Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(113,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.20322144469993472.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Root | \(-0.729858 - 1.57077i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.113 |
Dual form | 912.2.f.i.113.4 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.729858 | − | 1.57077i | −0.421383 | − | 0.906883i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22502i | 0.547843i | 0.961752 | + | 0.273922i | \(0.0883209\pi\) | ||||
−0.961752 | + | 0.273922i | \(0.911679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.80880 | 1.06163 | 0.530814 | − | 0.847488i | \(-0.321886\pi\) | ||||
0.530814 | + | 0.847488i | \(0.321886\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.93462 | + | 2.29287i | −0.644872 | + | 0.764291i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.49828i | − | 0.753259i | −0.926364 | − | 0.376630i | \(-0.877083\pi\) | ||
0.926364 | − | 0.376630i | \(-0.122917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.86827i | − | 0.518165i | −0.965855 | − | 0.259082i | \(-0.916580\pi\) | ||
0.965855 | − | 0.259082i | \(-0.0834201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.92421 | − | 0.894087i | 0.496830 | − | 0.230852i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.88146i | 1.18393i | 0.805965 | + | 0.591964i | \(0.201647\pi\) | ||||
−0.805965 | + | 0.591964i | \(0.798353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.12897 | − | 1.39700i | 0.947251 | − | 0.320493i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.05003 | − | 4.41197i | −0.447352 | − | 0.962772i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.424059i | − | 0.0884224i | −0.999022 | − | 0.0442112i | \(-0.985923\pi\) | ||
0.999022 | − | 0.0442112i | \(-0.0140775\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.49934 | 0.699868 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.01356 | + | 1.36536i | 0.964860 | + | 0.262764i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.86923 | 0.718498 | 0.359249 | − | 0.933242i | \(-0.383033\pi\) | ||||
0.359249 | + | 0.933242i | \(0.383033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.514909i | 0.0924805i | 0.998930 | + | 0.0462402i | \(0.0147240\pi\) | ||||
−0.998930 | + | 0.0462402i | \(0.985276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.92421 | + | 1.82339i | −0.683118 | + | 0.317411i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44083i | 0.581606i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.16750i | − | 0.849532i | −0.905303 | − | 0.424766i | \(-0.860356\pi\) | ||
0.905303 | − | 0.424766i | \(-0.139644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.93462 | + | 1.36357i | −0.469915 | + | 0.218346i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.40952 | 0.376303 | 0.188152 | − | 0.982140i | \(-0.439750\pi\) | ||||
0.188152 | + | 0.982140i | \(0.439750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.420092 | −0.0640635 | −0.0320317 | − | 0.999487i | \(-0.510198\pi\) | ||||
−0.0320317 | + | 0.999487i | \(0.510198\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.80880 | − | 2.36993i | −0.418712 | − | 0.353289i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.7405i | − | 1.56666i | −0.621607 | − | 0.783329i | \(-0.713520\pi\) | ||
0.621607 | − | 0.783329i | \(-0.286480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.889372 | 0.127053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.66763 | − | 3.56277i | 1.07368 | − | 0.498887i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.71766 | 1.06010 | 0.530051 | − | 0.847966i | \(-0.322173\pi\) | ||||
0.530051 | + | 0.847966i | \(0.322173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.06043 | 0.412668 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.20792 | − | 5.46604i | −0.689805 | − | 0.723995i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.63841 | 0.473681 | 0.236840 | − | 0.971549i | \(-0.423888\pi\) | ||||
0.236840 | + | 0.971549i | \(0.423888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85900 | −0.238021 | −0.119010 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119010 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.43395 | + | 6.44022i | −0.684614 | + | 0.811392i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.28866 | 0.283873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.1012i | − | 1.72274i | −0.507982 | − | 0.861368i | \(-0.669608\pi\) | ||
0.507982 | − | 0.861368i | \(-0.330392\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.666098 | + | 0.309503i | −0.0801888 | + | 0.0372598i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.5869 | −1.84982 | −0.924912 | − | 0.380182i | \(-0.875861\pi\) | ||||
−0.924912 | + | 0.380182i | \(0.875861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9862 | 1.40288 | 0.701438 | − | 0.712731i | \(-0.252542\pi\) | ||||
0.701438 | + | 0.712731i | \(0.252542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.55402 | − | 5.49664i | −0.294913 | − | 0.634698i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.01717i | − | 0.799681i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.61516i | − | 0.181719i | −0.995864 | − | 0.0908597i | \(-0.971039\pi\) | ||
0.995864 | − | 0.0908597i | \(-0.0289615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.51452 | − | 8.87165i | −0.168280 | − | 0.985739i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.68241i | 0.623726i | 0.950127 | + | 0.311863i | \(0.100953\pi\) | ||||
−0.950127 | + | 0.311863i | \(0.899047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.97986 | −0.648607 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82399 | − | 6.07766i | −0.302763 | − | 0.651594i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4660 | 1.21540 | 0.607698 | − | 0.794168i | \(-0.292093\pi\) | ||||
0.607698 | + | 0.794168i | \(0.292093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.24760i | − | 0.550098i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.808803 | − | 0.375811i | 0.0838689 | − | 0.0389697i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.71134 | + | 5.05805i | 0.175580 | + | 0.518945i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.48325i | − | 0.252136i | −0.992022 | − | 0.126068i | \(-0.959764\pi\) | ||
