Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.37 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.10 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.82354i | 1.05282i | 0.850230 | + | 0.526411i | \(0.176463\pi\) | ||||
−0.850230 | + | 0.526411i | \(0.823537\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.284793i | 0.127363i | 0.997970 | + | 0.0636816i | \(0.0202842\pi\) | ||||
−0.997970 | + | 0.0636816i | \(0.979716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.645277i | 0.243892i | 0.992537 | + | 0.121946i | \(0.0389135\pi\) | ||||
−0.992537 | + | 0.121946i | \(0.961087\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.325298 | −0.108433 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.56411i | − | 0.471598i | −0.971802 | − | 0.235799i | \(-0.924229\pi\) | ||
0.971802 | − | 0.235799i | \(-0.0757707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.12492 | 0.311997 | 0.155999 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.155999 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.519331 | −0.134091 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35405 | + | 3.89443i | 0.328404 | + | 0.944537i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.845911 | −0.194065 | −0.0970327 | − | 0.995281i | \(-0.530935\pi\) | ||||
−0.0970327 | + | 0.995281i | \(0.530935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.17669 | −0.256775 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.49622i | − | 0.520498i | −0.965542 | − | 0.260249i | \(-0.916195\pi\) | ||
0.965542 | − | 0.260249i | \(-0.0838047\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.91889 | 0.983779 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.87743i | 0.938661i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.28760i | − | 1.72466i | −0.506344 | − | 0.862332i | \(-0.669003\pi\) | ||
0.506344 | − | 0.862332i | \(-0.330997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.94750i | 1.06820i | 0.845420 | + | 0.534102i | \(0.179350\pi\) | ||||
−0.845420 | + | 0.534102i | \(0.820650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.85222 | 0.496508 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.183770 | −0.0310629 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.09474i | 1.00197i | 0.865456 | + | 0.500985i | \(0.167029\pi\) | ||||
−0.865456 | + | 0.500985i | \(0.832971\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.05134i | 0.328477i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.30564i | 0.203907i | 0.994789 | + | 0.101954i | \(0.0325094\pi\) | ||||
−0.994789 | + | 0.101954i | \(0.967491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.23300 | 0.493028 | 0.246514 | − | 0.969139i | \(-0.420715\pi\) | ||||
0.246514 | + | 0.969139i | \(0.420715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 0.0926424i | − | 0.0138103i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.319650 | 0.0466257 | 0.0233128 | − | 0.999728i | \(-0.492579\pi\) | ||||
0.0233128 | + | 0.999728i | \(0.492579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58362 | 0.940517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.10164 | + | 2.46916i | −0.994429 | + | 0.345751i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.07538 | −0.422436 | −0.211218 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211218 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.445448 | 0.0600642 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.54255i | − | 0.204316i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.55451i | − | 0.583145i | −0.956549 | − | 0.291572i | \(-0.905822\pi\) | ||
0.956549 | − | 0.291572i | \(-0.0941785\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.209907i | − | 0.0264458i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.320370i | 0.0397370i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.98126 | 0.608558 | 0.304279 | − | 0.952583i | \(-0.401585\pi\) | ||||
0.304279 | + | 0.952583i | \(0.401585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.55196 | 0.547991 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3681i | 1.58650i | 0.608896 | + | 0.793250i | \(0.291613\pi\) | ||||
−0.608896 | + | 0.793250i | \(0.708387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2696i | 1.55309i | 0.630065 | + | 0.776543i | \(0.283028\pi\) | ||||
−0.630065 | + | 0.776543i | \(0.716972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.96980i | 1.03574i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00929 | 0.115019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.65938i | − | 0.186695i | −0.995634 | − | 0.0933476i | \(-0.970243\pi\) | ||
0.995634 | − | 0.0933476i | \(-0.0297568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.87007 | −1.09667 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.62138 | 0.507262 | 0.253631 | − | 0.967301i | \(-0.418375\pi\) | ||||
0.253631 | + | 0.967301i | \(0.418375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.10910 | + | 0.385622i | −0.120299 | + | 0.0418266i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.9363 | 1.81576 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.32179 | 0.140110 | 0.0700550 | − | 0.997543i | \(-0.477683\pi\) | ||||
0.0700550 | + | 0.997543i | \(0.477683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.725887i | 0.0760936i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8455 | −1.12463 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.240909i | − | 0.0247168i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.36118i | 0.645880i | 0.946419 | + | 0.322940i | \(0.104671\pi\) | ||||
−0.946419 | + | 0.322940i | \(0.895329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.508802i | 0.0511365i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.83767 | 0.182855 | 0.0914275 | − | 0.995812i | \(-0.470857\pi\) | ||||
0.0914275 | + | 0.995812i | \(0.470857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.66717 | −0.952535 | −0.476267 | − | 0.879301i | \(-0.658011\pi\) | ||||
−0.476267 | + | 0.879301i | \(0.658011\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.335113i | − | 0.0327036i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.8474i | − | 1.53202i | −0.642828 | − | 0.766011i | \(-0.722239\pi\) | ||
0.642828 | − | 0.766011i | \(-0.277761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.38945i | − | 0.324650i | −0.986737 | − | 0.162325i | \(-0.948101\pi\) | ||
0.986737 | − | 0.162325i | \(-0.0518994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.1140 | −1.05489 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2698i | 1.43647i | 0.695803 | + | 0.718233i | \(0.255049\pi\) | ||||
