Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(883,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3822.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.c (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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9144576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 883.2 | ||
Root | \(-0.339877i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.883 |
Dual form | 3822.2.c.j.883.5 |
$q$-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 \(\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times\).
\(n\) | \(1471\) | \(2549\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.339877i | − | 0.151998i | −0.997108 | − | 0.0759988i | \(-0.975785\pi\) | ||
0.997108 | − | 0.0759988i | \(-0.0242145\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.339877 | −0.107479 | ||||||||
\(11\) | 0.660123i | 0.199035i | 0.995036 | + | 0.0995173i | \(0.0317299\pi\) | ||||
−0.995036 | + | 0.0995173i | \(0.968270\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.660123 | − | 3.54461i | −0.183085 | − | 0.983097i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.339877i | 0.0877558i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.54461 | 1.58730 | 0.793650 | − | 0.608374i | \(-0.208178\pi\) | ||||
0.793650 | + | 0.608374i | \(0.208178\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 6.08921i | 1.39696i | 0.715629 | + | 0.698481i | \(0.246140\pi\) | ||||
−0.715629 | + | 0.698481i | \(0.753860\pi\) | |||||||
\(20\) | 0.339877i | 0.0759988i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.660123 | 0.140739 | ||||||||
\(23\) | −7.42909 | −1.54907 | −0.774536 | − | 0.632530i | \(-0.782017\pi\) | ||||
−0.774536 | + | 0.632530i | \(0.782017\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 4.88448 | 0.976897 | ||||||||
\(26\) | −3.54461 | + | 0.660123i | −0.695155 | + | 0.129461i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56424 | −0.661862 | −0.330931 | − | 0.943655i | \(-0.607363\pi\) | ||||
−0.330931 | + | 0.943655i | \(0.607363\pi\) | |||||||
\(30\) | 0.339877 | 0.0620527 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 0.660123i | − | 0.114913i | ||||||
\(34\) | − | 6.54461i | − | 1.12239i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 3.54461i | − | 0.582730i | −0.956612 | − | 0.291365i | \(-0.905891\pi\) | ||
0.956612 | − | 0.291365i | \(-0.0941094\pi\) | |||||||
\(38\) | 6.08921 | 0.987801 | ||||||||
\(39\) | 0.660123 | + | 3.54461i | 0.105704 | + | 0.567591i | ||||
\(40\) | 0.339877 | 0.0537393 | ||||||||
\(41\) | 0.864853i | 0.135067i | 0.997717 | + | 0.0675337i | \(0.0215130\pi\) | ||||
−0.997717 | + | 0.0675337i | \(0.978487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.08921 | −0.776098 | −0.388049 | − | 0.921639i | \(-0.626851\pi\) | ||||
−0.388049 | + | 0.921639i | \(0.626851\pi\) | |||||||
\(44\) | − | 0.660123i | − | 0.0995173i | ||||||
\(45\) | − | 0.339877i | − | 0.0506659i | ||||||
\(46\) | 7.42909i | 1.09536i | ||||||||
\(47\) | 9.44872i | 1.37824i | 0.724648 | + | 0.689119i | \(0.242002\pi\) | ||||
−0.724648 | + | 0.689119i | \(0.757998\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.88448i | − | 0.690770i | ||||||
\(51\) | −6.54461 | −0.916428 | ||||||||
\(52\) | 0.660123 | + | 3.54461i | 0.0915426 | + | 0.491549i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0.224361 | 0.0302528 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.08921i | − | 0.806536i | ||||||
\(58\) | 3.56424i | 0.468007i | ||||||||
\(59\) | − | 3.90411i | − | 0.508272i | −0.967168 | − | 0.254136i | \(-0.918209\pi\) | ||
0.967168 | − | 0.254136i | \(-0.0817911\pi\) | |||||||
\(60\) | − | 0.339877i | − | 0.0438779i | ||||||
\(61\) | −1.86485 | −0.238770 | −0.119385 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119385 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.20473 | + | 0.224361i | −0.149428 | + | 0.0278285i | ||||
\(66\) | −0.660123 | −0.0812555 | ||||||||
\(67\) | − | 7.44872i | − | 0.910006i | −0.890490 | − | 0.455003i | \(-0.849638\pi\) | ||
0.890490 | − | 0.455003i | \(-0.150362\pi\) | |||||||
\(68\) | −6.54461 | −0.793650 | ||||||||
\(69\) | 7.42909 | 0.894357 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.884484i | 0.104969i | 0.998622 | + | 0.0524845i | \(0.0167140\pi\) | ||||
−0.998622 | + | 0.0524845i | \(0.983286\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 10.0696i | 1.17856i | 0.807931 | + | 0.589278i | \(0.200588\pi\) | ||||
−0.807931 | + | 0.589278i | \(0.799412\pi\) | |||||||
\(74\) | −3.54461 | −0.412052 | ||||||||
\(75\) | −4.88448 | −0.564012 | ||||||||
\(76\) | − | 6.08921i | − | 0.698481i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.54461 | − | 0.660123i | 0.401348 | − | 0.0747442i | ||||
\(79\) | −12.4487 | −1.40059 | −0.700295 | − | 0.713853i | \(-0.746948\pi\) | ||||
−0.700295 | + | 0.713853i | \(0.746948\pi\) | |||||||
\(80\) | − | 0.339877i | − | 0.0379994i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.864853 | 0.0955070 | ||||||||
\(83\) | 16.2939i | 1.78849i | 0.447575 | + | 0.894246i | \(0.352288\pi\) | ||||
−0.447575 | + | 0.894246i | \(0.647712\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.22436i | − | 0.241266i | ||||||
\(86\) | 5.08921i | 0.548784i | ||||||||
\(87\) | 3.56424 | 0.382126 | ||||||||
\(88\) | −0.660123 | −0.0703694 | ||||||||
\(89\) | − | 4.45539i | − | 0.472271i | −0.971720 | − | 0.236135i | \(-0.924119\pi\) | ||
0.971720 | − | 0.236135i | \(-0.0758809\pi\) | |||||||
\(90\) | −0.339877 | −0.0358262 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.42909 | 0.774536 | ||||||||
\(93\) | − | 4.00000i | − | 0.414781i | ||||||
\(94\) | 9.44872 | 0.974561 | ||||||||
\(95\) | 2.06958 | 0.212335 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 16.1088i | 1.63561i | 0.575499 | + | 0.817803i | \(0.304808\pi\) | ||||
−0.575499 | + | 0.817803i | \(0.695192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.660123i | 0.0663449i | ||||||||
\(100\) | −4.88448 | −0.488448 | ||||||||
\(101\) | −2.79527 | −0.278140 | −0.139070 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139070 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(102\) | 6.54461i | 0.648013i | ||||||||
\(103\) | 7.53793 | 0.742735 | 0.371367 | − | 0.928486i | \(-0.378889\pi\) | ||||
0.371367 | + | 0.928486i | \(0.378889\pi\) | |||||||
\(104\) | 3.54461 | − | 0.660123i | 0.347577 | − | 0.0647304i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 3.00000i | − | 0.291386i | ||||||
\(107\) | −3.72971 | −0.360564 | −0.180282 | − | 0.983615i | \(-0.557701\pi\) | ||||
−0.180282 | + | 0.983615i | \(0.557701\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − | 14.4095i | − | 1.38018i | −0.723725 | − | 0.690088i | \(-0.757572\pi\) | ||
0.723725 | − | 0.690088i | \(-0.242428\pi\) | |||||||
\(110\) | − | 0.224361i | − | 0.0213919i | ||||||
\(111\) | 3.54461i | 0.336439i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5576 | 1.46353 | 0.731766 | − | 0.681556i | \(-0.238696\pi\) | ||||
0.731766 | + | 0.681556i | \(0.238696\pi\) | |||||||
\(114\) | −6.08921 | −0.570307 | ||||||||
\(115\) | 2.52498i | 0.235455i | ||||||||
\(116\) | 3.56424 | 0.330931 | ||||||||
\(117\) | −0.660123 | − | 3.54461i | −0.0610284 | − | 0.327699i | ||||
\(118\) | −3.90411 | −0.359403 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.339877 | −0.0310264 | ||||||||