0.992022 | − | 0.126068i | \(-0.0402358\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.72823 | + | 4.83321i | 0.575709 | + | 0.485756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.9455i | − | 1.58663i | −0.608809 | − | 0.793317i | \(-0.708353\pi\) | ||
0.608809 | − | 0.793317i | \(-0.291647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8913i | 1.76289i | 0.472290 | + | 0.881443i | \(0.343427\pi\) | ||||
−0.472290 | + | 0.881443i | \(0.656573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.40473 | − | 2.51131i | 0.527448 | − | 0.245079i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.33220 | −0.128788 | −0.0643941 | − | 0.997925i | \(-0.520511\pi\) | ||||
−0.0643941 | + | 0.997925i | \(0.520511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5645i | 1.58659i | 0.608838 | + | 0.793294i | \(0.291636\pi\) | ||||
−0.608838 | + | 0.793294i | \(0.708364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.11694 | + | 3.77154i | −0.770426 | + | 0.357979i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.7157 | −1.57248 | −0.786242 | − | 0.617919i | \(-0.787976\pi\) | ||||
−0.786242 | + | 0.617919i | \(0.787976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.519479 | 0.0484417 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.28370 | + | 3.61438i | 0.396029 | + | 0.334150i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.7111i | 1.25689i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.75860 | 0.432600 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75860 | − | 3.78479i | −0.158568 | − | 0.341263i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4118i | 0.931261i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.20314i | 0.639176i | 0.947557 | + | 0.319588i | \(0.103544\pi\) | ||||
−0.947557 | + | 0.319588i | \(0.896456\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.306608 | + | 0.659867i | 0.0269953 | + | 0.0580980i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.0482485i | − | 0.00421550i | −0.999998 | − | 0.00210775i | \(-0.999329\pi\) | ||
0.999998 | − | 0.00210775i | \(-0.000670917\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5975 | − | 3.92389i | 1.00563 | − | 0.340244i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.67259 | + | 6.14169i | −0.143953 | + | 0.528592i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.8562i | 1.44012i | 0.693912 | + | 0.720060i | \(0.255886\pi\) | ||||
−0.693912 | + | 0.720060i | \(0.744114\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5169 | −0.892031 | −0.446016 | − | 0.895025i | \(-0.647157\pi\) | ||||
−0.446016 | + | 0.895025i | \(0.647157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.8708 | + | 7.83901i | −1.42077 | + | 0.660164i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.66746 | −0.390312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.73987i | 0.393625i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.649115 | − | 1.39700i | −0.0535381 | − | 0.115222i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.61966i | − | 0.378457i | −0.981933 | − | 0.189229i | \(-0.939401\pi\) | ||
0.981933 | − | 0.189229i | \(-0.0605987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9811i | 1.46328i | 0.681690 | + | 0.731641i | \(0.261245\pi\) | ||||
−0.681690 | + | 0.731641i | \(0.738755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.1926 | − | 9.44375i | −0.904865 | − | 0.763482i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.630772 | −0.0506648 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.77874 | −0.141959 | −0.0709796 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709796 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.63279 | − | 12.1226i | −0.446709 | − | 0.961388i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.19110i | − | 0.0938717i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4565 | 1.21064 | 0.605322 | − | 0.795981i | \(-0.293044\pi\) | ||||
0.605322 | + | 0.795981i | \(0.293044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.23368 | − | 4.80722i | −0.173892 | − | 0.374242i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.46164 | 0.345252 | 0.172626 | − | 0.984987i | \(-0.444775\pi\) | ||||
0.172626 | + | 0.984987i | \(0.444775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.50957 | 0.731505 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.78484 | + | 12.1699i | −0.365906 | + | 0.930652i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.0529 | −1.44857 | −0.724283 | − | 0.689502i | \(-0.757829\pi\) | ||||
−0.724283 | + | 0.689502i | \(0.757829\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.82895 | 0.742999 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.65552 | − | 5.71510i | −0.199601 | − | 0.429573i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.9759 | −1.19410 | −0.597049 | − | 0.802205i | \(-0.703660\pi\) | ||||
−0.597049 | + | 0.802205i | \(0.703660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.25727i | − | 0.390770i | −0.980727 | − | 0.195385i | \(-0.937404\pi\) | ||
0.980727 | − | 0.195385i | \(-0.0625956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.35681 | + | 2.92006i | 0.100298 | + | 0.215857i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.33027 | 0.465411 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.1952 | 0.891804 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.0821 | + | 3.83503i | 1.02432 | + | 0.278957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.33309i | − | 0.385889i | −0.981210 | − | 0.192945i | \(-0.938196\pi\) | ||
0.981210 | − | 0.192945i | \(-0.0618038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2027i | 1.52621i | 0.646277 | + | 0.763103i | \(0.276325\pi\) | ||||
−0.646277 | + | 0.763103i | \(0.723675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.67039 | − | 3.59495i | −0.119619 | − | 0.257440i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.6853i | 1.47377i | 0.676019 | + | 0.736884i | \(0.263704\pi\) | ||||
