Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (of order \(4\), degree \(2\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.4 | ||
Root | \(-0.222191i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.265 |
Dual form | 546.2.o.b.307.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.864220 | + | 0.864220i | 0.386491 | + | 0.386491i | 0.873434 | − | 0.486943i | \(-0.161888\pi\) |
−0.486943 | + | 0.873434i | \(0.661888\pi\) | |||||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −2.02133 | − | 1.70711i | −0.763992 | − | 0.645226i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.22219 | 0.386491 | ||||||||
\(11\) | −3.50062 | − | 3.50062i | −1.05548 | − | 1.05548i | −0.998368 | − | 0.0571102i | \(-0.981811\pi\) |
−0.0571102 | − | 0.998368i | \(-0.518189\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.37930 | − | 1.25710i | 0.937250 | − | 0.348657i | ||||
\(14\) | −2.63640 | + | 0.222191i | −0.704609 | + | 0.0593831i | ||||
\(15\) | 0.864220 | − | 0.864220i | 0.223141 | − | 0.223141i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.322179 | −0.0781399 | −0.0390699 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390699 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −1.77219 | − | 1.77219i | −0.406567 | − | 0.406567i | 0.473972 | − | 0.880540i | \(-0.342820\pi\) |
−0.880540 | + | 0.473972i | \(0.842820\pi\) | |||||||
\(20\) | 0.864220 | − | 0.864220i | 0.193245 | − | 0.193245i | ||||
\(21\) | −1.70711 | + | 2.02133i | −0.372521 | + | 0.441091i | ||||
\(22\) | −4.95063 | −1.05548 | ||||||||
\(23\) | − | 2.70799i | − | 0.564655i | −0.959318 | − | 0.282328i | \(-0.908894\pi\) | ||
0.959318 | − | 0.282328i | \(-0.0911065\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | − | 3.50625i | − | 0.701250i | ||||||
\(26\) | 1.50062 | − | 3.27843i | 0.294297 | − | 0.642954i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.70711 | + | 2.02133i | −0.322613 | + | 0.381996i | ||||
\(29\) | 4.82047 | 0.895140 | 0.447570 | − | 0.894249i | \(-0.352290\pi\) | ||||
0.447570 | + | 0.894249i | \(0.352290\pi\) | |||||||
\(30\) | − | 1.22219i | − | 0.223141i | ||||||
\(31\) | 1.72844 | + | 1.72844i | 0.310437 | + | 0.310437i | 0.845079 | − | 0.534642i | \(-0.179553\pi\) |
−0.534642 | + | 0.845079i | \(0.679553\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.50062 | + | 3.50062i | −0.609381 | + | 0.609381i | ||||
\(34\) | −0.227815 | + | 0.227815i | −0.0390699 | + | 0.0390699i | ||||
\(35\) | −0.271560 | − | 3.22219i | −0.0459021 | − | 0.544650i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 2.27843 | + | 2.27843i | 0.374572 | + | 0.374572i | 0.869139 | − | 0.494567i | \(-0.164673\pi\) |
−0.494567 | + | 0.869139i | \(0.664673\pi\) | |||||||
\(38\) | −2.50625 | −0.406567 | ||||||||
\(39\) | −1.25710 | − | 3.37930i | −0.201297 | − | 0.541122i | ||||
\(40\) | − | 1.22219i | − | 0.193245i | ||||||
\(41\) | 6.46483 | + | 6.46483i | 1.00964 | + | 1.00964i | 0.999953 | + | 0.00968403i | \(0.00308257\pi\) |
0.00968403 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(42\) | 0.222191 | + | 2.63640i | 0.0342849 | + | 0.406806i | ||||
\(43\) | 0.393764i | 0.0600485i | 0.999549 | + | 0.0300242i | \(0.00955845\pi\) | ||||
−0.999549 | + | 0.0300242i | \(0.990442\pi\) | |||||||
\(44\) | −3.50062 | + | 3.50062i | −0.527739 | + | 0.527739i | ||||
\(45\) | −0.864220 | − | 0.864220i | −0.128830 | − | 0.128830i | ||||
\(46\) | −1.91484 | − | 1.91484i | −0.282328 | − | 0.282328i | ||||
\(47\) | −1.41421 | + | 1.41421i | −0.206284 | + | 0.206284i | −0.802686 | − | 0.596402i | \(-0.796597\pi\) |
0.596402 | + | 0.802686i | \(0.296597\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 1.17157 | + | 6.90126i | 0.167368 | + | 0.985895i | ||||
\(50\) | −2.47929 | − | 2.47929i | −0.350625 | − | 0.350625i | ||||
\(51\) | 0.322179i | 0.0451141i | ||||||||
\(52\) | −1.25710 | − | 3.37930i | −0.174328 | − | 0.468625i | ||||
\(53\) | −2.03142 | −0.279037 | −0.139518 | − | 0.990219i | \(-0.544555\pi\) | ||||
−0.139518 | + | 0.990219i | \(0.544555\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | − | 6.05062i | − | 0.815865i | ||||||
\(56\) | 0.222191 | + | 2.63640i | 0.0296916 | + | 0.352304i | ||||
\(57\) | −1.77219 | + | 1.77219i | −0.234732 | + | 0.234732i | ||||
\(58\) | 3.40859 | − | 3.40859i | 0.447570 | − | 0.447570i | ||||
\(59\) | −10.7599 | + | 10.7599i | −1.40081 | + | 1.40081i | −0.603300 | + | 0.797515i | \(0.706148\pi\) |
−0.797515 | + | 0.603300i | \(0.793852\pi\) | |||||||
\(60\) | −0.864220 | − | 0.864220i | −0.111570 | − | 0.111570i | ||||
\(61\) | − | 10.6389i | − | 1.36217i | −0.732203 | − | 0.681086i | \(-0.761508\pi\) | ||
0.732203 | − | 0.681086i | \(-0.238492\pi\) | |||||||
\(62\) | 2.44438 | 0.310437 | ||||||||
\(63\) | 2.02133 | + | 1.70711i | 0.254664 | + | 0.215075i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 4.00687 | + | 1.83405i | 0.496991 | + | 0.227486i | ||||
\(66\) | 4.95063i | 0.609381i | ||||||||
\(67\) | 5.38404 | − | 5.38404i | 0.657766 | − | 0.657766i | −0.297085 | − | 0.954851i | \(-0.596015\pi\) |
0.954851 | + | 0.297085i | \(0.0960146\pi\) | |||||||
\(68\) | 0.322179i | 0.0390699i | ||||||||
\(69\) | −2.70799 | −0.326004 | ||||||||
\(70\) | −2.47046 | − | 2.08641i | −0.295276 | − | 0.249374i | ||||
\(71\) | −0.647652 | + | 0.647652i | −0.0768621 | + | 0.0768621i | −0.744493 | − | 0.667631i | \(-0.767309\pi\) |
0.667631 | + | 0.744493i | \(0.267309\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.85297 | − | 6.85297i | 0.802080 | − | 0.802080i | −0.181341 | − | 0.983420i | \(-0.558044\pi\) |
0.983420 | + | 0.181341i | \(0.0580436\pi\) | |||||||
\(74\) | 3.22219 | 0.374572 | ||||||||
\(75\) | −3.50625 | −0.404867 | ||||||||
\(76\) | −1.77219 | + | 1.77219i | −0.203284 | + | 0.203284i | ||||
\(77\) | 1.09999 | + | 13.0519i | 0.125355 | + | 1.48740i | ||||
\(78\) | −3.27843 | − | 1.50062i | −0.371209 | − | 0.169912i | ||||
\(79\) | 8.81718 | 0.992010 | 0.496005 | − | 0.868320i | \(-0.334800\pi\) | ||||
0.496005 | + | 0.868320i | \(0.334800\pi\) | |||||||
\(80\) | −0.864220 | − | 0.864220i | −0.0966227 | − | 0.0966227i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.14265 | 1.00964 | ||||||||
\(83\) | 6.09203 | + | 6.09203i | 0.668688 | + | 0.668688i | 0.957412 | − | 0.288725i | \(-0.0932312\pi\) |
−0.288725 | + | 0.957412i | \(0.593231\pi\) | |||||||
\(84\) | 2.02133 | + | 1.70711i | 0.220545 | + | 0.186261i | ||||
\(85\) | −0.278433 | − | 0.278433i | −0.0302003 | − | 0.0302003i | ||||
\(86\) | 0.278433 | + | 0.278433i | 0.0300242 | + | 0.0300242i | ||||
\(87\) | − | 4.82047i | − | 0.516809i | ||||||
\(88\) | 4.95063i | 0.527739i | ||||||||
\(89\) | −3.68702 | + | 3.68702i | −0.390824 | + | 0.390824i | −0.874981 | − | 0.484157i | \(-0.839126\pi\) |
0.484157 | + | 0.874981i | \(0.339126\pi\) | |||||||
\(90\) | −1.22219 | −0.128830 | ||||||||
\(91\) | −8.97670 | − | 3.22781i | −0.941014 | − | 0.338367i | ||||
\(92\) | −2.70799 | −0.282328 | ||||||||
\(93\) | 1.72844 | − | 1.72844i | 0.179231 | − | 0.179231i | ||||
\(94\) | 2.00000i | 0.206284i | ||||||||
\(95\) | − | 3.06311i | − | 0.314269i | ||||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | −5.20299 | − | 5.20299i | −0.528284 | − | 0.528284i | 0.391777 | − | 0.920060i | \(-0.371861\pi\) |
−0.920060 | + | 0.391777i | \(0.871861\pi\) | |||||||
\(98\) | 5.70836 | + | 4.05150i | 0.576631 | + | 0.409264i | ||||
\(99\) | 3.50062 | + | 3.50062i | 0.351826 | + | 0.351826i | ||||
\(100\) | −3.50625 | −0.350625 | ||||||||
\(101\) | 7.82968 | 0.779082 | 0.389541 | − | 0.921009i | \(-0.372634\pi\) | ||||
0.389541 | + | 0.921009i | \(0.372634\pi\) | |||||||
\(102\) | 0.227815 | + | 0.227815i | 0.0225570 | + | 0.0225570i | ||||
\(103\) | 14.8501 | 1.46323 | 0.731613 | − | 0.681720i | \(-0.238768\pi\) | ||||
0.731613 | + | 0.681720i | \(0.238768\pi\) | |||||||
\(104\) | −3.27843 | − | 1.50062i | −0.321477 | − | 0.147148i | ||||
\(105\) | −3.22219 | + | 0.271560i | −0.314454 | + | 0.0265016i | ||||
\(106\) | −1.43643 | + | 1.43643i | −0.139518 | + | 0.139518i | ||||
\(107\) | 13.8184 | 1.33588 | 0.667939 | − | 0.744216i | \(-0.267177\pi\) | ||||
0.667939 | + | 0.744216i | \(0.267177\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 5.19435 | − | 5.19435i | 0.497529 | − | 0.497529i | −0.413139 | − | 0.910668i | \(-0.635568\pi\) |
0.910668 | + | 0.413139i | \(0.135568\pi\) | |||||||
\(110\) | −4.27843 | − | 4.27843i | −0.407933 | − | 0.407933i | ||||
\(111\) | 2.27843 | − | 2.27843i | 0.216259 | − | 0.216259i | ||||
\(112\) | 2.02133 | + | 1.70711i | 0.190998 | + | 0.161306i | ||||
\(113\) | 3.41598 | 0.321348 | 0.160674 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160674 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(114\) | 2.50625i | 0.234732i | ||||||||
\(115\) | 2.34030 | − | 2.34030i | 0.218234 | − | 0.218234i | ||||
\(116\) | − | 4.82047i | − | 0.447570i | ||||||
\(117\) | −3.37930 | + | 1.25710i | −0.312417 | + | 0.116219i | ||||
\(118\) | 15.2167i | 1.40081i | ||||||||
\(119\) | 0.651231 | + | 0.549994i | 0.0596982 | + | 0.0504178i | ||||
\(120\) | −1.22219 | −0.111570 | ||||||||
\(121\) | 13.5087i | 1.22807i | ||||||||
\(122\) | −7.52284 | − | 7.52284i | −0.681086 | − | 0.681086i | ||||
\(123\) | 6.46483 | − | 6.46483i | 0.582914 | − | 0.582914i | ||||
