Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 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("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (of order \(2\), degree \(1\), not 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.10 | ||
Root | \(1.66912 + 0.462633i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.l.881.9 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.462633 | + | 1.66912i | 0.267101 | + | 0.963669i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62879 | + | 2.08496i | −0.615624 | + | 0.788040i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.57194 | + | 1.54438i | −0.857314 | + | 0.514794i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.196087i | − | 0.0591224i | −0.999563 | − | 0.0295612i | \(-0.990589\pi\) | ||
0.999563 | − | 0.0295612i | \(-0.00941100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.37720i | − | 0.659318i | −0.944100 | − | 0.329659i | \(-0.893066\pi\) | ||
0.944100 | − | 0.329659i | \(-0.106934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.462633 | + | 1.66912i | 0.119451 | + | 0.430966i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.36987 | 0.817315 | 0.408657 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408657 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89268i | 0.663625i | 0.943345 | + | 0.331813i | \(0.107660\pi\) | ||||
−0.943345 | + | 0.331813i | \(0.892340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.23358 | − | 1.75408i | −0.923843 | − | 0.382772i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.80220i | 1.20984i | 0.796285 | + | 0.604921i | \(0.206795\pi\) | ||||
−0.796285 | + | 0.604921i | \(0.793205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.76763 | − | 3.57841i | −0.725080 | − | 0.688665i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.73415i | 1.06480i | 0.846491 | + | 0.532402i | \(0.178711\pi\) | ||||
−0.846491 | + | 0.532402i | \(0.821289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.66669i | 0.838162i | 0.907949 | + | 0.419081i | \(0.137648\pi\) | ||||
−0.907949 | + | 0.419081i | \(0.862352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.327293 | − | 0.0907162i | 0.0569744 | − | 0.0157917i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.62879 | + | 2.08496i | −0.275316 | + | 0.352422i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34774 | −1.20796 | −0.603980 | − | 0.796999i | \(-0.706419\pi\) | ||||
−0.603980 | + | 0.796999i | \(0.706419\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.96785 | − | 1.09977i | 0.635364 | − | 0.176104i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.59692 | −1.34261 | −0.671307 | − | 0.741180i | \(-0.734267\pi\) | ||||
−0.671307 | + | 0.741180i | \(0.734267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.444609 | 0.0678022 | 0.0339011 | − | 0.999425i | \(-0.489207\pi\) | ||||
0.0339011 | + | 0.999425i | \(0.489207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.57194 | + | 1.54438i | −0.383403 | + | 0.230223i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.43557 | −0.792860 | −0.396430 | − | 0.918065i | \(-0.629751\pi\) | ||||
−0.396430 | + | 0.918065i | \(0.629751\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.69409 | − | 6.79191i | −0.242013 | − | 0.970273i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.55901 | + | 5.62473i | 0.218306 | + | 0.787620i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.24643i | 0.308571i | 0.988026 | + | 0.154286i | \(0.0493076\pi\) | ||||
−0.988026 | + | 0.154286i | \(0.950692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.196087i | − | 0.0264403i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.82823 | + | 1.33825i | −0.639515 | + | 0.177255i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.10762 | −0.534767 | −0.267384 | − | 0.963590i | \(-0.586159\pi\) | ||||
−0.267384 | + | 0.963590i | \(0.586159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.24011i | − | 0.158780i | −0.996844 | − | 0.0793901i | \(-0.974703\pi\) | ||
0.996844 | − | 0.0793901i | \(-0.0252973\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.969183 | − | 7.87786i | 0.122106 | − | 0.992517i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.37720i | − | 0.294856i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.26282 | −0.887295 | −0.443648 | − | 0.896201i | \(-0.646316\pi\) | ||||
−0.443648 | + | 0.896201i | \(0.646316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.68459 | + | 2.68429i | −1.16589 | + | 0.323150i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.21455i | 0.974888i | 0.873154 | + | 0.487444i | \(0.162071\pi\) | ||||
−0.873154 | + | 0.487444i | \(0.837929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.5044i | − | 1.34649i | −0.739421 | − | 0.673243i | \(-0.764901\pi\) | ||
0.739421 | − | 0.673243i | \(-0.235099\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.462633 | + | 1.66912i | 0.0534202 | + | 0.192734i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.408833 | + | 0.319384i | 0.0465908 | + | 0.0363972i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.71013 | 1.09248 | 0.546238 | − | 0.837630i | \(-0.316060\pi\) | ||||
0.546238 | + | 0.837630i | \(0.316060\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.22977 | − | 7.94412i | 0.469975 | − | 0.882680i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.51467 | 0.605314 | 0.302657 | − | 0.953100i | \(-0.402126\pi\) | ||||
0.302657 | + | 0.953100i | \(0.402126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.36987 | 0.365514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.57100 | + | 2.65280i | −1.02612 | + | 0.284410i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.30915 | −0.244770 | −0.122385 | − | 0.992483i | \(-0.539054\pi\) | ||||
−0.122385 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.95637 | + | 3.87196i | 0.519569 | + | 0.405892i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.78927 | + | 2.15896i | −0.807710 | + | 0.223874i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.89268i | 0.296782i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.59507i | 0.669628i | 0.942284 | + | 0.334814i | \(0.108674\pi\) | ||||
−0.942284 | + | 0.334814i | \(0.891326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.302833 | + | 0.504324i | 0.0304358 | + | 0.0506865i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.709225 | 0.0705705 | 0.0352853 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352853 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.6159i | − | 1.14455i | −0.820062 | − | 0.572275i | \(-0.806061\pi\) | ||
0.820062 | − | 0.572275i | \(-0.193939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.23358 | − | 1.75408i | −0.413155 | − | 0.171181i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.85555i | − | 0.662751i | −0.943499 | − | 0.331375i | \(-0.892487\pi\) | ||
0.943499 | − | 0.331375i | \(-0.107513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.3995 | 1.76235 | 0.881174 | − | 0.472792i | \(-0.156754\pi\) | ||||
0.881174 | + | 0.472792i | \(0.156754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.39930 | − | 12.2643i | −0.322647 | − | 1.16407i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.13112i | 0.764911i | 0.923974 | + | 0.382456i | \(0.124922\pi\) | ||||