−0.676019 | + | 0.736884i | \(0.736296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.09080 | −0.219101 | −0.109550 | − | 0.993981i | \(-0.534941\pi\) | ||||
−0.109550 | + | 0.993981i | \(0.534941\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.1497 | + | 10.2919i | −1.56232 | + | 0.725932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.8679 | 0.762778 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.95169i | 0.206155i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.972313 | + | 0.820392i | 0.0675804 | + | 0.0570212i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.49009 | − | 10.3153i | −0.241414 | − | 0.713526i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.02995i | 0.415119i | 0.978222 | + | 0.207560i | \(0.0665521\pi\) | ||||
−0.978222 | + | 0.207560i | \(0.933448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3762 | + | 24.4834i | 0.779485 | + | 1.67757i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.514619i | − | 0.0350967i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.44628i | 0.0981798i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.74820 | − | 18.8275i | −0.591149 | − | 1.27224i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.11988 | 0.613470 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5462i | 0.840153i | 0.907489 | + | 0.420076i | \(0.137997\pi\) | ||||
−0.907489 | + | 0.420076i | \(0.862003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.76987 | + | 8.02353i | −0.451325 | + | 0.534902i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0562 | 1.53029 | 0.765146 | − | 0.643857i | \(-0.222667\pi\) | ||||
0.765146 | + | 0.643857i | \(0.222667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4971 | −0.759748 | −0.379874 | − | 0.925038i | \(-0.624033\pi\) | ||||
−0.379874 | + | 0.925038i | \(0.624033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.0223 | + | 5.12154i | −0.725217 | + | 0.336972i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.7204i | − | 0.964369i | −0.876070 | − | 0.482184i | \(-0.839844\pi\) | ||
0.876070 | − | 0.482184i | \(-0.160156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.1572 | 0.858283 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.53704 | + | 1.17884i | −0.164798 | + | 0.0765736i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.6025i | − | 1.65609i | −0.560663 | − | 0.828044i | \(-0.689454\pi\) | ||
0.560663 | − | 0.828044i | \(-0.310546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.66611i | 0.236155i | 0.993004 | + | 0.118077i | \(0.0376731\pi\) | ||||
−0.993004 | + | 0.118077i | \(0.962327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.8299 | + | 8.85401i | −0.823039 | + | 0.567985i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.08949i | 0.0696052i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.60997 | − | 7.71403i | −0.166068 | − | 0.490832i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.92575 | − | 4.14735i | 0.565646 | − | 0.262828i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.2774i | − | 1.72173i | −0.508832 | − | 0.860866i | \(-0.669923\pi\) | ||
0.508832 | − | 0.860866i | \(-0.330077\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.05942 | −0.0666050 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.36445 | + | 9.39296i | 0.273312 | + | 0.588210i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5562 | −0.658476 | −0.329238 | − | 0.944247i | \(-0.606792\pi\) | ||||
−0.329238 | + | 0.944247i | \(0.606792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 14.5145i | − | 0.901887i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.48548 | + | 8.87165i | −0.463339 | + | 0.549142i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8784i | 0.855780i | 0.903831 | + | 0.427890i | \(0.140743\pi\) | ||||
−0.903831 | + | 0.427890i | \(0.859257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.45425i | 0.580770i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.36857 | − | 18.0105i | −0.512148 | − | 1.10222i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.60804 | −0.585813 | −0.292906 | − | 0.956141i | \(-0.594622\pi\) | ||||
−0.292906 | + | 0.956141i | \(0.594622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5859 | −1.12901 | −0.564507 | − | 0.825428i | \(-0.690934\pi\) | ||||
−0.564507 | + | 0.825428i | \(0.690934\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.24276 | + | 3.83000i | −0.498874 | + | 0.231802i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 8.74232i | − | 0.527182i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4363 | −0.687142 | −0.343571 | − | 0.939127i | \(-0.611637\pi\) | ||||
−0.343571 | + | 0.939127i | \(0.611637\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.18062 | − | 0.996152i | −0.0706820 | − | 0.0596381i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1774 | −1.26334 | −0.631668 | − | 0.775239i | \(-0.717629\pi\) | ||||
−0.631668 | + | 0.775239i | \(0.717629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.67803 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.69598 | − | 6.37978i | 0.396636 | − | 0.377905i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.76786 | 0.399494 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.82863 | −0.401684 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.90061 | + | 1.81242i | −0.228658 | + | 0.106246i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4049 | −0.783125 | −0.391563 | − | 0.920151i | \(-0.628065\pi\) | ||||
−0.391563 | + | 0.920151i | \(0.628065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.45711i | 0.259503i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41105 | − | 12.5253i | 0.197929 | − | 0.726790i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.792257 | −0.0458174 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.17996 | −0.0680115 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.0466 | + | 11.6379i | −1.43889 | + | 0.668581i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.27730i | − | 0.130398i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2565i | 1.49854i | 0.662266 | + | 0.749269i | \(0.269595\pi\) | ||||