\(121\) | 10.5642 | 0.960385 | ||||||||
\(122\) | 1.86485i | 0.168836i | ||||||||
\(123\) | − | 0.864853i | − | 0.0779812i | ||||||
\(124\) | − | 4.00000i | − | 0.359211i | ||||||
\(125\) | − | 3.35951i | − | 0.300483i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4028 | 1.27804 | 0.639020 | − | 0.769190i | \(-0.279340\pi\) | ||||
0.639020 | + | 0.769190i | \(0.279340\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 5.08921 | 0.448080 | ||||||||
\(130\) | 0.224361 | + | 1.20473i | 0.0196777 | + | 0.105662i | ||||
\(131\) | 20.6731 | 1.80622 | 0.903108 | − | 0.429414i | \(-0.141280\pi\) | ||||
0.903108 | + | 0.429414i | \(0.141280\pi\) | |||||||
\(132\) | 0.660123i | 0.0574563i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.44872 | −0.643472 | ||||||||
\(135\) | 0.339877i | 0.0292519i | ||||||||
\(136\) | 6.54461i | 0.561195i | ||||||||
\(137\) | 14.2244i | 1.21527i | 0.794217 | + | 0.607635i | \(0.207881\pi\) | ||||
−0.794217 | + | 0.607635i | \(0.792119\pi\) | |||||||
\(138\) | − | 7.42909i | − | 0.632406i | ||||||
\(139\) | −9.42909 | −0.799765 | −0.399883 | − | 0.916566i | \(-0.630949\pi\) | ||||
−0.399883 | + | 0.916566i | \(0.630949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.44872i | − | 0.795726i | ||||||
\(142\) | 0.884484 | 0.0742242 | ||||||||
\(143\) | 2.33988 | − | 0.435763i | 0.195670 | − | 0.0364403i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.21140i | 0.100601i | ||||||||
\(146\) | 10.0696 | 0.833365 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.54461i | 0.291365i | ||||||||
\(149\) | 8.10884i | 0.664302i | 0.943226 | + | 0.332151i | \(0.107774\pi\) | ||||
−0.943226 | + | 0.332151i | \(0.892226\pi\) | |||||||
\(150\) | 4.88448i | 0.398816i | ||||||||
\(151\) | 5.30062i | 0.431358i | 0.976464 | + | 0.215679i | \(0.0691965\pi\) | ||||
−0.976464 | + | 0.215679i | \(0.930804\pi\) | |||||||
\(152\) | −6.08921 | −0.493900 | ||||||||
\(153\) | 6.54461 | 0.529100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.35951 | 0.109198 | ||||||||
\(156\) | −0.660123 | − | 3.54461i | −0.0528521 | − | 0.283796i | ||||
\(157\) | 23.0562 | 1.84009 | 0.920044 | − | 0.391815i | \(-0.128153\pi\) | ||||
0.920044 | + | 0.391815i | \(0.128153\pi\) | |||||||
\(158\) | 12.4487i | 0.990367i | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | −0.339877 | −0.0268696 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 13.5642i | 1.06243i | 0.847236 | + | 0.531217i | \(0.178265\pi\) | ||||
−0.847236 | + | 0.531217i | \(0.821735\pi\) | |||||||
\(164\) | − | 0.864853i | − | 0.0675337i | ||||||
\(165\) | −0.224361 | −0.0174664 | ||||||||
\(166\) | 16.2939 | 1.26466 | ||||||||
\(167\) | 15.7034i | 1.21517i | 0.794256 | + | 0.607583i | \(0.207861\pi\) | ||||
−0.794256 | + | 0.607583i | \(0.792139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1285 | + | 4.67975i | −0.932960 | + | 0.359981i | ||||
\(170\) | −2.22436 | −0.170601 | ||||||||
\(171\) | 6.08921i | 0.465654i | ||||||||
\(172\) | 5.08921 | 0.388049 | ||||||||
\(173\) | −13.6035 | −1.03425 | −0.517127 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517127 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(174\) | − | 3.56424i | − | 0.270204i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.660123i | 0.0497587i | ||||||||
\(177\) | 3.90411i | 0.293451i | ||||||||
\(178\) | −4.45539 | −0.333946 | ||||||||
\(179\) | 0.448721 | 0.0335390 | 0.0167695 | − | 0.999859i | \(-0.494662\pi\) | ||||
0.0167695 | + | 0.999859i | \(0.494662\pi\) | |||||||
\(180\) | 0.339877i | 0.0253329i | ||||||||
\(181\) | 15.9041 | 1.18214 | 0.591072 | − | 0.806619i | \(-0.298705\pi\) | ||||
0.591072 | + | 0.806619i | \(0.298705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.86485 | 0.137854 | ||||||||
\(184\) | − | 7.42909i | − | 0.547680i | ||||||
\(185\) | −1.20473 | −0.0885735 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 4.32025i | 0.315928i | ||||||||
\(188\) | − | 9.44872i | − | 0.689119i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 2.06958i | − | 0.150143i | ||||||
\(191\) | −10.4095 | −0.753202 | −0.376601 | − | 0.926376i | \(-0.622907\pi\) | ||||
−0.376601 | + | 0.926376i | \(0.622907\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.69938i | 0.554214i | 0.960839 | + | 0.277107i | \(0.0893756\pi\) | ||||
−0.960839 | + | 0.277107i | \(0.910624\pi\) | |||||||
\(194\) | 16.1088 | 1.15655 | ||||||||
\(195\) | 1.20473 | − | 0.224361i | 0.0862725 | − | 0.0160668i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.98037i | 0.639825i | 0.947447 | + | 0.319912i | \(0.103653\pi\) | ||||
−0.947447 | + | 0.319912i | \(0.896347\pi\) | |||||||
\(198\) | 0.660123 | 0.0469129 | ||||||||
\(199\) | 20.5946 | 1.45991 | 0.729955 | − | 0.683495i | \(-0.239541\pi\) | ||||
0.729955 | + | 0.683495i | \(0.239541\pi\) | |||||||
\(200\) | 4.88448i | 0.345385i | ||||||||
\(201\) | 7.44872i | 0.525392i | ||||||||
\(202\) | 2.79527i | 0.196675i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.54461 | 0.458214 | ||||||||
\(205\) | 0.293944 | 0.0205299 | ||||||||
\(206\) | − | 7.53793i | − | 0.525193i | ||||||
\(207\) | −7.42909 | −0.516357 | ||||||||
\(208\) | −0.660123 | − | 3.54461i | −0.0457713 | − | 0.245774i | ||||
\(209\) | −4.01963 | −0.278044 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3898 | 1.05948 | 0.529740 | − | 0.848160i | \(-0.322290\pi\) | ||||
0.529740 | + | 0.848160i | \(0.322290\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | − | 0.884484i | − | 0.0606038i | ||||||
\(214\) | 3.72971i | 0.254957i | ||||||||
\(215\) | 1.72971i | 0.117965i | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.4095 | −0.975932 | ||||||||
\(219\) | − | 10.0696i | − | 0.680439i | ||||||
\(220\) | −0.224361 | −0.0151264 | ||||||||
\(221\) | −4.32025 | − | 23.1981i | −0.290611 | − | 1.56047i | ||||
\(222\) | 3.54461 | 0.237898 | ||||||||
\(223\) | − | 18.0196i | − | 1.20668i | −0.797483 | − | 0.603342i | \(-0.793835\pi\) | ||
0.797483 | − | 0.603342i | \(-0.206165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.88448 | 0.325632 | ||||||||
\(226\) | − | 15.5576i | − | 1.03487i | ||||||
\(227\) | 0.231033i | 0.0153342i | 0.999971 | + | 0.00766709i | \(0.00244053\pi\) | ||||
−0.999971 | + | 0.00766709i | \(0.997559\pi\) | |||||||
\(228\) | 6.08921i | 0.403268i | ||||||||
\(229\) | 6.64049i | 0.438816i | 0.975633 | + | 0.219408i | \(0.0704126\pi\) | ||||
−0.975633 | + | 0.219408i | \(0.929587\pi\) | |||||||
\(230\) | 2.52498 | 0.166492 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.56424i | − | 0.234004i | ||||||
\(233\) | −29.5183 | −1.93381 | −0.966904 | − | 0.255140i | \(-0.917879\pi\) | ||||
−0.966904 | + | 0.255140i | \(0.917879\pi\) | |||||||
\(234\) | −3.54461 | + | 0.660123i | −0.231718 | + | 0.0431536i | ||||
\(235\) | 3.21140 | 0.209489 | ||||||||
\(236\) | 3.90411i | 0.254136i | ||||||||
\(237\) | 12.4487 | 0.808631 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0236i | 0.971799i | 0.874015 | + | 0.485900i | \(0.161508\pi\) | ||||
−0.874015 | + | 0.485900i | \(0.838492\pi\) | |||||||
\(240\) | 0.339877i | 0.0219390i | ||||||||
\(241\) | − | 4.44872i | − | 0.286567i | −0.989682 | − | 0.143284i | \(-0.954234\pi\) | ||
0.989682 | − | 0.143284i | \(-0.0457661\pi\) | |||||||
\(242\) | − | 10.5642i | − | 0.679095i | ||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.86485 | 0.119385 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.864853 | −0.0551410 | ||||||||
