Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(17,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bl (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.8 | ||
Root | \(-1.45333 + 1.51725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.89 |
Dual form | 504.2.bl.a.17.8 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45333 | − | 2.51725i | 0.649950 | − | 1.12575i | −0.333184 | − | 0.942862i | \(-0.608123\pi\) |
0.983134 | − | 0.182885i | \(-0.0585436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64571 | + | 0.0146827i | −0.999985 | + | 0.00554953i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.08853 | − | 0.628464i | 0.328205 | − | 0.189489i | −0.326839 | − | 0.945080i | \(-0.605984\pi\) |
0.655044 | + | 0.755591i | \(0.272650\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.32679i | − | 1.47739i | −0.674042 | − | 0.738693i | \(-0.735443\pi\) | ||
0.674042 | − | 0.738693i | \(-0.264557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.880708 | + | 1.52543i | 0.213603 | + | 0.369971i | 0.952840 | − | 0.303475i | \(-0.0981467\pi\) |
−0.739236 | + | 0.673446i | \(0.764813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.69849 | − | 3.86738i | −1.53674 | − | 0.887237i | −0.999027 | − | 0.0441085i | \(-0.985955\pi\) |
−0.537712 | − | 0.843128i | \(-0.680711\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43392 | + | 2.55992i | 0.924536 | + | 0.533781i | 0.885079 | − | 0.465440i | \(-0.154104\pi\) |
0.0394566 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.72435 | − | 2.98667i | −0.344871 | − | 0.597333i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.74013i | − | 1.62300i | −0.584352 | − | 0.811500i | \(-0.698651\pi\) | ||
0.584352 | − | 0.811500i | \(-0.301349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.18272 | − | 1.26019i | 0.392027 | − | 0.226337i | −0.291011 | − | 0.956720i | \(-0.593992\pi\) |
0.683038 | + | 0.730383i | \(0.260658\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.80814 | + | 6.68124i | −0.643693 | + | 1.12934i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.66400 | + | 6.34623i | −0.602358 | + | 1.04331i | 0.390106 | + | 0.920770i | \(0.372439\pi\) |
−0.992463 | + | 0.122544i | \(0.960895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.09603 | −0.483519 | −0.241760 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241760 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15729 | 0.176484 | 0.0882422 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882422 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.44334 | − | 5.96403i | 0.502262 | − | 0.869944i | −0.497734 | − | 0.867330i | \(-0.665835\pi\) |
0.999997 | − | 0.00261431i | \(-0.000832161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99957 | − | 0.0776922i | 0.999938 | − | 0.0110989i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3057 | − | 6.52735i | 1.55296 | − | 0.896600i | 0.555058 | − | 0.831811i | \(-0.312696\pi\) |
0.997899 | − | 0.0647890i | \(-0.0206374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.65347i | − | 0.492634i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13525 | + | 5.43042i | 0.408175 | + | 0.706980i | 0.994685 | − | 0.102962i | \(-0.0328319\pi\) |
−0.586510 | + | 0.809942i | \(0.699499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19449 | + | 1.26699i | 0.280976 | + | 0.162221i | 0.633865 | − | 0.773444i | \(-0.281467\pi\) |
−0.352889 | + | 0.935665i | \(0.614801\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.4088 | − | 7.74160i | −1.66316 | − | 0.960227i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.689860 | − | 1.19487i | −0.0842798 | − | 0.145977i | 0.820804 | − | 0.571210i | \(-0.193526\pi\) |
−0.905084 | + | 0.425233i | \(0.860192\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.65477i | 1.02713i | 0.858050 | + | 0.513566i | \(0.171676\pi\) | ||||
−0.858050 | + | 0.513566i | \(0.828324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.38121 | − | 2.52949i | 0.512782 | − | 0.296055i | −0.221195 | − | 0.975230i | \(-0.570996\pi\) |
0.733976 | + | 0.679175i | \(0.237662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.87071 | + | 1.67872i | −0.327148 | + | 0.191308i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.63142 | + | 13.2180i | −0.858602 | + | 1.48714i | 0.0146603 | + | 0.999893i | \(0.495333\pi\) |
−0.873262 | + | 0.487250i | \(0.838000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.75373 | 0.412025 | 0.206013 | − | 0.978549i | \(-0.433951\pi\) | ||||
0.206013 | + | 0.978549i | \(0.433951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.11985 | 0.555326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.55321 | + | 6.15434i | −0.376640 | + | 0.652359i | −0.990571 | − | 0.137001i | \(-0.956254\pi\) |
0.613931 | + | 0.789359i | \(0.289587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0782115 | + | 14.0931i | 0.00819880 | + | 1.47736i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.4703 | + | 11.2412i | −1.99761 | + | 1.15332i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.03874i | − | 0.410072i | −0.978754 | − | 0.205036i | \(-0.934269\pi\) | ||
0.978754 | − | 0.205036i | \(-0.0657311\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.39249 | + | 5.87597i | 0.337565 | + | 0.584681i | 0.983974 | − | 0.178311i | \(-0.0570632\pi\) |
−0.646409 | + | 0.762991i | \(0.723730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.39758 | − | 3.11629i | −0.531839 | − | 0.307057i | 0.209926 | − | 0.977717i | \(-0.432678\pi\) |
−0.741765 | + | 0.670660i | \(0.766011\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.41950 | − | 4.86100i | −0.813944 | − | 0.469931i | 0.0343796 | − | 0.999409i | \(-0.489054\pi\) |
−0.848324 | + | 0.529478i | \(0.822388\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.34463 | + | 12.7213i | 0.703488 | + | 1.21848i | 0.967234 | + | 0.253885i | \(0.0817086\pi\) |