−0.662266 | + | 0.749269i | \(0.730405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.1031 | − | 13.0581i | 1.59873 | − | 0.742851i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.4261i | − | 0.591213i | −0.955310 | − | 0.295606i | \(-0.904478\pi\) | ||
0.955310 | − | 0.295606i | \(-0.0955217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0678 | −0.625587 | −0.312793 | − | 0.949821i | \(-0.601265\pi\) | ||||
−0.312793 | + | 0.949821i | \(0.601265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.88937 | − | 6.65668i | −0.444516 | − | 0.375061i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.95937 | −0.166215 | −0.0831073 | − | 0.996541i | \(-0.526484\pi\) | ||||
−0.0831073 | + | 0.996541i | \(0.526484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.66642i | − | 0.541216i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.972313 | + | 2.09257i | 0.0542692 | + | 0.116796i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.81938 | + | 20.1554i | 0.379440 | + | 1.12148i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.53771i | − | 0.362647i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.0189 | − | 12.0897i | 1.43885 | − | 0.668562i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 30.1678i | − | 1.66321i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.55718i | − | 0.250485i | −0.992126 | − | 0.125243i | \(-0.960029\pi\) | ||
0.992126 | − | 0.125243i | \(-0.0399710\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.8484 | + | 9.99714i | 0.649290 | + | 0.547840i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2742 | 0.943789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.27943i | − | 0.451009i | −0.974242 | − | 0.225505i | \(-0.927597\pi\) | ||
0.974242 | − | 0.225505i | \(-0.0724031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.2001 | + | 26.2565i | 0.662619 | + | 1.42606i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.28639 | 0.0696618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1635 | −0.926744 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.379146 | − | 0.815980i | −0.0204125 | − | 0.0439309i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3626i | 0.985754i | 0.870099 | + | 0.492877i | \(0.164055\pi\) | ||||
−0.870099 | + | 0.492877i | \(0.835945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25535 | 0.174255 | 0.0871275 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871275 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.55086 | − | 9.36668i | 0.136155 | − | 0.499957i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.48890i | 0.132471i | 0.997804 | + | 0.0662354i | \(0.0210988\pi\) | ||||
−0.997804 | + | 0.0662354i | \(0.978901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 19.0942i | − | 1.01341i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.5369 | − | 10.0071i | 1.13985 | − | 0.529633i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.8512i | 1.41715i | 0.705634 | + | 0.708577i | \(0.250662\pi\) | ||||
−0.705634 | + | 0.708577i | \(0.749338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0968 | − | 11.5363i | 0.794569 | − | 0.607174i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.47310 | − | 7.47466i | −0.182291 | − | 0.392318i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6832i | 0.768556i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.67905 | −0.348643 | −0.174322 | − | 0.984689i | \(-0.555773\pi\) | ||||
−0.174322 | + | 0.984689i | \(0.555773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.66149 | + | 5.52471i | −0.242667 | + | 0.287605i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.6774 | 1.12543 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.6103i | − | 1.53317i | −0.642146 | − | 0.766583i | \(-0.721956\pi\) | ||
0.642146 | − | 0.766583i | \(-0.278044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.3545 | − | 7.59914i | 0.844545 | − | 0.392418i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.22877i | − | 0.372301i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.41300i | − | 0.175314i | −0.996151 | − | 0.0876570i | \(-0.972062\pi\) | ||
0.996151 | − | 0.0876570i | \(-0.0279379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3145 | − | 5.25727i | 0.579657 | − | 0.269338i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.40661 | −0.225167 | −0.112584 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112584 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.59614 | 0.438100 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.812717 | − | 0.963218i | 0.0413127 | − | 0.0489631i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.20661i | 0.162581i | 0.996690 | + | 0.0812907i | \(0.0259042\pi\) | ||||
−0.996690 | + | 0.0812907i | \(0.974096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.07003 | 0.104686 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0757872 | + | 0.0352146i | −0.00382296 | + | 0.00177634i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.97859 | 0.0995538 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.9925 | −0.802640 | −0.401320 | − | 0.915938i | \(-0.631448\pi\) | ||||
−0.401320 | + | 0.915938i | \(0.631448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6280 | − | 15.3530i | −0.732316 | − | 0.768613i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.7131 | 1.53374 | 0.766869 | − | 0.641804i | \(-0.221814\pi\) | ||||
0.766869 | + | 0.641804i | \(0.221814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.961990 | 0.0479201 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.8679 | − | 1.85531i | 0.540031 | − | 0.0921913i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.9099 | −0.639918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 36.9136i | − | 1.82526i | −0.408789 | − | 0.912629i | \(-0.634049\pi\) | ||