−0.695803 | + | 0.718233i | \(0.744951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.710906 | 0.0662923 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.365934 | −0.0338306 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.51299 | + | 0.873735i | −0.230365 | + | 0.0800951i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.55355 | 0.777595 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.38089 | −0.214678 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.82483i | 0.252660i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.76464 | 0.156586 | 0.0782931 | − | 0.996930i | \(-0.475053\pi\) | ||||
0.0782931 | + | 0.996930i | \(0.475053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.89550i | 0.519070i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.57745i | − | 0.836785i | −0.908266 | − | 0.418393i | \(-0.862594\pi\) | ||
0.908266 | − | 0.418393i | \(-0.137406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.545848i | − | 0.0473310i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.38906 | −0.119551 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.59426 | −0.563385 | −0.281693 | − | 0.959505i | \(-0.590896\pi\) | ||||
−0.281693 | + | 0.959505i | \(0.590896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.3298i | 1.89399i | 0.321247 | + | 0.946995i | \(0.395898\pi\) | ||||
−0.321247 | + | 0.946995i | \(0.604102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.582894i | 0.0490885i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.75951i | − | 0.147137i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.64504 | 0.219659 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0055i | 0.990196i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.9103 | 1.54919 | 0.774595 | − | 0.632458i | \(-0.217954\pi\) | ||||
0.774595 | + | 0.632458i | \(0.217954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.21004 | −0.749502 | −0.374751 | − | 0.927125i | \(-0.622272\pi\) | ||||
−0.374751 | + | 0.927125i | \(0.622272\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.440467 | − | 1.26685i | −0.0356097 | − | 0.102419i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.69381 | −0.136050 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.0359 | 1.04038 | 0.520190 | − | 0.854051i | \(-0.325861\pi\) | ||||
0.520190 | + | 0.854051i | \(0.325861\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.60808i | − | 0.444750i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61076 | 0.126945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.99477i | 0.782851i | 0.920210 | + | 0.391425i | \(0.128018\pi\) | ||||
−0.920210 | + | 0.391425i | \(0.871982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.812292i | 0.0632369i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8575i | 1.14971i | 0.818257 | + | 0.574853i | \(0.194941\pi\) | ||||
−0.818257 | + | 0.574853i | \(0.805059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7346 | −0.902658 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.275173 | 0.0210430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.62290i | 0.503530i | 0.967788 | + | 0.251765i | \(0.0810110\pi\) | ||||
−0.967788 | + | 0.251765i | \(0.918989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.17405i | 0.239936i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.82354i | 0.137066i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.6065 | −1.91392 | −0.956960 | − | 0.290219i | \(-0.906272\pi\) | ||||
−0.956960 | + | 0.290219i | \(0.906272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.4252i | − | 1.14655i | −0.819363 | − | 0.573275i | \(-0.805673\pi\) | ||
0.819363 | − | 0.573275i | \(-0.194327\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.30533 | 0.613947 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.73574 | −0.127614 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.09133 | − | 2.11788i | 0.445442 | − | 0.154875i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.14729 | −0.228932 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2292 | −1.46373 | −0.731867 | − | 0.681447i | \(-0.761351\pi\) | ||||
−0.731867 | + | 0.681447i | \(0.761351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.2173i | − | 1.02338i | −0.859169 | − | 0.511692i | \(-0.829019\pi\) | ||
0.859169 | − | 0.511692i | \(-0.170981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.584207 | −0.0418359 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.98969i | 0.711736i | 0.934536 | + | 0.355868i | \(0.115815\pi\) | ||||
−0.934536 | + | 0.355868i | \(0.884185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.47073i | − | 0.104257i | −0.998640 | − | 0.0521286i | \(-0.983399\pi\) | ||
0.998640 | − | 0.0521286i | \(-0.0166006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.08353i | 0.640703i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.99308 | 0.420631 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.371838 | −0.0259703 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.812015i | 0.0564389i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.32310i | 0.0915208i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.98113i | − | 0.411758i | −0.978577 | − | 0.205879i | \(-0.933995\pi\) | ||
0.978577 | − | 0.205879i | \(-0.0660053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.3772 | −1.67030 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.920735i | 0.0627936i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.83779 | −0.260526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.1976 | −1.63512 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.52320 | + | 4.38093i | 0.102461 | + | 0.294693i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.7405 | −1.85764 | −0.928822 | − | 0.370527i | \(-0.879177\pi\) | ||||
−0.928822 | + | 0.370527i | \(0.879177\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.60010 | −0.106674 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6734i | 0.774793i | 0.921913 | + | 0.387396i | \(0.126625\pi\) | ||||
−0.921913 | + | 0.387396i | \(0.873375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.25514 | −0.479433 | −0.239717 | − | 0.970843i | \(-0.577055\pi\) | ||||
−0.239717 | + | 0.970843i | \(0.577055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.84048i | 0.121094i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.5248i | − | 0.886038i | −0.896512 | − | 0.443019i | \(-0.853908\pi\) | ||
