Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(376,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.376");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.o (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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 376.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.376 |
Dual form | 525.3.o.b.451.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.46410i | 0.577350i | ||||||||
\(7\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.00000 | − | 8.66025i | −0.454545 | − | 0.787296i | 0.544116 | − | 0.839010i | \(-0.316865\pi\) |
−0.998662 | + | 0.0517139i | \(0.983532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.1244i | 0.932643i | 0.884615 | + | 0.466321i | \(0.154421\pi\) | ||||
−0.884615 | + | 0.466321i | \(0.845579\pi\) | |||||||
\(14\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.00000 | − | 13.8564i | 0.500000 | − | 0.866025i | ||||
\(17\) | 6.00000 | − | 3.46410i | 0.352941 | − | 0.203771i | −0.313039 | − | 0.949740i | \(-0.601347\pi\) |
0.665980 | + | 0.745970i | \(0.268014\pi\) | |||||||
\(18\) | 3.00000 | + | 5.19615i | 0.166667 | + | 0.288675i | ||||
\(19\) | 28.5000 | + | 16.4545i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 12.1244i | − | 0.577350i | ||||||
\(22\) | 20.0000 | 0.909091 | ||||||||
\(23\) | 20.0000 | − | 34.6410i | 0.869565 | − | 1.50613i | 0.00712357 | − | 0.999975i | \(-0.497732\pi\) |
0.862442 | − | 0.506157i | \(-0.168934\pi\) | |||||||
\(24\) | −12.0000 | + | 6.92820i | −0.500000 | + | 0.288675i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −21.0000 | − | 12.1244i | −0.807692 | − | 0.466321i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.0000 | 0.551724 | 0.275862 | − | 0.961197i | \(-0.411037\pi\) | ||||
0.275862 | + | 0.961197i | \(0.411037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | − | 2.59808i | 0.145161 | − | 0.0838089i | −0.425660 | − | 0.904883i | \(-0.639958\pi\) |
0.570822 | + | 0.821074i | \(0.306625\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.0000 | − | 8.66025i | −0.454545 | − | 0.262432i | ||||
\(34\) | 13.8564i | 0.407541i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.0675676 | − | 0.117030i | −0.830262 | − | 0.557373i | \(-0.811810\pi\) |
0.897830 | + | 0.440342i | \(0.145143\pi\) | |||||||
\(38\) | −57.0000 | + | 32.9090i | −1.50000 | + | 0.866025i | ||||
\(39\) | 10.5000 | + | 18.1865i | 0.269231 | + | 0.466321i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 24.2487i | − | 0.591432i | −0.955276 | − | 0.295716i | \(-0.904442\pi\) | ||
0.955276 | − | 0.295716i | \(-0.0955582\pi\) | |||||||
\(42\) | 21.0000 | + | 12.1244i | 0.500000 | + | 0.288675i | ||||
\(43\) | 19.0000 | 0.441860 | 0.220930 | − | 0.975290i | \(-0.429091\pi\) | ||||
0.220930 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.0000 | + | 69.2820i | 0.869565 | + | 1.50613i | ||||
\(47\) | 45.0000 | + | 25.9808i | 0.957447 | + | 0.552782i | 0.895386 | − | 0.445290i | \(-0.146899\pi\) |
0.0620605 | + | 0.998072i | \(0.480233\pi\) | |||||||
\(48\) | − | 27.7128i | − | 0.577350i | ||||||
\(49\) | −24.5000 | − | 42.4352i | −0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | − | 10.3923i | 0.117647 | − | 0.203771i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16.0000 | − | 27.7128i | −0.301887 | − | 0.522883i | 0.674677 | − | 0.738114i | \(-0.264283\pi\) |
−0.976563 | + | 0.215230i | \(0.930950\pi\) | |||||||
\(54\) | 9.00000 | + | 5.19615i | 0.166667 | + | 0.0962250i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −28.0000 | + | 48.4974i | −0.500000 | + | 0.866025i | ||||
\(57\) | 57.0000 | 1.00000 | ||||||||
\(58\) | −16.0000 | + | 27.7128i | −0.275862 | + | 0.477807i | ||||
\(59\) | 36.0000 | − | 20.7846i | 0.610169 | − | 0.352282i | −0.162862 | − | 0.986649i | \(-0.552073\pi\) |
0.773032 | + | 0.634367i | \(0.218739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.0000 | + | 10.3923i | 0.295082 | + | 0.170366i | 0.640231 | − | 0.768182i | \(-0.278838\pi\) |
−0.345149 | + | 0.938548i | \(0.612172\pi\) | |||||||
\(62\) | 10.3923i | 0.167618i | ||||||||
\(63\) | −10.5000 | − | 18.1865i | −0.166667 | − | 0.288675i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 30.0000 | − | 17.3205i | 0.454545 | − | 0.262432i | ||||
\(67\) | 29.5000 | + | 51.0955i | 0.440299 | + | 0.762619i | 0.997711 | − | 0.0676160i | \(-0.0215393\pi\) |
−0.557413 | + | 0.830235i | \(0.688206\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 69.2820i | − | 1.00409i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −26.0000 | −0.366197 | −0.183099 | − | 0.983095i | \(-0.558613\pi\) | ||||
−0.183099 | + | 0.983095i | \(0.558613\pi\) | |||||||
\(72\) | −12.0000 | + | 20.7846i | −0.166667 | + | 0.288675i | ||||
\(73\) | 16.5000 | − | 9.52628i | 0.226027 | − | 0.130497i | −0.382711 | − | 0.923868i | \(-0.625009\pi\) |
0.608738 | + | 0.793371i | \(0.291676\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.0675676 | + | 0.117030i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −70.0000 | −0.909091 | ||||||||
\(78\) | −42.0000 | −0.538462 | ||||||||
\(79\) | −23.5000 | + | 40.7032i | −0.297468 | + | 0.515230i | −0.975556 | − | 0.219751i | \(-0.929476\pi\) |
0.678088 | + | 0.734981i | \(0.262809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 42.0000 | + | 24.2487i | 0.512195 | + | 0.295716i | ||||
\(83\) | − | 24.2487i | − | 0.292153i | −0.989273 | − | 0.146077i | \(-0.953335\pi\) | ||
0.989273 | − | 0.146077i | \(-0.0466646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.0000 | + | 32.9090i | −0.220930 | + | 0.382662i | ||||
\(87\) | 24.0000 | − | 13.8564i | 0.275862 | − | 0.159269i | ||||
\(88\) | 40.0000 | + | 69.2820i | 0.454545 | + | 0.787296i | ||||
\(89\) | 102.000 | + | 58.8897i | 1.14607 | + | 0.661682i | 0.947926 | − | 0.318491i | \(-0.103176\pi\) |
0.198142 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 73.5000 | + | 42.4352i | 0.807692 | + | 0.466321i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50000 | − | 7.79423i | 0.0483871 | − | 0.0838089i | ||||
\(94\) | −90.0000 | + | 51.9615i | −0.957447 | + | 0.552782i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 48.4974i | − | 0.499973i | −0.968249 | − | 0.249987i | \(-0.919574\pi\) | ||
0.968249 | − | 0.249987i | \(-0.0804263\pi\) | |||||||
\(98\) | 98.0000 | 1.00000 | ||||||||
\(99\) | −30.0000 | −0.303030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −111.000 | + | 64.0859i | −1.09901 | + | 0.634514i | −0.935961 | − | 0.352104i | \(-0.885466\pi\) |
−0.163049 | + | 0.986618i | \(0.552133\pi\) | |||||||
\(102\) | 12.0000 | + | 20.7846i | 0.117647 | + | 0.203771i | ||||
\(103\) | −7.50000 | − | 4.33013i | −0.0728155 | − | 0.0420401i | 0.463150 | − | 0.886280i | \(-0.346719\pi\) |
−0.535966 | + | 0.844240i | \(0.680052\pi\) | |||||||
\(104\) | − | 96.9948i | − | 0.932643i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 64.0000 | 0.603774 | ||||||||
\(107\) | −106.000 | + | 183.597i | −0.990654 | + | 1.71586i | −0.377204 | + | 0.926130i | \(0.623114\pi\) |
−0.613451 | + | 0.789733i | \(0.710219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | − | 14.7224i | −0.0779817 | − | 0.135068i | 0.824397 | − | 0.566011i | \(-0.191514\pi\) |
−0.902379 | + | 0.430943i | \(0.858181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.66025i | − | 0.0780203i | ||||||
\(112\) | −56.0000 | − | 96.9948i | −0.500000 | − | 0.866025i | ||||
\(113\) | −142.000 | −1.25664 | −0.628319 | − | 0.777956i | \(-0.716257\pi\) | ||||
−0.628319 | + | 0.777956i | \(0.716257\pi\) | |||||||
\(114\) | −57.0000 | + | 98.7269i | −0.500000 | + | 0.866025i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31.5000 | + | 18.1865i | 0.269231 | + | 0.155440i | ||||
\(118\) | 83.1384i | 0.704563i | ||||||||
\(119\) | − | 48.4974i | − | 0.407541i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5000 | − | 18.1865i | 0.0867769 | − | 0.150302i | ||||
\(122\) | −36.0000 | + | 20.7846i | −0.295082 | + | 0.170366i | ||||
\(123\) | −21.0000 | − | 36.3731i | −0.170732 | − | 0.295716i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 42.0000 | 0.333333 | ||||||||
\(127\) | 145.000 | 1.14173 | 0.570866 | − | 0.821043i | \(-0.306608\pi\) | ||||
0.570866 | + | 0.821043i | \(0.306608\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.500000 | + | 0.866025i | ||||