−0.923974 | + | 0.382456i | \(0.875078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.80220i | 0.541058i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.67131 | + | 6.11403i | 0.339413 | + | 0.565242i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.48881 | + | 7.02604i | −0.503159 | + | 0.644076i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9615 | 0.996505 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.97722 | − | 14.3493i | −0.358613 | − | 1.29383i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7323 | −1.39601 | −0.698006 | − | 0.716092i | \(-0.745929\pi\) | ||||
−0.698006 | + | 0.716092i | \(0.745929\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.205691 | + | 0.742107i | 0.0181100 | + | 0.0653389i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.2013 | 1.93974 | 0.969869 | − | 0.243626i | \(-0.0783368\pi\) | ||||
0.969869 | + | 0.243626i | \(0.0783368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.03110 | − | 4.71156i | −0.522963 | − | 0.408544i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.76763 | − | 3.57841i | −0.324266 | − | 0.307980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.54886i | 0.559507i | 0.960072 | + | 0.279754i | \(0.0902528\pi\) | ||||
−0.960072 | + | 0.279754i | \(0.909747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.422584i | − | 0.0358431i | −0.999839 | − | 0.0179216i | \(-0.994295\pi\) | ||
0.999839 | − | 0.0179216i | \(-0.00570492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.51467 | − | 9.07264i | −0.211774 | − | 0.764054i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.466139 | −0.0389805 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.73415i | 0.476195i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.5528 | − | 5.96981i | 0.870380 | − | 0.492381i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.2743i | 1.98863i | 0.106497 | + | 0.994313i | \(0.466036\pi\) | ||||
−0.106497 | + | 0.994313i | \(0.533964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9630 | −1.62456 | −0.812282 | − | 0.583265i | \(-0.801775\pi\) | ||||
−0.812282 | + | 0.583265i | \(0.801775\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.66712 | + | 5.20437i | −0.700695 | + | 0.420748i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.66669i | 0.374837i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.46198i | 0.515722i | 0.966182 | + | 0.257861i | \(0.0830177\pi\) | ||||
−0.966182 | + | 0.257861i | \(0.916982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.74957 | + | 1.03927i | −0.297361 | + | 0.0824197i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0973 | − | 9.45056i | −0.953404 | − | 0.744809i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1360 | −0.793913 | −0.396956 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396956 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.327293 | − | 0.0907162i | 0.0254797 | − | 0.00706224i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.8061 | −1.68741 | −0.843704 | − | 0.536808i | \(-0.819630\pi\) | ||||
−0.843704 | + | 0.536808i | \(0.819630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.34890 | 0.565300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.46739 | − | 7.43979i | −0.341630 | − | 0.568935i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9989 | 1.21637 | 0.608186 | − | 0.793795i | \(-0.291898\pi\) | ||||
0.608186 | + | 0.793795i | \(0.291898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.62879 | + | 2.08496i | −0.123125 | + | 0.157608i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.90032 | − | 6.85613i | −0.142837 | − | 0.515338i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.6765i | − | 0.947488i | −0.880663 | − | 0.473744i | \(-0.842902\pi\) | ||
0.880663 | − | 0.473744i | \(-0.157098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.1474i | − | 0.902912i | −0.892293 | − | 0.451456i | \(-0.850905\pi\) | ||
0.892293 | − | 0.451456i | \(-0.149095\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.06990 | − | 0.573717i | 0.153011 | − | 0.0424103i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.34774 | −0.540216 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.660788i | − | 0.0483216i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5975 | − | 2.02687i | 0.989072 | − | 0.147433i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1461i | 1.38536i | 0.721244 | + | 0.692682i | \(0.243571\pi\) | ||||
−0.721244 | + | 0.692682i | \(0.756429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6408 | 1.55774 | 0.778868 | − | 0.627188i | \(-0.215794\pi\) | ||||
0.778868 | + | 0.627188i | \(0.215794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.96785 | − | 1.09977i | 0.284143 | − | 0.0787563i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8641i | 1.55775i | 0.627177 | + | 0.778877i | \(0.284210\pi\) | ||||
−0.627177 | + | 0.778877i | \(0.715790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.31869i | − | 0.377032i | −0.982070 | − | 0.188516i | \(-0.939632\pi\) | ||
0.982070 | − | 0.188516i | \(-0.0603678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.36002 | − | 12.1225i | −0.236997 | − | 0.855058i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.9555 | − | 9.33972i | −0.839109 | − | 0.655520i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.59692 | −0.600435 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.96081 | − | 14.9229i | −0.622819 | − | 1.03722i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.567216 | 0.0392351 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.72971 | −0.463292 | −0.231646 | − | 0.972800i | \(-0.574411\pi\) | ||||
−0.231646 | + | 0.972800i | \(0.574411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.7111 | + | 3.80032i | −0.939469 | + | 0.260394i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.444609 | 0.0303221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.72984 | − | 7.60105i | −0.660505 | − | 0.515993i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.2022 | − | 5.32230i | 1.29757 | − | 0.359648i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.01088i | − | 0.538870i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.90230i | − | 0.596142i | −0.954544 | − | 0.298071i | \(-0.903657\pi\) | ||
0.954544 | − | 0.298071i | \(-0.0963433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.57194 | + | 1.54438i | −0.171463 | + | 0.102959i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.1415 | 1.73507 | 0.867537 | − | 0.497373i | \(-0.165702\pi\) | ||||
0.867537 | + | 0.497373i | \(0.165702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8960i | 1.18260i | 0.806451 | + | 0.591301i | \(0.201386\pi\) | ||||
−0.806451 | + | 0.591301i | \(0.798614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.343952 | + | 0.830150i | −0.0226304 | + | 0.0546198i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.2856i | − | 1.72203i | −0.508582 | − | 0.861014i | \(-0.669830\pi\) | ||
0.508582 | − | 0.861014i | \(-0.330170\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.43557 | −0.354578 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.49222 | + | 16.2074i | 0.291801 | + | 1.05278i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3474i | 1.18679i | 0.804910 | + | 0.593397i | \(0.202213\pi\) | ||||
