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 | 451.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.451 |
Dual form | 525.3.o.b.376.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | −0.998662 | − | 0.0517139i | \(-0.983532\pi\) |
0.544116 | + | 0.839010i | \(0.316865\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 12.1244i | − | 0.932643i | −0.884615 | − | 0.466321i | \(-0.845579\pi\) | ||
0.884615 | − | 0.466321i | \(-0.154421\pi\) | |||||||
\(14\) | 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 | 0.665980 | − | 0.745970i | \(-0.268014\pi\) |
−0.313039 | + | 0.949740i | \(0.601347\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.166667 | − | 0.288675i | ||||
\(19\) | 28.5000 | − | 16.4545i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.1244i | 0.577350i | ||||||||
\(22\) | 20.0000 | 0.909091 | ||||||||
\(23\) | 20.0000 | + | 34.6410i | 0.869565 | + | 1.50613i | 0.862442 | + | 0.506157i | \(0.168934\pi\) |
0.00712357 | + | 0.999975i | \(0.497732\pi\) | |||||||
\(24\) | −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 | 0.570822 | − | 0.821074i | \(-0.306625\pi\) |
−0.425660 | + | 0.904883i | \(0.639958\pi\) | |||||||
\(32\) | 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 | 0.897830 | − | 0.440342i | \(-0.145143\pi\) |
−0.830262 | + | 0.557373i | \(0.811810\pi\) | |||||||
\(38\) | −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 | \(0.0955582\pi\) | ||||
−0.955276 | + | 0.295716i | \(0.904442\pi\) | |||||||
\(42\) | 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 | 0.0620605 | − | 0.998072i | \(-0.480233\pi\) |
0.895386 | + | 0.445290i | \(0.146899\pi\) | |||||||
\(48\) | 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 | −0.976563 | − | 0.215230i | \(-0.930950\pi\) |
0.674677 | + | 0.738114i | \(0.264283\pi\) | |||||||
\(54\) | 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 | 0.773032 | − | 0.634367i | \(-0.218739\pi\) |
−0.162862 | + | 0.986649i | \(0.552073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.0000 | − | 10.3923i | 0.295082 | − | 0.170366i | −0.345149 | − | 0.938548i | \(-0.612172\pi\) |
0.640231 | + | 0.768182i | \(0.278838\pi\) | |||||||
\(62\) | − | 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 | −0.557413 | − | 0.830235i | \(-0.688206\pi\) |
0.997711 | + | 0.0676160i | \(0.0215393\pi\) | |||||||
\(68\) | 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 | 0.608738 | − | 0.793371i | \(-0.291676\pi\) |
−0.382711 | + | 0.923868i | \(0.625009\pi\) | |||||||
\(74\) | 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 | 0.678088 | − | 0.734981i | \(-0.262809\pi\) |
−0.975556 | + | 0.219751i | \(0.929476\pi\) | |||||||
\(80\) | 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 | \(0.0466646\pi\) | ||||
−0.989273 | + | 0.146077i | \(0.953335\pi\) | |||||||
\(84\) | 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 | 0.198142 | − | 0.980173i | \(-0.436509\pi\) |
0.947926 | + | 0.318491i | \(0.103176\pi\) | |||||||
\(90\) | 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 | \(0.0804263\pi\) | ||||
−0.968249 | + | 0.249987i | \(0.919574\pi\) | |||||||
\(98\) | 98.0000 | 1.00000 | ||||||||
\(99\) | −30.0000 | −0.303030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −111.000 | − | 64.0859i | −1.09901 | − | 0.634514i | −0.163049 | − | 0.986618i | \(-0.552133\pi\) |
−0.935961 | + | 0.352104i | \(0.885466\pi\) | |||||||
\(102\) | 12.0000 | − | 20.7846i | 0.117647 | − | 0.203771i | ||||
\(103\) | −7.50000 | + | 4.33013i | −0.0728155 | + | 0.0420401i | −0.535966 | − | 0.844240i | \(-0.680052\pi\) |
0.463150 | + | 0.886280i | \(0.346719\pi\) | |||||||
\(104\) | 96.9948i | 0.932643i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 64.0000 | 0.603774 | ||||||||