\(247\) | 21.5839 | − | 4.01963i | 1.37335 | − | 0.255763i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | − | 16.2939i | − | 1.03259i | ||||||
\(250\) | −3.35951 | −0.212474 | ||||||||
\(251\) | 24.3961 | 1.53987 | 0.769935 | − | 0.638123i | \(-0.220289\pi\) | ||||
0.769935 | + | 0.638123i | \(0.220289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.90411i | − | 0.308319i | ||||||
\(254\) | − | 14.4028i | − | 0.903711i | ||||||
\(255\) | 2.22436i | 0.139295i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.4487 | −1.15080 | −0.575400 | − | 0.817872i | \(-0.695154\pi\) | ||||
−0.575400 | + | 0.817872i | \(0.695154\pi\) | |||||||
\(258\) | − | 5.08921i | − | 0.316841i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.20473 | − | 0.224361i | 0.0747142 | − | 0.0139143i | ||||
\(261\) | −3.56424 | −0.220621 | ||||||||
\(262\) | − | 20.6731i | − | 1.27719i | ||||||
\(263\) | −6.30062 | −0.388513 | −0.194256 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194256 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(264\) | 0.660123 | 0.0406278 | ||||||||
\(265\) | − | 1.01963i | − | 0.0626354i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.45539i | 0.272666i | ||||||||
\(268\) | 7.44872i | 0.455003i | ||||||||
\(269\) | 9.89517 | 0.603319 | 0.301660 | − | 0.953416i | \(-0.402459\pi\) | ||||
0.301660 | + | 0.953416i | \(0.402459\pi\) | |||||||
\(270\) | 0.339877 | 0.0206842 | ||||||||
\(271\) | − | 12.6994i | − | 0.771433i | −0.922617 | − | 0.385716i | \(-0.873954\pi\) | ||
0.922617 | − | 0.385716i | \(-0.126046\pi\) | |||||||
\(272\) | 6.54461 | 0.396825 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2244 | 0.859325 | ||||||||
\(275\) | 3.22436i | 0.194436i | ||||||||
\(276\) | −7.42909 | −0.447179 | ||||||||
\(277\) | 28.0433 | 1.68496 | 0.842479 | − | 0.538730i | \(-0.181096\pi\) | ||||
0.842479 | + | 0.538730i | \(0.181096\pi\) | |||||||
\(278\) | 9.42909i | 0.565519i | ||||||||
\(279\) | 4.00000i | 0.239474i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.82157i | − | 0.108666i | −0.998523 | − | 0.0543330i | \(-0.982697\pi\) | ||
0.998523 | − | 0.0543330i | \(-0.0173032\pi\) | |||||||
\(282\) | −9.44872 | −0.562663 | ||||||||
\(283\) | −8.98037 | −0.533828 | −0.266914 | − | 0.963720i | \(-0.586004\pi\) | ||||
−0.266914 | + | 0.963720i | \(0.586004\pi\) | |||||||
\(284\) | − | 0.884484i | − | 0.0524845i | ||||||
\(285\) | −2.06958 | −0.122592 | ||||||||
\(286\) | −0.435763 | − | 2.33988i | −0.0257672 | − | 0.138360i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 25.8319 | 1.51952 | ||||||||
\(290\) | 1.21140 | 0.0711360 | ||||||||
\(291\) | − | 16.1088i | − | 0.944317i | ||||||
\(292\) | − | 10.0696i | − | 0.589278i | ||||||
\(293\) | 2.80194i | 0.163691i | 0.996645 | + | 0.0818456i | \(0.0260814\pi\) | ||||
−0.996645 | + | 0.0818456i | \(0.973919\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.32692 | −0.0772562 | ||||||||
\(296\) | 3.54461 | 0.206026 | ||||||||
\(297\) | − | 0.660123i | − | 0.0383042i | ||||||
\(298\) | 8.10884 | 0.469733 | ||||||||
\(299\) | 4.90411 | + | 26.3332i | 0.283612 | + | 1.52289i | ||||
\(300\) | 4.88448 | 0.282006 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.30062 | 0.305016 | ||||||||
\(303\) | 2.79527 | 0.160584 | ||||||||
\(304\) | 6.08921i | 0.349240i | ||||||||
\(305\) | 0.633820i | 0.0362925i | ||||||||
\(306\) | − | 6.54461i | − | 0.374130i | ||||||
\(307\) | 9.21769i | 0.526081i | 0.964785 | + | 0.263041i | \(0.0847253\pi\) | ||||
−0.964785 | + | 0.263041i | \(0.915275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.53793 | −0.428818 | ||||||||
\(310\) | − | 1.35951i | − | 0.0772148i | ||||||
\(311\) | 11.4684 | 0.650311 | 0.325155 | − | 0.945661i | \(-0.394583\pi\) | ||||
0.325155 | + | 0.945661i | \(0.394583\pi\) | |||||||
\(312\) | −3.54461 | + | 0.660123i | −0.200674 | + | 0.0373721i | ||||
\(313\) | 22.5642 | 1.27541 | 0.637703 | − | 0.770282i | \(-0.279885\pi\) | ||||
0.637703 | + | 0.770282i | \(0.279885\pi\) | |||||||
\(314\) | − | 23.0562i | − | 1.30114i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.4487 | 0.700295 | ||||||||
\(317\) | 12.6271i | 0.709211i | 0.935016 | + | 0.354606i | \(0.115385\pi\) | ||||
−0.935016 | + | 0.354606i | \(0.884615\pi\) | |||||||
\(318\) | 3.00000i | 0.168232i | ||||||||
\(319\) | − | 2.35284i | − | 0.131733i | ||||||
\(320\) | 0.339877i | 0.0189997i | ||||||||
\(321\) | 3.72971 | 0.208172 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.8515i | 2.21740i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −3.22436 | − | 17.3136i | −0.178855 | − | 0.960384i | ||||
\(326\) | 13.5642 | 0.751254 | ||||||||
\(327\) | 14.4095i | 0.796845i | ||||||||
\(328\) | −0.864853 | −0.0477535 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.224361i | 0.0123506i | ||||||||
\(331\) | − | 26.8212i | − | 1.47423i | −0.675770 | − | 0.737113i | \(-0.736189\pi\) | ||
0.675770 | − | 0.737113i | \(-0.263811\pi\) | |||||||
\(332\) | − | 16.2939i | − | 0.894246i | ||||||
\(333\) | − | 3.54461i | − | 0.194243i | ||||||
\(334\) | 15.7034 | 0.859252 | ||||||||
\(335\) | −2.53165 | −0.138319 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.81892 | 0.534871 | 0.267435 | − | 0.963576i | \(-0.413824\pi\) | ||||
0.267435 | + | 0.963576i | \(0.413824\pi\) | |||||||
\(338\) | 4.67975 | + | 12.1285i | 0.254545 | + | 0.659702i | ||||
\(339\) | −15.5576 | −0.844971 | ||||||||
\(340\) | 2.22436i | 0.120633i | ||||||||
\(341\) | −2.64049 | −0.142991 | ||||||||
\(342\) | 6.08921 | 0.329267 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 5.08921i | − | 0.274392i | ||||||
\(345\) | − | 2.52498i | − | 0.135940i | ||||||
\(346\) | 13.6035i | 0.731329i | ||||||||
\(347\) | 19.0959 | 1.02512 | 0.512560 | − | 0.858651i | \(-0.328697\pi\) | ||||
0.512560 | + | 0.858651i | \(0.328697\pi\) | |||||||
\(348\) | −3.56424 | −0.191063 | ||||||||
\(349\) | − | 0.416132i | − | 0.0222750i | −0.999938 | − | 0.0111375i | \(-0.996455\pi\) | ||
0.999938 | − | 0.0111375i | \(-0.00354525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.660123 | + | 3.54461i | 0.0352348 | + | 0.189197i | ||||
\(352\) | 0.660123 | 0.0351847 | ||||||||
\(353\) | 16.4880i | 0.877567i | 0.898593 | + | 0.438783i | \(0.144590\pi\) | ||||
−0.898593 | + | 0.438783i | \(0.855410\pi\) | |||||||
\(354\) | 3.90411 | 0.207501 | ||||||||
\(355\) | 0.300616 | 0.0159550 | ||||||||
\(356\) | 4.45539i | 0.236135i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 0.448721i | − | 0.0237157i | ||||||
\(359\) | − | 24.4724i | − | 1.29160i | −0.763506 | − | 0.645801i | \(-0.776523\pi\) | ||
0.763506 | − | 0.645801i | \(-0.223477\pi\) | |||||||
\(360\) | 0.339877 | 0.0179131 | ||||||||
\(361\) | −18.0785 | −0.951501 | ||||||||
\(362\) | − | 15.9041i | − | 0.835902i | ||||||
\(363\) | −10.5642 | −0.554479 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.42242 | 0.179138 | ||||||||
\(366\) | − | 1.86485i | − | 0.0974774i | ||||||
\(367\) | 12.4880 | 0.651867 | 0.325934 | − | 0.945393i | \(-0.394321\pi\) | ||||
0.325934 | + | 0.945393i | \(0.394321\pi\) | |||||||
\(368\) | −7.42909 | −0.387268 | ||||||||
\(369\) | 0.864853i | 0.0450225i | ||||||||
\(370\) | 1.20473i | 0.0626309i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | −7.82786 | −0.405311 | −0.202656 | − | 0.979250i | \(-0.564957\pi\) | ||||