−0.804910 | + | 0.593397i | \(0.797787\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3756i | 1.44134i | 0.693278 | + | 0.720670i | \(0.256166\pi\) | ||||
−0.693278 | + | 0.720670i | \(0.743834\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2165 | + | 3.38481i | 0.976142 | + | 0.217135i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.69409 | − | 6.79191i | −0.108232 | − | 0.433919i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.87648 | 0.437540 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.55127 | + | 9.20466i | 0.161680 | + | 0.583322i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4170 | 1.35183 | 0.675914 | − | 0.736981i | \(-0.263749\pi\) | ||||
0.675914 | + | 0.736981i | \(0.263749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.13774 | 0.0715288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.55901 | + | 5.62473i | 0.0976292 | + | 0.352234i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.19079 | 0.261414 | 0.130707 | − | 0.991421i | \(-0.458275\pi\) | ||||
0.130707 | + | 0.991421i | \(0.458275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9679 | − | 15.3197i | 0.743650 | − | 0.951921i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.85571 | − | 14.7479i | −0.548155 | − | 0.912872i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.3154i | 1.25270i | 0.779541 | + | 0.626352i | \(0.215453\pi\) | ||||
−0.779541 | + | 0.626352i | \(0.784547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.24643i | 0.137997i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.06829 | − | 3.85426i | −0.0653782 | − | 0.235877i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.4004 | 1.60966 | 0.804831 | − | 0.593504i | \(-0.202256\pi\) | ||||
0.804831 | + | 0.593504i | \(0.202256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.59460i | 0.0968648i | 0.998826 | + | 0.0484324i | \(0.0154225\pi\) | ||||
−0.998826 | + | 0.0484324i | \(0.984577\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.16981 | + | 10.0641i | −0.252368 | + | 0.609106i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.196087i | − | 0.0118245i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.27229 | −0.196613 | −0.0983064 | − | 0.995156i | \(-0.531343\pi\) | ||||
−0.0983064 | + | 0.995156i | \(0.531343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.20714 | − | 12.0024i | −0.431480 | − | 0.718568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6152i | 1.46842i | 0.678921 | + | 0.734211i | \(0.262448\pi\) | ||||
−0.678921 | + | 0.734211i | \(0.737552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.38730i | − | 0.379686i | −0.981815 | − | 0.189843i | \(-0.939202\pi\) | ||
0.981815 | − | 0.189843i | \(-0.0607978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.82823 | + | 1.33825i | −0.286000 | + | 0.0792708i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.0026 | − | 17.9242i | 0.826546 | − | 1.05803i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.64395 | −0.331997 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0080 | + | 3.05110i | −0.645300 | + | 0.178858i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.71110 | 0.567329 | 0.283664 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283664 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.10762 | −0.239155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.701679 | + | 0.738782i | −0.0407155 | + | 0.0428685i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.7930 | 0.797671 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.724174 | + | 0.926991i | −0.0417407 | + | 0.0534309i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.328111 | + | 1.18378i | 0.0188495 | + | 0.0680066i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.24011i | − | 0.0710087i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1102i | 1.26190i | 0.775825 | + | 0.630949i | \(0.217334\pi\) | ||||
−0.775825 | + | 0.630949i | \(0.782666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3884 | − | 5.37390i | 1.10297 | − | 0.305711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6135 | 0.885359 | 0.442679 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442679 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.04206i | 0.0589009i | 0.999566 | + | 0.0294504i | \(0.00937572\pi\) | ||||
−0.999566 | + | 0.0294504i | \(0.990624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.969183 | − | 7.87786i | 0.0546073 | − | 0.443867i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.6828i | 0.880836i | 0.897793 | + | 0.440418i | \(0.145170\pi\) | ||||
−0.897793 | + | 0.440418i | \(0.854830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.12439 | 0.0629538 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.4428 | − | 3.17160i | 0.638672 | − | 0.177021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.74795i | 0.542391i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.37720i | − | 0.131864i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.51219 | + | 30.7110i | 0.470725 | + | 1.69832i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.85340 | − | 11.3329i | 0.488104 | − | 0.624805i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2221 | 1.71612 | 0.858061 | − | 0.513548i | \(-0.171669\pi\) | ||||
0.858061 | + | 0.513548i | \(0.171669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.8980 | − | 11.3477i | 1.03560 | − | 0.621850i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.26282 | −0.396810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.7126 | −1.50960 | −0.754800 | − | 0.655955i | \(-0.772266\pi\) | ||||
−0.754800 | + | 0.655955i | \(0.772266\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.5718 | + | 3.76172i | −0.737121 | + | 0.204309i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.915076 | 0.0495541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9202 | + | 7.53048i | 0.913603 | + | 0.406608i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.68459 | + | 2.68429i | −0.521401 | + | 0.144517i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.0936i | − | 1.13236i | −0.824281 | − | 0.566181i | \(-0.808420\pi\) | ||
0.824281 | − | 0.566181i | \(-0.191580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34.2739i | − | 1.83464i | −0.398148 | − | 0.917321i | \(-0.630347\pi\) | ||
0.398148 | − | 0.917321i | \(-0.369653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.50660 | + | 8.95642i | −0.454049 | + | 0.478058i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.0053 | 1.91637 | 0.958183 | − | 0.286155i | \(-0.0923774\pi\) | ||||
0.958183 | + | 0.286155i | \(0.0923774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.21455i | 0.435983i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.2666 | − | 5.91103i | −0.755070 | − | 0.312845i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.46402i | − | 0.235602i | −0.993037 | − | 0.117801i | \(-0.962416\pi\) | ||
0.993037 | − | 0.117801i | \(-0.0375845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6324 | 0.559602 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.07117 | + | 18.2962i | 0.266167 | + | 0.960300i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11.5044i | − | 0.602167i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.327460i | 0.0170933i | 0.999963 | + | 0.00854663i | \(0.00272051\pi\) | ||||