0.408789 | − | 0.912629i | \(-0.365951\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.4771 | − | 12.3026i | 1.30602 | − | 0.606842i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.2196 | 0.502873 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.96104 | −0.341704 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.67584 | + | 16.5196i | 0.375887 | + | 0.808968i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7287i | 0.719546i | 0.933040 | + | 0.359773i | \(0.117146\pi\) | ||||
−0.933040 | + | 0.359773i | \(0.882854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.4457i | 1.14267i | 0.820716 | + | 0.571337i | \(0.193575\pi\) | ||||
−0.820716 | + | 0.571337i | \(0.806425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.6265 | + | 20.7787i | 1.19738 | + | 1.01029i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.0819i | 0.828592i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.22157 | −0.252689 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.40658 | + | 7.33149i | 0.164471 | + | 0.353968i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.4449 | −1.22564 | −0.612818 | − | 0.790224i | \(-0.709964\pi\) | ||||
−0.612818 | + | 0.790224i | \(0.709964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2027i | 1.01894i | 0.860489 | + | 0.509469i | \(0.170158\pi\) | ||||
−0.860489 | + | 0.509469i | \(0.829842\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.44522 | − | 3.45943i | 0.356971 | − | 0.165867i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.592409 | − | 1.75093i | −0.0283388 | − | 0.0837582i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.5578i | − | 1.31526i | −0.753341 | − | 0.657630i | \(-0.771559\pi\) | ||
0.753341 | − | 0.657630i | \(-0.228441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.72059 | + | 2.03922i | −0.0819330 | + | 0.0971056i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.8168i | 1.13157i | 0.824552 | + | 0.565786i | \(0.191427\pi\) | ||||
−0.824552 | + | 0.565786i | \(0.808573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0461i | 0.665847i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.25641 | + | 3.37169i | −0.343216 | + | 0.159476i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.3561 | 1.66856 | 0.834278 | − | 0.551344i | \(-0.185885\pi\) | ||||
0.834278 | + | 0.551344i | \(0.185885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.01964i | − | 0.283454i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.2441 | − | 13.1236i | 1.32702 | − | 0.616603i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.42839 | 0.301368 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1233 | 1.22199 | 0.610997 | − | 0.791633i | \(-0.290769\pi\) | ||||
0.610997 | + | 0.791633i | \(0.290769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.66495 | + | 24.4735i | −0.311093 | + | 1.14232i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.1158i | − | 0.797162i | −0.917133 | − | 0.398581i | \(-0.869503\pi\) | ||
0.917133 | − | 0.398581i | \(-0.130497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.341102 | −0.0158524 | −0.00792618 | − | 0.999969i | \(-0.502523\pi\) | ||||
−0.00792618 | + | 0.999969i | \(0.502523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.460374 | + | 0.990795i | 0.0213493 | + | 0.0459470i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.7092i | − | 1.42105i | −0.703671 | − | 0.710526i | \(-0.748457\pi\) | ||
0.703671 | − | 0.710526i | \(-0.251543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 39.6075i | − | 1.82890i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29823 | + | 2.79399i | 0.0598193 | + | 0.128740i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.04951i | 0.0482564i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.4487 | − | 4.88856i | 0.662950 | − | 0.224303i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.9307 | + | 17.6956i | −0.683630 | + | 0.810226i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.2160i | 1.38060i | 0.723522 | + | 0.690302i | \(0.242522\pi\) | ||||
−0.723522 | + | 0.690302i | \(0.757478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.65429 | −0.440198 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.87094 | + | 0.869332i | −0.0851306 | + | 0.0395560i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.04202 | 0.138131 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.1534i | − | 1.59295i | −0.604670 | − | 0.796476i | \(-0.706695\pi\) | ||
0.604670 | − | 0.796476i | \(-0.293305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2810 | − | 24.2785i | −0.510145 | − | 1.09791i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8286i | 1.21076i | 0.795937 | + | 0.605379i | \(0.206978\pi\) | ||||
−0.795937 | + | 0.605379i | \(0.793022\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.8875i | 0.850650i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.92075 | + | 7.01717i | −0.266118 | + | 0.315398i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.7805 | −1.96382 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.1309 | −1.79651 | −0.898253 | − | 0.439479i | \(-0.855163\pi\) | ||||
−0.898253 | + | 0.439479i | \(0.855163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.25636 | − | 7.00820i | −0.145484 | − | 0.313103i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 29.4746i | − | 1.31421i | −0.753801 | − | 0.657103i | \(-0.771782\pi\) | ||
0.753801 | − | 0.657103i | \(-0.228218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5334 | 0.869226 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.94063 | − | 14.9373i | −0.308244 | − | 0.663389i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.81464 | −0.257729 | −0.128865 | − | 0.991662i | \(-0.541133\pi\) | ||||
−0.128865 | + | 0.991662i | \(0.541133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.6668 | 1.48933 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.6082 | − | 1.36639i | 0.998179 | − | 0.0603278i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.9172 | −0.965785 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.8327 | −1.18010 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9059 | + | 29.9277i | 0.610402 | + | 1.31368i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.2332 | 1.67503 | 0.837513 | − | 0.546417i | \(-0.184009\pi\) | ||||