−0.202656 | + | 0.979250i | \(0.564957\pi\) | |||||||
\(374\) | 4.32025 | 0.223395 | ||||||||
\(375\) | 3.35951i | 0.173484i | ||||||||
\(376\) | −9.44872 | −0.487281 | ||||||||
\(377\) | 2.35284 | + | 12.6338i | 0.121177 | + | 0.650675i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.67975i | − | 0.445849i | −0.974836 | − | 0.222925i | \(-0.928440\pi\) | ||
0.974836 | − | 0.222925i | \(-0.0715603\pi\) | |||||||
\(380\) | −2.06958 | −0.106167 | ||||||||
\(381\) | −14.4028 | −0.737877 | ||||||||
\(382\) | 10.4095i | 0.532594i | ||||||||
\(383\) | − | 23.4224i | − | 1.19683i | −0.801186 | − | 0.598415i | \(-0.795797\pi\) | ||
0.801186 | − | 0.598415i | \(-0.204203\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.69938 | 0.391888 | ||||||||
\(387\) | −5.08921 | −0.258699 | ||||||||
\(388\) | − | 16.1088i | − | 0.817803i | ||||||
\(389\) | −30.1914 | −1.53076 | −0.765382 | − | 0.643576i | \(-0.777450\pi\) | ||||
−0.765382 | + | 0.643576i | \(0.777450\pi\) | |||||||
\(390\) | −0.224361 | − | 1.20473i | −0.0113609 | − | 0.0610039i | ||||
\(391\) | −48.6205 | −2.45884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.6731 | −1.04282 | ||||||||
\(394\) | 8.98037 | 0.452424 | ||||||||
\(395\) | 4.23103i | 0.212886i | ||||||||
\(396\) | − | 0.660123i | − | 0.0331724i | ||||||
\(397\) | 8.49465i | 0.426334i | 0.977016 | + | 0.213167i | \(0.0683779\pi\) | ||||
−0.977016 | + | 0.213167i | \(0.931622\pi\) | |||||||
\(398\) | − | 20.5946i | − | 1.03231i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.88448 | 0.244224 | ||||||||
\(401\) | 20.1718i | 1.00733i | 0.863899 | + | 0.503665i | \(0.168015\pi\) | ||||
−0.863899 | + | 0.503665i | \(0.831985\pi\) | |||||||
\(402\) | 7.44872 | 0.371508 | ||||||||
\(403\) | 14.1784 | − | 2.64049i | 0.706278 | − | 0.131532i | ||||
\(404\) | 2.79527 | 0.139070 | ||||||||
\(405\) | − | 0.339877i | − | 0.0168886i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.33988 | 0.115983 | ||||||||
\(408\) | − | 6.54461i | − | 0.324006i | ||||||
\(409\) | 4.30062i | 0.212652i | 0.994331 | + | 0.106326i | \(0.0339087\pi\) | ||||
−0.994331 | + | 0.106326i | \(0.966091\pi\) | |||||||
\(410\) | − | 0.293944i | − | 0.0145168i | ||||||
\(411\) | − | 14.2244i | − | 0.701636i | ||||||
\(412\) | −7.53793 | −0.371367 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.42909i | 0.365120i | ||||||||
\(415\) | 5.53793 | 0.271847 | ||||||||
\(416\) | −3.54461 | + | 0.660123i | −0.173789 | + | 0.0323652i | ||||
\(417\) | 9.42909 | 0.461745 | ||||||||
\(418\) | 4.01963i | 0.196607i | ||||||||
\(419\) | 32.8974 | 1.60715 | 0.803573 | − | 0.595207i | \(-0.202930\pi\) | ||||
0.803573 | + | 0.595207i | \(0.202930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.7230i | − | 1.05872i | −0.848399 | − | 0.529358i | \(-0.822433\pi\) | ||
0.848399 | − | 0.529358i | \(-0.177567\pi\) | |||||||
\(422\) | − | 15.3898i | − | 0.749165i | ||||||
\(423\) | 9.44872i | 0.459413i | ||||||||
\(424\) | 3.00000i | 0.145693i | ||||||||
\(425\) | 31.9670 | 1.55063 | ||||||||
\(426\) | −0.884484 | −0.0428534 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.72971 | 0.180282 | ||||||||
\(429\) | −2.33988 | + | 0.435763i | −0.112970 | + | 0.0210388i | ||||
\(430\) | 1.72971 | 0.0834138 | ||||||||
\(431\) | 6.06291i | 0.292040i | 0.989282 | + | 0.146020i | \(0.0466464\pi\) | ||||
−0.989282 | + | 0.146020i | \(0.953354\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.1392 | −0.535314 | −0.267657 | − | 0.963514i | \(-0.586249\pi\) | ||||
−0.267657 | + | 0.963514i | \(0.586249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 1.21140i | − | 0.0580823i | ||||||
\(436\) | 14.4095i | 0.690088i | ||||||||
\(437\) | − | 45.2373i | − | 2.16399i | ||||||
\(438\) | −10.0696 | −0.481143 | ||||||||
\(439\) | −11.6231 | −0.554742 | −0.277371 | − | 0.960763i | \(-0.589463\pi\) | ||||
−0.277371 | + | 0.960763i | \(0.589463\pi\) | |||||||
\(440\) | 0.224361i | 0.0106960i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.1981 | + | 4.32025i | −1.10342 | + | 0.205493i | ||||
\(443\) | −4.67308 | −0.222025 | −0.111012 | − | 0.993819i | \(-0.535409\pi\) | ||||
−0.111012 | + | 0.993819i | \(0.535409\pi\) | |||||||
\(444\) | − | 3.54461i | − | 0.168220i | ||||||
\(445\) | −1.51429 | −0.0717840 | ||||||||
\(446\) | −18.0196 | −0.853254 | ||||||||
\(447\) | − | 8.10884i | − | 0.383535i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6271i | 1.72854i | 0.503026 | + | 0.864271i | \(0.332220\pi\) | ||||
−0.503026 | + | 0.864271i | \(0.667780\pi\) | |||||||
\(450\) | − | 4.88448i | − | 0.230257i | ||||||
\(451\) | −0.570909 | −0.0268831 | ||||||||
\(452\) | −15.5576 | −0.731766 | ||||||||
\(453\) | − | 5.30062i | − | 0.249045i | ||||||
\(454\) | 0.231033 | 0.0108429 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.08921 | 0.285154 | ||||||||
\(457\) | 31.3372i | 1.46589i | 0.680286 | + | 0.732947i | \(0.261856\pi\) | ||||
−0.680286 | + | 0.732947i | \(0.738144\pi\) | |||||||
\(458\) | 6.64049 | 0.310290 | ||||||||
\(459\) | −6.54461 | −0.305476 | ||||||||
\(460\) | − | 2.52498i | − | 0.117728i | ||||||
\(461\) | − | 0.601231i | − | 0.0280021i | −0.999902 | − | 0.0140011i | \(-0.995543\pi\) | ||
0.999902 | − | 0.0140011i | \(-0.00445682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.5013i | − | 0.488038i | −0.969770 | − | 0.244019i | \(-0.921534\pi\) | ||
0.969770 | − | 0.244019i | \(-0.0784659\pi\) | |||||||
\(464\) | −3.56424 | −0.165466 | ||||||||
\(465\) | −1.35951 | −0.0630457 | ||||||||
\(466\) | 29.5183i | 1.36741i | ||||||||
\(467\) | −27.2217 | −1.25967 | −0.629835 | − | 0.776729i | \(-0.716878\pi\) | ||||
−0.629835 | + | 0.776729i | \(0.716878\pi\) | |||||||
\(468\) | 0.660123 | + | 3.54461i | 0.0305142 | + | 0.163850i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 3.21140i | − | 0.148131i | ||||||
\(471\) | −23.0562 | −1.06238 | ||||||||
\(472\) | 3.90411 | 0.179701 | ||||||||
\(473\) | − | 3.35951i | − | 0.154470i | ||||||
\(474\) | − | 12.4487i | − | 0.571789i | ||||||
\(475\) | 29.7427i | 1.36469i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 15.0236 | 0.687166 | ||||||||
\(479\) | 28.8711i | 1.31916i | 0.751636 | + | 0.659578i | \(0.229265\pi\) | ||||
−0.751636 | + | 0.659578i | \(0.770735\pi\) | |||||||
\(480\) | 0.339877 | 0.0155132 | ||||||||
\(481\) | −12.5642 | + | 2.33988i | −0.572880 | + | 0.106689i | ||||
\(482\) | −4.44872 | −0.202634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5642 | −0.480193 | ||||||||
\(485\) | 5.47502 | 0.248608 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 3.91746i | 0.177517i | 0.996053 | + | 0.0887585i | \(0.0282899\pi\) | ||||
−0.996053 | + | 0.0887585i | \(0.971710\pi\) | |||||||
\(488\) | − | 1.86485i | − | 0.0844179i | ||||||
\(489\) | − | 13.5642i | − | 0.613396i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4202 | −0.605643 | −0.302821 | − | 0.953047i | \(-0.597929\pi\) | ||||
−0.302821 | + | 0.953047i | \(0.597929\pi\) | |||||||
\(492\) | 0.864853i | 0.0389906i | ||||||||
\(493\) | −23.3265 | −1.05057 | ||||||||
\(494\) | −4.01963 | − | 21.5839i | −0.180852 | − | 0.971104i | ||||
\(495\) | 0.224361 | 0.0100843 | ||||||||
\(496\) | 4.00000i | 0.179605i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.2939 | −0.730149 | ||||||||
\(499\) | 32.7819i | 1.46752i | 0.679408 | + | 0.733760i | \(0.262236\pi\) | ||||