−0.999963 | + | 0.00854663i | \(0.997279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.1108 | − | 13.2769i | 1.15104 | − | 0.691169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.68372 | − | 3.65897i | −0.243167 | − | 0.189964i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3788 | −0.537393 | −0.268696 | − | 0.963225i | \(-0.586593\pi\) | ||||
−0.268696 | + | 0.963225i | \(0.586593\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.462633 | + | 1.66912i | 0.0238902 | + | 0.0861931i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.6312 | 0.702045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.7360 | −0.602837 | −0.301419 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301419 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.27825 | − | 26.2591i | −0.372876 | − | 1.34529i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9198 | −0.609073 | −0.304536 | − | 0.952501i | \(-0.598501\pi\) | ||||
−0.304536 | + | 0.952501i | \(0.598501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.408833 | + | 0.319384i | 0.0208360 | + | 0.0162773i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.14351 | + | 0.686646i | −0.0581278 | + | 0.0349042i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10.4525i | − | 0.529965i | −0.964253 | − | 0.264982i | \(-0.914634\pi\) | ||
0.964253 | − | 0.264982i | \(-0.0853662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5527i | 0.988822i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2711 | + | 37.0567i | 0.518106 | + | 1.86927i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.71013 | 0.488570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7169i | 0.989563i | 0.869017 | + | 0.494781i | \(0.164752\pi\) | ||||
−0.869017 | + | 0.494781i | \(0.835248\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.07398 | − | 12.2464i | 0.254017 | − | 0.613086i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.2315i | − | 0.560872i | −0.959873 | − | 0.280436i | \(-0.909521\pi\) | ||
0.959873 | − | 0.280436i | \(-0.0904790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0937 | 0.552615 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.22977 | − | 7.94412i | 0.210179 | − | 0.394746i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.44079i | 0.0714175i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.61432i | − | 0.0798229i | −0.999203 | − | 0.0399114i | \(-0.987292\pi\) | ||
0.999203 | − | 0.0399114i | \(-0.0127076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9309 | + | 3.02972i | −0.539179 | + | 0.149445i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.69045 | − | 8.56422i | 0.329216 | − | 0.421418i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.51467 | 0.270705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.705345 | − | 0.195501i | 0.0345409 | − | 0.00957374i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8474 | 1.45814 | 0.729071 | − | 0.684438i | \(-0.239952\pi\) | ||||
0.729071 | + | 0.684438i | \(0.239952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.87115 | −0.334879 | −0.167440 | − | 0.985882i | \(-0.553550\pi\) | ||||
−0.167440 | + | 0.985882i | \(0.553550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.9800 | − | 8.39460i | 0.679730 | − | 0.408159i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.36987 | 0.163463 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.58558 | + | 2.01988i | 0.125125 | + | 0.0977489i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.215651 | − | 0.778042i | −0.0104117 | − | 0.0375642i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.3572i | − | 1.70310i | −0.524275 | − | 0.851549i | \(-0.675664\pi\) | ||
0.524275 | − | 0.851549i | \(-0.324336\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.5668i | − | 0.844207i | −0.906548 | − | 0.422104i | \(-0.861292\pi\) | ||
0.906548 | − | 0.422104i | \(-0.138708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.57100 | + | 2.65280i | −0.458894 | + | 0.127192i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.7839 | −0.802882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.33236i | − | 0.254500i | −0.991871 | − | 0.127250i | \(-0.959385\pi\) | ||
0.991871 | − | 0.127250i | \(-0.0406150\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8464 | + | 14.8521i | 0.706972 | + | 0.707242i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.57620i | 0.407468i | 0.979026 | + | 0.203734i | \(0.0653077\pi\) | ||||
−0.979026 | + | 0.203734i | \(0.934692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.30915 | −0.109464 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −40.5167 | + | 11.2301i | −1.91638 | + | 0.531164i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.56437i | − | 0.262599i | −0.991343 | − | 0.131299i | \(-0.958085\pi\) | ||
0.991343 | − | 0.131299i | \(-0.0419149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68574i | 0.0793786i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.23552 | − | 33.3206i | −0.433923 | − | 1.56554i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.95637 | + | 3.87196i | 0.232358 | + | 0.181520i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.4095 | −0.861160 | −0.430580 | − | 0.902552i | \(-0.641691\pi\) | ||||
−0.430580 | + | 0.902552i | \(0.641691\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6964 | − | 12.0588i | −0.592618 | − | 0.562856i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2709 | 0.571511 | 0.285755 | − | 0.958303i | \(-0.407756\pi\) | ||||
0.285755 | + | 0.958303i | \(0.407756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6465 | 1.00600 | 0.502999 | − | 0.864287i | \(-0.332230\pi\) | ||||
0.502999 | + | 0.864287i | \(0.332230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.78927 | + | 2.15896i | −0.361219 | + | 0.100119i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.4338 | −0.621644 | −0.310822 | − | 0.950468i | \(-0.600604\pi\) | ||||
−0.310822 | + | 0.950468i | \(0.600604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8296 | − | 15.1427i | 0.546241 | − | 0.699224i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.7858 | + | 2.98952i | −0.496985 | + | 0.137750i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.0871820i | − | 0.00400863i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.89268i | 0.132725i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.46935 | − | 5.77770i | −0.158851 | − | 0.264543i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.59941 | 0.255844 | 0.127922 | − | 0.991784i | \(-0.459169\pi\) | ||||
0.127922 | + | 0.991784i | \(0.459169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4671i | 0.796430i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1775 | − | 24.5641i | 0.463093 | − | 1.11770i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.59507i | 0.299467i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.9111 | −1.49134 | −0.745671 | − | 0.666314i | \(-0.767871\pi\) | ||||
−0.745671 | + | 0.666314i | \(0.767871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.68924 | − | 16.9182i | −0.212055 | − | 0.765069i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.88974i | − | 0.310929i | −0.987841 | − | 0.155465i | \(-0.950313\pi\) | ||