\(124\) | 1.72844 | − | 1.72844i | 0.155218 | − | 0.155218i | ||||
\(125\) | 7.35127 | − | 7.35127i | 0.657517 | − | 0.657517i | ||||
\(126\) | 2.63640 | − | 0.222191i | 0.234870 | − | 0.0197944i | ||||
\(127\) | 9.70595i | 0.861263i | 0.902528 | + | 0.430632i | \(0.141709\pi\) | ||||
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0.393764 | 0.0346690 | ||||||||
\(130\) | 4.13016 | − | 1.53642i | 0.362239 | − | 0.134753i | ||||
\(131\) | 18.3963i | 1.60729i | 0.595110 | + | 0.803644i | \(0.297109\pi\) | ||||
−0.595110 | + | 0.803644i | \(0.702891\pi\) | |||||||
\(132\) | 3.50062 | + | 3.50062i | 0.304690 | + | 0.304690i | ||||
\(133\) | 0.556867 | + | 6.60749i | 0.0482865 | + | 0.572942i | ||||
\(134\) | − | 7.61419i | − | 0.657766i | ||||||
\(135\) | −0.864220 | + | 0.864220i | −0.0743802 | + | 0.0743802i | ||||
\(136\) | 0.227815 | + | 0.227815i | 0.0195350 | + | 0.0195350i | ||||
\(137\) | −1.93705 | − | 1.93705i | −0.165494 | − | 0.165494i | 0.619502 | − | 0.784995i | \(-0.287335\pi\) |
−0.784995 | + | 0.619502i | \(0.787335\pi\) | |||||||
\(138\) | −1.91484 | + | 1.91484i | −0.163002 | + | 0.163002i | ||||
\(139\) | − | 15.4569i | − | 1.31104i | −0.755180 | − | 0.655518i | \(-0.772450\pi\) | ||
0.755180 | − | 0.655518i | \(-0.227550\pi\) | |||||||
\(140\) | −3.22219 | + | 0.271560i | −0.272325 | + | 0.0229510i | ||||
\(141\) | 1.41421 | + | 1.41421i | 0.119098 | + | 0.119098i | ||||
\(142\) | 0.915918i | 0.0768621i | ||||||||
\(143\) | −16.2303 | − | 7.42904i | −1.35725 | − | 0.621247i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.16595 | + | 4.16595i | 0.345963 | + | 0.345963i | ||||
\(146\) | − | 9.69157i | − | 0.802080i | ||||||
\(147\) | 6.90126 | − | 1.17157i | 0.569206 | − | 0.0966297i | ||||
\(148\) | 2.27843 | − | 2.27843i | 0.187286 | − | 0.187286i | ||||
\(149\) | −3.16185 | + | 3.16185i | −0.259029 | + | 0.259029i | −0.824659 | − | 0.565630i | \(-0.808633\pi\) |
0.565630 | + | 0.824659i | \(0.308633\pi\) | |||||||
\(150\) | −2.47929 | + | 2.47929i | −0.202433 | + | 0.202433i | ||||
\(151\) | −15.8872 | − | 15.8872i | −1.29288 | − | 1.29288i | −0.932998 | − | 0.359881i | \(-0.882817\pi\) |
−0.359881 | − | 0.932998i | \(-0.617183\pi\) | |||||||
\(152\) | 2.50625i | 0.203284i | ||||||||
\(153\) | 0.322179 | 0.0260466 | ||||||||
\(154\) | 10.0069 | + | 8.45126i | 0.806377 | + | 0.681022i | ||||
\(155\) | 2.98750i | 0.239962i | ||||||||
\(156\) | −3.37930 | + | 1.25710i | −0.270561 | + | 0.100649i | ||||
\(157\) | 10.9376i | 0.872917i | 0.899724 | + | 0.436458i | \(0.143767\pi\) | ||||
−0.899724 | + | 0.436458i | \(0.856233\pi\) | |||||||
\(158\) | 6.23469 | − | 6.23469i | 0.496005 | − | 0.496005i | ||||
\(159\) | 2.03142i | 0.161102i | ||||||||
\(160\) | −1.22219 | −0.0966227 | ||||||||
\(161\) | −4.62283 | + | 5.47375i | −0.364330 | + | 0.431392i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −0.687541 | − | 0.687541i | −0.0538524 | − | 0.0538524i | 0.679668 | − | 0.733520i | \(-0.262124\pi\) |
−0.733520 | + | 0.679668i | \(0.762124\pi\) | |||||||
\(164\) | 6.46483 | − | 6.46483i | 0.504819 | − | 0.504819i | ||||
\(165\) | −6.05062 | −0.471040 | ||||||||
\(166\) | 8.61544 | 0.668688 | ||||||||
\(167\) | −11.5592 | + | 11.5592i | −0.894477 | + | 0.894477i | −0.994941 | − | 0.100463i | \(-0.967967\pi\) |
0.100463 | + | 0.994941i | \(0.467967\pi\) | |||||||
\(168\) | 2.63640 | − | 0.222191i | 0.203403 | − | 0.0171424i | ||||
\(169\) | 9.83940 | − | 8.49625i | 0.756877 | − | 0.653558i | ||||
\(170\) | −0.393764 | −0.0302003 | ||||||||
\(171\) | 1.77219 | + | 1.77219i | 0.135522 | + | 0.135522i | ||||
\(172\) | 0.393764 | 0.0300242 | ||||||||
\(173\) | −10.4694 | −0.795972 | −0.397986 | − | 0.917392i | \(-0.630291\pi\) | ||||
−0.397986 | + | 0.917392i | \(0.630291\pi\) | |||||||
\(174\) | −3.40859 | − | 3.40859i | −0.258405 | − | 0.258405i | ||||
\(175\) | −5.98554 | + | 7.08729i | −0.452464 | + | 0.535749i | ||||
\(176\) | 3.50062 | + | 3.50062i | 0.263870 | + | 0.263870i | ||||
\(177\) | 10.7599 | + | 10.7599i | 0.808760 | + | 0.808760i | ||||
\(178\) | 5.21424i | 0.390824i | ||||||||
\(179\) | − | 22.4990i | − | 1.68166i | −0.541302 | − | 0.840828i | \(-0.682068\pi\) | ||
0.541302 | − | 0.840828i | \(-0.317932\pi\) | |||||||
\(180\) | −0.864220 | + | 0.864220i | −0.0644151 | + | 0.0644151i | ||||
\(181\) | −24.5008 | −1.82113 | −0.910565 | − | 0.413366i | \(-0.864353\pi\) | ||||
−0.910565 | + | 0.413366i | \(0.864353\pi\) | |||||||
\(182\) | −8.62990 | + | 4.06508i | −0.639691 | + | 0.301324i | ||||
\(183\) | −10.6389 | −0.786450 | ||||||||
\(184\) | −1.91484 | + | 1.91484i | −0.141164 | + | 0.141164i | ||||
\(185\) | 3.93813i | 0.289537i | ||||||||
\(186\) | − | 2.44438i | − | 0.179231i | ||||||
\(187\) | 1.12783 | + | 1.12783i | 0.0824749 | + | 0.0824749i | ||||
\(188\) | 1.41421 | + | 1.41421i | 0.103142 | + | 0.103142i | ||||
\(189\) | 1.70711 | − | 2.02133i | 0.124174 | − | 0.147030i | ||||
\(190\) | −2.16595 | − | 2.16595i | −0.157134 | − | 0.157134i | ||||
\(191\) | 0.869566 | 0.0629196 | 0.0314598 | − | 0.999505i | \(-0.489984\pi\) | ||||
0.0314598 | + | 0.999505i | \(0.489984\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −6.38377 | − | 6.38377i | −0.459514 | − | 0.459514i | 0.438982 | − | 0.898496i | \(-0.355339\pi\) |
−0.898496 | + | 0.438982i | \(0.855339\pi\) | |||||||
\(194\) | −7.35814 | −0.528284 | ||||||||
\(195\) | 1.83405 | − | 4.00687i | 0.131339 | − | 0.286938i | ||||
\(196\) | 6.90126 | − | 1.17157i | 0.492947 | − | 0.0836838i | ||||
\(197\) | −10.5087 | + | 10.5087i | −0.748717 | + | 0.748717i | −0.974238 | − | 0.225521i | \(-0.927592\pi\) |
0.225521 | + | 0.974238i | \(0.427592\pi\) | |||||||
\(198\) | 4.95063 | 0.351826 | ||||||||
\(199\) | 16.9105 | 1.19875 | 0.599376 | − | 0.800468i | \(-0.295416\pi\) | ||||
0.599376 | + | 0.800468i | \(0.295416\pi\) | |||||||
\(200\) | −2.47929 | + | 2.47929i | −0.175312 | + | 0.175312i | ||||
\(201\) | −5.38404 | − | 5.38404i | −0.379761 | − | 0.379761i | ||||
\(202\) | 5.53642 | − | 5.53642i | 0.389541 | − | 0.389541i | ||||
\(203\) | −9.74378 | − | 8.22906i | −0.683879 | − | 0.577567i | ||||
\(204\) | 0.322179 | 0.0225570 | ||||||||
\(205\) | 11.1741i | 0.780431i | ||||||||
\(206\) | 10.5006 | − | 10.5006i | 0.731613 | − | 0.731613i | ||||
\(207\) | 2.70799i | 0.188218i | ||||||||
\(208\) | −3.37930 | + | 1.25710i | −0.234313 | + | 0.0871642i | ||||
\(209\) | 12.4075i | 0.858245i | ||||||||
\(210\) | −2.08641 | + | 2.47046i | −0.143976 | + | 0.170478i | ||||
\(211\) | 4.96188 | 0.341590 | 0.170795 | − | 0.985307i | \(-0.445366\pi\) | ||||
0.170795 | + | 0.985307i | \(0.445366\pi\) | |||||||
\(212\) | 2.03142i | 0.139518i | ||||||||
\(213\) | 0.647652 | + | 0.647652i | 0.0443764 | + | 0.0443764i | ||||
\(214\) | 9.77111 | − | 9.77111i | 0.667939 | − | 0.667939i | ||||
\(215\) | −0.340299 | + | 0.340299i | −0.0232082 | + | 0.0232082i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | −0.543121 | − | 6.44438i | −0.0368694 | − | 0.437473i | ||||
\(218\) | − | 7.34592i | − | 0.497529i | ||||||
\(219\) | −6.85297 | − | 6.85297i | −0.463081 | − | 0.463081i | ||||
\(220\) | −6.05062 | −0.407933 | ||||||||
\(221\) | −1.08874 | + | 0.405011i | −0.0732366 | + | 0.0272440i | ||||
\(222\) | − | 3.22219i | − | 0.216259i | ||||||
\(223\) | 5.69799 | + | 5.69799i | 0.381566 | + | 0.381566i | 0.871666 | − | 0.490100i | \(-0.163040\pi\) |
−0.490100 | + | 0.871666i | \(0.663040\pi\) | |||||||
\(224\) | 2.63640 | − | 0.222191i | 0.176152 | − | 0.0148458i | ||||
\(225\) | 3.50625i | 0.233750i | ||||||||
\(226\) | 2.41546 | − | 2.41546i | 0.160674 | − | 0.160674i | ||||
\(227\) | −0.501705 | − | 0.501705i | −0.0332993 | − | 0.0332993i | 0.690261 | − | 0.723560i | \(-0.257496\pi\) |
−0.723560 | + | 0.690261i | \(0.757496\pi\) | |||||||
\(228\) | 1.77219 | + | 1.77219i | 0.117366 | + | 0.117366i | ||||
\(229\) | 12.5167 | − | 12.5167i | 0.827127 | − | 0.827127i | −0.159992 | − | 0.987118i | \(-0.551147\pi\) |
0.987118 | + | 0.159992i | \(0.0511467\pi\) | |||||||
\(230\) | − | 3.30968i | − | 0.218234i | ||||||
\(231\) | 13.0519 | − | 1.09999i | 0.858750 | − | 0.0723739i | ||||
\(232\) | −3.40859 | − | 3.40859i | −0.223785 | − | 0.223785i | ||||
\(233\) | 5.52846i | 0.362182i | 0.983466 | + | 0.181091i | \(0.0579628\pi\) | ||||
−0.983466 | + | 0.181091i | \(0.942037\pi\) | |||||||
\(234\) | −1.50062 | + | 3.27843i | −0.0980989 | + | 0.214318i | ||||
\(235\) | −2.44438 | −0.159454 | ||||||||
\(236\) | 10.7599 | + | 10.7599i | 0.700407 | + | 0.700407i | ||||
\(237\) | − | 8.81718i | − | 0.572737i | ||||||
\(238\) | 0.849394 | − | 0.0715854i | 0.0550580 | − | 0.00464019i | ||||
\(239\) | 10.2332 | − | 10.2332i | 0.661928 | − | 0.661928i | −0.293906 | − | 0.955834i | \(-0.594955\pi\) |
0.955834 | + | 0.293906i | \(0.0949553\pi\) | |||||||
\(240\) | −0.864220 | + | 0.864220i | −0.0557851 | + | 0.0557851i | ||||
\(241\) | −16.8108 | + | 16.8108i | −1.08288 | + | 1.08288i | −0.0866358 | + | 0.996240i | \(0.527612\pi\) |
−0.996240 | + | 0.0866358i | \(0.972388\pi\) | |||||||
\(242\) | 9.55213 | + | 9.55213i | 0.614034 | + | 0.614034i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −10.6389 | −0.681086 | ||||||||
\(245\) | −4.95171 | + | 6.97670i | −0.316353 | + | 0.445725i | ||||
\(246\) | − | 9.14265i | − | 0.582914i | ||||||