−0.263746 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.1169i | 1.79837i | 0.437572 | + | 0.899184i | \(0.355839\pi\) | ||||
−0.437572 | + | 0.899184i | \(0.644161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.8879 | − | 7.44084i | 1.20180 | − | 0.693862i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.35250 | − | 4.02292i | −0.215653 | − | 0.368780i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.71007 | + | 8.15807i | −0.428188 | + | 0.741643i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.50909 | 0.403305 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2906 | 1.26808 | 0.634041 | − | 0.773299i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773299i | \(0.281395\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.07057 | − | 10.5145i | 0.530388 | − | 0.918659i | −0.468983 | − | 0.883207i | \(-0.655380\pi\) |
0.999371 | − | 0.0354521i | \(-0.0112871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.7791 | + | 10.1336i | 1.54164 | + | 0.878695i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.986259 | + | 0.569417i | −0.0842618 | + | 0.0486486i | −0.541539 | − | 0.840676i | \(-0.682158\pi\) |
0.457277 | + | 0.889324i | \(0.348825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6610i | 1.75245i | 0.481906 | + | 0.876223i | \(0.339945\pi\) | ||||
−0.481906 | + | 0.876223i | \(0.660055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.34770 | − | 5.79838i | −0.279948 | − | 0.484885i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.0011 | − | 12.7023i | −1.82709 | − | 1.05487i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.28425 | − | 3.05086i | −0.432903 | − | 0.249936i | 0.267680 | − | 0.963508i | \(-0.413743\pi\) |
−0.700582 | + | 0.713572i | \(0.747076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.66443 | − | 6.34698i | −0.298207 | − | 0.516510i | 0.677519 | − | 0.735505i | \(-0.263055\pi\) |
−0.975726 | + | 0.218996i | \(0.929722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.32591i | − | 0.588432i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.32800 | − | 1.92142i | 0.265603 | − | 0.153346i | −0.361285 | − | 0.932456i | \(-0.617662\pi\) |
0.626888 | + | 0.779110i | \(0.284328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7685 | − | 6.70772i | −0.927484 | − | 0.528642i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.97206 | − | 13.8080i | 0.624420 | − | 1.08153i | −0.364233 | − | 0.931308i | \(-0.618669\pi\) |
0.988653 | − | 0.150219i | \(-0.0479978\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.1419 | 1.86816 | 0.934079 | − | 0.357067i | \(-0.116223\pi\) | ||||
0.934079 | + | 0.357067i | \(0.116223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.3747 | −1.18267 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.78641 | − | 11.7544i | 0.515962 | − | 0.893672i | −0.483867 | − | 0.875142i | \(-0.660768\pi\) |
0.999828 | − | 0.0185299i | \(-0.00589860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.60599 | + | 7.87654i | 0.348180 | + | 0.595410i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.62646 | − | 0.939035i | 0.121567 | − | 0.0701868i | −0.437983 | − | 0.898983i | \(-0.644307\pi\) |
0.559550 | + | 0.828796i | \(0.310974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36975i | 0.399130i | 0.979885 | + | 0.199565i | \(0.0639530\pi\) | ||||
−0.979885 | + | 0.199565i | \(0.936047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.6500 | + | 18.4464i | 0.783005 | + | 1.35620i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.91736 | + | 1.10699i | 0.140211 | + | 0.0809509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3153 | − | 8.26495i | −1.03582 | − | 0.598031i | −0.117173 | − | 0.993111i | \(-0.537383\pi\) |
−0.918646 | + | 0.395081i | \(0.870717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.24013 | − | 10.8082i | −0.449174 | − | 0.777993i | 0.549158 | − | 0.835718i | \(-0.314948\pi\) |
−0.998332 | + | 0.0577258i | \(0.981615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7258i | 1.40541i | 0.711482 | + | 0.702704i | \(0.248024\pi\) | ||||
−0.711482 | + | 0.702704i | \(0.751976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2771 | − | 12.2844i | 1.50830 | − | 0.870815i | 0.508343 | − | 0.861155i | \(-0.330258\pi\) |
0.999953 | − | 0.00966023i | \(-0.00307500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.128328 | + | 23.1238i | 0.00900689 | + | 1.62298i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.49957 | + | 7.79348i | −0.314264 | + | 0.544320i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.72203 | −0.672487 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0173 | −1.10267 | −0.551337 | − | 0.834283i | \(-0.685882\pi\) | ||||
−0.551337 | + | 0.834283i | \(0.685882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.68192 | − | 2.91317i | 0.114706 | − | 0.198677i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.75633 | + | 3.36615i | −0.390765 | + | 0.228509i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.12565 | − | 4.69135i | 0.546590 | − | 0.315574i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.7358i | − | 1.65643i | −0.560410 | − | 0.828215i | \(-0.689356\pi\) | ||
0.560410 | − | 0.828215i | \(-0.310644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1431 | − | 19.3005i | −0.739597 | − | 1.28102i | −0.952677 | − | 0.303984i | \(-0.901683\pi\) |
0.213080 | − | 0.977035i | \(-0.431650\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5011 | − | 8.37219i | −0.958257 | − | 0.553250i | −0.0626207 | − | 0.998037i | \(-0.519946\pi\) |
−0.895636 | + | 0.444788i | \(0.853279\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.45707 | + | 0.841243i | 0.0954561 | + | 0.0551116i | 0.546968 | − | 0.837153i | \(-0.315782\pi\) |
−0.451512 | + | 0.892265i | \(0.649115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0086 | − | 17.3355i | −0.652891 | − | 1.13084i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.79777i | − | 0.504396i | −0.967676 | − | 0.252198i | \(-0.918847\pi\) | ||