\(107\) | −106.000 | − | 183.597i | −0.990654 | − | 1.71586i | −0.613451 | − | 0.789733i | \(-0.710219\pi\) |
−0.377204 | − | 0.926130i | \(-0.623114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | + | 14.7224i | −0.0779817 | + | 0.135068i | −0.902379 | − | 0.430943i | \(-0.858181\pi\) |
0.824397 | + | 0.566011i | \(0.191514\pi\) | |||||||
\(110\) | 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 | −0.903696 | − | 0.428175i | \(-0.859157\pi\) |
−0.0810371 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(132\) | 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 | −0.996265 | − | 0.0863428i | \(-0.972482\pi\) |
0.572908 | + | 0.819620i | \(0.305815\pi\) | |||||||
\(138\) | 120.000 | − | 69.2820i | 0.869565 | − | 0.502044i | ||||
\(139\) | 84.8705i | 0.610579i | 0.952260 | + | 0.305290i | \(0.0987532\pi\) | ||||
−0.952260 | + | 0.305290i | \(0.901247\pi\) | |||||||
\(140\) | 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 | 0.579437 | − | 0.815017i | \(-0.303273\pi\) |
−0.995544 | + | 0.0942982i | \(0.969939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0000 | − | 39.8372i | 0.152318 | − | 0.263822i | −0.779761 | − | 0.626077i | \(-0.784660\pi\) |
0.932079 | + | 0.362255i | \(0.117993\pi\) | |||||||
\(152\) | −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 | −0.114334 | − | 0.993442i | \(-0.536473\pi\) |
−0.917513 | + | 0.397705i | \(0.869807\pi\) | |||||||
\(158\) | −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 | 0.763252 | − | 0.646101i | \(-0.223602\pi\) |
−0.941166 | + | 0.337945i | \(0.890268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 42.0000 | − | 24.2487i | 0.253012 | − | 0.146077i | ||||
\(167\) | 266.736i | 1.59722i | 0.601849 | + | 0.798610i | \(0.294431\pi\) | ||||
−0.601849 | + | 0.798610i | \(0.705569\pi\) | |||||||
\(168\) | − | 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 | −0.154255 | − | 0.988031i | \(-0.549298\pi\) |
0.778532 | + | 0.627604i | \(0.215964\pi\) | |||||||
\(174\) | − | 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 | −0.879654 | − | 0.475614i | \(-0.842226\pi\) |
0.851721 | + | 0.523996i | \(0.175559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 327.358i | 1.80861i | 0.426892 | + | 0.904303i | \(0.359609\pi\) | ||||
−0.426892 | + | 0.904303i | \(0.640391\pi\) | |||||||
\(182\) | −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 | 0.868631 | − | 0.495459i | \(-0.165000\pi\) |
−0.863396 | + | 0.504527i | \(0.831667\pi\) | |||||||
\(192\) | 96.0000 | + | 55.4256i | 0.500000 | + | 0.288675i | ||||
\(193\) | −117.500 | + | 203.516i | −0.608808 | + | 1.05449i | 0.382629 | + | 0.923902i | \(0.375019\pi\) |
−0.991437 | + | 0.130585i | \(0.958315\pi\) | |||||||
\(194\) | 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 | −0.00557327 | − | 0.999984i | \(-0.501774\pi\) |
−0.868799 | + | 0.495166i | \(0.835107\pi\) | |||||||
\(200\) | 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 | \(0.275375\pi\) | ||||
−0.648552 | + | 0.761170i | \(0.724625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 142.000 | + | 245.951i | 0.628319 | + | 1.08828i | ||||
\(227\) | −141.000 | − | 81.4064i | −0.621145 | − | 0.358618i | 0.156169 | − | 0.987730i | \(-0.450085\pi\) |
−0.777315 | + | 0.629112i | \(0.783419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.50000 | − | 4.33013i | 0.0327511 | − | 0.0189089i | −0.483535 | − | 0.875325i | \(-0.660647\pi\) |
0.516286 | + | 0.856416i | \(0.327314\pi\) | |||||||
\(230\) | 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 | 0.623938 | − | 0.781474i | \(-0.285532\pi\) |
−0.988745 | + | 0.149610i | \(0.952198\pi\) | |||||||
\(234\) | −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 | 0.200483 | − | 0.979697i | \(-0.435749\pi\) |
−0.748201 | + | 0.663472i | \(0.769082\pi\) | |||||||