0.896512 | − | 0.443019i | \(-0.146092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0910339i | 0.00593840i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.02595 | 0.196557 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.89559 | 0.187300 | 0.0936501 | − | 0.995605i | \(-0.470146\pi\) | ||||
0.0936501 | + | 0.995605i | \(0.470146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.2515i | − | 0.660356i | −0.943919 | − | 0.330178i | \(-0.892891\pi\) | ||
0.943919 | − | 0.330178i | \(-0.107109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.36619i | − | 0.215941i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.87497i | 0.119787i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.951584 | −0.0605479 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.42727i | 0.534057i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3824 | 0.844691 | 0.422345 | − | 0.906435i | \(-0.361207\pi\) | ||||
0.422345 | + | 0.906435i | \(0.361207\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.90437 | −0.245466 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.703197 | − | 2.02250i | −0.0440359 | − | 0.126654i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.1868 | 1.38397 | 0.691987 | − | 0.721910i | \(-0.256736\pi\) | ||||
0.691987 | + | 0.721910i | \(0.256736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.93280 | −0.244372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.02123i | 0.187010i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.12333 | −0.130930 | −0.0654651 | − | 0.997855i | \(-0.520853\pi\) | ||||
−0.0654651 | + | 0.997855i | \(0.520853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.875847i | − | 0.0538028i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.41034i | 0.147511i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8565i | 0.783877i | 0.919991 | + | 0.391939i | \(0.128195\pi\) | ||||
−0.919991 | + | 0.391939i | \(0.871805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.5328 | −1.55101 | −0.775504 | − | 0.631342i | \(-0.782504\pi\) | ||||
−0.775504 | + | 0.631342i | \(0.782504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.32368 | −0.0801130 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 7.69371i | − | 0.463948i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8770i | 0.953954i | 0.878916 | + | 0.476977i | \(0.158267\pi\) | ||||
−0.878916 | + | 0.476977i | \(0.841733\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.93471i | − | 0.115828i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1720 | 1.62095 | 0.810474 | − | 0.585775i | \(-0.199210\pi\) | ||||
0.810474 | + | 0.585775i | \(0.199210\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.03060i | 0.239594i | 0.992798 | + | 0.119797i | \(0.0382244\pi\) | ||||
−0.992798 | + | 0.119797i | \(0.961776\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.439308 | 0.0260224 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.842503 | −0.0497314 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3331 | + | 10.5465i | −0.784301 | + | 0.620380i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.5999 | −0.679996 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.89615 | −0.110774 | −0.0553870 | − | 0.998465i | \(-0.517639\pi\) | ||||
−0.0553870 | + | 0.998465i | \(0.517639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.284793i | 0.0165813i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.62885 | 0.442671 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2.80805i | − | 0.162394i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08618i | 0.120245i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.35107i | 0.192514i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.29709 | 0.0742712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.01367 | 0.229072 | 0.114536 | − | 0.993419i | \(-0.463462\pi\) | ||||
0.114536 | + | 0.993419i | \(0.463462\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 17.6285i | − | 1.00285i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.3227i | − | 0.755464i | −0.925915 | − | 0.377732i | \(-0.876704\pi\) | ||
0.925915 | − | 0.377732i | \(-0.123296\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.7398i | 1.28533i | 0.766147 | + | 0.642665i | \(0.222171\pi\) | ||||
−0.766147 | + | 0.642665i | \(0.777829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0597800 | 0.00336822 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.0591i | − | 1.29513i | −0.762010 | − | 0.647565i | \(-0.775787\pi\) | ||
0.762010 | − | 0.647565i | \(-0.224213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5269 | −0.813348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.8983 | 1.61294 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.14540 | − | 3.29434i | −0.0637319 | − | 0.183302i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.53337 | 0.306936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.18080 | 0.341799 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.206263i | 0.0113716i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.41739 | −0.297767 | −0.148883 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148883 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.98261i | − | 0.108646i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.41863i | 0.0775079i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.00668662i | 0.000364243i | 1.00000 | 0.000182122i | \(5.79711e-5\pi\) | |||||
−1.00000 | 0.000182122i | \(0.999942\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.8452 | −1.51234 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.30257 | 0.503763 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.76520i | 0.473276i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.29636i | 0.0697939i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.1057i | 0.757236i | 0.925553 | + | 0.378618i | \(0.123601\pi\) | ||||
−0.925553 | + | 0.378618i | \(0.876399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9796 | 1.28360 | 0.641800 | − | 0.766872i | \(-0.278188\pi\) | ||||
0.641800 | + | 0.766872i | \(0.278188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.48672i | 0.292860i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8194 | −0.788755 | −0.394378 | − | 0.918948i | \(-0.629040\pi\) | ||||
−0.394378 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.80713 | −0.202062 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.59329 | − | 4.58253i | −0.0843259 | − | 0.242533i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1611 | −0.747393 | −0.373697 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373697 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2844 | −0.962339 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.5977i | 0.818669i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.77908 | −0.197806 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.8046i | − | 0.720596i | −0.932837 | − | 0.360298i | \(-0.882675\pi\) | ||