0.967676 | − | 0.252198i | \(-0.0811534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1503 | + | 7.01500i | −0.782672 | + | 0.451876i | −0.837377 | − | 0.546627i | \(-0.815912\pi\) |
0.0547042 | + | 0.998503i | \(0.482578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.97713 | − | 17.7326i | 0.637416 | − | 1.13289i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.6007 | + | 35.6815i | −1.31079 | + | 2.27036i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.34078 | 0.589585 | 0.294792 | − | 0.955561i | \(-0.404749\pi\) | ||||
0.294792 | + | 0.955561i | \(0.404749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.43528 | 0.404583 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.12814 | + | 7.15016i | −0.257507 | + | 0.446015i | −0.965573 | − | 0.260131i | \(-0.916234\pi\) |
0.708067 | + | 0.706146i | \(0.249568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.60070 | − | 16.8441i | 0.596558 | − | 1.04664i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7171 | − | 10.2290i | 1.09248 | − | 0.630746i | 0.158248 | − | 0.987399i | \(-0.449416\pi\) |
0.934237 | + | 0.356653i | \(0.116082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 37.9456i | − | 2.33098i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1726 | + | 26.2797i | 0.925088 | + | 1.60230i | 0.791420 | + | 0.611273i | \(0.209342\pi\) |
0.133668 | + | 0.991026i | \(0.457324\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.16870 | − | 2.98415i | −0.313976 | − | 0.181274i | 0.334728 | − | 0.942315i | \(-0.391355\pi\) |
−0.648704 | + | 0.761041i | \(0.724689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.75403 | − | 2.16739i | −0.226376 | − | 0.130698i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11836 | + | 1.93706i | 0.0671958 | + | 0.116387i | 0.897666 | − | 0.440677i | \(-0.145261\pi\) |
−0.830470 | + | 0.557063i | \(0.811928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.2683i | − | 0.970484i | −0.874380 | − | 0.485242i | \(-0.838732\pi\) | ||
0.874380 | − | 0.485242i | \(-0.161268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.84235 | − | 2.21838i | 0.228404 | − | 0.131869i | −0.381432 | − | 0.924397i | \(-0.624569\pi\) |
0.609836 | + | 0.792528i | \(0.291235\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.19121 | − | 0.0454581i | 0.483512 | − | 0.00268331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.94871 | − | 12.0355i | 0.408747 | − | 0.707971i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.48448 | 0.495669 | 0.247834 | − | 0.968802i | \(-0.420281\pi\) | ||||
0.247834 | + | 0.968802i | \(0.420281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.2263 | 1.06117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.6362 | − | 23.6186i | 0.788601 | − | 1.36590i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.06184 | + | 0.0169920i | −0.176482 | + | 0.000979405i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.37865 | − | 3.68272i | 0.365241 | − | 0.210872i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.06321i | 0.117753i | 0.998265 | + | 0.0588767i | \(0.0187519\pi\) | ||||
−0.998265 | + | 0.0588767i | \(0.981248\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4339 | − | 23.2683i | −0.761768 | − | 1.31942i | −0.941938 | − | 0.335786i | \(-0.890998\pi\) |
0.180170 | − | 0.983635i | \(-0.442335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6333 | − | 6.13912i | −0.601028 | − | 0.347004i | 0.168418 | − | 0.985716i | \(-0.446134\pi\) |
−0.769446 | + | 0.638712i | \(0.779468\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.29866 | + | 0.749784i | 0.0729403 | + | 0.0421121i | 0.536027 | − | 0.844201i | \(-0.319925\pi\) |
−0.463086 | + | 0.886313i | \(0.653258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.49286 | − | 9.51391i | −0.307541 | − | 0.532676i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.6241i | − | 0.758066i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.9094 | + | 9.18527i | −0.882492 | + | 0.509507i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.02251 | + | 15.8297i | −0.497427 | + | 0.872718i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.53641 | + | 13.0534i | −0.414239 | + | 0.717482i | −0.995348 | − | 0.0963430i | \(-0.969285\pi\) |
0.581110 | + | 0.813825i | \(0.302619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.01039 | −0.219111 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.3414 | 0.835700 | 0.417850 | − | 0.908516i | \(-0.362784\pi\) | ||||
0.417850 | + | 0.908516i | \(0.362784\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.58397 | − | 2.74352i | 0.0857768 | − | 0.148570i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5177 | + | 0.308324i | −0.999861 | + | 0.0166479i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4995 | + | 7.79393i | −0.724691 | + | 0.418400i | −0.816477 | − | 0.577378i | \(-0.804076\pi\) |
0.0917861 | + | 0.995779i | \(0.470742\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.35182i | 0.0723613i | 0.999345 | + | 0.0361806i | \(0.0115192\pi\) | ||||
−0.999345 | + | 0.0361806i | \(0.988481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.91110 | + | 17.1665i | 0.527515 | + | 0.913682i | 0.999486 | + | 0.0320680i | \(0.0102093\pi\) |
−0.471971 | + | 0.881614i | \(0.656457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.7862 | + | 12.5783i | 1.15629 | + | 0.667585i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.9382 | + | 10.9340i | 0.999521 | + | 0.577074i | 0.908107 | − | 0.418739i | \(-0.137528\pi\) |
0.0914146 | + | 0.995813i | \(0.470861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.4132 | + | 35.3567i | 1.07438 | + | 1.86088i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 14.7048i | − | 0.769683i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.591012 | − | 0.341221i | 0.0308506 | − | 0.0178116i | −0.484495 | − | 0.874794i | \(-0.660997\pi\) |