\(242\) | 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 | \(-0.803189\pi\) | ||
0.814865 | − | 0.579650i | \(-0.196811\pi\) | |||||||
\(252\) | 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 | 0.482688 | − | 0.875792i | \(-0.339661\pi\) |
0.999802 | + | 0.0198763i | \(0.00632725\pi\) | |||||||
\(258\) | − | 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 | −0.707300 | − | 0.706914i | \(-0.750087\pi\) |
0.965855 | + | 0.259083i | \(0.0834203\pi\) | |||||||
\(264\) | 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 | 0.0916490 | − | 0.995791i | \(-0.470786\pi\) |
−0.816556 | + | 0.577266i | \(0.804120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −318.000 | + | 183.597i | −1.17343 | + | 0.677481i | −0.954486 | − | 0.298256i | \(-0.903595\pi\) |
−0.218946 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(272\) | 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 | −0.250731 | − | 0.968057i | \(-0.580671\pi\) |
0.963727 | − | 0.266889i | \(-0.0859958\pi\) | |||||||
\(278\) | 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 | 0.935477 | − | 0.353387i | \(-0.114970\pi\) |
0.161696 | + | 0.986841i | \(0.448304\pi\) | |||||||
\(284\) | 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 | \(-0.864201\pi\) | ||
0.910368 | − | 0.413801i | \(-0.135799\pi\) | |||||||
\(294\) | 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 | \(-0.904281\pi\) | ||
0.955127 | − | 0.296198i | \(-0.0957187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.0485437 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 477.000 | + | 275.396i | 1.53376 | + | 0.885518i | 0.999184 | + | 0.0403991i | \(0.0128629\pi\) |
0.534578 | + | 0.845119i | \(0.320470\pi\) | |||||||
\(312\) | −84.0000 | + | 145.492i | −0.269231 | + | 0.466321i | ||||
\(313\) | −175.500 | + | 101.325i | −0.560703 | + | 0.323722i | −0.753428 | − | 0.657531i | \(-0.771601\pi\) |
0.192725 | + | 0.981253i | \(0.438268\pi\) | |||||||
\(314\) | 374.123i | 1.19147i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 146.000 | + | 252.879i | 0.460568 | + | 0.797727i | 0.998989 | − | 0.0449488i | \(-0.0143125\pi\) |
−0.538421 | + | 0.842676i | \(0.680979\pi\) | |||||||
\(318\) | 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 | 0.862224 | − | 0.506527i | \(-0.169071\pi\) |
−0.869777 | + | 0.493445i | \(0.835738\pi\) | |||||||
\(332\) | 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 | −0.662858 | − | 0.748745i | \(-0.730657\pi\) |
0.979861 | + | 0.199680i | \(0.0639902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 339.482i | − | 0.972728i | −0.873756 | − | 0.486364i | \(-0.838323\pi\) | ||
0.873756 | − | 0.486364i | \(-0.161677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 63.0000 | 0.179487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −267.000 | − | 154.153i | −0.756374 | − | 0.436693i | 0.0716184 | − | 0.997432i | \(-0.477184\pi\) |
−0.827992 | + | 0.560739i | \(0.810517\pi\) | |||||||
\(354\) | 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 | 0.587831 | − | 0.808984i | \(-0.299982\pi\) |
−0.994516 | + | 0.104584i | \(0.966649\pi\) | |||||||
\(360\) | 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 | −0.295919 | − | 0.955213i | \(-0.595626\pi\) |
−0.975198 | + | 0.221333i | \(0.928959\pi\) | |||||||
\(368\) | −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 | 0.695285 | − | 0.718734i | \(-0.255278\pi\) |
−0.970084 | + | 0.242768i | \(0.921945\pi\) | |||||||
\(374\) | 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 | −0.411357 | − | 0.911474i | \(-0.634945\pi\) |
0.583681 | + | 0.811983i | \(0.301612\pi\) | |||||||
\(384\) | − | 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 | −0.814541 | − | 0.580106i | \(-0.803011\pi\) |