\(129\) | 28.5000 | − | 16.4545i | 0.220930 | − | 0.127554i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.000 | − | 74.4782i | −0.984733 | − | 0.568536i | −0.0810371 | − | 0.996711i | \(-0.525823\pi\) |
−0.903696 | + | 0.428175i | \(0.859157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 199.500 | − | 115.181i | 1.50000 | − | 0.866025i | ||||
\(134\) | −118.000 | −0.880597 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −48.0000 | + | 27.7128i | −0.352941 | + | 0.203771i | ||||
\(137\) | −58.0000 | − | 100.459i | −0.423358 | − | 0.733277i | 0.572908 | − | 0.819620i | \(-0.305815\pi\) |
−0.996265 | + | 0.0863428i | \(0.972482\pi\) | |||||||
\(138\) | 120.000 | + | 69.2820i | 0.869565 | + | 0.502044i | ||||
\(139\) | − | 84.8705i | − | 0.610579i | −0.952260 | − | 0.305290i | \(-0.901247\pi\) | ||
0.952260 | − | 0.305290i | \(-0.0987532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 90.0000 | 0.638298 | ||||||||
\(142\) | 26.0000 | − | 45.0333i | 0.183099 | − | 0.317136i | ||||
\(143\) | 105.000 | − | 60.6218i | 0.734266 | − | 0.423929i | ||||
\(144\) | −24.0000 | − | 41.5692i | −0.166667 | − | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 38.1051i | 0.260994i | ||||||||
\(147\) | −73.5000 | − | 42.4352i | −0.500000 | − | 0.288675i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −62.0000 | + | 107.387i | −0.416107 | + | 0.720719i | −0.995544 | − | 0.0942982i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0000 | + | 39.8372i | 0.152318 | + | 0.263822i | 0.932079 | − | 0.362255i | \(-0.117993\pi\) |
−0.779761 | + | 0.626077i | \(0.784660\pi\) | |||||||
\(152\) | −228.000 | − | 131.636i | −1.50000 | − | 0.866025i | ||||
\(153\) | − | 20.7846i | − | 0.135847i | ||||||
\(154\) | 70.0000 | − | 121.244i | 0.454545 | − | 0.787296i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −162.000 | + | 93.5307i | −1.03185 | + | 0.595737i | −0.917513 | − | 0.397705i | \(-0.869807\pi\) |
−0.114334 | + | 0.993442i | \(0.536473\pi\) | |||||||
\(158\) | −47.0000 | − | 81.4064i | −0.297468 | − | 0.515230i | ||||
\(159\) | −48.0000 | − | 27.7128i | −0.301887 | − | 0.174294i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −140.000 | − | 242.487i | −0.869565 | − | 1.50613i | ||||
\(162\) | 18.0000 | 0.111111 | ||||||||
\(163\) | −29.0000 | + | 50.2295i | −0.177914 | + | 0.308156i | −0.941166 | − | 0.337945i | \(-0.890268\pi\) |
0.763252 | + | 0.646101i | \(0.223602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 42.0000 | + | 24.2487i | 0.253012 | + | 0.146077i | ||||
\(167\) | − | 266.736i | − | 1.59722i | −0.601849 | − | 0.798610i | \(-0.705569\pi\) | ||
0.601849 | − | 0.798610i | \(-0.294431\pi\) | |||||||
\(168\) | 96.9948i | 0.577350i | ||||||||
\(169\) | 22.0000 | 0.130178 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 85.5000 | − | 49.3634i | 0.500000 | − | 0.288675i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 108.000 | + | 62.3538i | 0.624277 | + | 0.360427i | 0.778532 | − | 0.627604i | \(-0.215964\pi\) |
−0.154255 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(174\) | 55.4256i | 0.318538i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −160.000 | −0.909091 | ||||||||
\(177\) | 36.0000 | − | 62.3538i | 0.203390 | − | 0.352282i | ||||
\(178\) | −204.000 | + | 117.779i | −1.14607 | + | 0.661682i | ||||
\(179\) | −5.00000 | − | 8.66025i | −0.0279330 | − | 0.0483813i | 0.851721 | − | 0.523996i | \(-0.175559\pi\) |
−0.879654 | + | 0.475614i | \(0.842226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 327.358i | − | 1.80861i | −0.426892 | − | 0.904303i | \(-0.640391\pi\) | ||
0.426892 | − | 0.904303i | \(-0.359609\pi\) | |||||||
\(182\) | −147.000 | + | 84.8705i | −0.807692 | + | 0.466321i | ||||
\(183\) | 36.0000 | 0.196721 | ||||||||
\(184\) | −160.000 | + | 277.128i | −0.869565 | + | 1.50613i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.00000 | + | 15.5885i | 0.0483871 | + | 0.0838089i | ||||
\(187\) | −60.0000 | − | 34.6410i | −0.320856 | − | 0.185246i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −31.5000 | − | 18.1865i | −0.166667 | − | 0.0962250i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00000 | − | 1.73205i | 0.00523560 | − | 0.00906833i | −0.863396 | − | 0.504527i | \(-0.831667\pi\) |
0.868631 | + | 0.495459i | \(0.165000\pi\) | |||||||
\(192\) | 96.0000 | − | 55.4256i | 0.500000 | − | 0.288675i | ||||
\(193\) | −117.500 | − | 203.516i | −0.608808 | − | 1.05449i | −0.991437 | − | 0.130585i | \(-0.958315\pi\) |
0.382629 | − | 0.923902i | \(-0.375019\pi\) | |||||||
\(194\) | 84.0000 | + | 48.4974i | 0.432990 | + | 0.249987i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −100.000 | −0.507614 | −0.253807 | − | 0.967255i | \(-0.581683\pi\) | ||||
−0.253807 | + | 0.967255i | \(0.581683\pi\) | |||||||
\(198\) | 30.0000 | − | 51.9615i | 0.151515 | − | 0.262432i | ||||
\(199\) | −174.000 | + | 100.459i | −0.874372 | + | 0.504819i | −0.868799 | − | 0.495166i | \(-0.835107\pi\) |
−0.00557327 | + | 0.999984i | \(0.501774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 88.5000 | + | 51.0955i | 0.440299 | + | 0.254206i | ||||
\(202\) | − | 256.344i | − | 1.26903i | ||||||
\(203\) | 56.0000 | − | 96.9948i | 0.275862 | − | 0.477807i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.0000 | − | 8.66025i | 0.0728155 | − | 0.0420401i | ||||
\(207\) | −60.0000 | − | 103.923i | −0.289855 | − | 0.502044i | ||||
\(208\) | 168.000 | + | 96.9948i | 0.807692 | + | 0.466321i | ||||
\(209\) | − | 329.090i | − | 1.57459i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.00947867 | 0.00473934 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00473934 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −39.0000 | + | 22.5167i | −0.183099 | + | 0.105712i | ||||
\(214\) | −212.000 | − | 367.195i | −0.990654 | − | 1.71586i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 41.5692i | 0.192450i | ||||||||
\(217\) | − | 36.3731i | − | 0.167618i | ||||||
\(218\) | 34.0000 | 0.155963 | ||||||||
\(219\) | 16.5000 | − | 28.5788i | 0.0753425 | − | 0.130497i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.0000 | + | 72.7461i | 0.190045 | + | 0.329168i | ||||
\(222\) | 15.0000 | + | 8.66025i | 0.0675676 | + | 0.0390102i | ||||
\(223\) | − | 339.482i | − | 1.52234i | −0.648552 | − | 0.761170i | \(-0.724625\pi\) | ||
0.648552 | − | 0.761170i | \(-0.275375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 142.000 | − | 245.951i | 0.628319 | − | 1.08828i | ||||
\(227\) | −141.000 | + | 81.4064i | −0.621145 | + | 0.358618i | −0.777315 | − | 0.629112i | \(-0.783419\pi\) |
0.156169 | + | 0.987730i | \(0.450085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.50000 | + | 4.33013i | 0.0327511 | + | 0.0189089i | 0.516286 | − | 0.856416i | \(-0.327314\pi\) |
−0.483535 | + | 0.875325i | \(0.660647\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −105.000 | + | 60.6218i | −0.454545 | + | 0.262432i | ||||
\(232\) | −128.000 | −0.551724 | ||||||||
\(233\) | −85.0000 | + | 147.224i | −0.364807 | + | 0.631864i | −0.988745 | − | 0.149610i | \(-0.952198\pi\) |
0.623938 | + | 0.781474i | \(0.285532\pi\) | |||||||
\(234\) | −63.0000 | + | 36.3731i | −0.269231 | + | 0.155440i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 81.4064i | 0.343487i | ||||||||
\(238\) | 84.0000 | + | 48.4974i | 0.352941 | + | 0.203771i | ||||
\(239\) | 142.000 | 0.594142 | 0.297071 | − | 0.954855i | \(-0.403990\pi\) | ||||
0.297071 | + | 0.954855i | \(0.403990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −132.000 | + | 76.2102i | −0.547718 | + | 0.316225i | −0.748201 | − | 0.663472i | \(-0.769082\pi\) |
0.200483 | + | 0.979697i | \(0.435749\pi\) | |||||||
\(242\) | 21.0000 | + | 36.3731i | 0.0867769 | + | 0.150302i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 84.0000 | 0.341463 | ||||||||
\(247\) | −199.500 | + | 345.544i | −0.807692 | + | 1.39896i | ||||
\(248\) | −36.0000 | + | 20.7846i | −0.145161 | + | 0.0838089i | ||||
\(249\) | −21.0000 | − | 36.3731i | −0.0843373 | − | 0.146077i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 290.985i | 1.15930i | 0.814865 | + | 0.579650i | \(0.196811\pi\) | ||||
−0.814865 | + | 0.579650i | \(0.803189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −400.000 | −1.58103 | ||||||||