0.932837 | − | 0.360298i | \(-0.117325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.424723i | − | 0.0221102i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.98448i | − | 0.103029i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.7891 | 1.80131 | 0.900655 | − | 0.434534i | \(-0.143087\pi\) | ||||
0.900655 | + | 0.434534i | \(0.143087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.15119 | −0.266006 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.4478i | − | 0.538090i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.91747i | 0.509426i | 0.967017 | + | 0.254713i | \(0.0819810\pi\) | ||||
−0.967017 | + | 0.254713i | \(0.918019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.21788i | 0.164857i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4705 | 1.45477 | 0.727386 | − | 0.686228i | \(-0.240735\pi\) | ||||
0.727386 | + | 0.686228i | \(0.240735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.287438i | 0.0146492i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.05169 | −0.0534602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.3610 | −1.69147 | −0.845734 | − | 0.533604i | \(-0.820837\pi\) | ||||
−0.845734 | + | 0.533604i | \(0.820837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.72135 | − | 3.38000i | 0.491630 | − | 0.170934i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4649 | 0.880985 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.472580 | 0.0237781 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.4188i | − | 0.673472i | −0.941599 | − | 0.336736i | \(-0.890677\pi\) | ||
0.941599 | − | 0.336736i | \(-0.109323\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.995375 | 0.0498311 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 35.3351i | − | 1.76455i | −0.470734 | − | 0.882275i | \(-0.656011\pi\) | ||
0.470734 | − | 0.882275i | \(-0.343989\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.69048i | 0.333277i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 2.81093i | − | 0.139676i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.53287 | 0.472527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.4471 | 1.25828 | 0.629139 | − | 0.777293i | \(-0.283407\pi\) | ||||
0.629139 | + | 0.777293i | \(0.283407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 12.0249i | − | 0.593144i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.645277i | 0.0317520i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.31614i | 0.0646066i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.7193 | −1.99403 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.0810i | 1.22529i | 0.790360 | + | 0.612643i | \(0.209894\pi\) | ||||
−0.790360 | + | 0.612643i | \(0.790106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.09469 | 0.150826 | 0.0754131 | − | 0.997152i | \(-0.475972\pi\) | ||||
0.0754131 | + | 0.997152i | \(0.475972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.103981 | −0.00505574 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.66040 | + | 19.1563i | 0.323077 | + | 0.929216i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93892 | 0.142224 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.20853 | 0.154909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.19055i | 0.298189i | 0.988823 | + | 0.149094i | \(0.0476358\pi\) | ||||
−0.988823 | + | 0.149094i | \(0.952364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.71795 | −0.130616 | −0.0653081 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653081 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.82334i | 0.231261i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.11158i | 0.101011i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.8137i | 0.945658i | 0.881154 | + | 0.472829i | \(0.156767\pi\) | ||||
−0.881154 | + | 0.472829i | \(0.843233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.14163 | −0.101983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.6289 | 1.36020 | 0.680101 | − | 0.733118i | \(-0.261936\pi\) | ||||
0.680101 | + | 0.733118i | \(0.261936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.376437i | 0.0178448i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.4836i | 1.63102i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.7766i | − | 1.07489i | −0.843298 | − | 0.537447i | \(-0.819389\pi\) | ||
0.843298 | − | 0.537447i | \(-0.180611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.04218 | 0.0961623 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 16.7949i | − | 0.789092i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.206727 | −0.00969153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1381 | −1.22269 | −0.611345 | − | 0.791364i | \(-0.709371\pi\) | ||||
−0.611345 | + | 0.791364i | \(0.709371\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.9948 | + | 6.60426i | −0.886600 | + | 0.308260i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.1242 | −1.21672 | −0.608362 | − | 0.793660i | \(-0.708173\pi\) | ||||
−0.608362 | + | 0.793660i | \(0.708173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0320 | −0.930964 | −0.465482 | − | 0.885057i | \(-0.654119\pi\) | ||||
−0.465482 | + | 0.885057i | \(0.654119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3.08872i | − | 0.143236i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.7634 | −1.00709 | −0.503544 | − | 0.863970i | \(-0.667971\pi\) | ||||
−0.503544 | + | 0.863970i | \(0.667971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.21430i | 0.148422i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.7715i | 1.09533i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.05678i | − | 0.232511i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.16095 | −0.190917 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.00041 | 0.0458058 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 7.90053i | − | 0.360984i | −0.983576 | − | 0.180492i | \(-0.942231\pi\) | ||
0.983576 | − | 0.180492i | \(-0.0577691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.85611i | 0.312612i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.93728i | 0.133651i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.81162 | −0.0822613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.6887i | 0.574979i | 0.957784 | + | 0.287489i | \(0.0928206\pi\) | ||||