0.515346 | + | 0.856982i | \(0.327663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.8158 | + | 17.4355i | −1.54796 | + | 0.905205i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5153 | − | 21.6772i | 0.648020 | − | 1.12240i | −0.335575 | − | 0.942013i | \(-0.608931\pi\) |
0.983595 | − | 0.180390i | \(-0.0577360\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.5568 | −2.39780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7220 | −0.550752 | −0.275376 | − | 0.961337i | \(-0.588802\pi\) | ||||
−0.275376 | + | 0.961337i | \(0.588802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8748 | + | 20.5677i | −0.606772 | + | 1.05096i | 0.384997 | + | 0.922918i | \(0.374203\pi\) |
−0.991769 | + | 0.128042i | \(0.959131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0536427 | + | 9.66602i | 0.00273389 | + | 0.492626i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6648 | − | 7.88939i | 0.692834 | − | 0.400008i | −0.111839 | − | 0.993726i | \(-0.535674\pi\) |
0.804673 | + | 0.593718i | \(0.202341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.01818i | 0.456069i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.1820 | + | 38.4203i | 1.11610 | + | 1.93314i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9468 | − | 8.05218i | −0.699969 | − | 0.404127i | 0.107367 | − | 0.994219i | \(-0.465758\pi\) |
−0.807336 | + | 0.590092i | \(0.799091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4857 | + | 8.36335i | 0.723384 | + | 0.417646i | 0.815997 | − | 0.578056i | \(-0.196189\pi\) |
−0.0926131 | + | 0.995702i | \(0.529522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.71278 | − | 11.6269i | −0.334387 | − | 0.579176i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.21076i | 0.456561i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1106 | − | 5.83733i | 0.499935 | − | 0.288637i | −0.228752 | − | 0.973485i | \(-0.573464\pi\) |
0.728687 | + | 0.684847i | \(0.240131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.37471 | − | 14.3213i | −0.412092 | − | 0.704704i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.45542 | − | 9.44906i | 0.267796 | − | 0.463836i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.16399 | −0.398837 | −0.199419 | − | 0.979914i | \(-0.563905\pi\) | ||||
−0.199419 | + | 0.979914i | \(0.563905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.71744 | −0.376125 | −0.188063 | − | 0.982157i | \(-0.560221\pi\) | ||||
−0.188063 | + | 0.982157i | \(0.560221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.03730 | − | 5.26076i | 0.147331 | − | 0.255185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.82459 | − | 3.31987i | −0.281872 | − | 0.160660i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.1483 | + | 13.9420i | −1.16318 | + | 0.671563i | −0.952064 | − | 0.305898i | \(-0.901043\pi\) |
−0.211117 | + | 0.977461i | \(0.567710\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8885i | 0.955779i | 0.878420 | + | 0.477889i | \(0.158598\pi\) | ||||
−0.878420 | + | 0.477889i | \(0.841402\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.8004 | − | 34.2953i | −0.947180 | − | 1.64056i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.61654 | + | 3.82006i | 0.315790 | + | 0.182322i | 0.649515 | − | 0.760349i | \(-0.274972\pi\) |
−0.333724 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4681 | + | 10.0852i | 0.829933 | + | 0.479162i | 0.853830 | − | 0.520553i | \(-0.174274\pi\) |
−0.0238969 | + | 0.999714i | \(0.507607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3280 | + | 17.8886i | 0.489594 | + | 0.848002i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.27122i | 0.107185i | 0.998563 | + | 0.0535926i | \(0.0170672\pi\) | ||||
−0.998563 | + | 0.0535926i | \(0.982933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.37013 | + | 1.94575i | −0.158693 | + | 0.0916216i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.5896 | + | 20.2852i | 1.66847 | + | 0.950983i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.74056 | + | 9.94294i | −0.268532 | + | 0.465111i | −0.968483 | − | 0.249080i | \(-0.919872\pi\) |
0.699951 | + | 0.714191i | \(0.253205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2339 | −1.17526 | −0.587630 | − | 0.809130i | \(-0.699939\pi\) | ||||
−0.587630 | + | 0.809130i | \(0.699939\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8323 | 0.828736 | 0.414368 | − | 0.910110i | \(-0.364003\pi\) | ||||
0.414368 | + | 0.910110i | \(0.364003\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.62598 | − | 4.54833i | 0.121516 | − | 0.210472i | −0.798850 | − | 0.601531i | \(-0.794558\pi\) |
0.920366 | + | 0.391059i | \(0.127891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.84271 | + | 3.15116i | 0.0850887 | + | 0.145507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.25974 | − | 0.727312i | 0.0579230 | − | 0.0334419i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.6749i | 1.22393i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.2216 | − | 29.8287i | −0.786875 | − | 1.36291i | −0.927873 | − | 0.372898i | \(-0.878364\pi\) |
0.140997 | − | 0.990010i | \(-0.454969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.8050 | + | 19.5173i | 1.54138 | + | 0.889915i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1665 | − | 5.86963i | −0.461637 | − | 0.266526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.3207 | + | 21.3401i | 0.558304 | + | 0.967010i | 0.997638 | + | 0.0686868i | \(0.0218809\pi\) |
−0.439335 | + | 0.898324i | \(0.644786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.90125i | 0.311449i | 0.987801 | + | 0.155725i | \(0.0497712\pi\) | ||||
−0.987801 | + | 0.155725i | \(0.950229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3325 | − | 7.69750i | 0.600464 | − | 0.346678i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.127075 | − | 22.8980i | −0.00570010 | − | 1.02712i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.72644 | − | 6.45437i | 0.166818 | − | 0.288938i | −0.770481 | − | 0.637463i | \(-0.779984\pi\) |