\(254\) | −145.000 | + | 251.147i | −0.570866 | + | 0.988769i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 381.000 | + | 219.970i | 1.48249 | + | 0.855916i | 0.999802 | − | 0.0198763i | \(-0.00632725\pi\) |
0.482688 | + | 0.875792i | \(0.339661\pi\) | |||||||
\(258\) | 65.8179i | 0.255108i | ||||||||
\(259\) | −17.5000 | − | 30.3109i | −0.0675676 | − | 0.117030i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.0000 | − | 41.5692i | 0.0919540 | − | 0.159269i | ||||
\(262\) | 258.000 | − | 148.956i | 0.984733 | − | 0.568536i | ||||
\(263\) | 68.0000 | + | 117.779i | 0.258555 | + | 0.447831i | 0.965855 | − | 0.259083i | \(-0.0834203\pi\) |
−0.707300 | + | 0.706914i | \(0.750087\pi\) | |||||||
\(264\) | 120.000 | + | 69.2820i | 0.454545 | + | 0.262432i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 460.726i | 1.73205i | ||||||||
\(267\) | 204.000 | 0.764045 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −195.000 | + | 112.583i | −0.724907 | + | 0.418525i | −0.816556 | − | 0.577266i | \(-0.804120\pi\) |
0.0916490 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −318.000 | − | 183.597i | −1.17343 | − | 0.677481i | −0.218946 | − | 0.975737i | \(-0.570262\pi\) |
−0.954486 | + | 0.298256i | \(0.903595\pi\) | |||||||
\(272\) | − | 110.851i | − | 0.407541i | ||||||
\(273\) | 147.000 | 0.538462 | ||||||||
\(274\) | 232.000 | 0.846715 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 197.500 | + | 342.080i | 0.712996 | + | 1.23495i | 0.963727 | + | 0.266889i | \(0.0859958\pi\) |
−0.250731 | + | 0.968057i | \(0.580671\pi\) | |||||||
\(278\) | 147.000 | + | 84.8705i | 0.528777 | + | 0.305290i | ||||
\(279\) | − | 15.5885i | − | 0.0558726i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 100.000 | 0.355872 | 0.177936 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177936 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(282\) | −90.0000 | + | 155.885i | −0.319149 | + | 0.552782i | ||||
\(283\) | 310.500 | − | 179.267i | 1.09717 | − | 0.633453i | 0.161696 | − | 0.986841i | \(-0.448304\pi\) |
0.935477 | + | 0.353387i | \(0.114970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 242.487i | 0.847857i | ||||||||
\(287\) | −147.000 | − | 84.8705i | −0.512195 | − | 0.295716i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −120.500 | + | 208.712i | −0.416955 | + | 0.722187i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42.0000 | − | 72.7461i | −0.144330 | − | 0.249987i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 242.487i | 0.827601i | 0.910368 | + | 0.413801i | \(0.135799\pi\) | ||||
−0.910368 | + | 0.413801i | \(0.864201\pi\) | |||||||
\(294\) | 147.000 | − | 84.8705i | 0.500000 | − | 0.288675i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.0000 | + | 34.6410i | −0.0675676 | + | 0.117030i | ||||
\(297\) | −45.0000 | + | 25.9808i | −0.151515 | + | 0.0874773i | ||||
\(298\) | −124.000 | − | 214.774i | −0.416107 | − | 0.720719i | ||||
\(299\) | 420.000 | + | 242.487i | 1.40468 | + | 0.810994i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 66.5000 | − | 115.181i | 0.220930 | − | 0.382662i | ||||
\(302\) | −92.0000 | −0.304636 | ||||||||
\(303\) | −111.000 | + | 192.258i | −0.366337 | + | 0.634514i | ||||
\(304\) | 456.000 | − | 263.272i | 1.50000 | − | 0.866025i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 36.0000 | + | 20.7846i | 0.117647 | + | 0.0679236i | ||||
\(307\) | 181.865i | 0.592395i | 0.955127 | + | 0.296198i | \(0.0957187\pi\) | ||||
−0.955127 | + | 0.296198i | \(0.904281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.0485437 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 477.000 | − | 275.396i | 1.53376 | − | 0.885518i | 0.534578 | − | 0.845119i | \(-0.320470\pi\) |
0.999184 | − | 0.0403991i | \(-0.0128629\pi\) | |||||||
\(312\) | −84.0000 | − | 145.492i | −0.269231 | − | 0.466321i | ||||
\(313\) | −175.500 | − | 101.325i | −0.560703 | − | 0.323722i | 0.192725 | − | 0.981253i | \(-0.438268\pi\) |
−0.753428 | + | 0.657531i | \(0.771601\pi\) | |||||||
\(314\) | − | 374.123i | − | 1.19147i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 146.000 | − | 252.879i | 0.460568 | − | 0.797727i | −0.538421 | − | 0.842676i | \(-0.680979\pi\) |
0.998989 | + | 0.0449488i | \(0.0143125\pi\) | |||||||
\(318\) | 96.0000 | − | 55.4256i | 0.301887 | − | 0.174294i | ||||
\(319\) | −80.0000 | − | 138.564i | −0.250784 | − | 0.434370i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 367.195i | 1.14391i | ||||||||
\(322\) | 560.000 | 1.73913 | ||||||||
\(323\) | 228.000 | 0.705882 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −58.0000 | − | 100.459i | −0.177914 | − | 0.308156i | ||||
\(327\) | −25.5000 | − | 14.7224i | −0.0779817 | − | 0.0450227i | ||||
\(328\) | 193.990i | 0.591432i | ||||||||
\(329\) | 315.000 | − | 181.865i | 0.957447 | − | 0.552782i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.50000 | + | 4.33013i | −0.00755287 | + | 0.0130820i | −0.869777 | − | 0.493445i | \(-0.835738\pi\) |
0.862224 | + | 0.506527i | \(0.169071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.50000 | − | 12.9904i | −0.0225225 | − | 0.0390102i | ||||
\(334\) | 462.000 | + | 266.736i | 1.38323 | + | 0.798610i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −168.000 | − | 96.9948i | −0.500000 | − | 0.288675i | ||||
\(337\) | 439.000 | 1.30267 | 0.651335 | − | 0.758790i | \(-0.274209\pi\) | ||||
0.651335 | + | 0.758790i | \(0.274209\pi\) | |||||||
\(338\) | −22.0000 | + | 38.1051i | −0.0650888 | + | 0.112737i | ||||
\(339\) | −213.000 | + | 122.976i | −0.628319 | + | 0.362760i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.0000 | − | 25.9808i | −0.131965 | − | 0.0761899i | ||||
\(342\) | 197.454i | 0.577350i | ||||||||
\(343\) | −343.000 | −1.00000 | ||||||||
\(344\) | −152.000 | −0.441860 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −216.000 | + | 124.708i | −0.624277 | + | 0.360427i | ||||
\(347\) | 110.000 | + | 190.526i | 0.317003 | + | 0.549065i | 0.979861 | − | 0.199680i | \(-0.0639902\pi\) |
−0.662858 | + | 0.748745i | \(0.730657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 339.482i | 0.972728i | 0.873756 | + | 0.486364i | \(0.161677\pi\) | ||||
−0.873756 | + | 0.486364i | \(0.838323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 63.0000 | 0.179487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −267.000 | + | 154.153i | −0.756374 | + | 0.436693i | −0.827992 | − | 0.560739i | \(-0.810517\pi\) |
0.0716184 | + | 0.997432i | \(0.477184\pi\) | |||||||
\(354\) | 72.0000 | + | 124.708i | 0.203390 | + | 0.352282i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −42.0000 | − | 72.7461i | −0.117647 | − | 0.203771i | ||||
\(358\) | 20.0000 | 0.0558659 | ||||||||
\(359\) | −146.000 | + | 252.879i | −0.406685 | + | 0.704399i | −0.994516 | − | 0.104584i | \(-0.966649\pi\) |
0.587831 | + | 0.808984i | \(0.299982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | + | 625.270i | 1.00000 | + | 1.73205i | ||||
\(362\) | 567.000 | + | 327.358i | 1.56630 | + | 0.904303i | ||||
\(363\) | − | 36.3731i | − | 0.100201i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −36.0000 | + | 62.3538i | −0.0983607 | + | 0.170366i | ||||
\(367\) | −466.500 | + | 269.334i | −1.27112 | + | 0.733880i | −0.975198 | − | 0.221333i | \(-0.928959\pi\) |
−0.295919 | + | 0.955213i | \(0.595626\pi\) | |||||||
\(368\) | −320.000 | − | 554.256i | −0.869565 | − | 1.50613i | ||||
\(369\) | −63.0000 | − | 36.3731i | −0.170732 | − | 0.0985720i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −224.000 | −0.603774 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −102.500 | + | 177.535i | −0.274799 | + | 0.475966i | −0.970084 | − | 0.242768i | \(-0.921945\pi\) |
0.695285 | + | 0.718734i | \(0.255278\pi\) | |||||||
\(374\) | 120.000 | − | 69.2820i | 0.320856 | − | 0.185246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −360.000 | − | 207.846i | −0.957447 | − | 0.552782i | ||||
\(377\) | 193.990i | 0.514562i | ||||||||
\(378\) | 63.0000 | − | 36.3731i | 0.166667 | − | 0.0962250i | ||||
\(379\) | −523.000 | −1.37995 | −0.689974 | − | 0.723835i | \(-0.742378\pi\) | ||||
−0.689974 | + | 0.723835i | \(0.742378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 217.500 | − | 125.574i | 0.570866 | − | 0.329590i | ||||
\(382\) | 2.00000 | + | 3.46410i | 0.00523560 | + | 0.00906833i | ||||