0.909657 | + | 0.415361i | \(0.136345\pi\) | |||||||
\(390\) | 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 | −0.809782 | − | 0.586731i | \(-0.800415\pi\) |
0.103233 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(398\) | 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 | 0.934725 | − | 0.355372i | \(-0.115646\pi\) |
−0.775124 | + | 0.631809i | \(0.782313\pi\) | |||||||
\(402\) | −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 | 0.779643 | − | 0.626224i | \(-0.215400\pi\) |
−0.152504 | + | 0.988303i | \(0.548734\pi\) | |||||||
\(410\) | 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 | \(-0.836296\pi\) | ||
0.870641 | − | 0.491919i | \(-0.163704\pi\) | |||||||
\(420\) | 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 | −0.977026 | − | 0.213121i | \(-0.931637\pi\) |
0.673081 | + | 0.739568i | \(0.264970\pi\) | |||||||
\(432\) | −72.0000 | + | 41.5692i | −0.166667 | + | 0.0962250i | ||||
\(433\) | 36.3731i | 0.0840025i | 0.999118 | + | 0.0420012i | \(0.0133733\pi\) | ||||
−0.999118 | + | 0.0420012i | \(0.986627\pi\) | |||||||
\(434\) | 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 | −0.159899 | − | 0.987133i | \(-0.551117\pi\) |
0.774933 | + | 0.632043i | \(0.217784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −147.000 | −0.333333 | ||||||||
\(442\) | −168.000 | −0.380090 | ||||||||
\(443\) | −106.000 | − | 183.597i | −0.239278 | − | 0.414441i | 0.721230 | − | 0.692696i | \(-0.243577\pi\) |
−0.960507 | + | 0.278255i | \(0.910244\pi\) | |||||||
\(444\) | 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 | 0.952177 | + | 0.305547i | \(0.0988394\pi\) |
−0.211477 | + | 0.977383i | \(0.567827\pi\) | |||||||
\(458\) | −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 | \(0.176310\pi\) | ||||
−0.850483 | + | 0.526002i | \(0.823690\pi\) | |||||||
\(462\) | 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 | −0.541174 | − | 0.840910i | \(-0.682020\pi\) |
0.457663 | + | 0.889126i | \(0.348687\pi\) | |||||||
\(468\) | 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 | 0.449058 | − | 0.893503i | \(-0.351760\pi\) |
−0.549267 | + | 0.835647i | \(0.685093\pi\) | |||||||
\(480\) | 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 | −0.898368 | − | 0.439243i | \(-0.855247\pi\) |
0.829580 | + | 0.558388i | \(0.188580\pi\) | |||||||
\(488\) | −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 | −0.999933 | − | 0.0116091i | \(-0.996305\pi\) |
0.489913 | − | 0.871772i | \(-0.337029\pi\) | |||||||
\(500\) | 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 | \(-0.774429\pi\) | ||
0.759240 | − | 0.650810i | \(-0.225571\pi\) | |||||||
\(504\) | 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 | 0.479644 | − | 0.877463i | \(-0.340766\pi\) |
0.999727 | + | 0.0233478i | \(0.00743251\pi\) | |||||||
\(510\) | 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 | 0.812545 | − | 0.582899i | \(-0.198082\pi\) |
−0.0985331 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(522\) | 48.0000 | − | 83.1384i | 0.0919540 | − | 0.159269i | ||||
\(523\) | 853.500 | − | 492.768i | 1.63193 | − | 0.942196i | 0.648434 | − | 0.761271i | \(-0.275424\pi\) |
0.983497 | − | 0.180925i | \(-0.0579092\pi\) | |||||||
\(524\) | 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 | 0.916508 | − | 0.400016i | \(-0.130995\pi\) |
−0.804678 | + | 0.593711i | \(0.797662\pi\) | |||||||
\(542\) | 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 | 0.399397 | + | 0.916778i | \(0.369220\pi\) |
−0.993652 | + | 0.112502i | \(0.964114\pi\) | |||||||
\(558\) | 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 | 0.726878 | − | 0.686767i | \(-0.240971\pi\) |
−0.231318 | + | 0.972878i | \(0.574304\pi\) | |||||||
\(564\) | 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 | 0.978991 | + | 0.203903i | \(0.0653628\pi\) |