0.937299 | + | 0.348525i | \(0.113317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0638301 | −0.00284605 | −0.00142302 | − | 0.999999i | \(-0.500453\pi\) | ||||
−0.00142302 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.7217 | 0.877603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.76796 | + | 11.7225i | −0.299985 | + | 0.519588i | −0.976132 | − | 0.217178i | \(-0.930315\pi\) |
0.676148 | + | 0.736766i | \(0.263648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.5543 | + | 6.75663i | −0.511131 | + | 0.298896i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.6890 | + | 9.05802i | −0.691338 | + | 0.399144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.65605i | − | 0.380693i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.01202 | − | 10.4131i | −0.263391 | − | 0.456207i | 0.703750 | − | 0.710448i | \(-0.251508\pi\) |
−0.967141 | + | 0.254241i | \(0.918174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1014 | + | 10.4508i | 0.791517 | + | 0.456983i | 0.840496 | − | 0.541817i | \(-0.182263\pi\) |
−0.0489792 | + | 0.998800i | \(0.515597\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.84467 | + | 2.21972i | 0.167477 | + | 0.0966926i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.60642 | + | 2.78241i | 0.0698445 | + | 0.120974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.4919i | 0.714345i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.4727 | + | 14.1293i | −1.05805 | + | 0.610863i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.57043 | − | 4.48355i | 0.326081 | − | 0.193120i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.07613 | + | 8.79211i | −0.218240 | + | 0.378003i | −0.954270 | − | 0.298946i | \(-0.903365\pi\) |
0.736030 | + | 0.676949i | \(0.236698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.6968 | 1.82893 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.99041 | −0.170618 | −0.0853088 | − | 0.996355i | \(-0.527188\pi\) | ||||
−0.0853088 | + | 0.996355i | \(0.527188\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.8014 | + | 58.5457i | −1.43999 | + | 2.49413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.9965 | − | 35.0831i | 0.850336 | − | 1.49188i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.41758 | − | 3.70519i | 0.271921 | − | 0.156994i | −0.357839 | − | 0.933783i | \(-0.616486\pi\) |
0.629760 | + | 0.776789i | \(0.283153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.16462i | − | 0.260736i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.851583 | − | 1.47499i | −0.0358899 | − | 0.0621632i | 0.847522 | − | 0.530759i | \(-0.178093\pi\) |
−0.883412 | + | 0.468596i | \(0.844760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.1220 | + | 27.7832i | 2.02451 | + | 1.16885i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3339 | − | 8.27566i | −0.600907 | − | 0.346934i | 0.168491 | − | 0.985703i | \(-0.446110\pi\) |
−0.769398 | + | 0.638769i | \(0.779444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.49034 | + | 6.04545i | 0.146066 | + | 0.252994i | 0.929770 | − | 0.368140i | \(-0.120005\pi\) |
−0.783704 | + | 0.621135i | \(0.786672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 17.6569i | − | 0.736342i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5904 | + | 16.5067i | −1.19023 | + | 0.687182i | −0.958360 | − | 0.285564i | \(-0.907819\pi\) |
−0.231875 | + | 0.972746i | \(0.574486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.93128 | + | 0.0551148i | −0.412019 | + | 0.00228655i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.20441 | − | 14.2105i | 0.339792 | − | 0.588537i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.1690 | 1.16266 | 0.581330 | − | 0.813668i | \(-0.302533\pi\) | ||||
0.581330 | + | 0.813668i | \(0.302533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.4945 | −0.803259 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.04923 | + | 12.2096i | −0.289477 | + | 0.501389i | −0.973685 | − | 0.227898i | \(-0.926815\pi\) |
0.684208 | + | 0.729287i | \(0.260148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.5456 | + | 0.0751731i | −0.555317 | + | 0.00308180i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.9852 | + | 16.1573i | −1.14345 | + | 0.660169i | −0.947282 | − | 0.320402i | \(-0.896182\pi\) |
−0.196164 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9359i | 0.486877i | 0.969916 | + | 0.243439i | \(0.0782754\pi\) | ||||
−0.969916 | + | 0.243439i | \(0.921725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.6906 | + | 23.7128i | 0.556602 | + | 0.964062i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.8863 | − | 11.4813i | −0.807159 | − | 0.466013i | 0.0388095 | − | 0.999247i | \(-0.487643\pi\) |
−0.845968 | + | 0.533233i | \(0.820977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.7692 | − | 18.3419i | −1.28524 | − | 0.742035i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5772 | − | 32.1766i | −0.750325 | − | 1.29960i | −0.947665 | − | 0.319267i | \(-0.896563\pi\) |
0.197339 | − | 0.980335i | \(-0.436770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.34437i | 0.0943806i | 0.998886 | + | 0.0471903i | \(0.0150267\pi\) | ||||
−0.998886 | + | 0.0471903i | \(0.984973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9709 | + | 14.9943i | −1.04386 | + | 0.602673i | −0.920924 | − | 0.389742i | \(-0.872564\pi\) |
−0.122936 | + | 0.992415i | \(0.539231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.31040 | − | 16.3348i | 0.373013 | − | 0.654439i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1750 | − | 26.2838i | 0.606999 | − | 1.05135i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.9077 | −0.514662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.6780 | −1.73879 | −0.869396 | − | 0.494116i | \(-0.835492\pi\) | ||||
−0.869396 | + | 0.494116i | \(0.835492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.7689 | − | 35.9729i | 0.824190 | − | 1.42754i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.413850 | − | 37.2852i | −0.0163973 | − | 1.47729i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.6850 | − | 8.47841i | 0.580024 | − | 0.334877i | −0.181119 | − | 0.983461i | \(-0.557972\pi\) |