\(383\) | 66.0000 | + | 38.1051i | 0.172324 | + | 0.0994912i | 0.583681 | − | 0.811983i | \(-0.301612\pi\) |
−0.411357 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(384\) | 221.703i | 0.577350i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 470.000 | 1.21762 | ||||||||
\(387\) | 28.5000 | − | 49.3634i | 0.0736434 | − | 0.127554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.0000 | + | 64.0859i | 0.0951157 | + | 0.164745i | 0.909657 | − | 0.415361i | \(-0.136345\pi\) |
−0.814541 | + | 0.580106i | \(0.803011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 277.128i | − | 0.708768i | ||||||
\(392\) | 196.000 | + | 339.482i | 0.500000 | + | 0.866025i | ||||
\(393\) | −258.000 | −0.656489 | ||||||||
\(394\) | 100.000 | − | 173.205i | 0.253807 | − | 0.439607i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −280.500 | − | 161.947i | −0.706549 | − | 0.407926i | 0.103233 | − | 0.994657i | \(-0.467081\pi\) |
−0.809782 | + | 0.586731i | \(0.800415\pi\) | |||||||
\(398\) | − | 401.836i | − | 1.00964i | ||||||
\(399\) | 199.500 | − | 345.544i | 0.500000 | − | 0.866025i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 64.0000 | − | 110.851i | 0.159601 | − | 0.276437i | −0.775124 | − | 0.631809i | \(-0.782313\pi\) |
0.934725 | + | 0.355372i | \(0.115646\pi\) | |||||||
\(402\) | −177.000 | + | 102.191i | −0.440299 | + | 0.254206i | ||||
\(403\) | 31.5000 | + | 54.5596i | 0.0781638 | + | 0.135384i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 112.000 | + | 193.990i | 0.275862 | + | 0.477807i | ||||
\(407\) | −50.0000 | −0.122850 | ||||||||
\(408\) | −48.0000 | + | 83.1384i | −0.117647 | + | 0.203771i | ||||
\(409\) | 256.500 | − | 148.090i | 0.627139 | − | 0.362079i | −0.152504 | − | 0.988303i | \(-0.548734\pi\) |
0.779643 | + | 0.626224i | \(0.215400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −174.000 | − | 100.459i | −0.423358 | − | 0.244426i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 290.985i | − | 0.704563i | ||||||
\(414\) | 240.000 | 0.579710 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −73.5000 | − | 127.306i | −0.176259 | − | 0.305290i | ||||
\(418\) | 570.000 | + | 329.090i | 1.36364 | + | 0.787296i | ||||
\(419\) | 412.228i | 0.983838i | 0.870641 | + | 0.491919i | \(0.163704\pi\) | ||||
−0.870641 | + | 0.491919i | \(0.836296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 107.000 | 0.254157 | 0.127078 | − | 0.991893i | \(-0.459440\pi\) | ||||
0.127078 | + | 0.991893i | \(0.459440\pi\) | |||||||
\(422\) | −2.00000 | + | 3.46410i | −0.00473934 | + | 0.00820877i | ||||
\(423\) | 135.000 | − | 77.9423i | 0.319149 | − | 0.184261i | ||||
\(424\) | 128.000 | + | 221.703i | 0.301887 | + | 0.522883i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 90.0666i | − | 0.211424i | ||||||
\(427\) | 126.000 | − | 72.7461i | 0.295082 | − | 0.170366i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 105.000 | − | 181.865i | 0.244755 | − | 0.423929i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −131.000 | − | 226.899i | −0.303944 | − | 0.526447i | 0.673081 | − | 0.739568i | \(-0.264970\pi\) |
−0.977026 | + | 0.213121i | \(0.931637\pi\) | |||||||
\(432\) | −72.0000 | − | 41.5692i | −0.166667 | − | 0.0962250i | ||||
\(433\) | − | 36.3731i | − | 0.0840025i | −0.999118 | − | 0.0420012i | \(-0.986627\pi\) | ||
0.999118 | − | 0.0420012i | \(-0.0133733\pi\) | |||||||
\(434\) | 63.0000 | + | 36.3731i | 0.145161 | + | 0.0838089i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1140.00 | − | 658.179i | 2.60870 | − | 1.50613i | ||||
\(438\) | 33.0000 | + | 57.1577i | 0.0753425 | + | 0.130497i | ||||
\(439\) | 270.000 | + | 155.885i | 0.615034 | + | 0.355090i | 0.774933 | − | 0.632043i | \(-0.217784\pi\) |
−0.159899 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −147.000 | −0.333333 | ||||||||
\(442\) | −168.000 | −0.380090 | ||||||||
\(443\) | −106.000 | + | 183.597i | −0.239278 | + | 0.414441i | −0.960507 | − | 0.278255i | \(-0.910244\pi\) |
0.721230 | + | 0.692696i | \(0.243577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 588.000 | + | 339.482i | 1.31839 | + | 0.761170i | ||||
\(447\) | 214.774i | 0.480479i | ||||||||
\(448\) | 224.000 | − | 387.979i | 0.500000 | − | 0.866025i | ||||
\(449\) | −782.000 | −1.74165 | −0.870824 | − | 0.491595i | \(-0.836414\pi\) | ||||
−0.870824 | + | 0.491595i | \(0.836414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −210.000 | + | 121.244i | −0.465632 | + | 0.268833i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 69.0000 | + | 39.8372i | 0.152318 | + | 0.0879408i | ||||
\(454\) | − | 325.626i | − | 0.717237i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −456.000 | −1.00000 | ||||||||
\(457\) | 338.500 | − | 586.299i | 0.740700 | − | 1.28293i | −0.211477 | − | 0.977383i | \(-0.567827\pi\) |
0.952177 | − | 0.305547i | \(-0.0988394\pi\) | |||||||
\(458\) | −15.0000 | + | 8.66025i | −0.0327511 | + | 0.0189089i | ||||
\(459\) | −18.0000 | − | 31.1769i | −0.0392157 | − | 0.0679236i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 484.974i | − | 1.05200i | −0.850483 | − | 0.526002i | \(-0.823690\pi\) | ||
0.850483 | − | 0.526002i | \(-0.176310\pi\) | |||||||
\(462\) | − | 242.487i | − | 0.524864i | ||||||
\(463\) | −443.000 | −0.956803 | −0.478402 | − | 0.878141i | \(-0.658784\pi\) | ||||
−0.478402 | + | 0.878141i | \(0.658784\pi\) | |||||||
\(464\) | 128.000 | − | 221.703i | 0.275862 | − | 0.477807i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −170.000 | − | 294.449i | −0.364807 | − | 0.631864i | ||||
\(467\) | −39.0000 | − | 22.5167i | −0.0835118 | − | 0.0482155i | 0.457663 | − | 0.889126i | \(-0.348687\pi\) |
−0.541174 | + | 0.840910i | \(0.682020\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 413.000 | 0.880597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −162.000 | + | 280.592i | −0.343949 | + | 0.595737i | ||||
\(472\) | −288.000 | + | 166.277i | −0.610169 | + | 0.352282i | ||||
\(473\) | −95.0000 | − | 164.545i | −0.200846 | − | 0.347875i | ||||
\(474\) | −141.000 | − | 81.4064i | −0.297468 | − | 0.171743i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −96.0000 | −0.201258 | ||||||||
\(478\) | −142.000 | + | 245.951i | −0.297071 | + | 0.514542i | ||||
\(479\) | −48.0000 | + | 27.7128i | −0.100209 | + | 0.0578556i | −0.549267 | − | 0.835647i | \(-0.685093\pi\) |
0.449058 | + | 0.893503i | \(0.351760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.5000 | + | 30.3109i | 0.109148 | + | 0.0630164i | ||||
\(482\) | − | 304.841i | − | 0.632450i | ||||||
\(483\) | −420.000 | − | 242.487i | −0.869565 | − | 0.502044i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 27.0000 | − | 15.5885i | 0.0555556 | − | 0.0320750i | ||||
\(487\) | −33.5000 | − | 58.0237i | −0.0687885 | − | 0.119145i | 0.829580 | − | 0.558388i | \(-0.188580\pi\) |
−0.898368 | + | 0.439243i | \(0.855247\pi\) | |||||||
\(488\) | −144.000 | − | 83.1384i | −0.295082 | − | 0.170366i | ||||
\(489\) | 100.459i | 0.205438i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −68.0000 | −0.138493 | −0.0692464 | − | 0.997600i | \(-0.522059\pi\) | ||||
−0.0692464 | + | 0.997600i | \(0.522059\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 96.0000 | − | 55.4256i | 0.194726 | − | 0.112425i | ||||
\(494\) | −399.000 | − | 691.088i | −0.807692 | − | 1.39896i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 83.1384i | − | 0.167618i | ||||||
\(497\) | −91.0000 | + | 157.617i | −0.183099 | + | 0.317136i | ||||
\(498\) | 84.0000 | 0.168675 | ||||||||
\(499\) | −254.500 | + | 440.807i | −0.510020 | + | 0.883381i | 0.489913 | + | 0.871772i | \(0.337029\pi\) |
−0.999933 | + | 0.0116091i | \(0.996305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −231.000 | − | 400.104i | −0.461078 | − | 0.798610i | ||||
\(502\) | −504.000 | − | 290.985i | −1.00398 | − | 0.579650i | ||||
\(503\) | 654.715i | 1.30162i | 0.759240 | + | 0.650810i | \(0.225571\pi\) | ||||
−0.759240 | + | 0.650810i | \(0.774429\pi\) | |||||||
\(504\) | 84.0000 | + | 145.492i | 0.166667 | + | 0.288675i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 400.000 | − | 692.820i | 0.790514 | − | 1.36921i | ||||
\(507\) | 33.0000 | − | 19.0526i | 0.0650888 | − | 0.0375790i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 753.000 | + | 434.745i | 1.47937 | + | 0.854115i | 0.999727 | − | 0.0233478i | \(-0.00743251\pi\) |