\(247\) | −8.21657 | − | 3.76094i | −0.522808 | − | 0.239303i | ||||
\(248\) | − | 2.44438i | − | 0.155218i | ||||||
\(249\) | 6.09203 | − | 6.09203i | 0.386067 | − | 0.386067i | ||||
\(250\) | − | 10.3963i | − | 0.657517i | ||||||
\(251\) | 13.3838 | 0.844776 | 0.422388 | − | 0.906415i | \(-0.361192\pi\) | ||||
0.422388 | + | 0.906415i | \(0.361192\pi\) | |||||||
\(252\) | 1.70711 | − | 2.02133i | 0.107538 | − | 0.127332i | ||||
\(253\) | −9.47966 | + | 9.47966i | −0.595981 | + | 0.595981i | ||||
\(254\) | 6.86314 | + | 6.86314i | 0.430632 | + | 0.430632i | ||||
\(255\) | −0.278433 | + | 0.278433i | −0.0174362 | + | 0.0174362i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.3581 | 0.708501 | 0.354251 | − | 0.935150i | \(-0.384736\pi\) | ||||
0.354251 | + | 0.935150i | \(0.384736\pi\) | |||||||
\(258\) | 0.278433 | − | 0.278433i | 0.0173345 | − | 0.0173345i | ||||
\(259\) | −0.715943 | − | 8.49500i | −0.0444865 | − | 0.527854i | ||||
\(260\) | 1.83405 | − | 4.00687i | 0.113743 | − | 0.248496i | ||||
\(261\) | −4.82047 | −0.298380 | ||||||||
\(262\) | 13.0081 | + | 13.0081i | 0.803644 | + | 0.803644i | ||||
\(263\) | −28.4021 | −1.75135 | −0.875673 | − | 0.482905i | \(-0.839582\pi\) | ||||
−0.875673 | + | 0.482905i | \(0.839582\pi\) | |||||||
\(264\) | 4.95063 | 0.304690 | ||||||||
\(265\) | −1.75559 | − | 1.75559i | −0.107845 | − | 0.107845i | ||||
\(266\) | 5.06596 | + | 4.27843i | 0.310614 | + | 0.262328i | ||||
\(267\) | 3.68702 | + | 3.68702i | 0.225642 | + | 0.225642i | ||||
\(268\) | −5.38404 | − | 5.38404i | −0.328883 | − | 0.328883i | ||||
\(269\) | − | 22.3912i | − | 1.36522i | −0.730785 | − | 0.682608i | \(-0.760846\pi\) | ||
0.730785 | − | 0.682608i | \(-0.239154\pi\) | |||||||
\(270\) | 1.22219i | 0.0743802i | ||||||||
\(271\) | −1.82388 | + | 1.82388i | −0.110793 | + | 0.110793i | −0.760330 | − | 0.649537i | \(-0.774963\pi\) |
0.649537 | + | 0.760330i | \(0.274963\pi\) | |||||||
\(272\) | 0.322179 | 0.0195350 | ||||||||
\(273\) | −3.22781 | + | 8.97670i | −0.195356 | + | 0.543295i | ||||
\(274\) | −2.73941 | −0.165494 | ||||||||
\(275\) | −12.2741 | + | 12.2741i | −0.740154 | + | 0.740154i | ||||
\(276\) | 2.70799i | 0.163002i | ||||||||
\(277\) | 16.7343i | 1.00547i | 0.864441 | + | 0.502735i | \(0.167673\pi\) | ||||
−0.864441 | + | 0.502735i | \(0.832327\pi\) | |||||||
\(278\) | −10.9297 | − | 10.9297i | −0.655518 | − | 0.655518i | ||||
\(279\) | −1.72844 | − | 1.72844i | −0.103479 | − | 0.103479i | ||||
\(280\) | −2.08641 | + | 2.47046i | −0.124687 | + | 0.147638i | ||||
\(281\) | −5.38706 | − | 5.38706i | −0.321365 | − | 0.321365i | 0.527926 | − | 0.849291i | \(-0.322970\pi\) |
−0.849291 | + | 0.527926i | \(0.822970\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 17.0421 | 1.01305 | 0.506525 | − | 0.862225i | \(-0.330930\pi\) | ||||
0.506525 | + | 0.862225i | \(0.330930\pi\) | |||||||
\(284\) | 0.647652 | + | 0.647652i | 0.0384311 | + | 0.0384311i | ||||
\(285\) | −3.06311 | −0.181443 | ||||||||
\(286\) | −16.7297 | + | 6.22344i | −0.989247 | + | 0.368000i | ||||
\(287\) | −2.03142 | − | 24.1037i | −0.119911 | − | 1.42280i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | −16.8962 | −0.993894 | ||||||||
\(290\) | 5.89154 | 0.345963 | ||||||||
\(291\) | −5.20299 | + | 5.20299i | −0.305005 | + | 0.305005i | ||||
\(292\) | −6.85297 | − | 6.85297i | −0.401040 | − | 0.401040i | ||||
\(293\) | 4.20174 | − | 4.20174i | 0.245468 | − | 0.245468i | −0.573639 | − | 0.819108i | \(-0.694469\pi\) |
0.819108 | + | 0.573639i | \(0.194469\pi\) | |||||||
\(294\) | 4.05150 | − | 5.70836i | 0.236288 | − | 0.332918i | ||||
\(295\) | −18.5978 | −1.08280 | ||||||||
\(296\) | − | 3.22219i | − | 0.187286i | ||||||
\(297\) | 3.50062 | − | 3.50062i | 0.203127 | − | 0.203127i | ||||
\(298\) | 4.47154i | 0.259029i | ||||||||
\(299\) | −3.40422 | − | 9.15112i | −0.196871 | − | 0.529223i | ||||
\(300\) | 3.50625i | 0.202433i | ||||||||
\(301\) | 0.672198 | − | 0.795929i | 0.0387448 | − | 0.0458766i | ||||
\(302\) | −22.4678 | −1.29288 | ||||||||
\(303\) | − | 7.82968i | − | 0.449803i | ||||||
\(304\) | 1.77219 | + | 1.77219i | 0.101642 | + | 0.101642i | ||||
\(305\) | 9.19435 | − | 9.19435i | 0.526467 | − | 0.526467i | ||||
\(306\) | 0.227815 | − | 0.227815i | 0.0130233 | − | 0.0130233i | ||||
\(307\) | −17.0150 | + | 17.0150i | −0.971097 | + | 0.971097i | −0.999594 | − | 0.0284968i | \(-0.990928\pi\) |
0.0284968 | + | 0.999594i | \(0.490928\pi\) | |||||||
\(308\) | 13.0519 | − | 1.09999i | 0.743699 | − | 0.0626776i | ||||
\(309\) | − | 14.8501i | − | 0.844794i | ||||||
\(310\) | 2.11248 | + | 2.11248i | 0.119981 | + | 0.119981i | ||||
\(311\) | −13.7090 | −0.777366 | −0.388683 | − | 0.921372i | \(-0.627070\pi\) | ||||
−0.388683 | + | 0.921372i | \(0.627070\pi\) | |||||||
\(312\) | −1.50062 | + | 3.27843i | −0.0849561 | + | 0.185605i | ||||
\(313\) | 17.4456i | 0.986085i | 0.870005 | + | 0.493043i | \(0.164115\pi\) | ||||
−0.870005 | + | 0.493043i | \(0.835885\pi\) | |||||||
\(314\) | 7.73406 | + | 7.73406i | 0.436458 | + | 0.436458i | ||||
\(315\) | 0.271560 | + | 3.22219i | 0.0153007 | + | 0.181550i | ||||
\(316\) | − | 8.81718i | − | 0.496005i | ||||||
\(317\) | −21.4771 | + | 21.4771i | −1.20627 | + | 1.20627i | −0.234046 | + | 0.972226i | \(0.575197\pi\) |
−0.972226 | + | 0.234046i | \(0.924803\pi\) | |||||||
\(318\) | 1.43643 | + | 1.43643i | 0.0805510 | + | 0.0805510i | ||||
\(319\) | −16.8747 | − | 16.8747i | −0.944800 | − | 0.944800i | ||||
\(320\) | −0.864220 | + | 0.864220i | −0.0483114 | + | 0.0483114i | ||||
\(321\) | − | 13.8184i | − | 0.771270i | ||||||
\(322\) | 0.601692 | + | 7.13936i | 0.0335310 | + | 0.397861i | ||||
\(323\) | 0.570961 | + | 0.570961i | 0.0317691 | + | 0.0317691i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −4.40771 | − | 11.8487i | −0.244496 | − | 0.657247i | ||||
\(326\) | −0.972330 | −0.0538524 | ||||||||
\(327\) | −5.19435 | − | 5.19435i | −0.287248 | − | 0.287248i | ||||
\(328\) | − | 9.14265i | − | 0.504819i | ||||||
\(329\) | 5.27281 | − | 0.444383i | 0.290699 | − | 0.0244996i | ||||
\(330\) | −4.27843 | + | 4.27843i | −0.235520 | + | 0.235520i | ||||
\(331\) | −5.19998 | + | 5.19998i | −0.285816 | + | 0.285816i | −0.835423 | − | 0.549607i | \(-0.814778\pi\) |
0.549607 | + | 0.835423i | \(0.314778\pi\) | |||||||
\(332\) | 6.09203 | − | 6.09203i | 0.334344 | − | 0.334344i | ||||
\(333\) | −2.27843 | − | 2.27843i | −0.124857 | − | 0.124857i | ||||
\(334\) | 16.3472i | 0.894477i | ||||||||
\(335\) | 9.30600 | 0.508441 | ||||||||
\(336\) | 1.70711 | − | 2.02133i | 0.0931303 | − | 0.110273i | ||||
\(337\) | 1.35058i | 0.0735708i | 0.999323 | + | 0.0367854i | \(0.0117118\pi\) | ||||
−0.999323 | + | 0.0367854i | \(0.988288\pi\) | |||||||
\(338\) | 0.949747 | − | 12.9653i | 0.0516595 | − | 0.705217i | ||||
\(339\) | − | 3.41598i | − | 0.185531i | ||||||
\(340\) | −0.278433 | + | 0.278433i | −0.0151002 | + | 0.0151002i | ||||
\(341\) | − | 12.1012i | − | 0.655319i | ||||||
\(342\) | 2.50625 | 0.135522 | ||||||||
\(343\) | 9.41305 | − | 15.9497i | 0.508257 | − | 0.861205i | ||||
\(344\) | 0.278433 | − | 0.278433i | 0.0150121 | − | 0.0150121i | ||||
\(345\) | −2.34030 | − | 2.34030i | −0.125997 | − | 0.125997i | ||||
\(346\) | −7.40297 | + | 7.40297i | −0.397986 | + | 0.397986i | ||||
\(347\) | 21.6050 | 1.15982 | 0.579910 | − | 0.814681i | \(-0.303088\pi\) | ||||
0.579910 | + | 0.814681i | \(0.303088\pi\) | |||||||
\(348\) | −4.82047 | −0.258405 | ||||||||
\(349\) | −25.7255 | + | 25.7255i | −1.37705 | + | 1.37705i | −0.527496 | + | 0.849557i | \(0.676869\pi\) |
−0.849557 | + | 0.527496i | \(0.823131\pi\) | |||||||
\(350\) | 0.779058 | + | 9.24389i | 0.0416424 | + | 0.494107i | ||||
\(351\) | 1.25710 | + | 3.37930i | 0.0670991 | + | 0.180374i | ||||
\(352\) | 4.95063 | 0.263870 | ||||||||
\(353\) | 9.77451 | + | 9.77451i | 0.520245 | + | 0.520245i | 0.917645 | − | 0.397400i | \(-0.130088\pi\) |
−0.397400 | + | 0.917645i | \(0.630088\pi\) | |||||||
\(354\) | 15.2167 | 0.808760 | ||||||||
\(355\) | −1.11943 | −0.0594130 | ||||||||
\(356\) | 3.68702 | + | 3.68702i | 0.195412 | + | 0.195412i | ||||
\(357\) | 0.549994 | − | 0.651231i | 0.0291088 | − | 0.0344668i | ||||
\(358\) | −15.9092 | − | 15.9092i | −0.840828 | − | 0.840828i | ||||
\(359\) | −4.56016 | − | 4.56016i | −0.240676 | − | 0.240676i | 0.576454 | − | 0.817130i | \(-0.304436\pi\) |
−0.817130 | + | 0.576454i | \(0.804436\pi\) | |||||||
\(360\) | 1.22219i | 0.0644151i | ||||||||
\(361\) | − | 12.7187i | − | 0.669406i | ||||||
\(362\) | −17.3247 | + | 17.3247i | −0.910565 | + | 0.910565i | ||||
\(363\) | 13.5087 | 0.709025 | ||||||||
\(364\) | −3.22781 | + | 8.97670i | −0.169183 | + | 0.470507i | ||||
\(365\) | 11.8449 | 0.619993 | ||||||||
\(366\) | −7.52284 | + | 7.52284i | −0.393225 | + | 0.393225i | ||||
\(367\) | 14.4983i | 0.756805i | 0.925641 | + | 0.378402i | \(0.123526\pi\) | ||||
−0.925641 | + | 0.378402i | \(0.876474\pi\) | |||||||
\(368\) | 2.70799i | 0.141164i | ||||||||
\(369\) | −6.46483 | − | 6.46483i | −0.336546 | − | 0.336546i | ||||
\(370\) | 2.78468 | + | 2.78468i | 0.144769 | + | 0.144769i | ||||
\(371\) | 4.10617 | + | 3.46785i | 0.213182 | + | 0.180042i | ||||
\(372\) | −1.72844 | − | 1.72844i | −0.0896154 | − | 0.0896154i | ||||