0.761143 | + | 0.648584i | \(0.224639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2731i | 0.602311i | 0.953575 | + | 0.301156i | \(0.0973723\pi\) | ||||
−0.953575 | + | 0.301156i | \(0.902628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.66472 | + | 2.88338i | 0.0654469 | + | 0.113357i | 0.896892 | − | 0.442249i | \(-0.145819\pi\) |
−0.831445 | + | 0.555607i | \(0.812486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.82565 | + | 3.94079i | 0.267930 | + | 0.154689i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0441 | + | 6.37633i | 0.432190 | + | 0.249525i | 0.700279 | − | 0.713869i | \(-0.253059\pi\) |
−0.268089 | + | 0.963394i | \(0.586392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6451 | − | 30.5622i | −0.689452 | − | 1.19417i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.3768i | 1.76763i | 0.467837 | + | 0.883815i | \(0.345033\pi\) | ||||
−0.467837 | + | 0.883815i | \(0.654967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0610 | + | 6.96341i | −0.469118 | + | 0.270845i | −0.715870 | − | 0.698233i | \(-0.753970\pi\) |
0.246753 | + | 0.969079i | \(0.420637\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51.3477 | − | 30.0268i | 1.99118 | − | 1.16439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.3741 | − | 38.7530i | 0.866327 | − | 1.50052i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18503 | 0.122957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2388 | −1.01143 | −0.505716 | − | 0.862700i | \(-0.668772\pi\) | ||||
−0.505716 | + | 0.862700i | \(0.668772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6453 | + | 37.4908i | −0.831897 | + | 1.44089i | 0.0646342 | + | 0.997909i | \(0.479412\pi\) |
−0.896532 | + | 0.442980i | \(0.853921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0592995 | + | 10.6853i | 0.00227571 | + | 0.410066i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.5578 | − | 13.6011i | 0.901416 | − | 0.520433i | 0.0237567 | − | 0.999718i | \(-0.492437\pi\) |
0.877659 | + | 0.479285i | \(0.159104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.31021i | 0.126477i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.7698 | − | 60.2231i | −1.32462 | − | 2.29432i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.16588 | + | 1.82782i | 0.120436 | + | 0.0695336i | 0.559008 | − | 0.829162i | \(-0.311182\pi\) |
−0.438572 | + | 0.898696i | \(0.644516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.0089 | + | 30.0274i | 1.97281 | + | 1.13900i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.72670 | − | 4.72279i | −0.103281 | − | 0.178888i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.5686i | − | 1.19233i | −0.802863 | − | 0.596164i | \(-0.796691\pi\) | ||
0.802863 | − | 0.596164i | \(-0.203309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.0865 | − | 28.3401i | 1.85133 | − | 1.06887i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.06182 | − | 15.4963i | −0.340805 | − | 0.582798i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1056 | − | 27.8956i | 0.604857 | − | 1.04764i | −0.387217 | − | 0.921989i | \(-0.626564\pi\) |
0.992074 | − | 0.125655i | \(-0.0401031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9040 | 0.483258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.4613 | −0.727810 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.07969 | + | 3.60213i | −0.0775595 | + | 0.134337i | −0.902196 | − | 0.431325i | \(-0.858046\pi\) |
0.824637 | + | 0.565662i | \(0.191379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3262 | + | 8.16556i | 0.533535 | + | 0.304101i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.1039 | + | 15.0711i | −0.969473 | + | 0.559725i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.3925i | 1.57225i | 0.618067 | + | 0.786125i | \(0.287916\pi\) | ||||
−0.618067 | + | 0.786125i | \(0.712084\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.01923 | + | 1.76536i | 0.0376976 | + | 0.0652942i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.7565 | − | 6.78764i | −0.434237 | − | 0.250707i | 0.266913 | − | 0.963721i | \(-0.413996\pi\) |
−0.701150 | + | 0.713014i | \(0.747330\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.50187 | − | 0.867105i | −0.0553221 | − | 0.0319402i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.46273 | + | 11.1938i | 0.237735 | + | 0.411770i | 0.960064 | − | 0.279780i | \(-0.0902616\pi\) |
−0.722329 | + | 0.691550i | \(0.756928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.9462i | − | 0.695068i | −0.937667 | − | 0.347534i | \(-0.887019\pi\) | ||
0.937667 | − | 0.347534i | \(-0.112981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.3595 | + | 8.86784i | −0.562730 | + | 0.324892i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.3469 | + | 12.7372i | 0.816539 | + | 0.465407i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4733 | − | 19.8723i | 0.418666 | − | 0.725150i | −0.577140 | − | 0.816645i | \(-0.695831\pi\) |
0.995806 | + | 0.0914950i | \(0.0291646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.3025 | −0.775279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.87010 | −0.249698 | −0.124849 | − | 0.992176i | \(-0.539845\pi\) | ||||
−0.124849 | + | 0.992176i | \(0.539845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.6164 | − | 32.2445i | 0.674843 | − | 1.16886i | −0.301671 | − | 0.953412i | \(-0.597545\pi\) |
0.976515 | − | 0.215451i | \(-0.0691221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.6186 | − | 33.5490i | −0.710239 | − | 1.21455i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9267 | − | 16.7008i | 1.04448 | − | 0.603032i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5757i | 0.669856i | 0.942244 | + | 0.334928i | \(0.108712\pi\) | ||||