−0.679408 | + | 0.733760i | \(0.737764\pi\) | |||||||
\(500\) | 3.35951i | 0.150242i | ||||||||
\(501\) | − | 15.7034i | − | 0.701576i | ||||||
\(502\) | − | 24.3961i | − | 1.08885i | ||||||
\(503\) | −22.8582 | −1.01920 | −0.509598 | − | 0.860413i | \(-0.670206\pi\) | ||||
−0.509598 | + | 0.860413i | \(0.670206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.950048i | 0.0422766i | ||||||||
\(506\) | −4.90411 | −0.218014 | ||||||||
\(507\) | 12.1285 | − | 4.67975i | 0.538644 | − | 0.207835i | ||||
\(508\) | −14.4028 | −0.639020 | ||||||||
\(509\) | − | 32.8448i | − | 1.45582i | −0.685672 | − | 0.727911i | \(-0.740491\pi\) | ||
0.685672 | − | 0.727911i | \(-0.259509\pi\) | |||||||
\(510\) | 2.22436 | 0.0984963 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 6.08921i | − | 0.268845i | ||||||
\(514\) | 18.4487i | 0.813738i | ||||||||
\(515\) | − | 2.56197i | − | 0.112894i | ||||||
\(516\) | −5.08921 | −0.224040 | ||||||||
\(517\) | −6.23732 | −0.274317 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6035 | 0.597127 | ||||||||
\(520\) | −0.224361 | − | 1.20473i | −0.00983886 | − | 0.0528309i | ||||
\(521\) | −2.81892 | −0.123499 | −0.0617496 | − | 0.998092i | \(-0.519668\pi\) | ||||
−0.0617496 | + | 0.998092i | \(0.519668\pi\) | |||||||
\(522\) | 3.56424i | 0.156002i | ||||||||
\(523\) | 5.62980 | 0.246174 | 0.123087 | − | 0.992396i | \(-0.460721\pi\) | ||||
0.123087 | + | 0.992396i | \(0.460721\pi\) | |||||||
\(524\) | −20.6731 | −0.903108 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.30062i | 0.274720i | ||||||||
\(527\) | 26.1784i | 1.14035i | ||||||||
\(528\) | − | 0.660123i | − | 0.0287282i | ||||||
\(529\) | 32.1914 | 1.39963 | ||||||||
\(530\) | −1.01963 | −0.0442899 | ||||||||
\(531\) | − | 3.90411i | − | 0.169424i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.06556 | − | 0.570909i | 0.132784 | − | 0.0247288i | ||||
\(534\) | 4.45539 | 0.192804 | ||||||||
\(535\) | 1.26764i | 0.0548049i | ||||||||
\(536\) | 7.44872 | 0.321736 | ||||||||
\(537\) | −0.448721 | −0.0193637 | ||||||||
\(538\) | − | 9.89517i | − | 0.426611i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 0.339877i | − | 0.0146260i | ||||||
\(541\) | − | 24.7123i | − | 1.06247i | −0.847226 | − | 0.531233i | \(-0.821729\pi\) | ||
0.847226 | − | 0.531233i | \(-0.178271\pi\) | |||||||
\(542\) | −12.6994 | −0.545485 | ||||||||
\(543\) | −15.9041 | −0.682511 | ||||||||
\(544\) | − | 6.54461i | − | 0.280598i | ||||||
\(545\) | −4.89744 | −0.209783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1874 | 0.777636 | 0.388818 | − | 0.921315i | \(-0.372884\pi\) | ||||
0.388818 | + | 0.921315i | \(0.372884\pi\) | |||||||
\(548\) | − | 14.2244i | − | 0.607635i | ||||||
\(549\) | −1.86485 | −0.0795900 | ||||||||
\(550\) | 3.22436 | 0.137487 | ||||||||
\(551\) | − | 21.7034i | − | 0.924596i | ||||||
\(552\) | 7.42909i | 0.316203i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 28.0433i | − | 1.19144i | ||||||
\(555\) | 1.20473 | 0.0511379 | ||||||||
\(556\) | 9.42909 | 0.399883 | ||||||||
\(557\) | 26.6405i | 1.12879i | 0.825504 | + | 0.564397i | \(0.190891\pi\) | ||||
−0.825504 | + | 0.564397i | \(0.809109\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 3.35951 | + | 18.0393i | 0.142092 | + | 0.762979i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 4.32025i | − | 0.182401i | ||||||
\(562\) | −1.82157 | −0.0768384 | ||||||||
\(563\) | −27.6771 | −1.16645 | −0.583225 | − | 0.812310i | \(-0.698210\pi\) | ||||
−0.583225 | + | 0.812310i | \(0.698210\pi\) | |||||||
\(564\) | 9.44872i | 0.397863i | ||||||||
\(565\) | − | 5.28766i | − | 0.222453i | ||||||
\(566\) | 8.98037i | 0.377473i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.884484 | −0.0371121 | ||||||||
\(569\) | −20.3898 | −0.854786 | −0.427393 | − | 0.904066i | \(-0.640568\pi\) | ||||
−0.427393 | + | 0.904066i | \(0.640568\pi\) | |||||||
\(570\) | 2.06958i | 0.0866853i | ||||||||
\(571\) | 38.2043 | 1.59880 | 0.799401 | − | 0.600798i | \(-0.205150\pi\) | ||||
0.799401 | + | 0.600798i | \(0.205150\pi\) | |||||||
\(572\) | −2.33988 | + | 0.435763i | −0.0978352 | + | 0.0182201i | ||||
\(573\) | 10.4095 | 0.434861 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.2873 | −1.51328 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 11.3595i | 0.472902i | 0.971643 | + | 0.236451i | \(0.0759844\pi\) | ||||
−0.971643 | + | 0.236451i | \(0.924016\pi\) | |||||||
\(578\) | − | 25.8319i | − | 1.07446i | ||||||
\(579\) | − | 7.69938i | − | 0.319975i | ||||||
\(580\) | − | 1.21140i | − | 0.0503007i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.1088 | −0.667733 | ||||||||
\(583\) | 1.98037i | 0.0820185i | ||||||||
\(584\) | −10.0696 | −0.416682 | ||||||||
\(585\) | −1.20473 | + | 0.224361i | −0.0498095 | + | 0.00927617i | ||||
\(586\) | 2.80194 | 0.115747 | ||||||||
\(587\) | 37.2347i | 1.53684i | 0.639946 | + | 0.768420i | \(0.278957\pi\) | ||||
−0.639946 | + | 0.768420i | \(0.721043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.3569 | −1.00361 | ||||||||
\(590\) | 1.32692i | 0.0546284i | ||||||||
\(591\) | − | 8.98037i | − | 0.369403i | ||||||
\(592\) | − | 3.54461i | − | 0.145682i | ||||||
\(593\) | 24.2110i | 0.994227i | 0.867685 | + | 0.497114i | \(0.165607\pi\) | ||||
−0.867685 | + | 0.497114i | \(0.834393\pi\) | |||||||
\(594\) | −0.660123 | −0.0270852 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 8.10884i | − | 0.332151i | ||||||
\(597\) | −20.5946 | −0.842879 | ||||||||
\(598\) | 26.3332 | − | 4.90411i | 1.07684 | − | 0.200544i | ||||
\(599\) | −6.47904 | −0.264727 | −0.132363 | − | 0.991201i | \(-0.542257\pi\) | ||||
−0.132363 | + | 0.991201i | \(0.542257\pi\) | |||||||
\(600\) | − | 4.88448i | − | 0.199408i | ||||||
\(601\) | −41.4354 | −1.69018 | −0.845092 | − | 0.534621i | \(-0.820454\pi\) | ||||
−0.845092 | + | 0.534621i | \(0.820454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.44872i | − | 0.303335i | ||||||
\(604\) | − | 5.30062i | − | 0.215679i | ||||||
\(605\) | − | 3.59054i | − | 0.145976i | ||||||
\(606\) | − | 2.79527i | − | 0.113550i | ||||||
\(607\) | 8.40279 | 0.341059 | 0.170529 | − | 0.985353i | \(-0.445452\pi\) | ||||
0.170529 | + | 0.985353i | \(0.445452\pi\) | |||||||
\(608\) | 6.08921 | 0.246950 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.633820 | 0.0256626 | ||||||||
\(611\) | 33.4920 | − | 6.23732i | 1.35494 | − | 0.252335i | ||||
\(612\) | −6.54461 | −0.264550 | ||||||||
\(613\) | − | 46.8974i | − | 1.89417i | −0.320983 | − | 0.947085i | \(-0.604013\pi\) | ||
0.320983 | − | 0.947085i | \(-0.395987\pi\) | |||||||
\(614\) | 9.21769 | 0.371996 | ||||||||
\(615\) | −0.293944 | −0.0118529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.6271i | − | 1.31352i | −0.754100 | − | 0.656760i | \(-0.771927\pi\) | ||
0.754100 | − | 0.656760i | \(-0.228073\pi\) | |||||||
\(618\) | 7.53793i | 0.303220i | ||||||||
\(619\) | − | 5.46168i | − | 0.219523i | −0.993958 | − | 0.109762i | \(-0.964991\pi\) | ||
0.993958 | − | 0.109762i | \(-0.0350088\pi\) | |||||||
\(620\) | −1.35951 | −0.0545991 | ||||||||
\(621\) | 7.42909 | 0.298119 | ||||||||
\(622\) | − | 11.4684i | − | 0.459839i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.660123 | + | 3.54461i | 0.0264261 | + | 0.141898i | ||||
\(625\) | 23.2806 | 0.931224 | ||||||||
\(626\) | − | 22.5642i | − | 0.901848i | ||||||
\(627\) | 4.01963 | 0.160529 | ||||||||