0.837513 | + | 0.546417i | \(0.184009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.17499i | − | 0.0951055i | −0.998869 | − | 0.0475528i | \(-0.984858\pi\) | ||
0.998869 | − | 0.0475528i | \(-0.0151422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.17373 | − | 15.4390i | −0.313087 | − | 0.673813i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.51351 | −0.109490 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8202 | 0.992181 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.03893 | + | 8.34241i | −0.305463 | + | 0.362030i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.50163i | − | 0.194987i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.63196i | − | 0.0705558i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.6602 | + | 25.0945i | 0.503173 | + | 1.08291i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.22190i | − | 0.0957040i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.8781 | −1.15558 | −0.577791 | − | 0.816185i | \(-0.696085\pi\) | ||||
−0.577791 | + | 0.816185i | \(0.696085\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.25794 | + | 3.83706i | −0.354382 | + | 0.164664i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.2917 | −0.869202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0152i | 1.24060i | 0.784364 | + | 0.620300i | \(0.212989\pi\) | ||||
−0.784364 | + | 0.620300i | \(0.787011\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.59645 | − | 4.26245i | 0.153493 | − | 0.181917i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9759 | − | 5.40530i | 0.680598 | − | 0.230274i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.53666i | − | 0.192918i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.62020 | − | 9.94338i | −0.196116 | − | 0.422073i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19.5680i | − | 0.829122i | −0.910021 | − | 0.414561i | \(-0.863935\pi\) | ||
0.910021 | − | 0.414561i | \(-0.136065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.784846i | 0.0331954i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.90079 | − | 19.1559i | −0.375792 | − | 0.808762i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.3253 | −0.772321 | −0.386161 | − | 0.922432i | \(-0.626199\pi\) | ||||
−0.386161 | + | 0.922432i | \(0.626199\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 20.4770i | − | 0.861475i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.25400 | − | 24.9187i | −0.178651 | − | 1.04649i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7539 | −0.744282 | −0.372141 | − | 0.928176i | \(-0.621376\pi\) | ||||
−0.372141 | + | 0.928176i | \(0.621376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.25794 | −0.345584 | −0.172792 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172792 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.37705 | + | 3.89240i | −0.349956 | + | 0.162607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.48393i | − | 0.0618840i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.96477 | −0.414839 | −0.207419 | − | 0.978252i | \(-0.566506\pi\) | ||||
−0.207419 | + | 0.978252i | \(0.566506\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.3045 | − | 15.4750i | 1.38409 | − | 0.643118i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.9608i | 0.662165i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 19.2809i | − | 0.798532i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.42767 | + | 5.24760i | −0.183062 | + | 0.216962i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.1772i | − | 1.36937i | −0.728840 | − | 0.684685i | \(-0.759940\pi\) | ||
0.728840 | − | 0.684685i | \(-0.240060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.719327 | + | 2.12605i | 0.0296393 | + | 0.0876022i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.4918 | − | 15.0973i | 1.33654 | − | 0.621022i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.1507i | 0.950684i | 0.879801 | + | 0.475342i | \(0.157676\pi\) | ||||
−0.879801 | + | 0.475342i | \(0.842324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.7962 | −0.688579 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.25584 | + | 4.85493i | 0.0923255 | + | 0.198699i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.9672 | 1.75559 | 0.877796 | − | 0.479035i | \(-0.159013\pi\) | ||||
0.877796 | + | 0.479035i | \(0.159013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.0425i | − | 1.38862i | −0.719675 | − | 0.694311i | \(-0.755709\pi\) | ||
0.719675 | − | 0.694311i | \(-0.244291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.3322 | + | 27.2804i | 1.31667 | + | 1.11094i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.82936i | 0.236997i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7358i | 0.841641i | 0.907144 | + | 0.420821i | \(0.138258\pi\) | ||||
−0.907144 | + | 0.420821i | \(0.861742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.93203 | − | 17.0709i | −0.321422 | − | 0.691750i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.0661 | −0.811787 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2732 | −1.50545 | −0.752724 | − | 0.658336i | \(-0.771261\pi\) | ||||
−0.752724 | + | 0.658336i | \(0.771261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.63642 | − | 2.15432i | 0.186959 | − | 0.0868704i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.6733i | 1.27512i | 0.770402 | + | 0.637559i | \(0.220056\pi\) | ||||
−0.770402 | + | 0.637559i | \(0.779944\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.2177 | 1.13416 | 0.567082 | − | 0.823662i | \(-0.308072\pi\) | ||||
0.567082 | + | 0.823662i | \(0.308072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.578993 | − | 2.12605i | 0.0232342 | − | 0.0853153i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.2058 | 1.29030 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.74206 | 0.189682 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.6557 | + | 13.0108i | −0.545356 | + | 0.519602i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.2250 | 1.00578 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0994 | −0.481669 | −0.240834 | − | 0.970566i | \(-0.577421\pi\) | ||||