\(373\) | 21.2073 | 1.09807 | 0.549035 | − | 0.835799i | \(-0.314995\pi\) | ||||
0.549035 | + | 0.835799i | \(0.314995\pi\) | |||||||
\(374\) | 1.59499 | 0.0824749 | ||||||||
\(375\) | −7.35127 | − | 7.35127i | −0.379618 | − | 0.379618i | ||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 16.2899 | − | 6.05982i | 0.838970 | − | 0.312097i | ||||
\(378\) | −0.222191 | − | 2.63640i | −0.0114283 | − | 0.135602i | ||||
\(379\) | 25.0372 | − | 25.0372i | 1.28608 | − | 1.28608i | 0.348924 | − | 0.937151i | \(-0.386547\pi\) |
0.937151 | − | 0.348924i | \(-0.113453\pi\) | |||||||
\(380\) | −3.06311 | −0.157134 | ||||||||
\(381\) | 9.70595 | 0.497251 | ||||||||
\(382\) | 0.614876 | − | 0.614876i | 0.0314598 | − | 0.0314598i | ||||
\(383\) | −14.5420 | − | 14.5420i | −0.743064 | − | 0.743064i | 0.230103 | − | 0.973166i | \(-0.426094\pi\) |
−0.973166 | + | 0.230103i | \(0.926094\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −10.3291 | + | 12.2303i | −0.526417 | + | 0.623315i | ||||
\(386\) | −9.02801 | −0.459514 | ||||||||
\(387\) | − | 0.393764i | − | 0.0200162i | ||||||
\(388\) | −5.20299 | + | 5.20299i | −0.264142 | + | 0.264142i | ||||
\(389\) | − | 30.6758i | − | 1.55532i | −0.628683 | − | 0.777662i | \(-0.716406\pi\) | ||
0.628683 | − | 0.777662i | \(-0.283594\pi\) | |||||||
\(390\) | −1.53642 | − | 4.13016i | −0.0777995 | − | 0.209139i | ||||
\(391\) | 0.872457i | 0.0441221i | ||||||||
\(392\) | 4.05150 | − | 5.70836i | 0.204632 | − | 0.288316i | ||||
\(393\) | 18.3963 | 0.927969 | ||||||||
\(394\) | 14.8616i | 0.748717i | ||||||||
\(395\) | 7.61998 | + | 7.61998i | 0.383403 | + | 0.383403i | ||||
\(396\) | 3.50062 | − | 3.50062i | 0.175913 | − | 0.175913i | ||||
\(397\) | 1.78156 | − | 1.78156i | 0.0894138 | − | 0.0894138i | −0.660985 | − | 0.750399i | \(-0.729861\pi\) |
0.750399 | + | 0.660985i | \(0.229861\pi\) | |||||||
\(398\) | 11.9575 | − | 11.9575i | 0.599376 | − | 0.599376i | ||||
\(399\) | 6.60749 | − | 0.556867i | 0.330788 | − | 0.0278782i | ||||
\(400\) | 3.50625i | 0.175312i | ||||||||
\(401\) | −2.02017 | − | 2.02017i | −0.100883 | − | 0.100883i | 0.654864 | − | 0.755747i | \(-0.272726\pi\) |
−0.755747 | + | 0.654864i | \(0.772726\pi\) | |||||||
\(402\) | −7.61419 | −0.379761 | ||||||||
\(403\) | 8.01375 | + | 3.66810i | 0.399193 | + | 0.182721i | ||||
\(404\) | − | 7.82968i | − | 0.389541i | ||||||
\(405\) | 0.864220 | + | 0.864220i | 0.0429434 | + | 0.0429434i | ||||
\(406\) | −12.7087 | + | 1.07107i | −0.630723 | + | 0.0531562i | ||||
\(407\) | − | 15.9519i | − | 0.790705i | ||||||
\(408\) | 0.227815 | − | 0.227815i | 0.0112785 | − | 0.0112785i | ||||
\(409\) | −11.7667 | − | 11.7667i | −0.581827 | − | 0.581827i | 0.353578 | − | 0.935405i | \(-0.384965\pi\) |
−0.935405 | + | 0.353578i | \(0.884965\pi\) | |||||||
\(410\) | 7.90126 | + | 7.90126i | 0.390216 | + | 0.390216i | ||||
\(411\) | −1.93705 | + | 1.93705i | −0.0955479 | + | 0.0955479i | ||||
\(412\) | − | 14.8501i | − | 0.731613i | ||||||
\(413\) | 40.1175 | − | 3.38103i | 1.97405 | − | 0.166370i | ||||
\(414\) | 1.91484 | + | 1.91484i | 0.0941092 | + | 0.0941092i | ||||
\(415\) | 10.5297i | 0.516883i | ||||||||
\(416\) | −1.50062 | + | 3.27843i | −0.0735742 | + | 0.160738i | ||||
\(417\) | −15.4569 | −0.756927 | ||||||||
\(418\) | 8.77343 | + | 8.77343i | 0.429123 | + | 0.429123i | ||||
\(419\) | 9.34287i | 0.456429i | 0.973611 | + | 0.228214i | \(0.0732887\pi\) | ||||
−0.973611 | + | 0.228214i | \(0.926711\pi\) | |||||||
\(420\) | 0.271560 | + | 3.22219i | 0.0132508 | + | 0.157227i | ||||
\(421\) | 7.32190 | − | 7.32190i | 0.356848 | − | 0.356848i | −0.505802 | − | 0.862650i | \(-0.668803\pi\) |
0.862650 | + | 0.505802i | \(0.168803\pi\) | |||||||
\(422\) | 3.50858 | − | 3.50858i | 0.170795 | − | 0.170795i | ||||
\(423\) | 1.41421 | − | 1.41421i | 0.0687614 | − | 0.0687614i | ||||
\(424\) | 1.43643 | + | 1.43643i | 0.0697592 | + | 0.0697592i | ||||
\(425\) | 1.12964i | 0.0547955i | ||||||||
\(426\) | 0.915918 | 0.0443764 | ||||||||
\(427\) | −18.1617 | + | 21.5048i | −0.878908 | + | 1.04069i | ||||
\(428\) | − | 13.8184i | − | 0.667939i | ||||||
\(429\) | −7.42904 | + | 16.2303i | −0.358677 | + | 0.783607i | ||||
\(430\) | 0.481255i | 0.0232082i | ||||||||
\(431\) | −26.9180 | + | 26.9180i | −1.29660 | + | 1.29660i | −0.365968 | + | 0.930627i | \(0.619262\pi\) |
−0.930627 | + | 0.365968i | \(0.880738\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −30.8370 | −1.48193 | −0.740965 | − | 0.671544i | \(-0.765632\pi\) | ||||
−0.740965 | + | 0.671544i | \(0.765632\pi\) | |||||||
\(434\) | −4.94091 | − | 4.17282i | −0.237171 | − | 0.200302i | ||||
\(435\) | 4.16595 | − | 4.16595i | 0.199742 | − | 0.199742i | ||||
\(436\) | −5.19435 | − | 5.19435i | −0.248764 | − | 0.248764i | ||||
\(437\) | −4.79906 | + | 4.79906i | −0.229570 | + | 0.229570i | ||||
\(438\) | −9.69157 | −0.463081 | ||||||||
\(439\) | 14.3229 | 0.683595 | 0.341798 | − | 0.939774i | \(-0.388964\pi\) | ||||
0.341798 | + | 0.939774i | \(0.388964\pi\) | |||||||
\(440\) | −4.27843 | + | 4.27843i | −0.203966 | + | 0.203966i | ||||
\(441\) | −1.17157 | − | 6.90126i | −0.0557892 | − | 0.328632i | ||||
\(442\) | −0.483470 | + | 1.05624i | −0.0229963 | + | 0.0502403i | ||||
\(443\) | 21.5422 | 1.02350 | 0.511751 | − | 0.859134i | \(-0.328997\pi\) | ||||
0.511751 | + | 0.859134i | \(0.328997\pi\) | |||||||
\(444\) | −2.27843 | − | 2.27843i | −0.108130 | − | 0.108130i | ||||
\(445\) | −6.37280 | −0.302100 | ||||||||
\(446\) | 8.05818 | 0.381566 | ||||||||
\(447\) | 3.16185 | + | 3.16185i | 0.149551 | + | 0.149551i | ||||
\(448\) | 1.70711 | − | 2.02133i | 0.0806532 | − | 0.0954990i | ||||
\(449\) | 28.2383 | + | 28.2383i | 1.33265 | + | 1.33265i | 0.902995 | + | 0.429651i | \(0.141364\pi\) |
0.429651 | + | 0.902995i | \(0.358636\pi\) | |||||||
\(450\) | 2.47929 | + | 2.47929i | 0.116875 | + | 0.116875i | ||||
\(451\) | − | 45.2619i | − | 2.13130i | ||||||
\(452\) | − | 3.41598i | − | 0.160674i | ||||||
\(453\) | −15.8872 | + | 15.8872i | −0.746444 | + | 0.746444i | ||||
\(454\) | −0.709517 | −0.0332993 | ||||||||
\(455\) | −4.96830 | − | 10.5474i | −0.232918 | − | 0.494469i | ||||
\(456\) | 2.50625 | 0.117366 | ||||||||
\(457\) | −12.7653 | + | 12.7653i | −0.597136 | + | 0.597136i | −0.939549 | − | 0.342413i | \(-0.888756\pi\) |
0.342413 | + | 0.939549i | \(0.388756\pi\) | |||||||
\(458\) | − | 17.7013i | − | 0.827127i | ||||||
\(459\) | − | 0.322179i | − | 0.0150380i | ||||||
\(460\) | −2.34030 | − | 2.34030i | −0.109117 | − | 0.109117i | ||||
\(461\) | 13.3358 | + | 13.3358i | 0.621108 | + | 0.621108i | 0.945815 | − | 0.324707i | \(-0.105266\pi\) |
−0.324707 | + | 0.945815i | \(0.605266\pi\) | |||||||
\(462\) | 8.45126 | − | 10.0069i | 0.393188 | − | 0.465562i | ||||
\(463\) | 21.3712 | + | 21.3712i | 0.993204 | + | 0.993204i | 0.999977 | − | 0.00677317i | \(-0.00215598\pi\) |
−0.00677317 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(464\) | −4.82047 | −0.223785 | ||||||||
\(465\) | 2.98750 | 0.138542 | ||||||||
\(466\) | 3.90921 | + | 3.90921i | 0.181091 | + | 0.181091i | ||||
\(467\) | 41.0053 | 1.89750 | 0.948749 | − | 0.316031i | \(-0.102350\pi\) | ||||
0.948749 | + | 0.316031i | \(0.102350\pi\) | |||||||
\(468\) | 1.25710 | + | 3.37930i | 0.0581095 | + | 0.156208i | ||||
\(469\) | −20.0741 | + | 1.69181i | −0.926935 | + | 0.0781204i | ||||
\(470\) | −1.72844 | + | 1.72844i | −0.0797270 | + | 0.0797270i | ||||
\(471\) | 10.9376 | 0.503979 | ||||||||
\(472\) | 15.2167 | 0.700407 | ||||||||
\(473\) | 1.37842 | − | 1.37842i | 0.0633799 | − | 0.0633799i | ||||
\(474\) | −6.23469 | − | 6.23469i | −0.286369 | − | 0.286369i | ||||
\(475\) | −6.21372 | + | 6.21372i | −0.285105 | + | 0.285105i | ||||
\(476\) | 0.549994 | − | 0.651231i | 0.0252089 | − | 0.0298491i | ||||
\(477\) | 2.03142 | 0.0930123 | ||||||||
\(478\) | − | 14.4719i | − | 0.661928i | ||||||
\(479\) | −6.94553 | + | 6.94553i | −0.317349 | + | 0.317349i | −0.847748 | − | 0.530399i | \(-0.822042\pi\) |
0.530399 | + | 0.847748i | \(0.322042\pi\) | |||||||
\(480\) | 1.22219i | 0.0557851i | ||||||||
\(481\) | 10.5637 | + | 4.83530i | 0.481665 | + | 0.220471i | ||||
\(482\) | 23.7740i | 1.08288i | ||||||||
\(483\) | 5.47375 | + | 4.62283i | 0.249064 | + | 0.210346i | ||||
\(484\) | 13.5087 | 0.614034 | ||||||||
\(485\) | − | 8.99306i | − | 0.408354i | ||||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −23.1741 | + | 23.1741i | −1.05012 | + | 1.05012i | −0.0514414 | + | 0.998676i | \(0.516382\pi\) |
−0.998676 | + | 0.0514414i | \(0.983618\pi\) | |||||||
\(488\) | −7.52284 | + | 7.52284i | −0.340543 | + | 0.340543i | ||||
\(489\) | −0.687541 | + | 0.687541i | −0.0310917 | + | 0.0310917i | ||||
\(490\) | 1.43189 | + | 8.43466i | 0.0646860 | + | 0.381039i | ||||
\(491\) | 15.6206i | 0.704948i | 0.935822 | + | 0.352474i | \(0.114660\pi\) | ||||
−0.935822 | + | 0.352474i | \(0.885340\pi\) | |||||||
\(492\) | −6.46483 | − | 6.46483i | −0.291457 | − | 0.291457i | ||||
\(493\) | −1.55306 | −0.0699461 | ||||||||
\(494\) | −8.46938 | + | 3.15061i | −0.381055 | + | 0.141752i | ||||
\(495\) | 6.05062i | 0.271955i | ||||||||
\(496\) | −1.72844 | − | 1.72844i | −0.0776092 | − | 0.0776092i | ||||
\(497\) | 2.41473 | − | 0.203509i | 0.108315 | − | 0.00912863i | ||||
\(498\) | − | 8.61544i | − | 0.386067i | ||||||