\(628\) | −23.0562 | −0.920044 | ||||||||
\(629\) | − | 23.1981i | − | 0.924967i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.8845i | 1.66739i | 0.552221 | + | 0.833697i | \(0.313780\pi\) | ||||
−0.552221 | + | 0.833697i | \(0.686220\pi\) | |||||||
\(632\) | − | 12.4487i | − | 0.495184i | ||||||
\(633\) | −15.3898 | −0.611691 | ||||||||
\(634\) | 12.6271 | 0.501488 | ||||||||
\(635\) | − | 4.89517i | − | 0.194259i | ||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.35284 | −0.0931497 | ||||||||
\(639\) | 0.884484i | 0.0349896i | ||||||||
\(640\) | 0.339877 | 0.0134348 | ||||||||
\(641\) | 6.61684 | 0.261350 | 0.130675 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130675 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(642\) | − | 3.72971i | − | 0.147200i | ||||||
\(643\) | − | 23.7427i | − | 0.936319i | −0.883644 | − | 0.468160i | \(-0.844917\pi\) | ||
0.883644 | − | 0.468160i | \(-0.155083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.72971i | − | 0.0681071i | ||||||
\(646\) | 39.8515 | 1.56794 | ||||||||
\(647\) | −39.1285 | −1.53830 | −0.769150 | − | 0.639069i | \(-0.779320\pi\) | ||||
−0.769150 | + | 0.639069i | \(0.779320\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 2.57720 | 0.101164 | ||||||||
\(650\) | −17.3136 | + | 3.22436i | −0.679094 | + | 0.126470i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 13.5642i | − | 0.531217i | ||||||
\(653\) | 5.51429 | 0.215791 | 0.107895 | − | 0.994162i | \(-0.465589\pi\) | ||||
0.107895 | + | 0.994162i | \(0.465589\pi\) | |||||||
\(654\) | 14.4095 | 0.563454 | ||||||||
\(655\) | − | 7.02630i | − | 0.274540i | ||||||
\(656\) | 0.864853i | 0.0337668i | ||||||||
\(657\) | 10.0696i | 0.392852i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.2217 | −1.91741 | −0.958703 | − | 0.284410i | \(-0.908202\pi\) | ||||
−0.958703 | + | 0.284410i | \(0.908202\pi\) | |||||||
\(660\) | 0.224361 | 0.00873322 | ||||||||
\(661\) | − | 12.3243i | − | 0.479358i | −0.970852 | − | 0.239679i | \(-0.922958\pi\) | ||
0.970852 | − | 0.239679i | \(-0.0770423\pi\) | |||||||
\(662\) | −26.8212 | −1.04244 | ||||||||
\(663\) | 4.32025 | + | 23.1981i | 0.167784 | + | 0.900938i | ||||
\(664\) | −16.2939 | −0.632328 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.54461 | −0.137351 | ||||||||
\(667\) | 26.4790 | 1.02527 | ||||||||
\(668\) | − | 15.7034i | − | 0.607583i | ||||||
\(669\) | 18.0196i | 0.696679i | ||||||||
\(670\) | 2.53165i | 0.0978061i | ||||||||
\(671\) | − | 1.23103i | − | 0.0475235i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.79527 | 0.261938 | 0.130969 | − | 0.991386i | \(-0.458191\pi\) | ||||
0.130969 | + | 0.991386i | \(0.458191\pi\) | |||||||
\(674\) | − | 9.81892i | − | 0.378211i | ||||||
\(675\) | −4.88448 | −0.188004 | ||||||||
\(676\) | 12.1285 | − | 4.67975i | 0.466480 | − | 0.179991i | ||||
\(677\) | −16.6927 | −0.641553 | −0.320777 | − | 0.947155i | \(-0.603944\pi\) | ||||
−0.320777 | + | 0.947155i | \(0.603944\pi\) | |||||||
\(678\) | 15.5576i | 0.597485i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.22436 | 0.0853003 | ||||||||
\(681\) | − | 0.231033i | − | 0.00885319i | ||||||
\(682\) | 2.64049i | 0.101110i | ||||||||
\(683\) | 21.7164i | 0.830954i | 0.909604 | + | 0.415477i | \(0.136385\pi\) | ||||
−0.909604 | + | 0.415477i | \(0.863615\pi\) | |||||||
\(684\) | − | 6.08921i | − | 0.232827i | ||||||
\(685\) | 4.83453 | 0.184718 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.64049i | − | 0.253351i | ||||||
\(688\) | −5.08921 | −0.194024 | ||||||||
\(689\) | −1.98037 | − | 10.6338i | −0.0754461 | − | 0.405116i | ||||
\(690\) | −2.52498 | −0.0961242 | ||||||||
\(691\) | 46.9341i | 1.78546i | 0.450597 | + | 0.892728i | \(0.351211\pi\) | ||||
−0.450597 | + | 0.892728i | \(0.648789\pi\) | |||||||
\(692\) | 13.6035 | 0.517127 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 19.0959i | − | 0.724870i | ||||||
\(695\) | 3.20473i | 0.121562i | ||||||||
\(696\) | 3.56424i | 0.135102i | ||||||||
\(697\) | 5.66012i | 0.214392i | ||||||||
\(698\) | −0.416132 | −0.0157508 | ||||||||
\(699\) | 29.5183 | 1.11648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.32251 | −0.276568 | −0.138284 | − | 0.990393i | \(-0.544159\pi\) | ||||
−0.138284 | + | 0.990393i | \(0.544159\pi\) | |||||||
\(702\) | 3.54461 | − | 0.660123i | 0.133783 | − | 0.0249147i | ||||
\(703\) | 21.5839 | 0.814051 | ||||||||
\(704\) | − | 0.660123i | − | 0.0248793i | ||||||
\(705\) | −3.21140 | −0.120948 | ||||||||
\(706\) | 16.4880 | 0.620533 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 3.90411i | − | 0.146726i | ||||||
\(709\) | 6.64716i | 0.249640i | 0.992179 | + | 0.124820i | \(0.0398353\pi\) | ||||
−0.992179 | + | 0.124820i | \(0.960165\pi\) | |||||||
\(710\) | − | 0.300616i | − | 0.0112819i | ||||||
\(711\) | −12.4487 | −0.466864 | ||||||||
\(712\) | 4.45539 | 0.166973 | ||||||||
\(713\) | − | 29.7164i | − | 1.11289i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.148106 | − | 0.795270i | −0.00553884 | − | 0.0297414i | ||||
\(716\) | −0.448721 | −0.0167695 | ||||||||
\(717\) | − | 15.0236i | − | 0.561068i | ||||||
\(718\) | −24.4724 | −0.913301 | ||||||||
\(719\) | 4.87153 | 0.181677 | 0.0908386 | − | 0.995866i | \(-0.471045\pi\) | ||||
0.0908386 | + | 0.995866i | \(0.471045\pi\) | |||||||
\(720\) | − | 0.339877i | − | 0.0126665i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.0785i | 0.672813i | ||||||||
\(723\) | 4.44872i | 0.165450i | ||||||||
\(724\) | −15.9041 | −0.591072 | ||||||||
\(725\) | −17.4095 | −0.646571 | ||||||||
\(726\) | 10.5642i | 0.392076i | ||||||||
\(727\) | 4.98931 | 0.185043 | 0.0925216 | − | 0.995711i | \(-0.470507\pi\) | ||||
0.0925216 | + | 0.995711i | \(0.470507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 3.42242i | − | 0.126669i | ||||||
\(731\) | −33.3069 | −1.23190 | ||||||||
\(732\) | −1.86485 | −0.0689270 | ||||||||
\(733\) | 7.46608i | 0.275766i | 0.990449 | + | 0.137883i | \(0.0440298\pi\) | ||||
−0.990449 | + | 0.137883i | \(0.955970\pi\) | |||||||
\(734\) | − | 12.4880i | − | 0.460940i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.42909i | 0.273840i | ||||||||
\(737\) | 4.91707 | 0.181123 | ||||||||
\(738\) | 0.864853 | 0.0318357 | ||||||||
\(739\) | − | 1.46168i | − | 0.0537688i | −0.999639 | − | 0.0268844i | \(-0.991441\pi\) | ||
0.999639 | − | 0.0268844i | \(-0.00855860\pi\) | |||||||
\(740\) | 1.20473 | 0.0442868 | ||||||||
\(741\) | −21.5839 | + | 4.01963i | −0.792903 | + | 0.147665i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.67975i | − | 0.208370i | −0.994558 | − | 0.104185i | \(-0.966777\pi\) | ||
0.994558 | − | 0.104185i | \(-0.0332234\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 2.75601 | 0.100972 | ||||||||
\(746\) | 7.82786i | 0.286598i | ||||||||
\(747\) | 16.2939i | 0.596164i | ||||||||
\(748\) | − | 4.32025i | − | 0.157964i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.35951 | 0.122672 | ||||||||
\(751\) | 4.39612 | 0.160417 | 0.0802083 | − | 0.996778i | \(-0.474441\pi\) | ||||
0.0802083 | + | 0.996778i | \(0.474441\pi\) | |||||||
\(752\) | 9.44872i | 0.344559i | ||||||||
\(753\) | −24.3961 | −0.889044 | ||||||||
\(754\) | 12.6338 | − | 2.35284i | 0.460097 | − | 0.0856852i | ||||
\(755\) | 1.80156 | 0.0655654 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.0326 | 0.764442 | 0.382221 | − | 0.924071i | \(-0.375159\pi\) | ||||
