 | 0.281776 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.9240i | − | 0.439782i | −0.975524 | − | 0.219891i | \(-0.929430\pi\) | ||
0.975524 | − | 0.219891i | \(-0.0705701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8447 | −1.19956 | −0.599780 | − | 0.800165i | \(-0.704745\pi\) | ||||
−0.599780 | + | 0.800165i | \(0.704745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.42937 | − | 1.83865i | 0.177745 | − | 0.0737826i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 19.3981i | − | 0.777167i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.5108i | 0.619441i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.06068 | 0.241655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.26198 | 0.169667 | 0.0848333 | − | 0.996395i | \(-0.472964\pi\) | ||||
0.0848333 | + | 0.996395i | \(0.472964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1011 | 0.719455 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.35495 | −0.172821 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.52149 | 0.218769 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5262i | 0.535089i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.5638i | 1.72067i | 0.509731 | + | 0.860334i | \(0.329745\pi\) | ||||
−0.509731 | + | 0.860334i | \(0.670255\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.2217 | 0.442542 | 0.221271 | − | 0.975212i | \(-0.428979\pi\) | ||||
0.221271 | + | 0.975212i | \(0.428979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.06681 | −0.160131 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.7686i | 1.44552i | 0.691098 | + | 0.722761i | \(0.257127\pi\) | ||||
−0.691098 | + | 0.722761i | \(0.742873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.88147i | 0.270121i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09379 | 0.0428692 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.9401 | −1.24991 | −0.624957 | − | 0.780659i | \(-0.714883\pi\) | ||||
−0.624957 | + | 0.780659i | \(0.714883\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.92541 | −0.0752319 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.51828 | 0.371344 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.5902 | −1.69803 | −0.849016 | − | 0.528367i | \(-0.822804\pi\) | ||||
−0.849016 | + | 0.528367i | \(0.822804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.4393i | − | 0.406042i | −0.979174 | − | 0.203021i | \(-0.934924\pi\) | ||
0.979174 | − | 0.203021i | \(-0.0650759\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.54246 | −0.0599041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.34702i | 0.323684i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8783 | − | 33.4332i | −0.537369 | − | 1.29454i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.72334 | −0.105290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5680i | 0.600997i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.83519 | 0.109288 | 0.0546442 | − | 0.998506i | \(-0.482598\pi\) | ||||
0.0546442 | + | 0.998506i | \(0.482598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.3830i | − | 1.39831i | −0.714969 | − | 0.699156i | \(-0.753559\pi\) | ||
0.714969 | − | 0.699156i | \(-0.246441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12.2118i | − | 0.468647i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7426i | 0.833179i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.81755i | 0.107811i | 0.998546 | + | 0.0539053i | \(0.0171669\pi\) | ||||
−0.998546 | + | 0.0539053i | \(0.982833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9282 | −0.455754 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.81560 | −0.0692695 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.3901i | − | 0.510120i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 49.1990i | − | 1.87162i | −0.352506 | − | 0.935809i | \(-0.614670\pi\) | ||
0.352506 | − | 0.935809i | \(-0.385330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.66677 | 0.177276 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.31703 | 0.0499578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.76216i | 0.331890i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.1093i | 0.949720i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.5212i | − | 0.586228i | −0.956078 | − | 0.293114i | \(-0.905308\pi\) | ||
0.956078 | − | 0.293114i | \(-0.0946915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4582i | 0.960173i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.95368i | 0.337215i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.9537 | 0.562392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.54150i | 0.0578923i | 0.999581 | + | 0.0289462i | \(0.00921514\pi\) | ||||
−0.999581 | + | 0.0289462i | \(0.990785\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71307 | −0.139251 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.05718 | + | 1.26905i | −0.114492 | + | 0.0475263i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.62246i | − | 0.135472i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.5463 | 0.954044 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.00464i | 0.0747606i | 0.999301 | + | 0.0373803i | \(0.0119013\pi\) | ||||
−0.999301 | + | 0.0373803i | \(0.988099\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2151 | 0.417671 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.7500 | 0.660129 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.54806 | −0.280328 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3038 | 0.641761 | 0.320881 | − | 0.947120i | \(-0.396021\pi\) | ||||
0.320881 | + | 0.947120i | \(0.396021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.09944i | − | 0.188610i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.4881i | − | 0.978358i | −0.872183 | − | 0.489179i | \(-0.837296\pi\) | ||
0.872183 | − | 0.489179i | \(-0.162704\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.48861 | −0.165565 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.9569 | 1.02981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.11302i | − | 0.261657i | −0.991405 | − | 0.130828i | \(-0.958236\pi\) | ||
0.991405 | − | 0.130828i | \(-0.0417637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 6.47916i | − | 0.238018i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.7611 | −1.42201 | −0.711003 | − | 0.703189i | \(-0.751759\pi\) | ||||
−0.711003 | + | 0.703189i | \(0.751759\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.50615 | 0.275004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.5130 | 0.604178 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.83930 | 0.359520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4017 | −0.963412 | −0.481706 | − | 0.876333i | \(-0.659983\pi\) | ||||