\(499\) | 25.6581 | − | 25.6581i | 1.14861 | − | 1.14861i | 0.161789 | − | 0.986825i | \(-0.448274\pi\) |
0.986825 | − | 0.161789i | \(-0.0517264\pi\) | |||||||
\(500\) | −7.35127 | − | 7.35127i | −0.328759 | − | 0.328759i | ||||
\(501\) | 11.5592 | + | 11.5592i | 0.516427 | + | 0.516427i | ||||
\(502\) | 9.46375 | − | 9.46375i | 0.422388 | − | 0.422388i | ||||
\(503\) | − | 31.3187i | − | 1.39643i | −0.715887 | − | 0.698216i | \(-0.753977\pi\) | ||
0.715887 | − | 0.698216i | \(-0.246023\pi\) | |||||||
\(504\) | −0.222191 | − | 2.63640i | −0.00989719 | − | 0.117435i | ||||
\(505\) | 6.76656 | + | 6.76656i | 0.301108 | + | 0.301108i | ||||
\(506\) | 13.4063i | 0.595981i | ||||||||
\(507\) | −8.49625 | − | 9.83940i | −0.377332 | − | 0.436983i | ||||
\(508\) | 9.70595 | 0.430632 | ||||||||
\(509\) | −20.3793 | − | 20.3793i | −0.903296 | − | 0.903296i | 0.0924241 | − | 0.995720i | \(-0.470538\pi\) |
−0.995720 | + | 0.0924241i | \(0.970538\pi\) | |||||||
\(510\) | 0.393764i | 0.0174362i | ||||||||
\(511\) | −25.5509 | + | 2.15338i | −1.13031 | + | 0.0952600i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 1.77219 | − | 1.77219i | 0.0782439 | − | 0.0782439i | ||||
\(514\) | 8.03142 | − | 8.03142i | 0.354251 | − | 0.354251i | ||||
\(515\) | 12.8338 | + | 12.8338i | 0.565524 | + | 0.565524i | ||||
\(516\) | − | 0.393764i | − | 0.0173345i | ||||||
\(517\) | 9.90126 | 0.435457 | ||||||||
\(518\) | −6.51312 | − | 5.50062i | −0.286170 | − | 0.241684i | ||||
\(519\) | 10.4694i | 0.459555i | ||||||||
\(520\) | −1.53642 | − | 4.13016i | −0.0673764 | − | 0.181119i | ||||
\(521\) | 33.7078i | 1.47677i | 0.674382 | + | 0.738383i | \(0.264410\pi\) | ||||
−0.674382 | + | 0.738383i | \(0.735590\pi\) | |||||||
\(522\) | −3.40859 | + | 3.40859i | −0.149190 | + | 0.149190i | ||||
\(523\) | 19.2350i | 0.841086i | 0.907273 | + | 0.420543i | \(0.138160\pi\) | ||||
−0.907273 | + | 0.420543i | \(0.861840\pi\) | |||||||
\(524\) | 18.3963 | 0.803644 | ||||||||
\(525\) | 7.08729 | + | 5.98554i | 0.309315 | + | 0.261230i | ||||
\(526\) | −20.0833 | + | 20.0833i | −0.875673 | + | 0.875673i | ||||
\(527\) | −0.556867 | − | 0.556867i | −0.0242575 | − | 0.0242575i | ||||
\(528\) | 3.50062 | − | 3.50062i | 0.152345 | − | 0.152345i | ||||
\(529\) | 15.6668 | 0.681165 | ||||||||
\(530\) | −2.48278 | −0.107845 | ||||||||
\(531\) | 10.7599 | − | 10.7599i | 0.466938 | − | 0.466938i | ||||
\(532\) | 6.60749 | − | 0.556867i | 0.286471 | − | 0.0241432i | ||||
\(533\) | 29.9736 | + | 13.7197i | 1.29830 | + | 0.594266i | ||||
\(534\) | 5.21424 | 0.225642 | ||||||||
\(535\) | 11.9422 | + | 11.9422i | 0.516305 | + | 0.516305i | ||||
\(536\) | −7.61419 | −0.328883 | ||||||||
\(537\) | −22.4990 | −0.970905 | ||||||||
\(538\) | −15.8330 | − | 15.8330i | −0.682608 | − | 0.682608i | ||||
\(539\) | 20.0575 | − | 28.2600i | 0.863937 | − | 1.21724i | ||||
\(540\) | 0.864220 | + | 0.864220i | 0.0371901 | + | 0.0371901i | ||||
\(541\) | 24.8685 | + | 24.8685i | 1.06918 | + | 1.06918i | 0.997422 | + | 0.0717576i | \(0.0228608\pi\) |
0.0717576 | + | 0.997422i | \(0.477139\pi\) | |||||||
\(542\) | 2.57936i | 0.110793i | ||||||||
\(543\) | 24.5008i | 1.05143i | ||||||||
\(544\) | 0.227815 | − | 0.227815i | 0.00976748 | − | 0.00976748i | ||||
\(545\) | 8.97812 | 0.384581 | ||||||||
\(546\) | 4.06508 | + | 8.62990i | 0.173969 | + | 0.369326i | ||||
\(547\) | 31.2150 | 1.33466 | 0.667328 | − | 0.744764i | \(-0.267438\pi\) | ||||
0.667328 | + | 0.744764i | \(0.267438\pi\) | |||||||
\(548\) | −1.93705 | + | 1.93705i | −0.0827469 | + | 0.0827469i | ||||
\(549\) | 10.6389i | 0.454057i | ||||||||
\(550\) | 17.3581i | 0.740154i | ||||||||
\(551\) | −8.54277 | − | 8.54277i | −0.363934 | − | 0.363934i | ||||
\(552\) | 1.91484 | + | 1.91484i | 0.0815009 | + | 0.0815009i | ||||
\(553\) | −17.8225 | − | 15.0519i | −0.757888 | − | 0.640071i | ||||
\(554\) | 11.8330 | + | 11.8330i | 0.502735 | + | 0.502735i | ||||
\(555\) | 3.93813 | 0.167165 | ||||||||
\(556\) | −15.4569 | −0.655518 | ||||||||
\(557\) | 5.05010 | + | 5.05010i | 0.213980 | + | 0.213980i | 0.805956 | − | 0.591976i | \(-0.201652\pi\) |
−0.591976 | + | 0.805956i | \(0.701652\pi\) | |||||||
\(558\) | −2.44438 | −0.103479 | ||||||||
\(559\) | 0.495001 | + | 1.33065i | 0.0209363 | + | 0.0562805i | ||||
\(560\) | 0.271560 | + | 3.22219i | 0.0114755 | + | 0.136162i | ||||
\(561\) | 1.12783 | − | 1.12783i | 0.0476169 | − | 0.0476169i | ||||
\(562\) | −7.61845 | −0.321365 | ||||||||
\(563\) | −33.9410 | −1.43044 | −0.715221 | − | 0.698899i | \(-0.753674\pi\) | ||||
−0.715221 | + | 0.698899i | \(0.753674\pi\) | |||||||
\(564\) | 1.41421 | − | 1.41421i | 0.0595491 | − | 0.0595491i | ||||
\(565\) | 2.95216 | + | 2.95216i | 0.124198 | + | 0.124198i | ||||
\(566\) | 12.0506 | − | 12.0506i | 0.506525 | − | 0.506525i | ||||
\(567\) | −2.02133 | − | 1.70711i | −0.0848880 | − | 0.0716917i | ||||
\(568\) | 0.915918 | 0.0384311 | ||||||||
\(569\) | − | 1.28622i | − | 0.0539210i | −0.999636 | − | 0.0269605i | \(-0.991417\pi\) | ||
0.999636 | − | 0.0269605i | \(-0.00858283\pi\) | |||||||
\(570\) | −2.16595 | + | 2.16595i | −0.0907216 | + | 0.0907216i | ||||
\(571\) | 36.5188i | 1.52826i | 0.645060 | + | 0.764132i | \(0.276833\pi\) | ||||
−0.645060 | + | 0.764132i | \(0.723167\pi\) | |||||||
\(572\) | −7.42904 | + | 16.2303i | −0.310624 | + | 0.678624i | ||||
\(573\) | − | 0.869566i | − | 0.0363266i | ||||||
\(574\) | −18.4803 | − | 15.6075i | −0.771355 | − | 0.651444i | ||||
\(575\) | −9.49489 | −0.395964 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 9.37228 | + | 9.37228i | 0.390173 | + | 0.390173i | 0.874749 | − | 0.484576i | \(-0.161026\pi\) |
−0.484576 | + | 0.874749i | \(0.661026\pi\) | |||||||
\(578\) | −11.9474 | + | 11.9474i | −0.496947 | + | 0.496947i | ||||
\(579\) | −6.38377 | + | 6.38377i | −0.265300 | + | 0.265300i | ||||
\(580\) | 4.16595 | − | 4.16595i | 0.172982 | − | 0.172982i | ||||
\(581\) | −1.91428 | − | 22.7138i | −0.0794176 | − | 0.942327i | ||||
\(582\) | 7.35814i | 0.305005i | ||||||||
\(583\) | 7.11123 | + | 7.11123i | 0.294517 | + | 0.294517i | ||||
\(584\) | −9.69157 | −0.401040 | ||||||||
\(585\) | −4.00687 | − | 1.83405i | −0.165664 | − | 0.0758287i | ||||
\(586\) | − | 5.94216i | − | 0.245468i | ||||||
\(587\) | −19.0646 | − | 19.0646i | −0.786880 | − | 0.786880i | 0.194101 | − | 0.980982i | \(-0.437821\pi\) |
−0.980982 | + | 0.194101i | \(0.937821\pi\) | |||||||
\(588\) | −1.17157 | − | 6.90126i | −0.0483149 | − | 0.284603i | ||||
\(589\) | − | 6.12623i | − | 0.252427i | ||||||
\(590\) | −13.1506 | + | 13.1506i | −0.541402 | + | 0.541402i | ||||
\(591\) | 10.5087 | + | 10.5087i | 0.432272 | + | 0.432272i | ||||
\(592\) | −2.27843 | − | 2.27843i | −0.0936430 | − | 0.0936430i | ||||
\(593\) | 25.5883 | − | 25.5883i | 1.05078 | − | 1.05078i | 0.0521454 | − | 0.998640i | \(-0.483394\pi\) |
0.998640 | − | 0.0521454i | \(-0.0166059\pi\) | |||||||
\(594\) | − | 4.95063i | − | 0.203127i | ||||||
\(595\) | 0.0874910 | + | 1.03812i | 0.00358678 | + | 0.0425589i | ||||
\(596\) | 3.16185 | + | 3.16185i | 0.129515 | + | 0.129515i | ||||
\(597\) | − | 16.9105i | − | 0.692099i | ||||||
\(598\) | −8.87797 | − | 4.06368i | −0.363047 | − | 0.166176i | ||||
\(599\) | 4.67868 | 0.191166 | 0.0955828 | − | 0.995421i | \(-0.469529\pi\) | ||||
0.0955828 | + | 0.995421i | \(0.469529\pi\) | |||||||
\(600\) | 2.47929 | + | 2.47929i | 0.101217 | + | 0.101217i | ||||
\(601\) | − | 18.8059i | − | 0.767110i | −0.923518 | − | 0.383555i | \(-0.874700\pi\) | ||
0.923518 | − | 0.383555i | \(-0.125300\pi\) | |||||||
\(602\) | −0.0874910 | − | 1.03812i | −0.00356587 | − | 0.0423107i | ||||
\(603\) | −5.38404 | + | 5.38404i | −0.219255 | + | 0.219255i | ||||
\(604\) | −15.8872 | + | 15.8872i | −0.646440 | + | 0.646440i | ||||
\(605\) | −11.6745 | + | 11.6745i | −0.474637 | + | 0.474637i | ||||
\(606\) | −5.53642 | − | 5.53642i | −0.224902 | − | 0.224902i | ||||
\(607\) | 4.66106i | 0.189187i | 0.995516 | + | 0.0945933i | \(0.0301551\pi\) | ||||
−0.995516 | + | 0.0945933i | \(0.969845\pi\) | |||||||
\(608\) | 2.50625 | 0.101642 | ||||||||
\(609\) | −8.22906 | + | 9.74378i | −0.333459 | + | 0.394838i | ||||
\(610\) | − | 13.0028i | − | 0.526467i | ||||||
\(611\) | −3.00125 | + | 6.55687i | −0.121418 | + | 0.265262i | ||||
\(612\) | − | 0.322179i | − | 0.0130233i | ||||||
\(613\) | 31.7107 | − | 31.7107i | 1.28078 | − | 1.28078i | 0.340558 | − | 0.940224i | \(-0.389384\pi\) |
0.940224 | − | 0.340558i | \(-0.110616\pi\) | |||||||
\(614\) | 24.0628i | 0.971097i | ||||||||
\(615\) | 11.1741 | 0.450582 | ||||||||
\(616\) | 8.45126 | − | 10.0069i | 0.340511 | − | 0.403188i | ||||
\(617\) | −5.26417 | + | 5.26417i | −0.211927 | + | 0.211927i | −0.805086 | − | 0.593158i | \(-0.797881\pi\) |
0.593158 | + | 0.805086i | \(0.297881\pi\) | |||||||
\(618\) | −10.5006 | − | 10.5006i | −0.422397 | − | 0.422397i | ||||
\(619\) | 9.61527 | − | 9.61527i | 0.386470 | − | 0.386470i | −0.486956 | − | 0.873426i | \(-0.661893\pi\) |
0.873426 | + | 0.486956i | \(0.161893\pi\) | |||||||
\(620\) | 2.98750 | 0.119981 | ||||||||
\(621\) | 2.70799 | 0.108668 | ||||||||
\(622\) | −9.69373 | + | 9.69373i | −0.388683 | + | 0.388683i | ||||
\(623\) | 13.7468 | − | 1.15856i | 0.550756 | − | 0.0464167i | ||||
\(624\) | 1.25710 | + | 3.37930i | 0.0503243 | + | 0.135280i | ||||