0.479644 | + | 0.877463i | \(0.340766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 133.368i | − | 0.260994i | ||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 85.5000 | − | 148.090i | 0.166667 | − | 0.288675i | ||||
\(514\) | −762.000 | + | 439.941i | −1.48249 | + | 0.855916i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 519.615i | − | 1.00506i | ||||||
\(518\) | 70.0000 | 0.135135 | ||||||||
\(519\) | 216.000 | 0.416185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 372.000 | − | 214.774i | 0.714012 | − | 0.412235i | −0.0985331 | − | 0.995134i | \(-0.531415\pi\) |
0.812545 | + | 0.582899i | \(0.198082\pi\) | |||||||
\(522\) | 48.0000 | + | 83.1384i | 0.0919540 | + | 0.159269i | ||||
\(523\) | 853.500 | + | 492.768i | 1.63193 | + | 0.942196i | 0.983497 | + | 0.180925i | \(0.0579092\pi\) |
0.648434 | + | 0.761271i | \(0.275424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −272.000 | −0.517110 | ||||||||
\(527\) | 18.0000 | − | 31.1769i | 0.0341556 | − | 0.0591592i | ||||
\(528\) | −240.000 | + | 138.564i | −0.454545 | + | 0.262432i | ||||
\(529\) | −535.500 | − | 927.513i | −1.01229 | − | 1.75333i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 124.708i | − | 0.234854i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 294.000 | 0.551595 | ||||||||
\(534\) | −204.000 | + | 353.338i | −0.382022 | + | 0.661682i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −236.000 | − | 408.764i | −0.440299 | − | 0.762619i | ||||
\(537\) | −15.0000 | − | 8.66025i | −0.0279330 | − | 0.0161271i | ||||
\(538\) | − | 450.333i | − | 0.837051i | ||||||
\(539\) | −245.000 | + | 424.352i | −0.454545 | + | 0.787296i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 60.5000 | − | 104.789i | 0.111830 | − | 0.193695i | −0.804678 | − | 0.593711i | \(-0.797662\pi\) |
0.916508 | + | 0.400016i | \(0.130995\pi\) | |||||||
\(542\) | 636.000 | − | 367.195i | 1.17343 | − | 0.677481i | ||||
\(543\) | −283.500 | − | 491.036i | −0.522099 | − | 0.904303i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −147.000 | + | 254.611i | −0.269231 | + | 0.466321i | ||||
\(547\) | −926.000 | −1.69287 | −0.846435 | − | 0.532492i | \(-0.821256\pi\) | ||||
−0.846435 | + | 0.532492i | \(0.821256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 54.0000 | − | 31.1769i | 0.0983607 | − | 0.0567886i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 456.000 | + | 263.272i | 0.827586 | + | 0.477807i | ||||
\(552\) | 554.256i | 1.00409i | ||||||||
\(553\) | 164.500 | + | 284.922i | 0.297468 | + | 0.515230i | ||||
\(554\) | −790.000 | −1.42599 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −331.000 | − | 573.309i | −0.594255 | − | 1.02928i | −0.993652 | − | 0.112502i | \(-0.964114\pi\) |
0.399397 | − | 0.916778i | \(-0.369220\pi\) | |||||||
\(558\) | 27.0000 | + | 15.5885i | 0.0483871 | + | 0.0279363i | ||||
\(559\) | 230.363i | 0.412098i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −120.000 | −0.213904 | ||||||||
\(562\) | −100.000 | + | 173.205i | −0.177936 | + | 0.308194i | ||||
\(563\) | 279.000 | − | 161.081i | 0.495560 | − | 0.286111i | −0.231318 | − | 0.972878i | \(-0.574304\pi\) |
0.726878 | + | 0.686767i | \(0.240971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 717.069i | 1.26691i | ||||||||
\(567\) | −63.0000 | −0.111111 | ||||||||
\(568\) | 208.000 | 0.366197 | ||||||||
\(569\) | 379.000 | − | 656.447i | 0.666081 | − | 1.15369i | −0.312910 | − | 0.949783i | \(-0.601304\pi\) |
0.978991 | − | 0.203903i | \(-0.0653628\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 432.500 | + | 749.112i | 0.757443 | + | 1.31193i | 0.944151 | + | 0.329514i | \(0.106885\pi\) |
−0.186707 | + | 0.982416i | \(0.559782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.46410i | − | 0.00604555i | ||||||
\(574\) | 294.000 | − | 169.741i | 0.512195 | − | 0.295716i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 96.0000 | − | 166.277i | 0.166667 | − | 0.288675i | ||||
\(577\) | −928.500 | + | 536.070i | −1.60919 | + | 0.929064i | −0.619633 | + | 0.784892i | \(0.712718\pi\) |
−0.989553 | + | 0.144172i | \(0.953948\pi\) | |||||||
\(578\) | −241.000 | − | 417.424i | −0.416955 | − | 0.722187i | ||||
\(579\) | −352.500 | − | 203.516i | −0.608808 | − | 0.351496i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −147.000 | − | 84.8705i | −0.253012 | − | 0.146077i | ||||
\(582\) | 168.000 | 0.288660 | ||||||||
\(583\) | −160.000 | + | 277.128i | −0.274443 | + | 0.475348i | ||||
\(584\) | −132.000 | + | 76.2102i | −0.226027 | + | 0.130497i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −420.000 | − | 242.487i | −0.716724 | − | 0.413801i | ||||
\(587\) | 339.482i | 0.578334i | 0.957279 | + | 0.289167i | \(0.0933783\pi\) | ||||
−0.957279 | + | 0.289167i | \(0.906622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 171.000 | 0.290323 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −150.000 | + | 86.6025i | −0.253807 | + | 0.146536i | ||||
\(592\) | −40.0000 | − | 69.2820i | −0.0675676 | − | 0.117030i | ||||
\(593\) | 213.000 | + | 122.976i | 0.359191 | + | 0.207379i | 0.668726 | − | 0.743509i | \(-0.266840\pi\) |
−0.309535 | + | 0.950888i | \(0.600173\pi\) | |||||||
\(594\) | − | 103.923i | − | 0.174955i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −174.000 | + | 301.377i | −0.291457 | + | 0.504819i | ||||
\(598\) | −840.000 | + | 484.974i | −1.40468 | + | 0.810994i | ||||
\(599\) | 142.000 | + | 245.951i | 0.237062 | + | 0.410603i | 0.959870 | − | 0.280446i | \(-0.0904823\pi\) |
−0.722808 | + | 0.691049i | \(0.757149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 594.093i | 0.988508i | 0.869317 | + | 0.494254i | \(0.164559\pi\) | ||||
−0.869317 | + | 0.494254i | \(0.835441\pi\) | |||||||
\(602\) | 133.000 | + | 230.363i | 0.220930 | + | 0.382662i | ||||
\(603\) | 177.000 | 0.293532 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −222.000 | − | 384.515i | −0.366337 | − | 0.634514i | ||||
\(607\) | −7.50000 | − | 4.33013i | −0.0123558 | − | 0.00713365i | 0.493809 | − | 0.869570i | \(-0.335604\pi\) |
−0.506165 | + | 0.862437i | \(0.668937\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 193.990i | − | 0.318538i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −315.000 | + | 545.596i | −0.515548 | + | 0.892956i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 439.000 | + | 760.370i | 0.716150 | + | 1.24041i | 0.962514 | + | 0.271231i | \(0.0874307\pi\) |
−0.246364 | + | 0.969177i | \(0.579236\pi\) | |||||||
\(614\) | −315.000 | − | 181.865i | −0.513029 | − | 0.296198i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 560.000 | 0.909091 | ||||||||
\(617\) | 194.000 | 0.314425 | 0.157212 | − | 0.987565i | \(-0.449749\pi\) | ||||
0.157212 | + | 0.987565i | \(0.449749\pi\) | |||||||
\(618\) | 15.0000 | − | 25.9808i | 0.0242718 | − | 0.0420401i | ||||
\(619\) | 529.500 | − | 305.707i | 0.855412 | − | 0.493872i | −0.00706124 | − | 0.999975i | \(-0.502248\pi\) |
0.862473 | + | 0.506103i | \(0.168914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −180.000 | − | 103.923i | −0.289855 | − | 0.167348i | ||||
\(622\) | 1101.58i | 1.77104i | ||||||||
\(623\) | 714.000 | − | 412.228i | 1.14607 | − | 0.661682i | ||||
\(624\) | 336.000 | 0.538462 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 351.000 | − | 202.650i | 0.560703 | − | 0.323722i | ||||
\(627\) | −285.000 | − | 493.634i | −0.454545 | − | 0.787296i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 34.6410i | − | 0.0550732i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −250.000 | −0.396197 | −0.198098 | − | 0.980182i | \(-0.563477\pi\) | ||||
−0.198098 | + | 0.980182i | \(0.563477\pi\) | |||||||
\(632\) | 188.000 | − | 325.626i | 0.297468 | − | 0.515230i | ||||
\(633\) | 3.00000 | − | 1.73205i | 0.00473934 | − | 0.00273626i | ||||
\(634\) | 292.000 | + | 505.759i | 0.460568 | + | 0.797727i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 514.500 | − | 297.047i | 0.807692 | − | 0.466321i | ||||
\(638\) | 320.000 | 0.501567 | ||||||||
\(639\) | −39.0000 | + | 67.5500i | −0.0610329 | + | 0.105712i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 562.000 | + | 973.413i | 0.876755 | + | 1.51858i | 0.854881 | + | 0.518824i | \(0.173630\pi\) |