0.987841 | − | 0.155465i | \(-0.0496875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3234i | 0.870280i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.302833 | + | 0.504324i | 0.0136113 | + | 0.0226677i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1270 | − | 13.3798i | −0.768251 | − | 0.600165i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9765 | 1.11810 | 0.559051 | − | 0.829133i | \(-0.311166\pi\) | ||||
0.559051 | + | 0.829133i | \(0.311166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0882 | − | 36.3971i | −0.450709 | − | 1.62610i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4820 | −0.913246 | −0.456623 | − | 0.889660i | \(-0.650941\pi\) | ||||
−0.456623 | + | 0.889660i | \(0.650941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.709225 | 0.0315601 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.39984 | + | 12.2662i | 0.150992 | + | 0.544762i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.1419 | −0.892773 | −0.446386 | − | 0.894840i | \(-0.647289\pi\) | ||||
−0.446386 | + | 0.894840i | \(0.647289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.9862 | + | 18.7382i | 1.06109 | + | 0.828930i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3512 | − | 10.8985i | 0.457015 | − | 0.481181i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 11.6159i | − | 0.511859i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.06584i | 0.0468758i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.40160 | + | 26.7041i | 0.324894 | + | 1.17218i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.1611 | −0.620410 | −0.310205 | − | 0.950670i | \(-0.600398\pi\) | ||||
−0.310205 | + | 0.950670i | \(0.600398\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.85547i | − | 0.343496i | −0.985141 | − | 0.171748i | \(-0.945059\pi\) | ||
0.985141 | − | 0.171748i | \(-0.0549414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.23358 | − | 1.75408i | −0.184769 | − | 0.0765543i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.7261i | 0.685042i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6655 | −0.463719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5646 | − | 6.34374i | 0.458463 | − | 0.275295i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.4366i | 0.885209i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.85555i | − | 0.296391i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.1587 | − | 5.86457i | 0.913064 | − | 0.253075i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.33180 | + | 0.332189i | −0.0573649 | + | 0.0143084i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9291 | 0.555866 | 0.277933 | − | 0.960600i | \(-0.410351\pi\) | ||||
0.277933 | + | 0.960600i | \(0.410351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2756 | − | 5.61980i | 0.870108 | − | 0.241169i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.3995 | 0.788146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.68245 | 0.0719366 | 0.0359683 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359683 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.91521 | + | 3.18950i | 0.0817390 | + | 0.136124i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5870 | −0.706631 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8158 | + | 20.2452i | −0.672554 | + | 0.860914i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.39930 | − | 12.2643i | −0.144292 | − | 0.520589i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 44.7979i | − | 1.89815i | −0.315055 | − | 0.949074i | \(-0.602023\pi\) | ||
0.315055 | − | 0.949074i | \(-0.397977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.05693i | − | 0.0447032i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10294 | − | 0.305702i | 0.0465660 | − | 0.0129068i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.5205 | −0.654112 | −0.327056 | − | 0.945005i | \(-0.606057\pi\) | ||||
−0.327056 | + | 0.945005i | \(0.606057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.13112i | 0.342079i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.67374 | + | 21.7582i | 0.406259 | + | 0.913758i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.3342i | 0.517077i | 0.966001 | + | 0.258538i | \(0.0832409\pi\) | ||||
−0.966001 | + | 0.258538i | \(0.916759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9050 | 1.25149 | 0.625743 | − | 0.780029i | \(-0.284796\pi\) | ||||
0.625743 | + | 0.780029i | \(0.284796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.9572 | + | 8.85761i | −1.33503 | + | 0.370032i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.80220i | 0.241968i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.8516i | − | 0.909695i | −0.890569 | − | 0.454847i | \(-0.849694\pi\) | ||
0.890569 | − | 0.454847i | \(-0.150306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.0117 | + | 36.1211i | 0.416073 | + | 1.50114i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.98224 | + | 11.4979i | −0.372646 | + | 0.477011i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.440496 | 0.0182435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.67131 | + | 6.11403i | 0.151790 | + | 0.252784i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.56025 | −0.105673 | −0.0528363 | − | 0.998603i | \(-0.516826\pi\) | ||||
−0.0528363 | + | 0.998603i | \(0.516826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4992 | −0.556225 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.4939 | + | 10.1151i | −1.50116 | + | 0.416078i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.3072 | −0.587528 | −0.293764 | − | 0.955878i | \(-0.594908\pi\) | ||||
−0.293764 | + | 0.955878i | \(0.594908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.48881 | + | 7.02604i | −0.225019 | + | 0.288040i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.87755 | − | 2.46060i | 0.363334 | − | 0.100706i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.7961i | − | 1.05400i | −0.849866 | − | 0.526999i | \(-0.823317\pi\) | ||
0.849866 | − | 0.526999i | \(-0.176683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.10158i | 0.289679i | 0.989455 | + | 0.144840i | \(0.0462667\pi\) | ||||
−0.989455 | + | 0.144840i | \(0.953733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.6796 | − | 11.2166i | 0.760691 | − | 0.456774i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9615 | 0.445650 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 37.7229i | − | 1.53112i | −0.643362 | − | 0.765562i | \(-0.722461\pi\) | ||
0.643362 | − | 0.765562i | \(-0.277539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0582 | − | 24.2760i | 0.407577 | − | 0.983712i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9215i | 0.522747i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8785 | 1.65107 | 0.825533 | − | 0.564353i | \(-0.190874\pi\) | ||||
0.825533 | + | 0.564353i | \(0.190874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.97722 | − | 14.3493i | −0.160377 | − | 0.578620i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.6969i | − | 0.511158i | −0.966788 | − | 0.255579i | \(-0.917734\pi\) | ||
0.966788 | − | 0.255579i | \(-0.0822662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 48.5788i | − | 1.95255i | −0.216545 | − | 0.976273i | \(-0.569479\pi\) | ||