−0.957784 | + | 0.287489i | \(0.907179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.2259 | −0.824202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8725 | 1.25787 | 0.628934 | − | 0.777459i | \(-0.283492\pi\) | ||||
0.628934 | + | 0.777459i | \(0.283492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.1699 | − | 12.5758i | 1.62901 | − | 0.566387i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.144903 | −0.00651291 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.62613 | −0.386935 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.1286i | − | 0.811546i | −0.913974 | − | 0.405773i | \(-0.867002\pi\) | ||
0.913974 | − | 0.405773i | \(-0.132998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0932 | −1.21043 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 37.0824i | − | 1.65342i | −0.562628 | − | 0.826710i | \(-0.690210\pi\) | ||
0.562628 | − | 0.826710i | \(-0.309790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.523355i | 0.0232890i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 21.3984i | − | 0.950337i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6485 | 0.782257 | 0.391129 | − | 0.920336i | \(-0.372085\pi\) | ||||
0.391129 | + | 0.920336i | \(0.372085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.56255 | −0.378785 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.12587i | − | 0.182162i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 2.75314i | − | 0.121318i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.499968i | − | 0.0219886i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0771 | −0.530127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.6418i | − | 1.29863i | −0.760520 | − | 0.649315i | \(-0.775056\pi\) | ||
0.760520 | − | 0.649315i | \(-0.224944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1883 | 1.36377 | 0.681884 | − | 0.731460i | \(-0.261161\pi\) | ||||
0.681884 | + | 0.731460i | \(0.261161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.78801 | −0.252609 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.1621 | + | 8.05319i | −1.00896 | + | 0.350802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.7689 | 0.729082 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.325298 | −0.0141167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.46875i | 0.0636185i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.51321 | 0.195123 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 46.6945i | − | 2.01502i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.2975i | − | 0.443546i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3276i | 1.73382i | 0.498466 | + | 0.866909i | \(0.333897\pi\) | ||||
−0.498466 | + | 0.866909i | \(0.666103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.1286 | 1.20711 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.965291 | 0.0413485 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.7138i | 1.44150i | 0.693196 | + | 0.720749i | \(0.256202\pi\) | ||||
−0.693196 | + | 0.720749i | \(0.743798\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.48157i | 0.0632319i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.85648i | 0.334697i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07076 | 0.0455334 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3.16519i | − | 0.134355i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.16460 | −0.0917171 | −0.0458586 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458586 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.63687 | 0.153823 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.86204 | + | 11.1078i | 0.163055 | + | 0.468971i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.2368 | 1.19004 | 0.595020 | − | 0.803711i | \(-0.297144\pi\) | ||||
0.595020 | + | 0.803711i | \(0.297144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.34874 | −0.182953 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 6.36894i | − | 0.267470i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.10346 | −0.0462596 | −0.0231298 | − | 0.999732i | \(-0.507363\pi\) | ||||
−0.0231298 | + | 0.999732i | \(0.507363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 25.9942i | − | 1.08782i | −0.839143 | − | 0.543911i | \(-0.816943\pi\) | ||
0.839143 | − | 0.543911i | \(-0.183057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 36.8888i | − | 1.54105i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 12.2786i | − | 0.512055i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6580 | 0.568588 | 0.284294 | − | 0.958737i | \(-0.408241\pi\) | ||||
0.284294 | + | 0.958737i | \(0.408241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.9258 | 1.07744 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.98207i | 0.123717i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.81025i | 0.199220i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.104215i | − | 0.00430878i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2472 | 0.959514 | 0.479757 | − | 0.877401i | \(-0.340725\pi\) | ||||
0.479757 | + | 0.877401i | \(0.340725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.03106i | − | 0.207301i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2166 | −0.749330 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.9531 | −1.64068 | −0.820338 | − | 0.571879i | \(-0.806215\pi\) | ||||
−0.820338 | + | 0.571879i | \(0.806215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.248833 | − | 0.715680i | −0.0102012 | − | 0.0293400i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.68193 | 0.109764 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.7706 | 1.91100 | 0.955498 | − | 0.294998i | \(-0.0953189\pi\) | ||||
0.955498 | + | 0.294998i | \(0.0953189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.0432i | − | 0.491252i | −0.969365 | − | 0.245626i | \(-0.921007\pi\) | ||
0.969365 | − | 0.245626i | \(-0.0789935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.62039 | −0.0659875 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.43599i | 0.0990370i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.1246i | − | 0.410945i | −0.978663 | − | 0.205472i | \(-0.934127\pi\) | ||
0.978663 | − | 0.205472i | \(-0.0658730\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.9286i | 0.442850i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.359581 | 0.0145471 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.63880 | 0.146970 | 0.0734848 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734848 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.678061i | − | 0.0273421i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.4331i | 0.701829i | 0.936407 | + | 0.350915i | \(0.114129\pi\) | ||||