0.0218737 | + | 0.999761i | \(0.493037\pi\) | |||||||
\(642\) | −636.000 | − | 367.195i | −0.990654 | − | 0.571954i | ||||
\(643\) | − | 569.845i | − | 0.886228i | −0.896465 | − | 0.443114i | \(-0.853874\pi\) | ||
0.896465 | − | 0.443114i | \(-0.146126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −228.000 | + | 394.908i | −0.352941 | + | 0.611312i | ||||
\(647\) | −939.000 | + | 542.132i | −1.45131 | + | 0.837916i | −0.998556 | − | 0.0537173i | \(-0.982893\pi\) |
−0.452758 | + | 0.891634i | \(0.649560\pi\) | |||||||
\(648\) | 36.0000 | + | 62.3538i | 0.0555556 | + | 0.0962250i | ||||
\(649\) | −360.000 | − | 207.846i | −0.554700 | − | 0.320256i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.5000 | − | 54.5596i | −0.0483871 | − | 0.0838089i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −505.000 | + | 874.686i | −0.773354 | + | 1.33949i | 0.162361 | + | 0.986731i | \(0.448089\pi\) |
−0.935715 | + | 0.352757i | \(0.885244\pi\) | |||||||
\(654\) | 51.0000 | − | 29.4449i | 0.0779817 | − | 0.0450227i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −336.000 | − | 193.990i | −0.512195 | − | 0.295716i | ||||
\(657\) | − | 57.1577i | − | 0.0869980i | ||||||
\(658\) | 727.461i | 1.10556i | ||||||||
\(659\) | −908.000 | −1.37785 | −0.688923 | − | 0.724835i | \(-0.741916\pi\) | ||||
−0.688923 | + | 0.724835i | \(0.741916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −625.500 | + | 361.133i | −0.946293 | + | 0.546343i | −0.891928 | − | 0.452178i | \(-0.850647\pi\) |
−0.0543659 | + | 0.998521i | \(0.517314\pi\) | |||||||
\(662\) | −5.00000 | − | 8.66025i | −0.00755287 | − | 0.0130820i | ||||
\(663\) | 126.000 | + | 72.7461i | 0.190045 | + | 0.109723i | ||||
\(664\) | 193.990i | 0.292153i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000 | 0.0450450 | ||||||||
\(667\) | 320.000 | − | 554.256i | 0.479760 | − | 0.830969i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −294.000 | − | 509.223i | −0.439462 | − | 0.761170i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 207.846i | − | 0.309756i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1027.00 | 1.52600 | 0.763001 | − | 0.646397i | \(-0.223725\pi\) | ||||
0.763001 | + | 0.646397i | \(0.223725\pi\) | |||||||
\(674\) | −439.000 | + | 760.370i | −0.651335 | + | 1.12815i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 486.000 | + | 280.592i | 0.717873 | + | 0.414464i | 0.813969 | − | 0.580908i | \(-0.197302\pi\) |
−0.0960963 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(678\) | − | 491.902i | − | 0.725520i | ||||||
\(679\) | −294.000 | − | 169.741i | −0.432990 | − | 0.249987i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −141.000 | + | 244.219i | −0.207048 | + | 0.358618i | ||||
\(682\) | 90.0000 | − | 51.9615i | 0.131965 | − | 0.0761899i | ||||
\(683\) | 488.000 | + | 845.241i | 0.714495 | + | 1.23754i | 0.963154 | + | 0.268950i | \(0.0866768\pi\) |
−0.248659 | + | 0.968591i | \(0.579990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 343.000 | − | 594.093i | 0.500000 | − | 0.866025i | ||||
\(687\) | 15.0000 | 0.0218341 | ||||||||
\(688\) | 152.000 | − | 263.272i | 0.220930 | − | 0.382662i | ||||
\(689\) | 336.000 | − | 193.990i | 0.487663 | − | 0.281553i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 490.500 | + | 283.190i | 0.709841 | + | 0.409827i | 0.811002 | − | 0.585043i | \(-0.198922\pi\) |
−0.101161 | + | 0.994870i | \(0.532256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −105.000 | + | 181.865i | −0.151515 | + | 0.262432i | ||||
\(694\) | −440.000 | −0.634006 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −192.000 | + | 110.851i | −0.275862 | + | 0.159269i | ||||
\(697\) | −84.0000 | − | 145.492i | −0.120516 | − | 0.208741i | ||||
\(698\) | −588.000 | − | 339.482i | −0.842407 | − | 0.486364i | ||||
\(699\) | 294.449i | 0.421243i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 352.000 | 0.502140 | 0.251070 | − | 0.967969i | \(-0.419218\pi\) | ||||
0.251070 | + | 0.967969i | \(0.419218\pi\) | |||||||
\(702\) | −63.0000 | + | 109.119i | −0.0897436 | + | 0.155440i | ||||
\(703\) | 142.500 | − | 82.2724i | 0.202703 | − | 0.117030i | ||||
\(704\) | −320.000 | − | 554.256i | −0.454545 | − | 0.787296i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 616.610i | − | 0.873385i | ||||||
\(707\) | 897.202i | 1.26903i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 575.000 | − | 995.929i | 0.811001 | − | 1.40470i | −0.101162 | − | 0.994870i | \(-0.532256\pi\) |
0.912164 | − | 0.409826i | \(-0.134410\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 70.5000 | + | 122.110i | 0.0991561 | + | 0.171743i | ||||
\(712\) | −816.000 | − | 471.118i | −1.14607 | − | 0.661682i | ||||
\(713\) | − | 207.846i | − | 0.291509i | ||||||
\(714\) | 168.000 | 0.235294 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 213.000 | − | 122.976i | 0.297071 | − | 0.171514i | ||||
\(718\) | −292.000 | − | 505.759i | −0.406685 | − | 0.704399i | ||||
\(719\) | −843.000 | − | 486.706i | −1.17246 | − | 0.676921i | −0.218203 | − | 0.975903i | \(-0.570020\pi\) |
−0.954259 | + | 0.298982i | \(0.903353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.5000 | + | 30.3109i | −0.0728155 | + | 0.0420401i | ||||
\(722\) | −1444.00 | −2.00000 | ||||||||
\(723\) | −132.000 | + | 228.631i | −0.182573 | + | 0.316225i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 63.0000 | + | 36.3731i | 0.0867769 | + | 0.0501006i | ||||
\(727\) | 206.114i | 0.283513i | 0.989902 | + | 0.141757i | \(0.0452750\pi\) | ||||
−0.989902 | + | 0.141757i | \(0.954725\pi\) | |||||||
\(728\) | −588.000 | − | 339.482i | −0.807692 | − | 0.466321i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 114.000 | − | 65.8179i | 0.155951 | − | 0.0900382i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1078.50 | − | 622.672i | −1.47135 | − | 0.849485i | −0.471869 | − | 0.881669i | \(-0.656420\pi\) |
−0.999482 | + | 0.0321842i | \(0.989754\pi\) | |||||||
\(734\) | − | 1077.34i | − | 1.46776i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 295.000 | − | 510.955i | 0.400271 | − | 0.693290i | ||||
\(738\) | 126.000 | − | 72.7461i | 0.170732 | − | 0.0985720i | ||||
\(739\) | −155.500 | − | 269.334i | −0.210419 | − | 0.364457i | 0.741426 | − | 0.671034i | \(-0.234150\pi\) |
−0.951846 | + | 0.306577i | \(0.900816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 691.088i | 0.932643i | ||||||||
\(742\) | 224.000 | − | 387.979i | 0.301887 | − | 0.522883i | ||||
\(743\) | −394.000 | −0.530283 | −0.265141 | − | 0.964210i | \(-0.585419\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585419\pi\) | |||||||
\(744\) | −36.0000 | + | 62.3538i | −0.0483871 | + | 0.0838089i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −205.000 | − | 355.070i | −0.274799 | − | 0.475966i | ||||
\(747\) | −63.0000 | − | 36.3731i | −0.0843373 | − | 0.0486922i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 742.000 | + | 1285.18i | 0.990654 | + | 1.71586i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.5000 | − | 68.4160i | 0.0525965 | − | 0.0910999i | −0.838528 | − | 0.544858i | \(-0.816584\pi\) |
0.891125 | + | 0.453758i | \(0.149917\pi\) | |||||||
\(752\) | 720.000 | − | 415.692i | 0.957447 | − | 0.552782i | ||||
\(753\) | 252.000 | + | 436.477i | 0.334661 | + | 0.579650i | ||||
\(754\) | −336.000 | − | 193.990i | −0.445623 | − | 0.257281i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 250.000 | 0.330251 | 0.165125 | − | 0.986273i | \(-0.447197\pi\) | ||||
0.165125 | + | 0.986273i | \(0.447197\pi\) | |||||||
\(758\) | 523.000 | − | 905.863i | 0.689974 | − | 1.19507i | ||||
\(759\) | −600.000 | + | 346.410i | −0.790514 | + | 0.456403i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −822.000 | − | 474.582i | −1.08016 | − | 0.623629i | −0.149219 | − | 0.988804i | \(-0.547676\pi\) |
−0.930939 | + | 0.365175i | \(0.881009\pi\) | |||||||
\(762\) | 502.295i | 0.659179i | ||||||||
\(763\) | −119.000 | −0.155963 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −132.000 | + | 76.2102i | −0.172324 | + | 0.0994912i | ||||
\(767\) | 252.000 | + | 436.477i | 0.328553 | + | 0.569070i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 860.829i | 1.11941i | 0.828691 | + | 0.559707i | \(0.189086\pi\) | ||||