−0.942244 | + | 0.334928i | \(0.891288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.99548 | + | 5.18832i | 0.107740 | + | 0.186611i | 0.914854 | − | 0.403784i | \(-0.132305\pi\) |
−0.807114 | + | 0.590395i | \(0.798972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.52755 | − | 4.34603i | −0.270398 | − | 0.156114i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7388 | + | 11.9735i | 0.743043 | + | 0.428996i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.43921 | + | 9.42099i | 0.194630 | + | 0.337110i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 11.1698i | − | 0.398669i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5679 | + | 12.4522i | −0.768813 | + | 0.443875i | −0.832451 | − | 0.554098i | \(-0.813063\pi\) |
0.0636377 | + | 0.997973i | \(0.479730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.280687 | − | 50.5778i | −0.00998009 | − | 1.79834i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.74899 | − | 11.6896i | 0.239664 | − | 0.415110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4955 | −0.442612 | −0.221306 | − | 0.975204i | \(-0.571032\pi\) | ||||
−0.221306 | + | 0.975204i | \(0.571032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.1303 | 0.429139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.17939 | − | 5.50686i | 0.112198 | − | 0.194333i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.9885 | + | 19.8755i | −1.19794 | + | 0.700521i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.8616 | − | 18.9727i | 1.15535 | − | 0.667043i | 0.205167 | − | 0.978727i | \(-0.434226\pi\) |
0.950186 | + | 0.311684i | \(0.100893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.7451i | − | 1.36053i | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||
0.732968 | − | 0.680263i | \(-0.238134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.1721 | − | 40.1353i | −0.811683 | − | 1.40588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.75207 | − | 4.47566i | −0.271210 | − | 0.156583i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.53706 | + | 3.77417i | 0.228145 | + | 0.131720i | 0.609716 | − | 0.792620i | \(-0.291283\pi\) |
−0.381571 | + | 0.924340i | \(0.624617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.6203 | + | 18.3949i | 0.370200 | + | 0.641205i | 0.989596 | − | 0.143874i | \(-0.0459559\pi\) |
−0.619396 | + | 0.785078i | \(0.712623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.9188i | 0.623098i | 0.950230 | + | 0.311549i | \(0.100848\pi\) | ||||
−0.950230 | + | 0.311549i | \(0.899152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.9593 | + | 15.5649i | −0.936334 | + | 0.540592i | −0.888809 | − | 0.458278i | \(-0.848467\pi\) |
−0.0475245 | + | 0.998870i | \(0.515133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.28309 | + | 10.6089i | 0.217696 | + | 0.367578i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.0862 | − | 60.7712i | 1.21421 | − | 2.10307i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.3438 | −0.633297 | −0.316649 | − | 0.948543i | \(-0.602558\pi\) | ||||
−0.316649 | + | 0.948543i | \(0.602558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −47.3898 | −1.63413 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.3446 | + | 38.7019i | −0.768676 | + | 1.33139i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.3417 | − | 21.6531i | 0.424065 | − | 0.744008i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.4917 | + | 18.7591i | −1.11380 | + | 0.643054i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 45.2905i | − | 1.55072i | −0.631521 | − | 0.775359i | \(-0.717569\pi\) | ||
0.631521 | − | 0.775359i | \(-0.282431\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.2703 | + | 36.8413i | 0.726581 | + | 1.25847i | 0.958320 | + | 0.285697i | \(0.0922250\pi\) |
−0.231739 | + | 0.972778i | \(0.574442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5225 | + | 11.8487i | 0.700218 | + | 0.404271i | 0.807429 | − | 0.589965i | \(-0.200859\pi\) |
−0.107210 | + | 0.994236i | \(0.534192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.4202 | + | 18.7178i | 1.10360 | + | 0.637162i | 0.937163 | − | 0.348891i | \(-0.113442\pi\) |
0.166433 | + | 0.986053i | \(0.446775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7258 | − | 34.1662i | −0.670699 | − | 1.16168i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.1843i | 0.650783i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.36484 | + | 3.67474i | −0.215664 | + | 0.124514i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.9298 | + | 0.0662055i | −0.403299 | + | 0.00223816i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.532842 | + | 0.922910i | −0.0179928 | + | 0.0311645i | −0.874882 | − | 0.484337i | \(-0.839061\pi\) |
0.856889 | + | 0.515501i | \(0.172394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4036 | 1.49600 | 0.747998 | − | 0.663701i | \(-0.231015\pi\) | ||||
0.747998 | + | 0.663701i | \(0.231015\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3117 | 0.885458 | 0.442729 | − | 0.896656i | \(-0.354010\pi\) | ||||
0.442729 | + | 0.896656i | \(0.354010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.4691 | − | 35.4536i | 0.687286 | − | 1.19041i | −0.285427 | − | 0.958400i | \(-0.592135\pi\) |
0.972713 | − | 0.232013i | \(-0.0745313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.8087 | + | 0.209824i | −1.26806 | + | 0.00703726i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.1303 | + | 26.6334i | −1.54369 | + | 0.891251i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.45892i | − | 0.182472i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.0142 | − | 19.0772i | −0.367345 | − | 0.636261i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.9140 | + | 11.4974i | 0.663433 | + | 0.383033i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.5170 | + | 7.80404i | 0.449320 | + | 0.259415i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8508 | + | 43.0428i | 0.825156 | + | 1.42921i | 0.901800 | + | 0.432153i | \(0.142246\pi\) |