\(625\) | −4.82502 | −0.193001 | ||||||||
\(626\) | 12.3359 | + | 12.3359i | 0.493043 | + | 0.493043i | ||||
\(627\) | 12.4075 | 0.495508 | ||||||||
\(628\) | 10.9376 | 0.436458 | ||||||||
\(629\) | −0.734063 | − | 0.734063i | −0.0292690 | − | 0.0292690i | ||||
\(630\) | 2.47046 | + | 2.08641i | 0.0984253 | + | 0.0831246i | ||||
\(631\) | −14.4462 | − | 14.4462i | −0.575094 | − | 0.575094i | 0.358454 | − | 0.933548i | \(-0.383304\pi\) |
−0.933548 | + | 0.358454i | \(0.883304\pi\) | |||||||
\(632\) | −6.23469 | − | 6.23469i | −0.248003 | − | 0.248003i | ||||
\(633\) | − | 4.96188i | − | 0.197217i | ||||||
\(634\) | 30.3731i | 1.20627i | ||||||||
\(635\) | −8.38807 | + | 8.38807i | −0.332870 | + | 0.332870i | ||||
\(636\) | 2.03142 | 0.0805510 | ||||||||
\(637\) | 12.6347 | + | 21.8487i | 0.500604 | + | 0.865676i | ||||
\(638\) | −23.8644 | −0.944800 | ||||||||
\(639\) | 0.647652 | − | 0.647652i | 0.0256207 | − | 0.0256207i | ||||
\(640\) | 1.22219i | 0.0483114i | ||||||||
\(641\) | − | 4.88105i | − | 0.192790i | −0.995343 | − | 0.0963950i | \(-0.969269\pi\) | ||
0.995343 | − | 0.0963950i | \(-0.0307312\pi\) | |||||||
\(642\) | −9.77111 | − | 9.77111i | −0.385635 | − | 0.385635i | ||||
\(643\) | 25.2403 | + | 25.2403i | 0.995381 | + | 0.995381i | 0.999989 | − | 0.00460867i | \(-0.00146699\pi\) |
−0.00460867 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(644\) | 5.47375 | + | 4.62283i | 0.215696 | + | 0.182165i | ||||
\(645\) | 0.340299 | + | 0.340299i | 0.0133993 | + | 0.0133993i | ||||
\(646\) | 0.807460 | 0.0317691 | ||||||||
\(647\) | −18.9818 | −0.746252 | −0.373126 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373126 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 75.3325 | 2.95706 | ||||||||
\(650\) | −11.4950 | − | 5.26156i | −0.450871 | − | 0.206375i | ||||
\(651\) | −6.44438 | + | 0.543121i | −0.252575 | + | 0.0212866i | ||||
\(652\) | −0.687541 | + | 0.687541i | −0.0269262 | + | 0.0269262i | ||||
\(653\) | 28.5652 | 1.11784 | 0.558921 | − | 0.829221i | \(-0.311216\pi\) | ||||
0.558921 | + | 0.829221i | \(0.311216\pi\) | |||||||
\(654\) | −7.34592 | −0.287248 | ||||||||
\(655\) | −15.8984 | + | 15.8984i | −0.621202 | + | 0.621202i | ||||
\(656\) | −6.46483 | − | 6.46483i | −0.252409 | − | 0.252409i | ||||
\(657\) | −6.85297 | + | 6.85297i | −0.267360 | + | 0.267360i | ||||
\(658\) | 3.41421 | − | 4.04267i | 0.133100 | − | 0.157600i | ||||
\(659\) | 11.6879 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(660\) | 6.05062i | 0.235520i | ||||||||
\(661\) | 16.7977 | − | 16.7977i | 0.653356 | − | 0.653356i | −0.300443 | − | 0.953800i | \(-0.597135\pi\) |
0.953800 | + | 0.300443i | \(0.0971346\pi\) | |||||||
\(662\) | 7.35388i | 0.285816i | ||||||||
\(663\) | 0.405011 | + | 1.08874i | 0.0157293 | + | 0.0422832i | ||||
\(664\) | − | 8.61544i | − | 0.334344i | ||||||
\(665\) | −5.22906 | + | 6.19157i | −0.202774 | + | 0.240099i | ||||
\(666\) | −3.22219 | −0.124857 | ||||||||
\(667\) | − | 13.0538i | − | 0.505445i | ||||||
\(668\) | 11.5592 | + | 11.5592i | 0.447239 | + | 0.447239i | ||||
\(669\) | 5.69799 | − | 5.69799i | 0.220297 | − | 0.220297i | ||||
\(670\) | 6.58033 | − | 6.58033i | 0.254220 | − | 0.254220i | ||||
\(671\) | −37.2428 | + | 37.2428i | −1.43774 | + | 1.43774i | ||||
\(672\) | −0.222191 | − | 2.63640i | −0.00857122 | − | 0.101702i | ||||
\(673\) | 35.7487i | 1.37801i | 0.724756 | + | 0.689006i | \(0.241953\pi\) | ||||
−0.724756 | + | 0.689006i | \(0.758047\pi\) | |||||||
\(674\) | 0.955005 | + | 0.955005i | 0.0367854 | + | 0.0367854i | ||||
\(675\) | 3.50625 | 0.134956 | ||||||||
\(676\) | −8.49625 | − | 9.83940i | −0.326779 | − | 0.378438i | ||||
\(677\) | − | 31.5694i | − | 1.21331i | −0.794966 | − | 0.606655i | \(-0.792511\pi\) | ||
0.794966 | − | 0.606655i | \(-0.207489\pi\) | |||||||
\(678\) | −2.41546 | − | 2.41546i | −0.0927653 | − | 0.0927653i | ||||
\(679\) | 1.63492 | + | 19.3990i | 0.0627423 | + | 0.744467i | ||||
\(680\) | 0.393764i | 0.0151002i | ||||||||
\(681\) | −0.501705 | + | 0.501705i | −0.0192254 | + | 0.0192254i | ||||
\(682\) | −8.55687 | − | 8.55687i | −0.327659 | − | 0.327659i | ||||
\(683\) | 23.7613 | + | 23.7613i | 0.909200 | + | 0.909200i | 0.996208 | − | 0.0870076i | \(-0.0277305\pi\) |
−0.0870076 | + | 0.996208i | \(0.527730\pi\) | |||||||
\(684\) | 1.77219 | − | 1.77219i | 0.0677612 | − | 0.0677612i | ||||
\(685\) | − | 3.34808i | − | 0.127924i | ||||||
\(686\) | −4.62214 | − | 17.9342i | −0.176474 | − | 0.684731i | ||||
\(687\) | −12.5167 | − | 12.5167i | −0.477542 | − | 0.477542i | ||||
\(688\) | − | 0.393764i | − | 0.0150121i | ||||||
\(689\) | −6.86478 | + | 2.55370i | −0.261527 | + | 0.0972881i | ||||
\(690\) | −3.30968 | −0.125997 | ||||||||
\(691\) | 2.90001 | + | 2.90001i | 0.110322 | + | 0.110322i | 0.760113 | − | 0.649791i | \(-0.225144\pi\) |
−0.649791 | + | 0.760113i | \(0.725144\pi\) | |||||||
\(692\) | 10.4694i | 0.397986i | ||||||||
\(693\) | −1.09999 | − | 13.0519i | −0.0417851 | − | 0.495799i | ||||
\(694\) | 15.2771 | − | 15.2771i | 0.579910 | − | 0.579910i | ||||
\(695\) | 13.3581 | − | 13.3581i | 0.506703 | − | 0.506703i | ||||
\(696\) | −3.40859 | + | 3.40859i | −0.129202 | + | 0.129202i | ||||
\(697\) | −2.08283 | − | 2.08283i | −0.0788929 | − | 0.0788929i | ||||
\(698\) | 36.3813i | 1.37705i | ||||||||
\(699\) | 5.52846 | 0.209106 | ||||||||
\(700\) | 7.08729 | + | 5.98554i | 0.267875 | + | 0.226232i | ||||
\(701\) | − | 25.6279i | − | 0.967954i | −0.875081 | − | 0.483977i | \(-0.839192\pi\) | ||
0.875081 | − | 0.483977i | \(-0.160808\pi\) | |||||||
\(702\) | 3.27843 | + | 1.50062i | 0.123736 | + | 0.0566374i | ||||
\(703\) | − | 8.07561i | − | 0.304577i | ||||||
\(704\) | 3.50062 | − | 3.50062i | 0.131935 | − | 0.131935i | ||||
\(705\) | 2.44438i | 0.0920608i | ||||||||
\(706\) | 13.8233 | 0.520245 | ||||||||
\(707\) | −15.8264 | − | 13.3661i | −0.595212 | − | 0.502684i | ||||
\(708\) | 10.7599 | − | 10.7599i | 0.404380 | − | 0.404380i | ||||
\(709\) | −31.7063 | − | 31.7063i | −1.19075 | − | 1.19075i | −0.976856 | − | 0.213899i | \(-0.931384\pi\) |
−0.213899 | − | 0.976856i | \(-0.568616\pi\) | |||||||
\(710\) | −0.791555 | + | 0.791555i | −0.0297065 | + | 0.0297065i | ||||
\(711\) | −8.81718 | −0.330670 | ||||||||
\(712\) | 5.21424 | 0.195412 | ||||||||
\(713\) | 4.68060 | − | 4.68060i | 0.175290 | − | 0.175290i | ||||
\(714\) | −0.0715854 | − | 0.849394i | −0.00267902 | − | 0.0317878i | ||||
\(715\) | −7.60624 | − | 20.4469i | −0.284457 | − | 0.764670i | ||||
\(716\) | −22.4990 | −0.840828 | ||||||||
\(717\) | −10.2332 | − | 10.2332i | −0.382164 | − | 0.382164i | ||||
\(718\) | −6.44904 | −0.240676 | ||||||||
\(719\) | 0.852526 | 0.0317938 | 0.0158969 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158969 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(720\) | 0.864220 | + | 0.864220i | 0.0322076 | + | 0.0322076i | ||||
\(721\) | −30.0170 | − | 25.3508i | −1.11789 | − | 0.944111i | ||||
\(722\) | −8.99349 | − | 8.99349i | −0.334703 | − | 0.334703i | ||||
\(723\) | 16.8108 | + | 16.8108i | 0.625199 | + | 0.625199i | ||||
\(724\) | 24.5008i | 0.910565i | ||||||||
\(725\) | − | 16.9018i | − | 0.627716i | ||||||
\(726\) | 9.55213 | − | 9.55213i | 0.354513 | − | 0.354513i | ||||
\(727\) | 8.14896 | 0.302228 | 0.151114 | − | 0.988516i | \(-0.451714\pi\) | ||||
0.151114 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(728\) | 4.06508 | + | 8.62990i | 0.150662 | + | 0.319845i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.37564 | − | 8.37564i | 0.309997 | − | 0.309997i | ||||
\(731\) | − | 0.126863i | − | 0.00469218i | ||||||
\(732\) | 10.6389i | 0.393225i | ||||||||
\(733\) | −6.44262 | − | 6.44262i | −0.237963 | − | 0.237963i | 0.578043 | − | 0.816006i | \(-0.303817\pi\) |
−0.816006 | + | 0.578043i | \(0.803817\pi\) | |||||||
\(734\) | 10.2518 | + | 10.2518i | 0.378402 | + | 0.378402i | ||||
\(735\) | 6.97670 | + | 4.95171i | 0.257340 | + | 0.182647i | ||||
\(736\) | 1.91484 | + | 1.91484i | 0.0705819 | + | 0.0705819i | ||||
\(737\) | −37.6950 | −1.38851 | ||||||||
\(738\) | −9.14265 | −0.336546 | ||||||||
\(739\) | 20.2641 | + | 20.2641i | 0.745426 | + | 0.745426i | 0.973616 | − | 0.228191i | \(-0.0732810\pi\) |
−0.228191 | + | 0.973616i | \(0.573281\pi\) | |||||||
\(740\) | 3.93813 | 0.144769 | ||||||||
\(741\) | −3.76094 | + | 8.21657i | −0.138162 | + | 0.301843i | ||||
\(742\) | 5.35564 | − | 0.451364i | 0.196612 | − | 0.0165701i | ||||
\(743\) | −32.6975 | + | 32.6975i | −1.19955 | + | 1.19955i | −0.225254 | + | 0.974300i | \(0.572321\pi\) |
−0.974300 | + | 0.225254i | \(0.927679\pi\) | |||||||
\(744\) | −2.44438 | −0.0896154 | ||||||||
\(745\) | −5.46507 | −0.200225 | ||||||||
\(746\) | 14.9958 | − | 14.9958i | 0.549035 | − | 0.549035i | ||||
\(747\) | −6.09203 | − | 6.09203i | −0.222896 | − | 0.222896i | ||||
\(748\) | 1.12783 | − | 1.12783i | 0.0412375 | − | 0.0412375i | ||||
\(749\) | −27.9316 | − | 23.5895i | −1.02060 | − | 0.861943i | ||||
\(750\) | −10.3963 | −0.379618 | ||||||||
\(751\) | − | 39.6528i | − | 1.44695i | −0.690351 | − | 0.723475i | \(-0.742544\pi\) | ||
0.690351 | − | 0.723475i | \(-0.257456\pi\) | |||||||
\(752\) | 1.41421 | − | 1.41421i | 0.0515711 | − | 0.0515711i | ||||
\(753\) | − | 13.3838i | − | 0.487732i | ||||||
\(754\) | 7.23372 | − | 15.8036i | 0.263437 | − | 0.575533i | ||||