−0.481706 | + | 0.876333i | \(0.659983\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8514i | 0.686984i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.78698 | 0.174216 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 19.6012i | − | 0.712419i | −0.934406 | − | 0.356210i | \(-0.884069\pi\) | ||
0.934406 | − | 0.356210i | \(-0.115931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.0437 | + | 5.41451i | −0.473457 | + | 0.196534i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.90461 | −0.0690421 | −0.0345211 | − | 0.999404i | \(-0.510991\pi\) | ||||
−0.0345211 | + | 0.999404i | \(0.510991\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.65554i | − | 0.313352i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.25392 | 0.0453355 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.87453i | − | 0.103793i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.1496i | − | 0.870858i | −0.900223 | − | 0.435429i | \(-0.856597\pi\) | ||
0.900223 | − | 0.435429i | \(-0.143403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 18.1245i | − | 0.652739i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35.9153i | − | 1.29179i | −0.763428 | − | 0.645893i | \(-0.776485\pi\) | ||
0.763428 | − | 0.645893i | \(-0.223515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.690205i | 0.0247929i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.65967 | 0.274789 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.8058 | −1.31871 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.8323i | − | 1.42531i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.54806i | 0.269746i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.01182 | −0.214571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.6536 | 0.914452 | 0.457226 | − | 0.889351i | \(-0.348843\pi\) | ||||
0.457226 | + | 0.889351i | \(0.348843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 29.0810i | − | 1.03531i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.14646i | − | 0.111875i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.50308i | − | 0.230931i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.8852i | 0.386059i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11.6082i | − | 0.411185i | −0.978638 | − | 0.205592i | \(-0.934088\pi\) | ||
0.978638 | − | 0.205592i | \(-0.0659121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.2272 | −0.397189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.2406i | − | 0.432499i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.0297 | −0.989145 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.01939 | + | 2.91378i | −0.247401 | + | 0.102697i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.2290i | 0.747295i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.1262 | −1.16465 | −0.582327 | − | 0.812955i | \(-0.697858\pi\) | ||||
−0.582327 | + | 0.812955i | \(0.697858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.0060i | 1.58037i | 0.612867 | + | 0.790186i | \(0.290016\pi\) | ||||
−0.612867 | + | 0.790186i | \(0.709984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.18826 | 0.322246 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.41003 | −0.329619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.4204 | 0.749407 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.94940 | −0.0681177 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5182 | 0.925493 | 0.462746 | − | 0.886491i | \(-0.346864\pi\) | ||||
0.462746 | + | 0.886491i | \(0.346864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3626i | 0.361216i | 0.983555 | + | 0.180608i | \(0.0578066\pi\) | ||||
−0.983555 | + | 0.180608i | \(0.942193\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.94482i | 0.102526i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.8592 | −1.66423 | −0.832114 | − | 0.554605i | \(-0.812870\pi\) | ||||
−0.832114 | + | 0.554605i | \(0.812870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.3355 | −0.358968 | −0.179484 | − | 0.983761i | \(-0.557443\pi\) | ||||
−0.179484 | + | 0.983761i | \(0.557443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 23.9814i | − | 0.831906i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.62834i | − | 0.195011i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.39043 | 0.0827241 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.690205 | 0.0238570 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.62580 | 0.228748 | 0.114374 | − | 0.993438i | \(-0.463514\pi\) | ||||
0.114374 | + | 0.993438i | \(0.463514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9732 | 0.964594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.5638 | 0.639370 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 11.4868i | − | 0.395159i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.68929 | 0.126766 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.8548i | 0.441175i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.4089 | + | 8.88695i | −0.733889 | + | 0.304641i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.4991 | −1.52362 | −0.761810 | − | 0.647800i | \(-0.775689\pi\) | ||||
−0.761810 | + | 0.647800i | \(0.775689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.26714i | 0.180132i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.12506 | 0.311706 | 0.155853 | − | 0.987780i | \(-0.450187\pi\) | ||||
0.155853 | + | 0.987780i | \(0.450187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 30.9281i | − | 1.05525i | −0.849476 | − | 0.527627i | \(-0.823082\pi\) | ||
0.849476 | − | 0.527627i | \(-0.176918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.0739i | 0.377397i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.46438i | − | 0.288131i | −0.989568 | − | 0.144065i | \(-0.953982\pi\) | ||
0.989568 | − | 0.144065i | \(-0.0460176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.24943i | 0.246488i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.4277i | − | 0.523952i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9343 | 0.370922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6782 | −0.395700 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.70591i | − | 0.260806i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.58474i | 0.0535739i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0279 | 0.676295 | 0.338147 | − | 0.941093i | \(-0.390200\pi\) | ||||