−0.828691 | + | 0.559707i | \(0.810914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 762.000 | 0.988327 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 195.000 | − | 112.583i | 0.252264 | − | 0.145645i | −0.368537 | − | 0.929613i | \(-0.620141\pi\) |
0.620800 | + | 0.783969i | \(0.286808\pi\) | |||||||
\(774\) | 57.0000 | + | 98.7269i | 0.0736434 | + | 0.127554i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 387.979i | 0.499973i | ||||||||
\(777\) | −52.5000 | − | 30.3109i | −0.0675676 | − | 0.0390102i | ||||
\(778\) | −148.000 | −0.190231 | ||||||||
\(779\) | 399.000 | − | 691.088i | 0.512195 | − | 0.887148i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 130.000 | + | 225.167i | 0.166453 | + | 0.288306i | ||||
\(782\) | 480.000 | + | 277.128i | 0.613811 | + | 0.354384i | ||||
\(783\) | − | 83.1384i | − | 0.106179i | ||||||
\(784\) | −784.000 | −1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 258.000 | − | 446.869i | 0.328244 | − | 0.568536i | ||||
\(787\) | 216.000 | − | 124.708i | 0.274460 | − | 0.158460i | −0.356453 | − | 0.934313i | \(-0.616014\pi\) |
0.630913 | + | 0.775854i | \(0.282681\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 204.000 | + | 117.779i | 0.258555 | + | 0.149277i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −497.000 | + | 860.829i | −0.628319 | + | 1.08828i | ||||
\(792\) | 240.000 | 0.303030 | ||||||||
\(793\) | −126.000 | + | 218.238i | −0.158890 | + | 0.275206i | ||||
\(794\) | 561.000 | − | 323.894i | 0.706549 | − | 0.407926i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1357.93i | − | 1.70380i | −0.523705 | − | 0.851900i | \(-0.675451\pi\) | ||
0.523705 | − | 0.851900i | \(-0.324549\pi\) | |||||||
\(798\) | 399.000 | + | 691.088i | 0.500000 | + | 0.866025i | ||||
\(799\) | 360.000 | 0.450563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 306.000 | − | 176.669i | 0.382022 | − | 0.220561i | ||||
\(802\) | 128.000 | + | 221.703i | 0.159601 | + | 0.276437i | ||||
\(803\) | −165.000 | − | 95.2628i | −0.205479 | − | 0.118634i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −126.000 | −0.156328 | ||||||||
\(807\) | −195.000 | + | 337.750i | −0.241636 | + | 0.418525i | ||||
\(808\) | 888.000 | − | 512.687i | 1.09901 | − | 0.634514i | ||||
\(809\) | 709.000 | + | 1228.02i | 0.876391 | + | 1.51795i | 0.855274 | + | 0.518176i | \(0.173389\pi\) |
0.0211166 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 872.954i | − | 1.07639i | −0.842820 | − | 0.538196i | \(-0.819106\pi\) | ||
0.842820 | − | 0.538196i | \(-0.180894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −636.000 | −0.782288 | ||||||||
\(814\) | 50.0000 | − | 86.6025i | 0.0614251 | − | 0.106391i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −96.0000 | − | 166.277i | −0.117647 | − | 0.203771i | ||||
\(817\) | 541.500 | + | 312.635i | 0.662791 | + | 0.382662i | ||||
\(818\) | 592.361i | 0.724158i | ||||||||
\(819\) | 220.500 | − | 127.306i | 0.269231 | − | 0.155440i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −125.000 | + | 216.506i | −0.152253 | + | 0.263711i | −0.932056 | − | 0.362315i | \(-0.881986\pi\) |
0.779802 | + | 0.626026i | \(0.215320\pi\) | |||||||
\(822\) | 348.000 | − | 200.918i | 0.423358 | − | 0.244426i | ||||
\(823\) | 103.000 | + | 178.401i | 0.125152 | + | 0.216769i | 0.921792 | − | 0.387684i | \(-0.126725\pi\) |
−0.796640 | + | 0.604454i | \(0.793392\pi\) | |||||||
\(824\) | 60.0000 | + | 34.6410i | 0.0728155 | + | 0.0420401i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 504.000 | + | 290.985i | 0.610169 | + | 0.352282i | ||||
\(827\) | −1234.00 | −1.49214 | −0.746070 | − | 0.665867i | \(-0.768062\pi\) | ||||
−0.746070 | + | 0.665867i | \(0.768062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 298.500 | − | 172.339i | 0.360072 | − | 0.207888i | −0.309040 | − | 0.951049i | \(-0.600008\pi\) |
0.669113 | + | 0.743161i | \(0.266674\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 592.500 | + | 342.080i | 0.712996 | + | 0.411649i | ||||
\(832\) | 775.959i | 0.932643i | ||||||||
\(833\) | −294.000 | − | 169.741i | −0.352941 | − | 0.203771i | ||||
\(834\) | 294.000 | 0.352518 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5000 | − | 23.3827i | −0.0161290 | − | 0.0279363i | ||||
\(838\) | −714.000 | − | 412.228i | −0.852029 | − | 0.491919i | ||||
\(839\) | − | 484.974i | − | 0.578038i | −0.957323 | − | 0.289019i | \(-0.906671\pi\) | ||
0.957323 | − | 0.289019i | \(-0.0933291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −585.000 | −0.695600 | ||||||||
\(842\) | −107.000 | + | 185.329i | −0.127078 | + | 0.220106i | ||||
\(843\) | 150.000 | − | 86.6025i | 0.177936 | − | 0.102731i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 311.769i | 0.368521i | ||||||||
\(847\) | −73.5000 | − | 127.306i | −0.0867769 | − | 0.150302i | ||||
\(848\) | −512.000 | −0.603774 | ||||||||
\(849\) | 310.500 | − | 537.802i | 0.365724 | − | 0.633453i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −100.000 | − | 173.205i | −0.117509 | − | 0.203531i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 278.860i | 0.326917i | 0.986550 | + | 0.163458i | \(0.0522650\pi\) | ||||
−0.986550 | + | 0.163458i | \(0.947735\pi\) | |||||||
\(854\) | 290.985i | 0.340731i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 848.000 | − | 1468.78i | 0.990654 | − | 1.71586i | ||||
\(857\) | 552.000 | − | 318.697i | 0.644107 | − | 0.371876i | −0.142088 | − | 0.989854i | \(-0.545381\pi\) |
0.786195 | + | 0.617979i | \(0.212048\pi\) | |||||||
\(858\) | 210.000 | + | 363.731i | 0.244755 | + | 0.423929i | ||||
\(859\) | −528.000 | − | 304.841i | −0.614668 | − | 0.354879i | 0.160122 | − | 0.987097i | \(-0.448811\pi\) |
−0.774790 | + | 0.632218i | \(0.782145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −294.000 | −0.341463 | ||||||||
\(862\) | 524.000 | 0.607889 | ||||||||
\(863\) | 335.000 | − | 580.237i | 0.388181 | − | 0.672349i | −0.604024 | − | 0.796966i | \(-0.706437\pi\) |
0.992205 | + | 0.124617i | \(0.0397703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 63.0000 | + | 36.3731i | 0.0727483 | + | 0.0420012i | ||||
\(867\) | 417.424i | 0.481458i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 470.000 | 0.540852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −619.500 | + | 357.668i | −0.711251 | + | 0.410641i | ||||
\(872\) | 68.0000 | + | 117.779i | 0.0779817 | + | 0.135068i | ||||
\(873\) | −126.000 | − | 72.7461i | −0.144330 | − | 0.0833289i | ||||
\(874\) | 2632.72i | 3.01226i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −197.000 | + | 341.214i | −0.224629 | + | 0.389070i | −0.956208 | − | 0.292687i | \(-0.905450\pi\) |
0.731579 | + | 0.681757i | \(0.238784\pi\) | |||||||
\(878\) | −540.000 | + | 311.769i | −0.615034 | + | 0.355090i | ||||
\(879\) | 210.000 | + | 363.731i | 0.238908 | + | 0.413801i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1163.94i | − | 1.32116i | −0.750758 | − | 0.660578i | \(-0.770311\pi\) | ||
0.750758 | − | 0.660578i | \(-0.229689\pi\) | |||||||
\(882\) | 147.000 | − | 254.611i | 0.166667 | − | 0.288675i | ||||
\(883\) | −737.000 | −0.834655 | −0.417327 | − | 0.908756i | \(-0.637033\pi\) | ||||
−0.417327 | + | 0.908756i | \(0.637033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −212.000 | − | 367.195i | −0.239278 | − | 0.414441i | ||||
\(887\) | 633.000 | + | 365.463i | 0.713641 | + | 0.412021i | 0.812408 | − | 0.583090i | \(-0.198156\pi\) |
−0.0987664 | + | 0.995111i | \(0.531490\pi\) | |||||||
\(888\) | 69.2820i | 0.0780203i | ||||||||
\(889\) | 507.500 | − | 879.016i | 0.570866 | − | 0.988769i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.0000 | + | 77.9423i | −0.0505051 | + | 0.0874773i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 855.000 | + | 1480.90i | 0.957447 | + | 1.65835i | ||||
\(894\) | −372.000 | − | 214.774i | −0.416107 | − | 0.240240i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 448.000 | + | 775.959i | 0.500000 | + | 0.866025i | ||||
\(897\) | 840.000 | 0.936455 | ||||||||
\(898\) | 782.000 | − | 1354.46i | 0.870824 | − | 1.50831i | ||||
\(899\) | 72.0000 | − | 41.5692i | 0.0800890 | − | 0.0462394i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −192.000 | − | 110.851i | −0.213097 | − | 0.123031i | ||||
\(902\) | − | 484.974i | − | 0.537665i | ||||||
\(903\) | − | 230.363i | − | 0.255108i | ||||||