0.216545 | − | 0.976273i | \(-0.430521\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.7626 | − | 21.8605i | 0.833176 | − | 0.877233i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.76112 | − | 4.81449i | 0.150686 | − | 0.192888i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.262412 | + | 0.946753i | 0.0104797 | + | 0.0378097i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.7609 | −0.987284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.07013 | 0.0824106 | 0.0412053 | − | 0.999151i | \(-0.486880\pi\) | ||||
0.0412053 | + | 0.999151i | \(0.486880\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.11338 | − | 11.2327i | −0.123746 | − | 0.446460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.7323 | −0.624315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.1458 | + | 4.02720i | −0.639718 | + | 0.159564i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.6864 | − | 21.1274i | −0.501866 | − | 0.835785i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.5974i | 0.853045i | 0.904477 | + | 0.426523i | \(0.140262\pi\) | ||||
−0.904477 | + | 0.426523i | \(0.859738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.6759i | 1.48579i | 0.669407 | + | 0.742896i | \(0.266548\pi\) | ||||
−0.669407 | + | 0.742896i | \(0.733452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.205691 | + | 0.742107i | 0.00809906 | + | 0.0292204i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.7561 | 1.20915 | 0.604574 | − | 0.796549i | \(-0.293343\pi\) | ||||
0.604574 | + | 0.796549i | \(0.293343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.805451i | 0.0316167i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.18574 | − | 19.7568i | 0.320824 | − | 0.774330i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.26896i | − | 0.0496583i | −0.999692 | − | 0.0248292i | \(-0.992096\pi\) | ||
0.999692 | − | 0.0248292i | \(-0.00790418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.2013 | 0.867478 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.7672 | + | 29.5886i | 0.693163 | + | 1.15436i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.1535i | 1.29148i | 0.763559 | + | 0.645738i | \(0.223450\pi\) | ||||
−0.763559 | + | 0.645738i | \(0.776550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.99036i | 0.271894i | 0.990716 | + | 0.135947i | \(0.0434076\pi\) | ||||
−0.990716 | + | 0.135947i | \(0.956592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3711 | − | 3.70609i | 0.519292 | − | 0.143933i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.03110 | − | 4.71156i | −0.233876 | − | 0.182706i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.2707 | −1.28825 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8590 | − | 4.11850i | 0.574484 | − | 0.159230i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.243170 | −0.00938747 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7243 | −0.490484 | −0.245242 | − | 0.969462i | \(-0.578867\pi\) | ||||
−0.245242 | + | 0.969462i | \(0.578867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.76763 | − | 3.57841i | −0.145016 | − | 0.137733i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.7083 | −0.680585 | −0.340293 | − | 0.940320i | \(-0.610526\pi\) | ||||
−0.340293 | + | 0.940320i | \(0.610526\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.7504 | − | 10.7420i | −0.527694 | − | 0.412239i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0939 | + | 43.6334i | 0.463440 | + | 1.67204i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5608i | 0.595416i | 0.954657 | + | 0.297708i | \(0.0962221\pi\) | ||||
−0.954657 | + | 0.297708i | \(0.903778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.54886i | 0.250219i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.8707 | + | 8.27928i | −1.13964 | + | 0.315874i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.34023 | 0.203447 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 44.5595i | − | 1.69512i | −0.530696 | − | 0.847562i | \(-0.678069\pi\) | ||
0.530696 | − | 0.847562i | \(-0.321931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.54474 | − | 0.190044i | −0.0586800 | − | 0.00721918i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.422584i | − | 0.0160295i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9705 | −1.09734 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.8739 | − | 12.1606i | 1.65946 | − | 0.459955i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.5905i | 1.19316i | 0.802555 | + | 0.596578i | \(0.203473\pi\) | ||||
−0.802555 | + | 0.596578i | \(0.796527\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.2546i | − | 0.801633i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.51467 | − | 9.07264i | −0.0947081 | − | 0.341695i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.15518 | + | 1.47870i | −0.0434450 | + | 0.0556124i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.2268 | −0.872302 | −0.436151 | − | 0.899874i | \(-0.643659\pi\) | ||||
−0.436151 | + | 0.899874i | \(0.643659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.9739 | + | 14.9961i | −0.936594 | + | 0.562399i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0770 | −1.01404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.466139 | −0.0174326 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.6240 | + | 8.48809i | −1.14368 | + | 0.316994i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.0899 | −1.15946 | −0.579730 | − | 0.814809i | \(-0.696842\pi\) | ||||
−0.579730 | + | 0.814809i | \(0.696842\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.2187 | + | 18.9199i | 0.901951 | + | 0.704613i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.3477 | + | 10.3517i | −1.38897 | + | 0.384984i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.73415i | 0.212961i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.9826i | − | 0.963641i | −0.876270 | − | 0.481821i | \(-0.839976\pi\) | ||
0.876270 | − | 0.481821i | \(-0.160024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.39001 | + | 26.9642i | 0.0514819 | + | 0.998674i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.49828 | 0.0554158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.39842i | 0.0885875i | 0.999019 | + | 0.0442938i | \(0.0141038\pi\) | ||||
−0.999019 | + | 0.0442938i | \(0.985896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.5528 | − | 5.96981i | 0.389246 | − | 0.220200i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.42414i | 0.0524590i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6322 | 0.722183 | 0.361091 | − | 0.932530i | \(-0.382404\pi\) | ||||
0.361091 | + | 0.932530i | \(0.382404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.18128 | + | 11.4777i | 0.116867 | + | 0.421643i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.0639i | 0.846132i | 0.906099 | + | 0.423066i | \(0.139046\pi\) | ||||
−0.906099 | + | 0.423066i | \(0.860954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.2743i | 0.889341i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1834 | + | 8.51675i | −0.518944 | + | 0.311612i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.2935 | + | 11.1662i | 0.522274 | + | 0.408006i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.54259 | −0.202252 | −0.101126 | − | 0.994874i | \(-0.532245\pi\) | ||||