\(755\) | − | 27.4600i | − | 0.999372i | ||||||
\(756\) | −2.02133 | − | 1.70711i | −0.0735152 | − | 0.0620869i | ||||
\(757\) | −32.1926 | −1.17006 | −0.585030 | − | 0.811012i | \(-0.698917\pi\) | ||||
−0.585030 | + | 0.811012i | \(0.698917\pi\) | |||||||
\(758\) | − | 35.4080i | − | 1.28608i | ||||||
\(759\) | 9.47966 | + | 9.47966i | 0.344090 | + | 0.344090i | ||||
\(760\) | −2.16595 | + | 2.16595i | −0.0785672 | + | 0.0785672i | ||||
\(761\) | −22.8646 | + | 22.8646i | −0.828842 | + | 0.828842i | −0.987357 | − | 0.158514i | \(-0.949330\pi\) |
0.158514 | + | 0.987357i | \(0.449330\pi\) | |||||||
\(762\) | 6.86314 | − | 6.86314i | 0.248625 | − | 0.248625i | ||||
\(763\) | −19.3668 | + | 1.63220i | −0.701126 | + | 0.0590896i | ||||
\(764\) | − | 0.869566i | − | 0.0314598i | ||||||
\(765\) | 0.278433 | + | 0.278433i | 0.0100668 | + | 0.0100668i | ||||
\(766\) | −20.5656 | −0.743064 | ||||||||
\(767\) | −22.8346 | + | 49.8871i | −0.824510 | + | 1.80132i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −13.5311 | − | 13.5311i | −0.487943 | − | 0.487943i | 0.419714 | − | 0.907657i | \(-0.362130\pi\) |
−0.907657 | + | 0.419714i | \(0.862130\pi\) | |||||||
\(770\) | 1.34440 | + | 15.9519i | 0.0484486 | + | 0.574866i | ||||
\(771\) | − | 11.3581i | − | 0.409053i | ||||||
\(772\) | −6.38377 | + | 6.38377i | −0.229757 | + | 0.229757i | ||||
\(773\) | −9.19917 | − | 9.19917i | −0.330871 | − | 0.330871i | 0.522046 | − | 0.852917i | \(-0.325169\pi\) |
−0.852917 | + | 0.522046i | \(0.825169\pi\) | |||||||
\(774\) | −0.278433 | − | 0.278433i | −0.0100081 | − | 0.0100081i | ||||
\(775\) | 6.06034 | − | 6.06034i | 0.217694 | − | 0.217694i | ||||
\(776\) | 7.35814i | 0.264142i | ||||||||
\(777\) | −8.49500 | + | 0.715943i | −0.304756 | + | 0.0256843i | ||||
\(778\) | −21.6910 | − | 21.6910i | −0.777662 | − | 0.777662i | ||||
\(779\) | − | 22.9138i | − | 0.820971i | ||||||
\(780\) | −4.00687 | − | 1.83405i | −0.143469 | − | 0.0656695i | ||||
\(781\) | 4.53437 | 0.162253 | ||||||||
\(782\) | 0.616920 | + | 0.616920i | 0.0220610 | + | 0.0220610i | ||||
\(783\) | 4.82047i | 0.172270i | ||||||||
\(784\) | −1.17157 | − | 6.90126i | −0.0418419 | − | 0.246474i | ||||
\(785\) | −9.45251 | + | 9.45251i | −0.337374 | + | 0.337374i | ||||
\(786\) | 13.0081 | − | 13.0081i | 0.463984 | − | 0.463984i | ||||
\(787\) | 7.86571 | − | 7.86571i | 0.280382 | − | 0.280382i | −0.552879 | − | 0.833261i | \(-0.686471\pi\) |
0.833261 | + | 0.552879i | \(0.186471\pi\) | |||||||
\(788\) | 10.5087 | + | 10.5087i | 0.374359 | + | 0.374359i | ||||
\(789\) | 28.4021i | 1.01114i | ||||||||
\(790\) | 10.7763 | 0.383403 | ||||||||
\(791\) | −6.90483 | − | 5.83144i | −0.245508 | − | 0.207342i | ||||
\(792\) | − | 4.95063i | − | 0.175913i | ||||||
\(793\) | −13.3742 | − | 35.9521i | −0.474931 | − | 1.27670i | ||||
\(794\) | − | 2.51950i | − | 0.0894138i | ||||||
\(795\) | −1.75559 | + | 1.75559i | −0.0622644 | + | 0.0622644i | ||||
\(796\) | − | 16.9105i | − | 0.599376i | ||||||
\(797\) | 15.6097 | 0.552924 | 0.276462 | − | 0.961025i | \(-0.410838\pi\) | ||||
0.276462 | + | 0.961025i | \(0.410838\pi\) | |||||||
\(798\) | 4.27843 | − | 5.06596i | 0.151455 | − | 0.179333i | ||||
\(799\) | 0.455630 | − | 0.455630i | 0.0161190 | − | 0.0161190i | ||||
\(800\) | 2.47929 | + | 2.47929i | 0.0876562 | + | 0.0876562i | ||||
\(801\) | 3.68702 | − | 3.68702i | 0.130275 | − | 0.130275i | ||||
\(802\) | −2.85695 | −0.100883 | ||||||||
\(803\) | −47.9794 | −1.69316 | ||||||||
\(804\) | −5.38404 | + | 5.38404i | −0.189881 | + | 0.189881i | ||||
\(805\) | −8.72566 | + | 0.735383i | −0.307539 | + | 0.0259188i | ||||
\(806\) | 8.26031 | − | 3.07283i | 0.290957 | − | 0.108236i | ||||
\(807\) | −22.3912 | −0.788208 | ||||||||
\(808\) | −5.53642 | − | 5.53642i | −0.194770 | − | 0.194770i | ||||
\(809\) | −0.500062 | −0.0175813 | −0.00879063 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879063 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(810\) | 1.22219 | 0.0429434 | ||||||||
\(811\) | −1.13249 | − | 1.13249i | −0.0397670 | − | 0.0397670i | 0.686944 | − | 0.726711i | \(-0.258952\pi\) |
−0.726711 | + | 0.686944i | \(0.758952\pi\) | |||||||
\(812\) | −8.22906 | + | 9.74378i | −0.288784 | + | 0.341940i | ||||
\(813\) | 1.82388 | + | 1.82388i | 0.0639664 | + | 0.0639664i | ||||
\(814\) | −11.2797 | − | 11.2797i | −0.395353 | − | 0.395353i | ||||
\(815\) | − | 1.18837i | − | 0.0416269i | ||||||
\(816\) | − | 0.322179i | − | 0.0112785i | ||||||
\(817\) | 0.697823 | − | 0.697823i | 0.0244137 | − | 0.0244137i | ||||
\(818\) | −16.6407 | −0.581827 | ||||||||
\(819\) | 8.97670 | + | 3.22781i | 0.313671 | + | 0.112789i | ||||
\(820\) | 11.1741 | 0.390216 | ||||||||
\(821\) | 26.7861 | − | 26.7861i | 0.934841 | − | 0.934841i | −0.0631619 | − | 0.998003i | \(-0.520118\pi\) |
0.998003 | + | 0.0631619i | \(0.0201185\pi\) | |||||||
\(822\) | 2.73941i | 0.0955479i | ||||||||
\(823\) | 31.9038i | 1.11210i | 0.831150 | + | 0.556048i | \(0.187683\pi\) | ||||
−0.831150 | + | 0.556048i | \(0.812317\pi\) | |||||||
\(824\) | −10.5006 | − | 10.5006i | −0.365807 | − | 0.365807i | ||||
\(825\) | 12.2741 | + | 12.2741i | 0.427328 | + | 0.427328i | ||||
\(826\) | 25.9766 | − | 30.7581i | 0.903841 | − | 1.07021i | ||||
\(827\) | −10.2391 | − | 10.2391i | −0.356047 | − | 0.356047i | 0.506307 | − | 0.862354i | \(-0.331010\pi\) |
−0.862354 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(828\) | 2.70799 | 0.0941092 | ||||||||
\(829\) | 29.3502 | 1.01937 | 0.509687 | − | 0.860360i | \(-0.329761\pi\) | ||||
0.509687 | + | 0.860360i | \(0.329761\pi\) | |||||||
\(830\) | 7.44563 | + | 7.44563i | 0.258442 | + | 0.258442i | ||||
\(831\) | 16.7343 | 0.580508 | ||||||||
\(832\) | 1.25710 | + | 3.37930i | 0.0435821 | + | 0.117156i | ||||
\(833\) | −0.377456 | − | 2.22344i | −0.0130781 | − | 0.0770377i | ||||
\(834\) | −10.9297 | + | 10.9297i | −0.378463 | + | 0.378463i | ||||
\(835\) | −19.9794 | −0.691415 | ||||||||
\(836\) | 12.4075 | 0.429123 | ||||||||
\(837\) | −1.72844 | + | 1.72844i | −0.0597436 | + | 0.0597436i | ||||
\(838\) | 6.60641 | + | 6.60641i | 0.228214 | + | 0.228214i | ||||
\(839\) | −5.00302 | + | 5.00302i | −0.172723 | + | 0.172723i | −0.788175 | − | 0.615451i | \(-0.788974\pi\) |
0.615451 | + | 0.788175i | \(0.288974\pi\) | |||||||
\(840\) | 2.47046 | + | 2.08641i | 0.0852388 | + | 0.0719880i | ||||
\(841\) | −5.76303 | −0.198725 | ||||||||
\(842\) | − | 10.3547i | − | 0.356848i | ||||||
\(843\) | −5.38706 | + | 5.38706i | −0.185540 | + | 0.185540i | ||||
\(844\) | − | 4.96188i | − | 0.170795i | ||||||
\(845\) | 15.8460 | + | 1.16077i | 0.545120 | + | 0.0399318i | ||||
\(846\) | − | 2.00000i | − | 0.0687614i | ||||||
\(847\) | 23.0609 | − | 27.3057i | 0.792381 | − | 0.938234i | ||||
\(848\) | 2.03142 | 0.0697592 | ||||||||
\(849\) | − | 17.0421i | − | 0.584885i | ||||||
\(850\) | 0.798775 | + | 0.798775i | 0.0273978 | + | 0.0273978i | ||||
\(851\) | 6.16998 | − | 6.16998i | 0.211504 | − | 0.211504i | ||||
\(852\) | 0.647652 | − | 0.647652i | 0.0221882 | − | 0.0221882i | ||||
\(853\) | 1.25690 | − | 1.25690i | 0.0430356 | − | 0.0430356i | −0.685262 | − | 0.728297i | \(-0.740312\pi\) |
0.728297 | + | 0.685262i | \(0.240312\pi\) | |||||||
\(854\) | 2.36387 | + | 28.0485i | 0.0808901 | + | 0.959799i | ||||
\(855\) | 3.06311i | 0.104756i | ||||||||
\(856\) | −9.77111 | − | 9.77111i | −0.333970 | − | 0.333970i | ||||
\(857\) | −2.59639 | −0.0886910 | −0.0443455 | − | 0.999016i | \(-0.514120\pi\) | ||||
−0.0443455 | + | 0.999016i | \(0.514120\pi\) | |||||||
\(858\) | 6.22344 | + | 16.7297i | 0.212465 | + | 0.571142i | ||||
\(859\) | − | 15.8670i | − | 0.541376i | −0.962667 | − | 0.270688i | \(-0.912749\pi\) | ||
0.962667 | − | 0.270688i | \(-0.0872512\pi\) | |||||||
\(860\) | 0.340299 | + | 0.340299i | 0.0116041 | + | 0.0116041i | ||||
\(861\) | −24.1037 | + | 2.03142i | −0.821453 | + | 0.0692306i | ||||
\(862\) | 38.0678i | 1.29660i | ||||||||
\(863\) | 17.3932 | − | 17.3932i | 0.592073 | − | 0.592073i | −0.346118 | − | 0.938191i | \(-0.612500\pi\) |
0.938191 | + | 0.346118i | \(0.112500\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | −9.04784 | − | 9.04784i | −0.307636 | − | 0.307636i | ||||
\(866\) | −21.8050 | + | 21.8050i | −0.740965 | + | 0.740965i | ||||
\(867\) | 16.8962i | 0.573825i | ||||||||
\(868\) | −6.44438 | + | 0.543121i | −0.218737 | + | 0.0184347i | ||||
\(869\) | −30.8656 | − | 30.8656i | −1.04705 | − | 1.04705i | ||||
\(870\) | − | 5.89154i | − | 0.199742i | ||||||
\(871\) | 11.4260 | − | 24.9626i | 0.387157 | − | 0.845826i | ||||
\(872\) | −7.34592 | −0.248764 | ||||||||
\(873\) | 5.20299 | + | 5.20299i | 0.176095 | + | 0.176095i | ||||
\(874\) | 6.78690i | 0.229570i | ||||||||
\(875\) | −27.4088 | + | 2.30996i | −0.926585 | + | 0.0780909i | ||||
\(876\) | −6.85297 | + | 6.85297i | −0.231540 | + | 0.231540i | ||||
\(877\) | −4.65810 | + | 4.65810i | −0.157293 | + | 0.157293i | −0.781366 | − | 0.624073i | \(-0.785477\pi\) |
0.624073 | + | 0.781366i | \(0.285477\pi\) | |||||||
\(878\) | 10.1278 | − | 10.1278i | 0.341798 | − | 0.341798i | ||||
\(879\) | −4.20174 | − | 4.20174i | −0.141721 | − | 0.141721i | ||||
\(880\) | 6.05062i | 0.203966i | ||||||||
\(881\) | 15.3188 | 0.516102 | 0.258051 | − | 0.966131i | \(-0.416920\pi\) | ||||