0.382221 | + | 0.924071i | \(0.375159\pi\) | |||||||
\(758\) | −8.67975 | −0.315263 | ||||||||
\(759\) | 4.90411i | 0.178008i | ||||||||
\(760\) | 2.06958i | 0.0750717i | ||||||||
\(761\) | − | 12.6012i | − | 0.456794i | −0.973568 | − | 0.228397i | \(-0.926652\pi\) | ||
0.973568 | − | 0.228397i | \(-0.0733485\pi\) | |||||||
\(762\) | 14.4028i | 0.521758i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.4095 | 0.376601 | ||||||||
\(765\) | − | 2.22436i | − | 0.0804219i | ||||||
\(766\) | −23.4224 | −0.846286 | ||||||||
\(767\) | −13.8386 | + | 2.57720i | −0.499681 | + | 0.0930572i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − | 34.4398i | − | 1.24193i | −0.783838 | − | 0.620965i | \(-0.786741\pi\) | ||
0.783838 | − | 0.620965i | \(-0.213259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4487 | 0.664414 | ||||||||
\(772\) | − | 7.69938i | − | 0.277107i | ||||||
\(773\) | 16.7975i | 0.604165i | 0.953282 | + | 0.302083i | \(0.0976819\pi\) | ||||
−0.953282 | + | 0.302083i | \(0.902318\pi\) | |||||||
\(774\) | 5.08921i | 0.182928i | ||||||||
\(775\) | 19.5379i | 0.701823i | ||||||||
\(776\) | −16.1088 | −0.578274 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.1914i | 1.08241i | ||||||||
\(779\) | −5.26627 | −0.188684 | ||||||||
\(780\) | −1.20473 | + | 0.224361i | −0.0431363 | + | 0.00803340i | ||||
\(781\) | −0.583868 | −0.0208924 | ||||||||
\(782\) | 48.6205i | 1.73866i | ||||||||
\(783\) | 3.56424 | 0.127375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.83628i | − | 0.279689i | ||||||
\(786\) | 20.6731i | 0.737384i | ||||||||
\(787\) | 36.9474i | 1.31703i | 0.752567 | + | 0.658516i | \(0.228816\pi\) | ||||
−0.752567 | + | 0.658516i | \(0.771184\pi\) | |||||||
\(788\) | − | 8.98037i | − | 0.319912i | ||||||
\(789\) | 6.30062 | 0.224308 | ||||||||
\(790\) | 4.23103 | 0.150533 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.660123 | −0.0234565 | ||||||||
\(793\) | 1.23103 | + | 6.61017i | 0.0437152 | + | 0.234734i | ||||
\(794\) | 8.49465 | 0.301464 | ||||||||
\(795\) | 1.01963i | 0.0361626i | ||||||||
\(796\) | −20.5946 | −0.729955 | ||||||||
\(797\) | −38.7819 | −1.37373 | −0.686863 | − | 0.726787i | \(-0.741013\pi\) | ||||
−0.686863 | + | 0.726787i | \(0.741013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.8382i | 2.18768i | ||||||||
\(800\) | − | 4.88448i | − | 0.172693i | ||||||
\(801\) | − | 4.45539i | − | 0.157424i | ||||||
\(802\) | 20.1718 | 0.712289 | ||||||||
\(803\) | −6.64716 | −0.234573 | ||||||||
\(804\) | − | 7.44872i | − | 0.262696i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.64049 | − | 14.1784i | −0.0930074 | − | 0.499414i | ||||
\(807\) | −9.89517 | −0.348327 | ||||||||
\(808\) | − | 2.79527i | − | 0.0983373i | ||||||
\(809\) | 2.12180 | 0.0745986 | 0.0372993 | − | 0.999304i | \(-0.488125\pi\) | ||||
0.0372993 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(810\) | −0.339877 | −0.0119421 | ||||||||
\(811\) | − | 3.66680i | − | 0.128759i | −0.997926 | − | 0.0643793i | \(-0.979493\pi\) | ||
0.997926 | − | 0.0643793i | \(-0.0205067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6994i | 0.445387i | ||||||||
\(814\) | − | 2.33988i | − | 0.0820126i | ||||||
\(815\) | 4.61017 | 0.161487 | ||||||||
\(816\) | −6.54461 | −0.229107 | ||||||||
\(817\) | − | 30.9893i | − | 1.08418i | ||||||
\(818\) | 4.30062 | 0.150367 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.293944 | −0.0102650 | ||||||||
\(821\) | 21.5076i | 0.750621i | 0.926899 | + | 0.375310i | \(0.122464\pi\) | ||||
−0.926899 | + | 0.375310i | \(0.877536\pi\) | |||||||
\(822\) | −14.2244 | −0.496132 | ||||||||
\(823\) | −35.9541 | −1.25328 | −0.626640 | − | 0.779309i | \(-0.715570\pi\) | ||||
−0.626640 | + | 0.779309i | \(0.715570\pi\) | |||||||
\(824\) | 7.53793i | 0.262596i | ||||||||
\(825\) | − | 3.22436i | − | 0.112258i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.8778i | − | 1.14327i | −0.820507 | − | 0.571637i | \(-0.806309\pi\) | ||
0.820507 | − | 0.571637i | \(-0.193691\pi\) | |||||||
\(828\) | 7.42909 | 0.258179 | ||||||||
\(829\) | 9.82559 | 0.341257 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(830\) | − | 5.53793i | − | 0.192225i | ||||||
\(831\) | −28.0433 | −0.972811 | ||||||||
\(832\) | 0.660123 | + | 3.54461i | 0.0228857 | + | 0.122887i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 9.42909i | − | 0.326503i | ||||||
\(835\) | 5.33722 | 0.184702 | ||||||||
\(836\) | 4.01963 | 0.139022 | ||||||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | − | 32.8974i | − | 1.13642i | ||||||
\(839\) | 42.6008i | 1.47074i | 0.677663 | + | 0.735372i | \(0.262993\pi\) | ||||
−0.677663 | + | 0.735372i | \(0.737007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2962 | −0.561938 | ||||||||
\(842\) | −21.7230 | −0.748625 | ||||||||
\(843\) | 1.82157i | 0.0627383i | ||||||||
\(844\) | −15.3898 | −0.529740 | ||||||||
\(845\) | 1.59054 | + | 4.12219i | 0.0547162 | + | 0.141808i | ||||
\(846\) | 9.44872 | 0.324854 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 8.98037 | 0.308205 | ||||||||
\(850\) | − | 31.9670i | − | 1.09646i | ||||||
\(851\) | 26.3332i | 0.902691i | ||||||||
\(852\) | 0.884484i | 0.0303019i | ||||||||
\(853\) | − | 47.7490i | − | 1.63489i | −0.576005 | − | 0.817446i | \(-0.695389\pi\) | ||
0.576005 | − | 0.817446i | \(-0.304611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.06958 | 0.0707782 | ||||||||
\(856\) | − | 3.72971i | − | 0.127479i | ||||||
\(857\) | 6.89342 | 0.235475 | 0.117737 | − | 0.993045i | \(-0.462436\pi\) | ||||
0.117737 | + | 0.993045i | \(0.462436\pi\) | |||||||
\(858\) | 0.435763 | + | 2.33988i | 0.0148767 | + | 0.0798821i | ||||
\(859\) | −28.7797 | −0.981949 | −0.490975 | − | 0.871174i | \(-0.663359\pi\) | ||||
−0.490975 | + | 0.871174i | \(0.663359\pi\) | |||||||
\(860\) | − | 1.72971i | − | 0.0589825i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.06291 | 0.206504 | ||||||||
\(863\) | − | 48.5745i | − | 1.65350i | −0.562572 | − | 0.826748i | \(-0.690188\pi\) | ||
0.562572 | − | 0.826748i | \(-0.309812\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 4.62351i | 0.157204i | ||||||||
\(866\) | 11.1392i | 0.378524i | ||||||||
\(867\) | −25.8319 | −0.877297 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.21769i | − | 0.278766i | ||||||
\(870\) | −1.21140 | −0.0410704 | ||||||||
\(871\) | −26.4028 | + | 4.91707i | −0.894624 | + | 0.166609i | ||||
\(872\) | 14.4095 | 0.487966 | ||||||||
\(873\) | 16.1088i | 0.545202i | ||||||||
\(874\) | −45.2373 | −1.53018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.0696i | 0.340220i | ||||||||
\(877\) | 9.23505i | 0.311846i | 0.987769 | + | 0.155923i | \(0.0498351\pi\) | ||||
−0.987769 | + | 0.155923i | \(0.950165\pi\) | |||||||
\(878\) | 11.6231i | 0.392262i | ||||||||
\(879\) | − | 2.80194i | − | 0.0945072i | ||||||
\(880\) | 0.224361 | 0.00756319 | ||||||||
\(881\) | 14.9108 | 0.502357 | 0.251179 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251179 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.9171 | −1.27601 | −0.638006 | − | 0.770032i | \(-0.720240\pi\) | ||||
−0.638006 | + | 0.770032i | \(0.720240\pi\) | |||||||
\(884\) | 4.32025 | + | 23.1981i | 0.145306 | + | 0.780235i | ||||
\(885\) | 1.32692 | 0.0446039 | ||||||||
\(886\) | 4.67308i | 0.156995i | ||||||||
\(887\) | −11.1285 | −0.373658 | −0.186829 | − | 0.982392i | \(-0.559821\pi\) | ||||