−0.312910 | + | 0.949783i | \(0.601304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 432.500 | − | 749.112i | 0.757443 | − | 1.31193i | −0.186707 | − | 0.982416i | \(-0.559782\pi\) |
0.944151 | − | 0.329514i | \(-0.106885\pi\) | |||||||
\(572\) | 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 | −0.989553 | − | 0.144172i | \(-0.953948\pi\) |
−0.619633 | − | 0.784892i | \(-0.712718\pi\) | |||||||
\(578\) | −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 | \(-0.906622\pi\) | ||
0.957279 | − | 0.289167i | \(-0.0933783\pi\) | |||||||
\(588\) | 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 | −0.309535 | − | 0.950888i | \(-0.600173\pi\) |
0.668726 | + | 0.743509i | \(0.266840\pi\) | |||||||
\(594\) | 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 | −0.722808 | − | 0.691049i | \(-0.757149\pi\) |
0.959870 | + | 0.280446i | \(0.0904823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 594.093i | − | 0.988508i | −0.869317 | − | 0.494254i | \(-0.835441\pi\) | ||
0.869317 | − | 0.494254i | \(-0.164559\pi\) | |||||||
\(602\) | 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 | −0.506165 | − | 0.862437i | \(-0.668937\pi\) |
0.493809 | + | 0.869570i | \(0.335604\pi\) | |||||||
\(608\) | 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 | −0.246364 | − | 0.969177i | \(-0.579236\pi\) |
0.962514 | − | 0.271231i | \(-0.0874307\pi\) | |||||||
\(614\) | −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 | 0.862473 | − | 0.506103i | \(-0.168914\pi\) |
−0.00706124 | + | 0.999975i | \(0.502248\pi\) | |||||||
\(620\) | 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 | 0.0218737 | − | 0.999761i | \(-0.493037\pi\) |
0.854881 | − | 0.518824i | \(-0.173630\pi\) | |||||||
\(642\) | −636.000 | + | 367.195i | −0.990654 | + | 0.571954i | ||||
\(643\) | 569.845i | 0.886228i | 0.896465 | + | 0.443114i | \(0.146126\pi\) | ||||
−0.896465 | + | 0.443114i | \(0.853874\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −228.000 | − | 394.908i | −0.352941 | − | 0.611312i | ||||
\(647\) | −939.000 | − | 542.132i | −1.45131 | − | 0.837916i | −0.452758 | − | 0.891634i | \(-0.649560\pi\) |
−0.998556 | + | 0.0537173i | \(0.982893\pi\) | |||||||
\(648\) | 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 | −0.935715 | − | 0.352757i | \(-0.885244\pi\) |
0.162361 | − | 0.986731i | \(-0.448089\pi\) | |||||||
\(654\) | 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 | −0.0543659 | − | 0.998521i | \(-0.517314\pi\) |
−0.891928 | + | 0.452178i | \(0.850647\pi\) | |||||||
\(662\) | −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 | −0.0960963 | − | 0.995372i | \(-0.530636\pi\) |
0.813969 | + | 0.580908i | \(0.197302\pi\) | |||||||
\(678\) | 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 | −0.248659 | − | 0.968591i | \(-0.579990\pi\) |
0.963154 | − | 0.268950i | \(-0.0866768\pi\) | |||||||
\(684\) | 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 | −0.101161 | − | 0.994870i | \(-0.532256\pi\) |
0.811002 | + | 0.585043i | \(0.198922\pi\) | |||||||
\(692\) | 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 | 0.912164 | + | 0.409826i | \(0.134410\pi\) |
−0.101162 | + | 0.994870i | \(0.532256\pi\) | |||||||
\(710\) | 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 | −0.954259 | − | 0.298982i | \(-0.903353\pi\) |
−0.218203 | + | 0.975903i | \(0.570020\pi\) | |||||||
\(720\) | 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 | \(-0.954725\pi\) | ||
0.989902 | − | 0.141757i | \(-0.0452750\pi\) | |||||||
\(728\) | −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 | −0.999482 | − | 0.0321842i | \(-0.989754\pi\) |
−0.471869 | + | 0.881669i | \(0.656420\pi\) | |||||||
\(734\) | 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 | −0.951846 | − | 0.306577i | \(-0.900816\pi\) |