0.338147 | + | 0.941093i | \(0.390200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.3576 | 0.855292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.0341i | 1.28140i | 0.767790 | + | 0.640701i | \(0.221356\pi\) | ||||
−0.767790 | + | 0.640701i | \(0.778644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.9644i | − | 0.503592i | −0.967780 | − | 0.251796i | \(-0.918979\pi\) | ||
0.967780 | − | 0.251796i | \(-0.0810211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.33680i | 0.0785508i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.728725i | − | 0.0244682i | −0.999925 | − | 0.0122341i | \(-0.996106\pi\) | ||
0.999925 | − | 0.0122341i | \(-0.00389433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.90144i | − | 0.231467i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.94482 | 0.0986553 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 47.1602i | − | 1.57816i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2088 | 0.408097 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.44862 | − | 2.26175i | 0.181924 | − | 0.0755176i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 5.20971i | − | 0.173754i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6492 | −0.454720 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.44483i | − | 0.214470i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.9328 | −0.562865 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.84373 | 0.127629 | 0.0638145 | − | 0.997962i | \(-0.479673\pi\) | ||||
0.0638145 | + | 0.997962i | \(0.479673\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.43609 | 0.312975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.8963 | 1.85193 | 0.925964 | − | 0.377611i | \(-0.123254\pi\) | ||||
0.925964 | + | 0.377611i | \(0.123254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.6278 | −1.60935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.28658i | 0.174769i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.05126i | − | 0.100762i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.643465 | 0.0212260 | 0.0106130 | − | 0.999944i | \(-0.496622\pi\) | ||||
0.0106130 | + | 0.999944i | \(0.496622\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.7630 | 0.420555 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.6388i | 0.547672i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.83340i | 0.158921i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.07692 | 0.232437 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.92764 | −0.0632440 | −0.0316220 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316220 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.6421 | 0.774839 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.7842 | −0.484012 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.69256 | −0.120760 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6541i | 0.609404i | 0.952448 | + | 0.304702i | \(0.0985568\pi\) | ||||
−0.952448 | + | 0.304702i | \(0.901443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.48723 | −0.0485339 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7327i | 0.675868i | 0.941170 | + | 0.337934i | \(0.109728\pi\) | ||||
−0.941170 | + | 0.337934i | \(0.890272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.8482 | − | 30.9517i | −0.418395 | − | 1.00793i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.58474 | 0.0515515 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34.9977i | − | 1.13727i | −0.822589 | − | 0.568636i | \(-0.807471\pi\) | ||
0.822589 | − | 0.568636i | \(-0.192529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.7086 | 0.380076 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.771575i | − | 0.0250200i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.1023i | − | 1.36383i | −0.731433 | − | 0.681914i | \(-0.761148\pi\) | ||
0.731433 | − | 0.681914i | \(-0.238852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.46417i | 0.209176i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.2277i | − | 0.718520i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 18.9031i | − | 0.610412i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.5236 | 0.984633 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.20879 | 0.200076 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 21.5952i | − | 0.695173i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6032i | 0.694711i | 0.937734 | + | 0.347355i | \(0.112920\pi\) | ||||
−0.937734 | + | 0.347355i | \(0.887080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.60455 | −0.212169 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.8071 | 1.24538 | 0.622690 | − | 0.782469i | \(-0.286040\pi\) | ||||
0.622690 | + | 0.782469i | \(0.286040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.08715i | 0.0669108i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.23011i | − | 0.0393951i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.0657i | 1.05787i | 0.848664 | + | 0.528933i | \(0.177408\pi\) | ||||
−0.848664 | + | 0.528933i | \(0.822592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0463i | 1.15204i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 5.46182i | − | 0.174382i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.4381 | −0.619980 | −0.309990 | − | 0.950740i | \(-0.600326\pi\) | ||||
−0.309990 | + | 0.950740i | \(0.600326\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.11055i | − | 0.130973i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.1892 | −0.451648 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.47746 | + | 18.0134i | 0.237769 | + | 0.572794i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.60244i | 0.0509033i | 0.999676 | + | 0.0254517i | \(0.00810239\pi\) | ||||
−0.999676 | + | 0.0254517i | \(0.991898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.8360 | −1.07375 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.25603i | 0.103223i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.4207 | 0.330026 | 0.165013 | − | 0.986291i | \(-0.447233\pi\) | ||||
0.165013 | + | 0.986291i | \(0.447233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.83340 | 0.152922 |
(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.be.a.1471.3 | ✓ | 16 | |
4.3 | odd | 2 | 5520.2.be.b.1471.14 | yes | 16 | ||
23.22 | odd | 2 | 5520.2.be.b.1471.6 | yes | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.a.1471.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
5520.2.be.a.1471.11 | yes | 16 | 92.91 | even | 2 | inner | |
5520.2.be.b.1471.6 | yes | 16 | 23.22 | odd | 2 | ||
5520.2.be.b.1471.14 | yes | 16 | 4.3 | odd | 2 |