−0.0766447 | + | 0.997058i | \(0.524421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.2074i | − | 0.470713i | −0.971909 | − | 0.235356i | \(-0.924374\pi\) | ||
0.971909 | − | 0.235356i | \(-0.0756257\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.08605 | − | 2.35908i | 0.135229 | − | 0.0780743i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.9066 | + | 27.9075i | −0.525282 | + | 0.921588i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5364 | + | 37.3022i | −0.710421 | + | 1.23048i | 0.254279 | + | 0.967131i | \(0.418162\pi\) |
−0.964699 | + | 0.263354i | \(0.915171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.1022 | 1.51747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2721 | 0.830942 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.8978 | + | 25.8038i | −0.488782 | + | 0.846595i | −0.999917 | − | 0.0129053i | \(-0.995892\pi\) |
0.511135 | + | 0.859501i | \(0.329225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47.1870 | − | 26.5495i | −1.54649 | − | 0.870126i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.57312 | − | 3.21764i | 0.182260 | − | 0.105228i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.6131i | 1.49012i | 0.667000 | + | 0.745058i | \(0.267578\pi\) | ||||
−0.667000 | + | 0.745058i | \(0.732422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.94839 | − | 13.7670i | −0.259110 | − | 0.448792i | 0.706894 | − | 0.707320i | \(-0.250096\pi\) |
−0.966004 | + | 0.258528i | \(0.916763\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7276 | − | 7.92561i | −0.447031 | − | 0.258093i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.1286 | − | 24.3229i | −1.36900 | − | 0.790390i | −0.378195 | − | 0.925726i | \(-0.623455\pi\) |
−0.990800 | + | 0.135336i | \(0.956789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4741 | − | 23.3378i | −0.437387 | − | 0.757576i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.50929i | 0.113677i | 0.998383 | + | 0.0568386i | \(0.0181020\pi\) | ||||
−0.998383 | + | 0.0568386i | \(0.981898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.6098 | + | 24.0234i | −1.34646 | + | 0.777380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.60100 | − | 1.52099i | 0.0839906 | − | 0.0491155i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3238 | + | 21.3455i | −0.397543 | + | 0.688565i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.2759 | −1.16776 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6422 | 0.824599 | 0.412299 | − | 0.911048i | \(-0.364726\pi\) | ||||
0.412299 | + | 0.911048i | \(0.364726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.9164 | + | 37.9603i | −0.703331 | + | 1.21820i | 0.263960 | + | 0.964534i | \(0.414971\pi\) |
−0.967291 | + | 0.253671i | \(0.918362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.303359 | − | 54.6631i | −0.00972525 | − | 1.75242i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.5853 | + | 10.7303i | −0.594598 | + | 0.343291i | −0.766913 | − | 0.641750i | \(-0.778208\pi\) |
0.172315 | + | 0.985042i | \(0.444875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.93226i | 0.285476i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.50371 | + | 16.4609i | 0.303121 | + | 0.525022i | 0.976841 | − | 0.213965i | \(-0.0686379\pi\) |
−0.673720 | + | 0.738987i | \(0.735305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.6548 | + | 28.6682i | 1.58213 | + | 0.913445i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.13131 | + | 2.96256i | 0.163166 | + | 0.0942040i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.99686 | + | 12.1189i | 0.222262 | + | 0.384970i | 0.955495 | − | 0.295008i | \(-0.0953225\pi\) |
−0.733232 | + | 0.679978i | \(0.761989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 71.4131i | − | 2.26395i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.764764 | + | 0.441537i | −0.0242203 | + | 0.0139836i | −0.512061 | − | 0.858949i | \(-0.671118\pi\) |
0.487841 | + | 0.872933i | \(0.337785\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 504.2.bl.a.89.8 | yes | 16 | |
3.2 | odd | 2 | inner | 504.2.bl.a.89.1 | yes | 16 | |
4.3 | odd | 2 | 1008.2.bt.d.593.8 | 16 | |||
7.2 | even | 3 | 3528.2.k.b.881.2 | 16 | |||
7.3 | odd | 6 | inner | 504.2.bl.a.17.1 | ✓ | 16 | |
7.4 | even | 3 | 3528.2.bl.a.521.8 | 16 | |||
7.5 | odd | 6 | 3528.2.k.b.881.16 | 16 | |||
7.6 | odd | 2 | 3528.2.bl.a.1097.1 | 16 | |||
12.11 | even | 2 | 1008.2.bt.d.593.1 | 16 | |||
21.2 | odd | 6 | 3528.2.k.b.881.15 | 16 | |||
21.5 | even | 6 | 3528.2.k.b.881.1 | 16 | |||
21.11 | odd | 6 | 3528.2.bl.a.521.1 | 16 | |||
21.17 | even | 6 | inner | 504.2.bl.a.17.8 | yes | 16 | |
21.20 | even | 2 | 3528.2.bl.a.1097.8 | 16 | |||
28.3 | even | 6 | 1008.2.bt.d.17.1 | 16 | |||
28.19 | even | 6 | 7056.2.k.h.881.15 | 16 | |||
28.23 | odd | 6 | 7056.2.k.h.881.1 | 16 | |||
84.23 | even | 6 | 7056.2.k.h.881.16 | 16 | |||
84.47 | odd | 6 | 7056.2.k.h.881.2 | 16 | |||
84.59 | odd | 6 | 1008.2.bt.d.17.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bl.a.17.1 | ✓ | 16 | 7.3 | odd | 6 | inner | |
504.2.bl.a.17.8 | yes | 16 | 21.17 | even | 6 | inner | |
504.2.bl.a.89.1 | yes | 16 | 3.2 | odd | 2 | inner | |
504.2.bl.a.89.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1008.2.bt.d.17.1 | 16 | 28.3 | even | 6 | |||
1008.2.bt.d.17.8 | 16 | 84.59 | odd | 6 | |||
1008.2.bt.d.593.1 | 16 | 12.11 | even | 2 | |||
1008.2.bt.d.593.8 | 16 | 4.3 | odd | 2 | |||
3528.2.k.b.881.1 | 16 | 21.5 | even | 6 | |||
3528.2.k.b.881.2 | 16 | 7.2 | even | 3 | |||
3528.2.k.b.881.15 | 16 | 21.2 | odd | 6 | |||
3528.2.k.b.881.16 | 16 | 7.5 | odd | 6 | |||
3528.2.bl.a.521.1 | 16 | 21.11 | odd | 6 | |||
3528.2.bl.a.521.8 | 16 | 7.4 | even | 3 | |||
3528.2.bl.a.1097.1 | 16 | 7.6 | odd | 2 | |||
3528.2.bl.a.1097.8 | 16 | 21.20 | even | 2 | |||
7056.2.k.h.881.1 | 16 | 28.23 | odd | 6 | |||
7056.2.k.h.881.2 | 16 | 84.47 | odd | 6 | |||
7056.2.k.h.881.15 | 16 | 28.19 | even | 6 | |||
7056.2.k.h.881.16 | 16 | 84.23 | even | 6 |