0.741426 | + | 0.671034i | \(0.234150\pi\) | |||||||
\(740\) | 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 | 0.891125 | − | 0.453758i | \(-0.149917\pi\) |
−0.838528 | + | 0.544858i | \(0.816584\pi\) | |||||||
\(752\) | 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 | −0.930939 | − | 0.365175i | \(-0.881009\pi\) |
−0.149219 | + | 0.988804i | \(0.547676\pi\) | |||||||
\(762\) | − | 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 | \(-0.810914\pi\) | ||
0.828691 | − | 0.559707i | \(-0.189086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 762.000 | 0.988327 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 195.000 | + | 112.583i | 0.252264 | + | 0.145645i | 0.620800 | − | 0.783969i | \(-0.286808\pi\) |
−0.368537 | + | 0.929613i | \(0.620141\pi\) | |||||||
\(774\) | 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 | 0.630913 | − | 0.775854i | \(-0.282681\pi\) |
−0.356453 | + | 0.934313i | \(0.616014\pi\) | |||||||
\(788\) | 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 | \(0.324549\pi\) | ||||
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(798\) | 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 | 0.0211166 | − | 0.999777i | \(-0.493278\pi\) |
0.855274 | − | 0.518176i | \(-0.173389\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 872.954i | 1.07639i | 0.842820 | + | 0.538196i | \(0.180894\pi\) | ||||
−0.842820 | + | 0.538196i | \(0.819106\pi\) | |||||||
\(812\) | 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 | 0.779802 | − | 0.626026i | \(-0.215320\pi\) |
−0.932056 | + | 0.362315i | \(0.881986\pi\) | |||||||
\(822\) | 348.000 | + | 200.918i | 0.423358 | + | 0.244426i | ||||
\(823\) | 103.000 | − | 178.401i | 0.125152 | − | 0.216769i | −0.796640 | − | 0.604454i | \(-0.793392\pi\) |
0.921792 | + | 0.387684i | \(0.126725\pi\) | |||||||
\(824\) | 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 | 0.669113 | − | 0.743161i | \(-0.266674\pi\) |
−0.309040 | + | 0.951049i | \(0.600008\pi\) | |||||||
\(830\) | 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 | \(0.0933291\pi\) | ||||
−0.957323 | + | 0.289019i | \(0.906671\pi\) | |||||||
\(840\) | 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 | \(-0.947735\pi\) | ||
0.986550 | − | 0.163458i | \(-0.0522650\pi\) | |||||||
\(854\) | − | 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 | 0.786195 | − | 0.617979i | \(-0.212048\pi\) |
−0.142088 | + | 0.989854i | \(0.545381\pi\) | |||||||
\(858\) | 210.000 | − | 363.731i | 0.244755 | − | 0.423929i | ||||
\(859\) | −528.000 | + | 304.841i | −0.614668 | + | 0.354879i | −0.774790 | − | 0.632218i | \(-0.782145\pi\) |
0.160122 | + | 0.987097i | \(0.448811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −294.000 | −0.341463 | ||||||||
\(862\) | 524.000 | 0.607889 | ||||||||
\(863\) | 335.000 | + | 580.237i | 0.388181 | + | 0.672349i | 0.992205 | − | 0.124617i | \(-0.0397703\pi\) |
−0.604024 | + | 0.796966i | \(0.706437\pi\) | |||||||
\(864\) | 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 | 0.731579 | − | 0.681757i | \(-0.238784\pi\) |
−0.956208 | + | 0.292687i | \(0.905450\pi\) | |||||||
\(878\) | −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 | \(0.229689\pi\) | ||||
−0.750758 | + | 0.660578i | \(0.770311\pi\) | |||||||
\(882\) | 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 | −0.0987664 | − | 0.995111i | \(-0.531490\pi\) |
0.812408 | + | 0.583090i | \(0.198156\pi\) | |||||||
\(888\) | − | 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 | −0.923502 | − | 0.383595i | \(-0.874686\pi\) |
0.793954 | + | 0.607978i | \(0.208019\pi\) | |||||||
\(908\) | 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 | −0.901649 | − | 0.432469i | \(-0.857642\pi\) |