−0.101126 | + | 0.994874i | \(0.532245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.90819 | + | 35.7476i | 0.361075 | + | 1.30271i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.9630 | −0.726527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0408 | 0.728397 | 0.364198 | − | 0.931321i | \(-0.381343\pi\) | ||||
0.364198 | + | 0.931321i | \(0.381343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.526353 | + | 1.89902i | 0.0191054 | + | 0.0689301i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1864 | −0.840507 | −0.420254 | − | 0.907407i | \(-0.638059\pi\) | ||||
−0.420254 | + | 0.907407i | \(0.638059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.9688 | + | 38.3621i | −1.08494 | + | 1.38880i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.66712 | + | 5.20437i | −0.313360 | + | 0.188164i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.76466i | 0.352581i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.09763i | − | 0.292008i | −0.989284 | − | 0.146004i | \(-0.953359\pi\) | ||
0.989284 | − | 0.146004i | \(-0.0466412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.93879 | + | 6.99494i | 0.0698240 | + | 0.251917i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.7010 | 0.888432 | 0.444216 | − | 0.895920i | \(-0.353482\pi\) | ||||
0.444216 | + | 0.895920i | \(0.353482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.66669i | 0.167632i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.1072 | + | 12.8885i | 1.11597 | + | 0.462373i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.8681i | − | 0.890992i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.61077 | 0.0576377 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.5191 | − | 21.6041i | 0.733293 | − | 0.772069i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.46198i | 0.230638i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6.04084i | − | 0.215333i | −0.994187 | − | 0.107666i | \(-0.965662\pi\) | ||
0.994187 | − | 0.107666i | \(-0.0343378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.9090 | + | 9.39858i | −1.20719 | + | 0.334598i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.9530 | − | 13.2439i | −0.602780 | − | 0.470898i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.94800 | −0.104687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.74957 | + | 1.03927i | −0.132984 | + | 0.0368592i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.6745 | 1.61787 | 0.808937 | − | 0.587895i | \(-0.200043\pi\) | ||||
0.808937 | + | 0.587895i | \(0.200043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3172 | −0.648016 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.93901 | − | 3.56621i | 0.209845 | − | 0.126006i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.25586 | −0.0796075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0973 | − | 9.45056i | −0.426375 | − | 0.333089i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.2137 | + | 44.0656i | 0.429942 | + | 1.55118i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.65382i | − | 0.233936i | −0.993136 | − | 0.116968i | \(-0.962683\pi\) | ||
0.993136 | − | 0.116968i | \(-0.0373175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1472i | 0.461662i | 0.972994 | + | 0.230831i | \(0.0741445\pi\) | ||||
−0.972994 | + | 0.230831i | \(0.925856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.66158 | + | 0.737712i | −0.0933456 | + | 0.0258727i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1360 | −0.355049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.28611i | 0.0449953i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.7273 | − | 2.30395i | −0.654384 | − | 0.0805064i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.2991i | 1.37155i | 0.727814 | + | 0.685775i | \(0.240536\pi\) | ||||
−0.727814 | + | 0.685775i | \(0.759464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.2932 | 1.40453 | 0.702266 | − | 0.711915i | \(-0.252172\pi\) | ||||
0.702266 | + | 0.711915i | \(0.252172\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.327293 | − | 0.0907162i | 0.0113949 | − | 0.00315833i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.2044i | 1.08508i | 0.840029 | + | 0.542541i | \(0.182538\pi\) | ||||
−0.840029 | + | 0.542541i | \(0.817462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.3307i | − | 0.810308i | −0.914248 | − | 0.405154i | \(-0.867218\pi\) | ||
0.914248 | − | 0.405154i | \(-0.132782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.51387 | − | 5.46185i | −0.0525155 | − | 0.189470i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.70888 | − | 22.8879i | −0.197801 | − | 0.793018i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.8061 | −0.754632 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.6993 | − | 17.5823i | 0.577212 | − | 0.607734i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.7694 | 1.92537 | 0.962687 | − | 0.270618i | \(-0.0872281\pi\) | ||||
0.962687 | + | 0.270618i | \(0.0872281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.88047 | −0.133809 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −41.0859 | + | 11.3878i | −1.41507 | + | 0.392217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.34890 | 0.252810 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.8541 | + | 22.8544i | −0.613472 | + | 0.785285i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.6612 | − | 2.95497i | 0.365891 | − | 0.101414i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 42.6330i | − | 1.46144i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0999i | 1.03060i | 0.857010 | + | 0.515300i | \(0.172319\pi\) | ||||
−0.857010 | + | 0.515300i | \(0.827681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.46739 | − | 7.43979i | −0.152782 | − | 0.254436i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −51.3831 | −1.75521 | −0.877607 | − | 0.479382i | \(-0.840861\pi\) | ||||
−0.877607 | + | 0.479382i | \(0.840861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.3624i | − | 0.524160i | −0.965046 | − | 0.262080i | \(-0.915592\pi\) | ||
0.965046 | − | 0.262080i | \(-0.0844084\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.3958 | + | 15.0797i | 1.24036 | + | 0.513914i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.8347i | 0.743263i | 0.928380 | + | 0.371632i | \(0.121202\pi\) | ||||
−0.928380 | + | 0.371632i | \(0.878798\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.9989 | 0.543978 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.61107 | − | 9.42044i | −0.0886767 | − | 0.319935i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.90403i | − | 0.0645898i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2652i | 0.585010i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.1853 | − | 16.9621i | −0.344720 | − | 0.574082i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.62879 | + | 2.08496i | −0.0550631 | + | 0.0704844i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.8639 | 0.839593 | 0.419796 | − | 0.907618i | \(-0.362101\pi\) | ||||
0.419796 | + | 0.907618i | \(0.362101\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.49267 | + | 16.2090i | 0.151534 | + | 0.546717i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.5148 | −0.590088 | −0.295044 | − | 0.955484i | \(-0.595334\pi\) | ||||
−0.295044 | + | 0.955484i | \(0.595334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.7821 | −1.54069 | −0.770344 | − | 0.637628i | \(-0.779916\pi\) | ||||