−0.240834 | + | 0.970566i | \(0.577421\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.47165 | − | 4.40101i | 0.376464 | − | 0.174924i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.82396 | −0.350168 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.66159i | − | 0.0658345i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.1546 | − | 35.7387i | 1.19290 | − | 1.41380i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.2308 | 0.957060 | 0.478530 | − | 0.878071i | \(-0.341170\pi\) | ||||
0.478530 | + | 0.878071i | \(0.341170\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.0981 | −0.832026 | −0.416013 | − | 0.909359i | \(-0.636573\pi\) | ||||
−0.416013 | + | 0.909359i | \(0.636573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.808347 | + | 0.375599i | −0.0318286 | + | 0.0147892i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.254891i | − | 0.0100208i | −0.999987 | − | 0.00501039i | \(-0.998405\pi\) | ||
0.999987 | − | 0.00501039i | \(-0.00159486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.08977i | − | 0.356804i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.27177 | − | 1.05558i | 0.0890376 | − | 0.0413714i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.0777i | − | 0.942232i | −0.882071 | − | 0.471116i | \(-0.843851\pi\) | ||
0.882071 | − | 0.471116i | \(-0.156149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0591052 | 0.00230943 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.1886 | + | 27.4828i | −0.904675 | + | 1.07220i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.53072 | 0.332310 | 0.166155 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166155 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 38.4286i | − | 1.49470i | −0.664430 | − | 0.747350i | \(-0.731326\pi\) | ||
0.664430 | − | 0.747350i | \(-0.268674\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.65621 | − | 14.3252i | −0.258506 | − | 0.556345i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.80682 | + | 14.2071i | 0.186401 | + | 0.550926i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.64078i | − | 0.0635314i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.7071 | − | 9.15691i | 0.761920 | − | 0.354026i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.64430i | 0.179291i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.8954i | 1.80768i | 0.427867 | + | 0.903842i | \(0.359265\pi\) | ||||
−0.427867 | + | 0.903842i | \(0.640735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.5441 | + | 4.77786i | 0.675274 | + | 0.183900i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6890 | 0.833575 | 0.416787 | − | 0.909004i | \(-0.363156\pi\) | ||||
0.416787 | + | 0.909004i | \(0.363156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.97497i | − | 0.267675i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8277 | − | 36.2159i | −0.644840 | − | 1.38779i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.8523 | −1.48664 | −0.743321 | − | 0.668935i | \(-0.766750\pi\) | ||||
−0.743321 | + | 0.668935i | \(0.766750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.6491 | −0.788960 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.39122 | + | 18.0592i | 0.320145 | + | 0.689002i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 14.4187i | − | 0.549307i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.39377 | 0.281272 | 0.140636 | − | 0.990061i | \(-0.455085\pi\) | ||||
0.140636 | + | 0.990061i | \(0.455085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.0895 | + | 13.5755i | 0.611189 | + | 0.515692i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.8834i | − | 0.488693i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7620i | 0.445516i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.1224 | + | 10.7438i | −0.874569 | + | 0.406369i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.8613i | 1.20338i | 0.798728 | + | 0.601692i | \(0.205507\pi\) | ||||
−0.798728 | + | 0.601692i | \(0.794493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.21898 | − | 21.3365i | −0.272269 | − | 0.804720i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.60291 | − | 20.6669i | −0.361666 | − | 0.778362i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 44.7877i | − | 1.68441i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7371 | 0.553465 | 0.276732 | − | 0.960947i | \(-0.410748\pi\) | ||||
0.276732 | + | 0.960947i | \(0.410748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.70335 | + | 3.12471i | 0.138886 | + | 0.117186i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.218352 | 0.00817735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.71771i | − | 0.213830i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.2156 | + | 18.6862i | −1.50188 | + | 0.697848i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 21.7645i | − | 0.811678i | −0.913945 | − | 0.405839i | \(-0.866979\pi\) | ||
0.913945 | − | 0.405839i | \(-0.133021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.2532i | 1.87153i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.75860 | − | 2.67574i | 0.214165 | − | 0.0995118i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.5397 | 0.502854 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44554 | 0.0536123 | 0.0268061 | − | 0.999641i | \(-0.491466\pi\) | ||||
0.0268061 | + | 0.999641i | \(0.491466\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.2716 | + | 13.6906i | 0.861911 | + | 0.507060i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.05066i | − | 0.0758465i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6302 | −0.577316 | −0.288658 | − | 0.957432i | \(-0.593209\pi\) | ||||
−0.288658 | + | 0.957432i | \(0.593209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.71134 | − | 0.795176i | 0.0631238 | − | 0.0293305i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.2287 | −1.29767 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.1663 | −1.51433 | −0.757163 | − | 0.653226i | \(-0.773415\pi\) | ||||