0.0762951 | − | 0.997085i | \(-0.475691\pi\) | |||||||
\(920\) | 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 | 0.117731 | − | 0.993046i | \(-0.462438\pi\) |
0.918868 | + | 0.394565i | \(0.129105\pi\) | |||||||
\(930\) | 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 | \(0.147299\pi\) | ||||
−0.894826 | + | 0.446414i | \(0.852701\pi\) | |||||||
\(938\) | −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 | 0.307147 | − | 0.951662i | \(-0.400626\pi\) |
−0.670590 | + | 0.741828i | \(0.733959\pi\) | |||||||
\(942\) | −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 | 0.762894 | − | 0.646523i | \(-0.223778\pi\) |
−0.941353 | + | 0.337424i | \(0.890444\pi\) | |||||||
\(948\) | 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 | 0.195942 | − | 0.980615i | \(-0.437223\pi\) |
0.947209 | + | 0.320617i | \(0.103890\pi\) | |||||||
\(972\) | 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 | −0.791163 | − | 0.611605i | \(-0.790524\pi\) |
0.925247 | + | 0.379365i | \(0.123857\pi\) | |||||||
\(978\) | −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 | −0.0753596 | − | 0.997156i | \(-0.524010\pi\) |
−0.901243 | + | 0.433315i | \(0.857344\pi\) | |||||||
\(984\) | 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 | −0.848628 | − | 0.528990i | \(-0.822571\pi\) |
0.882433 | + | 0.470439i | \(0.155904\pi\) | |||||||
\(992\) | 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 | 0.863703 | − | 0.504001i | \(-0.168139\pi\) |
−0.00462594 | + | 0.999989i | \(0.501472\pi\) | |||||||
\(998\) | −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.451.1 | 2 | ||
5.2 | odd | 4 | 525.3.s.d.199.2 | 4 | |||
5.3 | odd | 4 | 525.3.s.d.199.1 | 4 | |||
5.4 | even | 2 | 21.3.f.c.10.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 525.3.o.b.376.1 | 2 | ||
15.14 | odd | 2 | 63.3.m.a.10.1 | 2 | |||
20.19 | odd | 2 | 336.3.bh.c.241.1 | 2 | |||
35.4 | even | 6 | 147.3.d.a.97.2 | 2 | |||
35.9 | even | 6 | 147.3.f.e.19.1 | 2 | |||
35.12 | even | 12 | 525.3.s.d.124.1 | 4 | |||
35.19 | odd | 6 | 21.3.f.c.19.1 | yes | 2 | ||
35.24 | odd | 6 | 147.3.d.a.97.1 | 2 | |||
35.33 | even | 12 | 525.3.s.d.124.2 | 4 | |||
35.34 | odd | 2 | 147.3.f.e.31.1 | 2 | |||
60.59 | even | 2 | 1008.3.cg.f.577.1 | 2 | |||
105.44 | odd | 6 | 441.3.m.b.19.1 | 2 | |||
105.59 | even | 6 | 441.3.d.d.244.1 | 2 | |||
105.74 | odd | 6 | 441.3.d.d.244.2 | 2 | |||
105.89 | even | 6 | 63.3.m.a.19.1 | 2 | |||
105.104 | even | 2 | 441.3.m.b.325.1 | 2 | |||
140.19 | even | 6 | 336.3.bh.c.145.1 | 2 | |||
140.39 | odd | 6 | 2352.3.f.b.97.1 | 2 | |||
140.59 | even | 6 | 2352.3.f.b.97.2 | 2 | |||
420.299 | odd | 6 | 1008.3.cg.f.145.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.c.10.1 | ✓ | 2 | 5.4 | even | 2 | ||
21.3.f.c.19.1 | yes | 2 | 35.19 | odd | 6 | ||
63.3.m.a.10.1 | 2 | 15.14 | odd | 2 | |||
63.3.m.a.19.1 | 2 | 105.89 | even | 6 | |||
147.3.d.a.97.1 | 2 | 35.24 | odd | 6 | |||
147.3.d.a.97.2 | 2 | 35.4 | even | 6 | |||
147.3.f.e.19.1 | 2 | 35.9 | even | 6 | |||
147.3.f.e.31.1 | 2 | 35.34 | odd | 2 | |||
336.3.bh.c.145.1 | 2 | 140.19 | even | 6 | |||
336.3.bh.c.241.1 | 2 | 20.19 | odd | 2 | |||
441.3.d.d.244.1 | 2 | 105.59 | even | 6 | |||
441.3.d.d.244.2 | 2 | 105.74 | odd | 6 | |||
441.3.m.b.19.1 | 2 | 105.44 | odd | 6 | |||
441.3.m.b.325.1 | 2 | 105.104 | even | 2 | |||
525.3.o.b.376.1 | 2 | 7.5 | odd | 6 | inner | ||
525.3.o.b.451.1 | 2 | 1.1 | even | 1 | trivial | ||
525.3.s.d.124.1 | 4 | 35.12 | even | 12 | |||
525.3.s.d.124.2 | 4 | 35.33 | even | 12 | |||
525.3.s.d.199.1 | 4 | 5.3 | odd | 4 | |||
525.3.s.d.199.2 | 4 | 5.2 | odd | 4 | |||
1008.3.cg.f.145.1 | 2 | 420.299 | odd | 6 | |||
1008.3.cg.f.577.1 | 2 | 60.59 | even | 2 | |||
2352.3.f.b.97.1 | 2 | 140.39 | odd | 6 | |||
2352.3.f.b.97.2 | 2 | 140.59 | even | 6 |