\(904\) | 1136.00 | 1.25664 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −138.000 | + | 79.6743i | −0.152318 | + | 0.0879408i | ||||
\(907\) | −117.500 | − | 203.516i | −0.129548 | − | 0.224384i | 0.793954 | − | 0.607978i | \(-0.208019\pi\) |
−0.923502 | + | 0.383595i | \(0.874686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 384.515i | 0.423009i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −740.000 | −0.812294 | −0.406147 | − | 0.913808i | \(-0.633128\pi\) | ||||
−0.406147 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(912\) | 456.000 | − | 789.815i | 0.500000 | − | 0.866025i | ||||
\(913\) | −210.000 | + | 121.244i | −0.230011 | + | 0.132797i | ||||
\(914\) | 677.000 | + | 1172.60i | 0.740700 | + | 1.28293i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −903.000 | + | 521.347i | −0.984733 | + | 0.568536i | ||||
\(918\) | 72.0000 | 0.0784314 | ||||||||
\(919\) | −758.500 | + | 1313.76i | −0.825354 | + | 1.42955i | 0.0762951 | + | 0.997085i | \(0.475691\pi\) |
−0.901649 | + | 0.432469i | \(0.857642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 157.500 | + | 272.798i | 0.171010 | + | 0.296198i | ||||
\(922\) | 840.000 | + | 484.974i | 0.911063 | + | 0.526002i | ||||
\(923\) | − | 315.233i | − | 0.341531i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 443.000 | − | 767.299i | 0.478402 | − | 0.828616i | ||||
\(927\) | −22.5000 | + | 12.9904i | −0.0242718 | + | 0.0140134i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 963.000 | + | 555.988i | 1.03660 | + | 0.598480i | 0.918868 | − | 0.394565i | \(-0.129105\pi\) |
0.117731 | + | 0.993046i | \(0.462438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1612.54i | − | 1.73205i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 477.000 | − | 826.188i | 0.511254 | − | 0.885518i | ||||
\(934\) | 78.0000 | − | 45.0333i | 0.0835118 | − | 0.0482155i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −252.000 | − | 145.492i | −0.269231 | − | 0.155440i | ||||
\(937\) | − | 836.581i | − | 0.892829i | −0.894826 | − | 0.446414i | \(-0.852701\pi\) | ||
0.894826 | − | 0.446414i | \(-0.147299\pi\) | |||||||
\(938\) | −413.000 | + | 715.337i | −0.440299 | + | 0.762619i | ||||
\(939\) | −351.000 | −0.373802 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −342.000 | + | 197.454i | −0.363443 | + | 0.209834i | −0.670590 | − | 0.741828i | \(-0.733959\pi\) |
0.307147 | + | 0.951662i | \(0.400626\pi\) | |||||||
\(942\) | −324.000 | − | 561.184i | −0.343949 | − | 0.595737i | ||||
\(943\) | −840.000 | − | 484.974i | −0.890774 | − | 0.514289i | ||||
\(944\) | − | 665.108i | − | 0.704563i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 380.000 | 0.401691 | ||||||||
\(947\) | −169.000 | + | 292.717i | −0.178458 | + | 0.309099i | −0.941353 | − | 0.337424i | \(-0.890444\pi\) |
0.762894 | + | 0.646523i | \(0.223778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 115.500 | + | 200.052i | 0.121707 | + | 0.210803i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 505.759i | − | 0.531818i | ||||||
\(952\) | 387.979i | 0.407541i | ||||||||
\(953\) | 1244.00 | 1.30535 | 0.652676 | − | 0.757637i | \(-0.273646\pi\) | ||||
0.652676 | + | 0.757637i | \(0.273646\pi\) | |||||||
\(954\) | 96.0000 | − | 166.277i | 0.100629 | − | 0.174294i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −240.000 | − | 138.564i | −0.250784 | − | 0.144790i | ||||
\(958\) | − | 110.851i | − | 0.115711i | ||||||
\(959\) | −812.000 | −0.846715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −467.000 | + | 808.868i | −0.485952 | + | 0.841694i | ||||
\(962\) | −105.000 | + | 60.6218i | −0.109148 | + | 0.0630164i | ||||
\(963\) | 318.000 | + | 550.792i | 0.330218 | + | 0.571954i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 840.000 | − | 484.974i | 0.869565 | − | 0.502044i | ||||
\(967\) | 1741.00 | 1.80041 | 0.900207 | − | 0.435463i | \(-0.143415\pi\) | ||||
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(968\) | −84.0000 | + | 145.492i | −0.0867769 | + | 0.150302i | ||||
\(969\) | 342.000 | − | 197.454i | 0.352941 | − | 0.203771i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1110.00 | + | 640.859i | 1.14315 | + | 0.659999i | 0.947209 | − | 0.320617i | \(-0.103890\pi\) |
0.195942 | + | 0.980615i | \(0.437223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −514.500 | − | 297.047i | −0.528777 | − | 0.305290i | ||||
\(974\) | 134.000 | 0.137577 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 288.000 | − | 166.277i | 0.295082 | − | 0.170366i | ||||
\(977\) | 131.000 | + | 226.899i | 0.134084 | + | 0.232240i | 0.925247 | − | 0.379365i | \(-0.123857\pi\) |
−0.791163 | + | 0.611605i | \(0.790524\pi\) | |||||||
\(978\) | −174.000 | − | 100.459i | −0.177914 | − | 0.102719i | ||||
\(979\) | − | 1177.79i | − | 1.20306i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.0000 | −0.0519878 | ||||||||
\(982\) | 68.0000 | − | 117.779i | 0.0692464 | − | 0.119938i | ||||
\(983\) | −960.000 | + | 554.256i | −0.976602 | + | 0.563842i | −0.901243 | − | 0.433315i | \(-0.857344\pi\) |
−0.0753596 | + | 0.997156i | \(0.524010\pi\) | |||||||
\(984\) | 168.000 | + | 290.985i | 0.170732 | + | 0.295716i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 221.703i | 0.224850i | ||||||||
\(987\) | 315.000 | − | 545.596i | 0.319149 | − | 0.552782i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 380.000 | − | 658.179i | 0.384226 | − | 0.665500i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.5000 | + | 58.0237i | 0.0338042 | + | 0.0585507i | 0.882433 | − | 0.470439i | \(-0.155904\pi\) |
−0.848628 | + | 0.528990i | \(0.822571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.66025i | 0.00872130i | ||||||||
\(994\) | −182.000 | − | 315.233i | −0.183099 | − | 0.317136i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 856.500 | − | 494.501i | 0.859077 | − | 0.495988i | −0.00462594 | − | 0.999989i | \(-0.501472\pi\) |
0.863703 | + | 0.504001i | \(0.168139\pi\) | |||||||
\(998\) | −509.000 | − | 881.614i | −0.510020 | − | 0.883381i | ||||
\(999\) | −22.5000 | − | 12.9904i | −0.0225225 | − | 0.0130034i |
(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 | 525.3.o.b.376.1 | 2 | ||
5.2 | odd | 4 | 525.3.s.d.124.1 | 4 | |||
5.3 | odd | 4 | 525.3.s.d.124.2 | 4 | |||
5.4 | even | 2 | 21.3.f.c.19.1 | yes | 2 | ||
7.3 | odd | 6 | inner | 525.3.o.b.451.1 | 2 | ||
15.14 | odd | 2 | 63.3.m.a.19.1 | 2 | |||
20.19 | odd | 2 | 336.3.bh.c.145.1 | 2 | |||
35.3 | even | 12 | 525.3.s.d.199.1 | 4 | |||
35.4 | even | 6 | 147.3.f.e.31.1 | 2 | |||
35.9 | even | 6 | 147.3.d.a.97.1 | 2 | |||
35.17 | even | 12 | 525.3.s.d.199.2 | 4 | |||
35.19 | odd | 6 | 147.3.d.a.97.2 | 2 | |||
35.24 | odd | 6 | 21.3.f.c.10.1 | ✓ | 2 | ||
35.34 | odd | 2 | 147.3.f.e.19.1 | 2 | |||
60.59 | even | 2 | 1008.3.cg.f.145.1 | 2 | |||
105.44 | odd | 6 | 441.3.d.d.244.1 | 2 | |||
105.59 | even | 6 | 63.3.m.a.10.1 | 2 | |||
105.74 | odd | 6 | 441.3.m.b.325.1 | 2 | |||
105.89 | even | 6 | 441.3.d.d.244.2 | 2 | |||
105.104 | even | 2 | 441.3.m.b.19.1 | 2 | |||
140.19 | even | 6 | 2352.3.f.b.97.1 | 2 | |||
140.59 | even | 6 | 336.3.bh.c.241.1 | 2 | |||
140.79 | odd | 6 | 2352.3.f.b.97.2 | 2 | |||
420.59 | odd | 6 | 1008.3.cg.f.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.c.10.1 | ✓ | 2 | 35.24 | odd | 6 | ||
21.3.f.c.19.1 | yes | 2 | 5.4 | even | 2 | ||
63.3.m.a.10.1 | 2 | 105.59 | even | 6 | |||
63.3.m.a.19.1 | 2 | 15.14 | odd | 2 | |||
147.3.d.a.97.1 | 2 | 35.9 | even | 6 | |||
147.3.d.a.97.2 | 2 | 35.19 | odd | 6 | |||
147.3.f.e.19.1 | 2 | 35.34 | odd | 2 | |||
147.3.f.e.31.1 | 2 | 35.4 | even | 6 | |||
336.3.bh.c.145.1 | 2 | 20.19 | odd | 2 | |||
336.3.bh.c.241.1 | 2 | 140.59 | even | 6 | |||
441.3.d.d.244.1 | 2 | 105.44 | odd | 6 | |||
441.3.d.d.244.2 | 2 | 105.89 | even | 6 | |||
441.3.m.b.19.1 | 2 | 105.104 | even | 2 | |||
441.3.m.b.325.1 | 2 | 105.74 | odd | 6 | |||
525.3.o.b.376.1 | 2 | 1.1 | even | 1 | trivial | ||
525.3.o.b.451.1 | 2 | 7.3 | odd | 6 | inner | ||
525.3.s.d.124.1 | 4 | 5.2 | odd | 4 | |||
525.3.s.d.124.2 | 4 | 5.3 | odd | 4 | |||
525.3.s.d.199.1 | 4 | 35.3 | even | 12 | |||
525.3.s.d.199.2 | 4 | 35.17 | even | 12 | |||
1008.3.cg.f.145.1 | 2 | 60.59 | even | 2 | |||
1008.3.cg.f.577.1 | 2 | 420.59 | odd | 6 | |||
2352.3.f.b.97.1 | 2 | 140.19 | even | 6 | |||
2352.3.f.b.97.2 | 2 | 140.79 | odd | 6 |