−0.936407 | + | 0.350915i | \(0.885871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.8289i | 0.515638i | 0.966193 | + | 0.257819i | \(0.0830038\pi\) | ||||
−0.966193 | + | 0.257819i | \(0.916996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.1751 | 0.488571 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.852924i | 0.0341717i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.7900 | 0.951599 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.41273 | −0.0963551 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.7355 | + | 8.25256i | −0.946398 | + | 0.329051i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7859 | 0.907091 | 0.453546 | − | 0.891233i | \(-0.350159\pi\) | ||||
0.453546 | + | 0.891233i | \(0.350159\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.9068 | 0.433507 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.502556i | 0.0199433i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.40606 | 0.293439 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.34861i | − | 0.172028i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.0217i | − | 1.10679i | −0.832919 | − | 0.553396i | \(-0.813332\pi\) | ||
0.832919 | − | 0.553396i | \(-0.186668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2975i | 0.761018i | 0.924777 | + | 0.380509i | \(0.124251\pi\) | ||||
−0.924777 | + | 0.380509i | \(0.875749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.67900 | −0.0661104 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3721 | −0.761597 | −0.380798 | − | 0.924658i | \(-0.624351\pi\) | ||||
−0.380798 | + | 0.924658i | \(0.624351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.56411i | − | 0.0613968i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 6.99836i | − | 0.274288i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8464i | 0.463587i | 0.972765 | + | 0.231794i | \(0.0744594\pi\) | ||||
−0.972765 | + | 0.231794i | \(0.925541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.72759 | 0.106576 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.31656i | − | 0.168405i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.9559 | −0.465737 | −0.232869 | − | 0.972508i | \(-0.574811\pi\) | ||||
−0.232869 | + | 0.972508i | \(0.574811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9669 | 0.737727 | 0.368863 | − | 0.929484i | \(-0.379747\pi\) | ||||
0.368863 | + | 0.929484i | \(0.379747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.98880 | + | 2.77761i | −0.310259 | + | 0.107873i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.155453 | 0.00602823 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.1839 | −0.897684 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 50.5860i | − | 1.95577i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.12377 | −0.275010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 25.6384i | − | 0.988287i | −0.869380 | − | 0.494144i | \(-0.835482\pi\) | ||
0.869380 | − | 0.494144i | \(-0.164518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 23.9915i | 0.923435i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.12360i | − | 0.196916i | −0.995141 | − | 0.0984580i | \(-0.968609\pi\) | ||
0.995141 | − | 0.0984580i | \(-0.0313910\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.10473 | −0.157525 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.2870 | −0.815718 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 23.8909i | − | 0.914162i | −0.889425 | − | 0.457081i | \(-0.848895\pi\) | ||
0.889425 | − | 0.457081i | \(-0.151105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.87800i | − | 0.0717546i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 13.2300i | − | 0.504758i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.45957 | −0.131799 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.91390i | 0.186934i | 0.995622 | + | 0.0934668i | \(0.0297949\pi\) | ||||
−0.995622 | + | 0.0934668i | \(0.970205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.328319 | −0.0124718 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.35937 | −0.241225 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.08474 | + | 1.76790i | −0.192598 | + | 0.0669640i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.6630 | 0.932839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.7046 | 1.34855 | 0.674273 | − | 0.738482i | \(-0.264457\pi\) | ||||
0.674273 | + | 0.738482i | \(0.264457\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.15561i | − | 0.194448i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.166004 | −0.00625207 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.18581i | 0.0445969i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.96839i | 0.261703i | 0.991402 | + | 0.130852i | \(0.0417712\pi\) | ||||
−0.991402 | + | 0.130852i | \(0.958229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.539793i | 0.0202438i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.8463 | 0.555998 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.501094 | 0.0187399 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.28023i | 0.197194i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.3544i | 0.796383i | 0.917302 | + | 0.398192i | \(0.130362\pi\) | ||||
−0.917302 | + | 0.398192i | \(0.869638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.23801i | − | 0.232316i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.6940 | 0.695237 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 45.6847i | − | 1.69669i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0508 | 0.632378 | 0.316189 | − | 0.948696i | \(-0.397597\pi\) | ||||
0.316189 | + | 0.948696i | \(0.397597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4718 | −0.869327 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.37763 | + | 12.5907i | 0.161912 | + | 0.465683i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8717 | 1.21414 | 0.607072 | − | 0.794647i | \(-0.292344\pi\) | ||||
0.607072 | + | 0.794647i | \(0.292344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.41908 | −0.126115 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.79126i | − | 0.286995i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.33927 | 0.343551 | 0.171775 | − | 0.985136i | \(-0.445050\pi\) | ||||
0.171775 | + | 0.985136i | \(0.445050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.73525i | − | 0.0637461i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.7678i | − | 0.505092i | −0.967585 | − | 0.252546i | \(-0.918732\pi\) | ||