−0.186829 | + | 0.982392i | \(0.559821\pi\) | |||||||
\(888\) | −3.54461 | −0.118949 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.51429i | 0.0507590i | ||||||||
\(891\) | 0.660123i | 0.0221150i | ||||||||
\(892\) | 18.0196i | 0.603342i | ||||||||
\(893\) | −57.5353 | −1.92534 | ||||||||
\(894\) | −8.10884 | −0.271200 | ||||||||
\(895\) | − | 0.152510i | − | 0.00509785i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.90411 | − | 26.3332i | −0.163744 | − | 0.879240i | ||||
\(898\) | 36.6271 | 1.22226 | ||||||||
\(899\) | − | 14.2569i | − | 0.475496i | ||||||
\(900\) | −4.88448 | −0.162816 | ||||||||
\(901\) | 19.6338 | 0.654097 | ||||||||
\(902\) | 0.570909i | 0.0190092i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.5576i | 0.517437i | ||||||||
\(905\) | − | 5.40544i | − | 0.179683i | ||||||
\(906\) | −5.30062 | −0.176101 | ||||||||
\(907\) | −12.1088 | −0.402068 | −0.201034 | − | 0.979584i | \(-0.564430\pi\) | ||||
−0.201034 | + | 0.979584i | \(0.564430\pi\) | |||||||
\(908\) | − | 0.231033i | − | 0.00766709i | ||||||
\(909\) | −2.79527 | −0.0927133 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4354 | −1.53847 | −0.769236 | − | 0.638964i | \(-0.779363\pi\) | ||||
−0.769236 | + | 0.638964i | \(0.779363\pi\) | |||||||
\(912\) | − | 6.08921i | − | 0.201634i | ||||||
\(913\) | −10.7560 | −0.355972 | ||||||||
\(914\) | 31.3372 | 1.03654 | ||||||||
\(915\) | − | 0.633820i | − | 0.0209535i | ||||||
\(916\) | − | 6.64049i | − | 0.219408i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.54461i | 0.216004i | ||||||||
\(919\) | 36.7797 | 1.21325 | 0.606624 | − | 0.794989i | \(-0.292523\pi\) | ||||
0.606624 | + | 0.794989i | \(0.292523\pi\) | |||||||
\(920\) | −2.52498 | −0.0832460 | ||||||||
\(921\) | − | 9.21769i | − | 0.303733i | ||||||
\(922\) | −0.601231 | −0.0198005 | ||||||||
\(923\) | 3.13515 | − | 0.583868i | 0.103195 | − | 0.0192183i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 17.3136i | − | 0.569267i | ||||||
\(926\) | −10.5013 | −0.345095 | ||||||||
\(927\) | 7.53793 | 0.247578 | ||||||||
\(928\) | 3.56424i | 0.117002i | ||||||||
\(929\) | 4.13917i | 0.135802i | 0.997692 | + | 0.0679008i | \(0.0216301\pi\) | ||||
−0.997692 | + | 0.0679008i | \(0.978370\pi\) | |||||||
\(930\) | 1.35951i | 0.0445800i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.5183 | 0.966904 | ||||||||
\(933\) | −11.4684 | −0.375457 | ||||||||
\(934\) | 27.2217i | 0.890721i | ||||||||
\(935\) | 1.46835 | 0.0480202 | ||||||||
\(936\) | 3.54461 | − | 0.660123i | 0.115859 | − | 0.0215768i | ||||
\(937\) | −45.2939 | −1.47969 | −0.739844 | − | 0.672778i | \(-0.765101\pi\) | ||||
−0.739844 | + | 0.672778i | \(0.765101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.5642 | −0.736356 | ||||||||
\(940\) | −3.21140 | −0.104744 | ||||||||
\(941\) | 47.8948i | 1.56133i | 0.624953 | + | 0.780663i | \(0.285118\pi\) | ||||
−0.624953 | + | 0.780663i | \(0.714882\pi\) | |||||||
\(942\) | 23.0562i | 0.751213i | ||||||||
\(943\) | − | 6.42507i | − | 0.209229i | ||||||
\(944\) | − | 3.90411i | − | 0.127068i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.35951 | −0.109227 | ||||||||
\(947\) | − | 21.4554i | − | 0.697207i | −0.937270 | − | 0.348603i | \(-0.886656\pi\) | ||
0.937270 | − | 0.348603i | \(-0.113344\pi\) | |||||||
\(948\) | −12.4487 | −0.404316 | ||||||||
\(949\) | 35.6927 | − | 6.64716i | 1.15863 | − | 0.215776i | ||||
\(950\) | 29.7427 | 0.964979 | ||||||||
\(951\) | − | 12.6271i | − | 0.409463i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.0433 | 1.55627 | 0.778137 | − | 0.628094i | \(-0.216165\pi\) | ||||
0.778137 | + | 0.628094i | \(0.216165\pi\) | |||||||
\(954\) | − | 3.00000i | − | 0.0971286i | ||||||
\(955\) | 3.53793i | 0.114485i | ||||||||
\(956\) | − | 15.0236i | − | 0.485900i | ||||||
\(957\) | 2.35284i | 0.0760564i | ||||||||
\(958\) | 28.8711 | 0.932784 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 0.339877i | − | 0.0109695i | ||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 2.33988 | + | 12.5642i | 0.0754407 | + | 0.405087i | ||||
\(963\) | −3.72971 | −0.120188 | ||||||||
\(964\) | 4.44872i | 0.143284i | ||||||||
\(965\) | 2.61684 | 0.0842392 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.91481i | 0.158049i | 0.996873 | + | 0.0790247i | \(0.0251806\pi\) | ||||
−0.996873 | + | 0.0790247i | \(0.974819\pi\) | |||||||
\(968\) | 10.5642i | 0.339547i | ||||||||
\(969\) | − | 39.8515i | − | 1.28021i | ||||||
\(970\) | − | 5.47502i | − | 0.175792i | ||||||
\(971\) | −30.1584 | −0.967829 | −0.483915 | − | 0.875115i | \(-0.660786\pi\) | ||||
−0.483915 | + | 0.875115i | \(0.660786\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.91746 | 0.125523 | ||||||||
\(975\) | 3.22436 | + | 17.3136i | 0.103262 | + | 0.554478i | ||||
\(976\) | −1.86485 | −0.0596925 | ||||||||
\(977\) | − | 34.4095i | − | 1.10086i | −0.834883 | − | 0.550428i | \(-0.814465\pi\) | ||
0.834883 | − | 0.550428i | \(-0.185535\pi\) | |||||||
\(978\) | −13.5642 | −0.433736 | ||||||||
\(979\) | 2.94111 | 0.0939982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.4095i | − | 0.460059i | ||||||
\(982\) | 13.4202i | 0.428254i | ||||||||
\(983\) | − | 19.9500i | − | 0.636308i | −0.948039 | − | 0.318154i | \(-0.896937\pi\) | ||
0.948039 | − | 0.318154i | \(-0.103063\pi\) | |||||||
\(984\) | 0.864853 | 0.0275705 | ||||||||
\(985\) | 3.05222 | 0.0972518 | ||||||||
\(986\) | 23.3265i | 0.742868i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.5839 | + | 4.01963i | −0.686674 | + | 0.127881i | ||||
\(989\) | 37.8082 | 1.20223 | ||||||||
\(990\) | − | 0.224361i | − | 0.00713065i | ||||||
\(991\) | −23.8948 | −0.759043 | −0.379521 | − | 0.925183i | \(-0.623911\pi\) | ||||
−0.379521 | + | 0.925183i | \(0.623911\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 26.8212i | 0.851145i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.99961i | − | 0.221903i | ||||||
\(996\) | 16.2939i | 0.516293i | ||||||||
\(997\) | −6.14545 | −0.194628 | −0.0973142 | − | 0.995254i | \(-0.531025\pi\) | ||||
−0.0973142 | + | 0.995254i | \(0.531025\pi\) | |||||||
\(998\) | 32.7819 | 1.03769 | ||||||||
\(999\) | 3.54461i | 0.112146i |
(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 | 3822.2.c.j.883.2 | 6 | ||
7.3 | odd | 6 | 546.2.bk.b.415.5 | yes | 12 | ||
7.5 | odd | 6 | 546.2.bk.b.25.2 | ✓ | 12 | ||
7.6 | odd | 2 | 3822.2.c.k.883.2 | 6 | |||
13.12 | even | 2 | inner | 3822.2.c.j.883.5 | 6 | ||
21.5 | even | 6 | 1638.2.dm.c.1117.5 | 12 | |||
21.17 | even | 6 | 1638.2.dm.c.415.2 | 12 | |||
91.12 | odd | 6 | 546.2.bk.b.25.5 | yes | 12 | ||
91.38 | odd | 6 | 546.2.bk.b.415.2 | yes | 12 | ||
91.90 | odd | 2 | 3822.2.c.k.883.5 | 6 | |||
273.38 | even | 6 | 1638.2.dm.c.415.5 | 12 | |||
273.194 | even | 6 | 1638.2.dm.c.1117.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.b.25.2 | ✓ | 12 | 7.5 | odd | 6 | ||
546.2.bk.b.25.5 | yes | 12 | 91.12 | odd | 6 | ||
546.2.bk.b.415.2 | yes | 12 | 91.38 | odd | 6 | ||
546.2.bk.b.415.5 | yes | 12 | 7.3 | odd | 6 | ||
1638.2.dm.c.415.2 | 12 | 21.17 | even | 6 | |||
1638.2.dm.c.415.5 | 12 | 273.38 | even | 6 | |||
1638.2.dm.c.1117.2 | 12 | 273.194 | even | 6 | |||
1638.2.dm.c.1117.5 | 12 | 21.5 | even | 6 | |||
3822.2.c.j.883.2 | 6 | 1.1 | even | 1 | trivial | ||
3822.2.c.j.883.5 | 6 | 13.12 | even | 2 | inner | ||
3822.2.c.k.883.2 | 6 | 7.6 | odd | 2 | |||
3822.2.c.k.883.5 | 6 | 91.90 | odd | 2 |