−0.770344 | + | 0.637628i | \(0.779916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.90032 | − | 6.85613i | −0.0638786 | − | 0.230466i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.8505 | −1.06944 | −0.534718 | − | 0.845031i | \(-0.679582\pi\) | ||||
−0.534718 | + | 0.845031i | \(0.679582\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.6245 | − | 32.8011i | 0.859419 | − | 1.10011i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.55774 | − | 0.829403i | −0.0521862 | − | 0.0277861i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 15.7233i | − | 0.526162i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12.6765i | − | 0.423729i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.38110 | + | 23.0222i | 0.213059 | + | 0.768690i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.7595 | −0.892478 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.57020i | 0.252200i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.88229 | − | 0.779880i | −0.0626386 | − | 0.0259528i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.1474i | − | 0.403795i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0152 | −0.365754 | −0.182877 | − | 0.983136i | \(-0.558541\pi\) | ||||
−0.182877 | + | 0.983136i | \(0.558541\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.82409 | + | 1.09531i | −0.0605011 | + | 0.0363293i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.6413i | − | 0.783272i | −0.920120 | − | 0.391636i | \(-0.871909\pi\) | ||
0.920120 | − | 0.391636i | \(-0.128091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.08135i | − | 0.0357876i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.06990 | − | 0.573717i | 0.0684288 | − | 0.0189665i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.1613 | + | 46.2888i | −1.19415 | + | 1.52859i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0966 | −0.794874 | −0.397437 | − | 0.917629i | \(-0.630100\pi\) | ||||
−0.397437 | + | 0.917629i | \(0.630100\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.9047 | + | 10.2289i | −1.21605 | + | 0.337054i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.5277 | 0.642761 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.34774 | −0.241592 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.9394 | + | 29.8755i | 0.589207 | + | 0.981239i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.2676 | −1.22271 | −0.611355 | − | 0.791356i | \(-0.709375\pi\) | ||||
−0.611355 | + | 0.791356i | \(0.709375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.6468 | − | 4.90046i | 0.643898 | − | 0.160606i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.22330 | + | 26.0608i | 0.236480 | + | 0.853193i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.660788i | − | 0.0216101i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.1767i | − | 0.365126i | −0.983194 | − | 0.182563i | \(-0.941561\pi\) | ||
0.983194 | − | 0.182563i | \(-0.0584394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.73933 | + | 0.482092i | −0.0567609 | + | 0.0157325i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.8782 | 0.843605 | 0.421803 | − | 0.906688i | \(-0.361398\pi\) | ||||
0.421803 | + | 0.906688i | \(0.361398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 49.8811i | − | 1.62435i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5975 | − | 2.02687i | 0.442326 | − | 0.0659341i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.08802i | 0.197834i | 0.995096 | + | 0.0989170i | \(0.0315378\pi\) | ||||
−0.995096 | + | 0.0989170i | \(0.968462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3483 | −0.887763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.1766 | + | 7.25539i | −0.848834 | + | 0.235272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.35040i | − | 0.0437438i | −0.999761 | − | 0.0218719i | \(-0.993037\pi\) | ||
0.999761 | − | 0.0218719i | \(-0.00696259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1461i | 0.619553i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.520180 | + | 1.87675i | 0.0168150 | + | 0.0606666i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.6541 | − | 10.6667i | −0.440914 | − | 0.344446i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.22204 | 0.297485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5876 | + | 17.6321i | 0.341180 | + | 0.568186i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.6408 | 0.696640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.25722 | 0.104745 | 0.0523726 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523726 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.2705 | + | 4.50972i | −0.522685 | + | 0.144873i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.6431 | −0.437827 | −0.218913 | − | 0.975744i | \(-0.570251\pi\) | ||||
−0.218913 | + | 0.975744i | \(0.570251\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.881070 | + | 0.688301i | 0.0282458 | + | 0.0220659i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.96785 | − | 1.09977i | 0.127073 | − | 0.0352209i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 43.7973i | − | 1.40120i | −0.713555 | − | 0.700599i | \(-0.752916\pi\) | ||
0.713555 | − | 0.700599i | \(-0.247084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.452795i | 0.0144714i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.3223 | + | 28.4158i | −1.51089 | + | 0.907246i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.68575 | −0.308927 | −0.154464 | − | 0.987998i | \(-0.549365\pi\) | ||||
−0.154464 | + | 0.987998i | \(0.549365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8641i | 0.696649i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.0119 | + | 9.53443i | 0.732478 | + | 0.303484i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.57971i | 0.0820300i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1780 | −0.609210 | −0.304605 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304605 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.4444 | + | 52.1135i | 0.458378 | + | 1.65377i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.31869i | − | 0.168614i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.756399i | 0.0239554i | 0.999928 | + | 0.0119777i | \(0.00381271\pi\) | ||||
−0.999928 | + | 0.0119777i | \(0.996187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.6835 | + | 26.2932i | 0.875868 | + | 0.831880i |
(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 | 1680.2.f.l.881.10 | 16 | ||
3.2 | odd | 2 | 1680.2.f.k.881.8 | 16 | |||
4.3 | odd | 2 | 840.2.f.b.41.7 | yes | 16 | ||
7.6 | odd | 2 | 1680.2.f.k.881.7 | 16 | |||
12.11 | even | 2 | 840.2.f.a.41.9 | ✓ | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.l.881.9 | 16 | ||
28.27 | even | 2 | 840.2.f.a.41.10 | yes | 16 | ||
84.83 | odd | 2 | 840.2.f.b.41.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.9 | ✓ | 16 | 12.11 | even | 2 | ||
840.2.f.a.41.10 | yes | 16 | 28.27 | even | 2 | ||
840.2.f.b.41.7 | yes | 16 | 4.3 | odd | 2 | ||
840.2.f.b.41.8 | yes | 16 | 84.83 | odd | 2 | ||
1680.2.f.k.881.7 | 16 | 7.6 | odd | 2 | |||
1680.2.f.k.881.8 | 16 | 3.2 | odd | 2 | |||
1680.2.f.l.881.9 | 16 | 21.20 | even | 2 | inner | ||
1680.2.f.l.881.10 | 16 | 1.1 | even | 1 | trivial |