0.967585 | − | 0.252546i | \(-0.0812679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.38551i | 0.197310i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50332 | −0.0550037 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2259 | 0.373648 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.6064i | − | 0.642467i | −0.947000 | − | 0.321233i | \(-0.895903\pi\) | ||
0.947000 | − | 0.321233i | \(-0.104097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.4034i | 0.889308i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.62295i | − | 0.0954590i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4997 | 0.817764 | 0.408882 | − | 0.912587i | \(-0.365919\pi\) | ||||
0.408882 | + | 0.912587i | \(0.365919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 7.11978i | − | 0.258432i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3751 | 0.883597 | 0.441798 | − | 0.897114i | \(-0.354341\pi\) | ||||
0.441798 | + | 0.897114i | \(0.354341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.18714 | 0.0791796 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.360789 | − | 0.125442i | 0.0130444 | − | 0.00453536i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.12492 | 0.0406186 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6146 | 1.06793 | 0.533965 | − | 0.845507i | \(-0.320702\pi\) | ||||
0.533965 | + | 0.845507i | \(0.320702\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.4585i | 1.45708i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.6428 | 1.74956 | 0.874781 | − | 0.484519i | \(-0.161005\pi\) | ||||
0.874781 | + | 0.484519i | \(0.161005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.2551i | 1.05088i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.17162i | − | 0.257280i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.10446i | − | 0.0395714i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.9092 | 0.748190 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.2996 | 1.61887 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.71253i | 0.132506i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3538i | 0.476012i | 0.971264 | + | 0.238006i | \(0.0764938\pi\) | ||||
−0.971264 | + | 0.238006i | \(0.923506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.87198i | − | 0.137846i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.85328 | −0.350342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.12347i | − | 0.181940i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.59714 | 0.0566448 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0532 | 0.604056 | 0.302028 | − | 0.953299i | \(-0.402336\pi\) | ||||
0.302028 | + | 0.953299i | \(0.402336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.432820 | + | 1.24485i | 0.0153121 | + | 0.0440397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.429976 | −0.0151925 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.7551 | 0.732432 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.458731i | 0.0161682i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.4444 | −0.825283 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.5820i | 0.723626i | 0.932251 | + | 0.361813i | \(0.117842\pi\) | ||||
−0.932251 | + | 0.361813i | \(0.882158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40.3759i | − | 1.41779i | −0.705315 | − | 0.708894i | \(-0.749194\pi\) | ||
0.705315 | − | 0.708894i | \(-0.250806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 46.5601i | − | 1.63294i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.84644 | −0.0997064 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73483 | −0.0956796 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 0.236129i | − | 0.00825102i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 35.5729i | − | 1.24150i | −0.784007 | − | 0.620752i | \(-0.786827\pi\) | ||
0.784007 | − | 0.620752i | \(-0.213173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4197i | 0.990648i | 0.868708 | + | 0.495324i | \(0.164951\pi\) | ||||
−0.868708 | + | 0.495324i | \(0.835049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.0298 | 0.488454 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.5000i | − | 0.608534i | −0.952587 | − | 0.304267i | \(-0.901588\pi\) | ||
0.952587 | − | 0.304267i | \(-0.0984116\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.8924 | 0.760354 | 0.380177 | − | 0.924914i | \(-0.375863\pi\) | ||||
0.380177 | + | 0.924914i | \(0.375863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.9523 | −1.00434 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.91451 | + | 25.6394i | 0.308870 | + | 0.888353i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.23130 | −0.146430 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.0085 | −1.00268 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40.6379i | − | 1.40298i | −0.712681 | − | 0.701489i | \(-0.752519\pi\) | ||
0.712681 | − | 0.701489i | \(-0.247481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −57.2594 | −1.97446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49.5493i | 1.70657i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.34191i | − | 0.114965i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.51941i | 0.189649i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.34995 | −0.252250 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2138 | 0.521523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.8928i | − | 0.783835i | −0.920000 | − | 0.391918i | \(-0.871812\pi\) | ||
0.920000 | − | 0.391918i | \(-0.128188\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0783672i | 0.00268010i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.50036i | 0.290367i | 0.989405 | + | 0.145183i | \(0.0463772\pi\) | ||||
−0.989405 | + | 0.145183i | \(0.953623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.9059 | −1.70277 | −0.851383 | − | 0.524545i | \(-0.824236\pi\) | ||||
−0.851383 | + | 0.524545i | \(0.824236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 1.53634i | − | 0.0523582i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0287 | −0.817945 | −0.408972 | − | 0.912547i | \(-0.634113\pi\) | ||||
−0.408972 | + | 0.912547i | \(0.634113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.88615 | −0.0641312 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.2319 | − | 24.3135i | −0.653149 | − | 0.825729i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.59546 | −0.0880451 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.60353 | 0.189868 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.06928i | − | 0.0700344i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.82280 | −0.0616218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.1739i | 0.917598i | 0.888540 | + | 0.458799i | \(0.151720\pi\) | ||||