0.258051 | + | 0.966131i | \(0.416920\pi\) | |||||||
\(882\) | −5.70836 | − | 4.05150i | −0.192210 | − | 0.136421i | ||||
\(883\) | 41.5251i | 1.39743i | 0.715399 | + | 0.698716i | \(0.246245\pi\) | ||||
−0.715399 | + | 0.698716i | \(0.753755\pi\) | |||||||
\(884\) | 0.405011 | + | 1.08874i | 0.0136220 | + | 0.0366183i | ||||
\(885\) | 18.5978i | 0.625157i | ||||||||
\(886\) | 15.2326 | − | 15.2326i | 0.511751 | − | 0.511751i | ||||
\(887\) | 45.8470i | 1.53939i | 0.638410 | + | 0.769697i | \(0.279592\pi\) | ||||
−0.638410 | + | 0.769697i | \(0.720408\pi\) | |||||||
\(888\) | −3.22219 | −0.108130 | ||||||||
\(889\) | 16.5691 | − | 19.6189i | 0.555709 | − | 0.657998i | ||||
\(890\) | −4.50625 | + | 4.50625i | −0.151050 | + | 0.151050i | ||||
\(891\) | −3.50062 | − | 3.50062i | −0.117275 | − | 0.117275i | ||||
\(892\) | 5.69799 | − | 5.69799i | 0.190783 | − | 0.190783i | ||||
\(893\) | 5.01250 | 0.167737 | ||||||||
\(894\) | 4.47154 | 0.149551 | ||||||||
\(895\) | 19.4441 | − | 19.4441i | 0.649945 | − | 0.649945i | ||||
\(896\) | −0.222191 | − | 2.63640i | −0.00742289 | − | 0.0880761i | ||||
\(897\) | −9.15112 | + | 3.40422i | −0.305547 | + | 0.113663i | ||||
\(898\) | 39.9349 | 1.33265 | ||||||||
\(899\) | 8.33190 | + | 8.33190i | 0.277884 | + | 0.277884i | ||||
\(900\) | 3.50625 | 0.116875 | ||||||||
\(901\) | 0.654480 | 0.0218039 | ||||||||
\(902\) | −32.0050 | − | 32.0050i | −1.06565 | − | 1.06565i | ||||
\(903\) | −0.795929 | − | 0.672198i | −0.0264868 | − | 0.0223693i | ||||
\(904\) | −2.41546 | − | 2.41546i | −0.0803371 | − | 0.0803371i | ||||
\(905\) | −21.1741 | − | 21.1741i | −0.703850 | − | 0.703850i | ||||
\(906\) | 22.4678i | 0.746444i | ||||||||
\(907\) | 19.6544i | 0.652612i | 0.945264 | + | 0.326306i | \(0.105804\pi\) | ||||
−0.945264 | + | 0.326306i | \(0.894196\pi\) | |||||||
\(908\) | −0.501705 | + | 0.501705i | −0.0166497 | + | 0.0166497i | ||||
\(909\) | −7.82968 | −0.259694 | ||||||||
\(910\) | −10.9712 | − | 3.94501i | −0.363693 | − | 0.130776i | ||||
\(911\) | −28.4979 | −0.944177 | −0.472089 | − | 0.881551i | \(-0.656500\pi\) | ||||
−0.472089 | + | 0.881551i | \(0.656500\pi\) | |||||||
\(912\) | 1.77219 | − | 1.77219i | 0.0586829 | − | 0.0586829i | ||||
\(913\) | − | 42.6519i | − | 1.41157i | ||||||
\(914\) | 18.0529i | 0.597136i | ||||||||
\(915\) | −9.19435 | − | 9.19435i | −0.303956 | − | 0.303956i | ||||
\(916\) | −12.5167 | − | 12.5167i | −0.413563 | − | 0.413563i | ||||
\(917\) | 31.4044 | − | 37.1850i | 1.03706 | − | 1.22796i | ||||
\(918\) | −0.227815 | − | 0.227815i | −0.00751901 | − | 0.00751901i | ||||
\(919\) | −6.44938 | −0.212745 | −0.106373 | − | 0.994326i | \(-0.533924\pi\) | ||||
−0.106373 | + | 0.994326i | \(0.533924\pi\) | |||||||
\(920\) | −3.30968 | −0.109117 | ||||||||
\(921\) | 17.0150 | + | 17.0150i | 0.560663 | + | 0.560663i | ||||
\(922\) | 18.8596 | 0.621108 | ||||||||
\(923\) | −1.37445 | + | 3.00278i | −0.0452406 | + | 0.0988376i | ||||
\(924\) | −1.09999 | − | 13.0519i | −0.0361869 | − | 0.429375i | ||||
\(925\) | 7.98875 | − | 7.98875i | 0.262669 | − | 0.262669i | ||||
\(926\) | 30.2234 | 0.993204 | ||||||||
\(927\) | −14.8501 | −0.487742 | ||||||||
\(928\) | −3.40859 | + | 3.40859i | −0.111892 | + | 0.111892i | ||||
\(929\) | −30.8995 | − | 30.8995i | −1.01378 | − | 1.01378i | −0.999904 | − | 0.0138758i | \(-0.995583\pi\) |
−0.0138758 | − | 0.999904i | \(-0.504417\pi\) | |||||||
\(930\) | 2.11248 | − | 2.11248i | 0.0692711 | − | 0.0692711i | ||||
\(931\) | 10.1541 | − | 14.3066i | 0.332786 | − | 0.468878i | ||||
\(932\) | 5.52846 | 0.181091 | ||||||||
\(933\) | 13.7090i | 0.448813i | ||||||||
\(934\) | 28.9951 | − | 28.9951i | 0.948749 | − | 0.948749i | ||||
\(935\) | 1.94938i | 0.0637516i | ||||||||
\(936\) | 3.27843 | + | 1.50062i | 0.107159 | + | 0.0490495i | ||||
\(937\) | − | 50.5081i | − | 1.65003i | −0.565112 | − | 0.825014i | \(-0.691167\pi\) | ||
0.565112 | − | 0.825014i | \(-0.308833\pi\) | |||||||
\(938\) | −12.9982 | + | 15.3908i | −0.424407 | + | 0.502528i | ||||
\(939\) | 17.4456 | 0.569317 | ||||||||
\(940\) | 2.44438i | 0.0797270i | ||||||||
\(941\) | 13.7563 | + | 13.7563i | 0.448443 | + | 0.448443i | 0.894837 | − | 0.446393i | \(-0.147292\pi\) |
−0.446393 | + | 0.894837i | \(0.647292\pi\) | |||||||
\(942\) | 7.73406 | − | 7.73406i | 0.251989 | − | 0.251989i | ||||
\(943\) | 17.5067 | − | 17.5067i | 0.570097 | − | 0.570097i | ||||
\(944\) | 10.7599 | − | 10.7599i | 0.350204 | − | 0.350204i | ||||
\(945\) | 3.22219 | − | 0.271560i | 0.104818 | − | 0.00883386i | ||||
\(946\) | − | 1.94938i | − | 0.0633799i | ||||||
\(947\) | −16.6588 | − | 16.6588i | −0.541338 | − | 0.541338i | 0.382583 | − | 0.923921i | \(-0.375035\pi\) |
−0.923921 | + | 0.382583i | \(0.875035\pi\) | |||||||
\(948\) | −8.81718 | −0.286369 | ||||||||
\(949\) | 14.5434 | − | 31.7732i | 0.472099 | − | 1.03140i | ||||
\(950\) | 8.78753i | 0.285105i | ||||||||
\(951\) | 21.4771 | + | 21.4771i | 0.696441 | + | 0.696441i | ||||
\(952\) | −0.0715854 | − | 0.849394i | −0.00232010 | − | 0.0275290i | ||||
\(953\) | − | 17.6456i | − | 0.571597i | −0.958290 | − | 0.285799i | \(-0.907741\pi\) | ||
0.958290 | − | 0.285799i | \(-0.0922589\pi\) | |||||||
\(954\) | 1.43643 | − | 1.43643i | 0.0465061 | − | 0.0465061i | ||||
\(955\) | 0.751496 | + | 0.751496i | 0.0243178 | + | 0.0243178i | ||||
\(956\) | −10.2332 | − | 10.2332i | −0.330964 | − | 0.330964i | ||||
\(957\) | −16.8747 | + | 16.8747i | −0.545481 | + | 0.545481i | ||||
\(958\) | 9.82246i | 0.317349i | ||||||||
\(959\) | 0.608673 | + | 7.22219i | 0.0196551 | + | 0.233217i | ||||
\(960\) | 0.864220 | + | 0.864220i | 0.0278926 | + | 0.0278926i | ||||
\(961\) | − | 25.0250i | − | 0.807258i | ||||||
\(962\) | 10.8888 | − | 4.05062i | 0.351068 | − | 0.130597i | ||||
\(963\) | −13.8184 | −0.445293 | ||||||||
\(964\) | 16.8108 | + | 16.8108i | 0.541438 | + | 0.541438i | ||||
\(965\) | − | 11.0340i | − | 0.355196i | ||||||
\(966\) | 7.13936 | − | 0.601692i | 0.229705 | − | 0.0193591i | ||||
\(967\) | −38.6204 | + | 38.6204i | −1.24195 | + | 1.24195i | −0.282756 | + | 0.959192i | \(0.591249\pi\) |
−0.959192 | + | 0.282756i | \(0.908751\pi\) | |||||||
\(968\) | 9.55213 | − | 9.55213i | 0.307017 | − | 0.307017i | ||||
\(969\) | 0.570961 | − | 0.570961i | 0.0183419 | − | 0.0183419i | ||||
\(970\) | −6.35905 | − | 6.35905i | −0.204177 | − | 0.204177i | ||||
\(971\) | − | 1.62095i | − | 0.0520189i | −0.999662 | − | 0.0260094i | \(-0.991720\pi\) | ||
0.999662 | − | 0.0260094i | \(-0.00828000\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −26.3865 | + | 31.2435i | −0.845914 | + | 1.00162i | ||||
\(974\) | 32.7731i | 1.05012i | ||||||||
\(975\) | −11.8487 | + | 4.40771i | −0.379461 | + | 0.141160i | ||||
\(976\) | 10.6389i | 0.340543i | ||||||||
\(977\) | −35.9201 | + | 35.9201i | −1.14919 | + | 1.14919i | −0.162473 | + | 0.986713i | \(0.551947\pi\) |
−0.986713 | + | 0.162473i | \(0.948053\pi\) | |||||||
\(978\) | 0.972330i | 0.0310917i | ||||||||
\(979\) | 25.8138 | 0.825012 | ||||||||
\(980\) | 6.97670 | + | 4.95171i | 0.222863 | + | 0.158177i | ||||
\(981\) | −5.19435 | + | 5.19435i | −0.165843 | + | 0.165843i | ||||
\(982\) | 11.0454 | + | 11.0454i | 0.352474 | + | 0.352474i | ||||
\(983\) | 7.99017 | − | 7.99017i | 0.254847 | − | 0.254847i | −0.568107 | − | 0.822954i | \(-0.692324\pi\) |
0.822954 | + | 0.568107i | \(0.192324\pi\) | |||||||
\(984\) | −9.14265 | −0.291457 | ||||||||
\(985\) | −18.1637 | −0.578745 | ||||||||
\(986\) | −1.09818 | + | 1.09818i | −0.0349730 | + | 0.0349730i | ||||
\(987\) | −0.444383 | − | 5.27281i | −0.0141449 | − | 0.167835i | ||||
\(988\) | −3.76094 | + | 8.21657i | −0.119651 | + | 0.261404i | ||||
\(989\) | 1.06631 | 0.0339067 | ||||||||
\(990\) | 4.27843 | + | 4.27843i | 0.135978 | + | 0.135978i | ||||
\(991\) | −20.8202 | −0.661377 | −0.330688 | − | 0.943740i | \(-0.607281\pi\) | ||||
−0.330688 | + | 0.943740i | \(0.607281\pi\) | |||||||
\(992\) | −2.44438 | −0.0776092 | ||||||||
\(993\) | 5.19998 | + | 5.19998i | 0.165016 | + | 0.165016i | ||||
\(994\) | 1.56357 | − | 1.85138i | 0.0495934 | − | 0.0587221i | ||||
\(995\) | 14.6144 | + | 14.6144i | 0.463306 | + | 0.463306i | ||||
\(996\) | −6.09203 | − | 6.09203i | −0.193034 | − | 0.193034i | ||||
\(997\) | 32.4465i | 1.02759i | 0.857913 | + | 0.513795i | \(0.171761\pi\) | ||||
−0.857913 | + | 0.513795i | \(0.828239\pi\) | |||||||
\(998\) | − | 36.2860i | − | 1.14861i | ||||||
\(999\) | −2.27843 | + | 2.27843i | −0.0720864 | + | 0.0720864i |
(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 | 546.2.o.b.265.4 | ✓ | 8 | |
3.2 | odd | 2 | 1638.2.x.c.811.1 | 8 | |||
7.6 | odd | 2 | 546.2.o.c.265.3 | yes | 8 | ||
13.8 | odd | 4 | 546.2.o.c.307.3 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.a.811.2 | 8 | |||
39.8 | even | 4 | 1638.2.x.a.307.2 | 8 | |||
91.34 | even | 4 | inner | 546.2.o.b.307.4 | yes | 8 | |
273.125 | odd | 4 | 1638.2.x.c.307.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
546.2.o.b.307.4 | yes | 8 | 91.34 | even | 4 | inner | |
546.2.o.c.265.3 | yes | 8 | 7.6 | odd | 2 | ||
546.2.o.c.307.3 | yes | 8 | 13.8 | odd | 4 | ||
1638.2.x.a.307.2 | 8 | 39.8 | even | 4 | |||
1638.2.x.a.811.2 | 8 | 21.20 | even | 2 | |||
1638.2.x.c.307.1 | 8 | 273.125 | odd | 4 | |||
1638.2.x.c.811.1 | 8 | 3.2 | odd | 2 |