−0.888540 | + | 0.458799i | \(0.848280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.45770i | − | 0.116625i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.53835i | 0.220283i | 0.993916 | + | 0.110141i | \(0.0351303\pi\) | ||||
−0.993916 | + | 0.110141i | \(0.964870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.8594 | −0.500060 | −0.250030 | − | 0.968238i | \(-0.580440\pi\) | ||||
−0.250030 | + | 0.968238i | \(0.580440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.519331 | −0.0174571 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.2486i | − | 0.982070i | −0.871140 | − | 0.491035i | \(-0.836619\pi\) | ||
0.871140 | − | 0.491035i | \(-0.163381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13868i | 0.0381901i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4379i | 0.517190i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.270395 | −0.00904843 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.29255i | − | 0.243763i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.12060 | 0.170972 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.2380 | 1.84229 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.16421 | − | 11.9769i | −0.138730 | − | 0.399007i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.80423 | −0.126597 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.39300 | 0.146028 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.1311i | − | 1.29933i | −0.760222 | − | 0.649664i | \(-0.774910\pi\) | ||
0.760222 | − | 0.649664i | \(-0.225090\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.597790 | −0.0198274 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27.5613i | − | 0.913146i | −0.889686 | − | 0.456573i | \(-0.849077\pi\) | ||
0.889686 | − | 0.456573i | \(-0.150923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.22836i | − | 0.239224i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.36530i | 0.0781943i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.18011 | 0.204085 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.4456 | 0.377557 | 0.188778 | − | 0.982020i | \(-0.439547\pi\) | ||||
0.188778 | + | 0.982020i | \(0.439547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.31909i | 0.241172i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.0381i | 0.494984i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.9794i | 0.985716i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.14471 | 0.103286 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 22.6214i | − | 0.742185i | −0.928596 | − | 0.371092i | \(-0.878983\pi\) | ||
0.928596 | − | 0.371092i | \(-0.121017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.56916 | −0.182522 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.2946 | 0.795368 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.603157 | + | 1.73477i | 0.0197253 | + | 0.0567329i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.4168 | −0.536313 | −0.268156 | − | 0.963375i | \(-0.586414\pi\) | ||||
−0.268156 | + | 0.963375i | \(0.586414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.4669 | −1.35322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 25.1873i | − | 0.821083i | −0.911842 | − | 0.410541i | \(-0.865340\pi\) | ||
0.911842 | − | 0.410541i | \(-0.134660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.25918 | 0.106133 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.896326i | − | 0.0291575i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 44.7188i | − | 1.45317i | −0.687079 | − | 0.726583i | \(-0.741107\pi\) | ||
0.687079 | − | 0.726583i | \(-0.258893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.9272i | 0.484558i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.0493 | 1.36354 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.2106 | 1.01101 | 0.505505 | − | 0.862824i | \(-0.331306\pi\) | ||||
0.505505 | + | 0.862824i | \(0.331306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.76113i | − | 0.186426i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26.4903i | − | 0.856310i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 4.25513i | − | 0.137405i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.37281 | −0.141059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.15510i | 0.166121i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.04899 | 0.130341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.3363 | −1.23281 | −0.616405 | − | 0.787429i | \(-0.711412\pi\) | ||||
−0.616405 | + | 0.787429i | \(0.711412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00736 | − | 2.08869i | 0.192984 | − | 0.0670983i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.73616 | 0.0878077 | 0.0439039 | − | 0.999036i | \(-0.486020\pi\) | ||||
0.0439039 | + | 0.999036i | \(0.486020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4089 | −0.461929 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.0903i | 0.323149i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.74239 | 0.183715 | 0.0918577 | − | 0.995772i | \(-0.470720\pi\) | ||||
0.0918577 | + | 0.995772i | \(0.470720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.06744i | − | 0.0660756i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.10258i | 0.0352027i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.59156i | 0.114553i | 0.998358 | + | 0.0572764i | \(0.0182416\pi\) | ||||
−0.998358 | + | 0.0572764i | \(0.981758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.84499 | −0.0906489 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.376128 | −0.0119723 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 8.07028i | − | 0.256620i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 19.4482i | − | 0.617792i | −0.951096 | − | 0.308896i | \(-0.900040\pi\) | ||
0.951096 | − | 0.308896i | \(-0.0999595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.87882i | − | 0.313495i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.418853 | 0.0132785 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 21.8618i | − | 0.692369i | −0.938167 | − | 0.346184i | \(-0.887477\pi\) | ||
0.938167 | − | 0.346184i | \(-0.112523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.7267 | −0.940510 |
(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 | 4012.2.b.b.237.37 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.10 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.10 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.37 | yes | 46 | 1.1 | even | 1 | trivial |