−0.757163 | + | 0.653226i | \(0.773415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2120 | + | 9.72979i | −0.375149 | + | 0.357433i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.2089 | −1.54849 | −0.774247 | − | 0.632884i | \(-0.781871\pi\) | ||||
−0.774247 | + | 0.632884i | \(0.781871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.65915 | 0.207335 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.0290 | − | 10.9933i | −0.476708 | − | 0.402223i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.74188 | −0.136725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.203487i | − | 0.00742536i | −0.999993 | − | 0.00371268i | \(-0.998818\pi\) | ||
0.999993 | − | 0.00371268i | \(-0.00118178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.8464 | + | 19.9086i | −1.56141 | + | 0.725509i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.0271 | −0.801649 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.0897 | −1.56612 | −0.783060 | − | 0.621946i | \(-0.786342\pi\) | ||||
−0.783060 | + | 0.621946i | \(0.786342\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.773224 | + | 1.66410i | 0.0280663 | + | 0.0604029i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.4848i | 0.633823i | 0.948455 | + | 0.316912i | \(0.102646\pi\) | ||||
−0.948455 | + | 0.316912i | \(0.897354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.5263i | 1.68437i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.5687 | − | 13.7111i | 0.418268 | − | 0.495724i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.79753i | − | 0.245445i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.9862 | −1.15345 | −0.576725 | − | 0.816938i | \(-0.695670\pi\) | ||||
−0.576725 | + | 0.816938i | \(0.695670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.70450 | + | 16.5813i | 0.277471 | + | 0.597160i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.1338 | 1.69529 | 0.847643 | − | 0.530567i | \(-0.178021\pi\) | ||||
0.847643 | + | 0.530567i | \(0.178021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.80184i | 0.0647241i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.7989 | + | 10.5935i | −0.817906 | + | 0.380040i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.94882 | − | 3.36609i | 0.356454 | − | 0.120603i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.9404i | 1.39340i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.3986 | + | 5.28289i | 0.693250 | + | 0.188795i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.17899i | − | 0.0777714i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.4779i | 1.01513i | 0.861614 | + | 0.507564i | \(0.169454\pi\) | ||||
−0.861614 | + | 0.507564i | \(0.830546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.7998 | − | 10.1293i | 0.776092 | − | 0.360612i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.9512 | −1.66939 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.47312i | 0.123334i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.8504 | − | 6.90025i | 0.526690 | − | 0.244727i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.8013 | −1.51610 | −0.758050 | − | 0.652197i | \(-0.773848\pi\) | ||||
−0.758050 | + | 0.652197i | \(0.773848\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.4291 | 1.85481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.1824 | + | 26.2901i | −0.783775 | + | 0.928916i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 29.9448i | − | 1.05673i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.45911 | 0.0514270 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.01250 | + | 15.0920i | 0.246852 | + | 0.531263i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 0.248801i | − | 0.00874739i | −0.999990 | − | 0.00437369i | \(-0.998608\pi\) | ||
0.999990 | − | 0.00437369i | \(-0.00139219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.07141i | 0.318540i | 0.987235 | + | 0.159270i | \(0.0509141\pi\) | ||||
−0.987235 | + | 0.159270i | \(0.949086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5651 | + | 29.1941i | 0.475748 | + | 1.02388i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9344i | 0.663243i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.73455 | + | 0.586867i | −0.0606842 | + | 0.0205319i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0321 | + | 10.1521i | 0.420435 | + | 0.354743i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.31807i | − | 0.220502i | −0.993904 | − | 0.110251i | \(-0.964835\pi\) | ||
0.993904 | − | 0.110251i | \(-0.0351655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.46537 | −0.329942 | −0.164971 | − | 0.986298i | \(-0.552753\pi\) | ||||
−0.164971 | + | 0.986298i | \(0.552753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.7321 | + | 6.38065i | −0.478092 | + | 0.222146i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.938117 | 0.0326215 | 0.0163108 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163108 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 47.9726i | − | 1.66616i | −0.553153 | − | 0.833079i | \(-0.686576\pi\) | ||
0.553153 | − | 0.833079i | \(-0.313424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.34689 | + | 17.9638i | 0.289550 | + | 0.623157i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.34143i | 0.150422i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.46558i | 0.189144i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.703037 | + | 2.58153i | −0.0243005 | + | 0.0892307i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.7186 | 0.508144 | 0.254072 | − | 0.967185i | \(-0.418230\pi\) | ||||
0.254072 | + | 0.967185i | \(0.418230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0290 | −0.483760 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.4565 | + | 33.2647i | 0.532349 | + | 1.14570i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.6494i | 0.400750i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.3660 | 0.459260 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.41430 | + | 7.34810i | 0.117178 | + | 0.252186i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.19133 | −0.0751177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.4691 | 1.41987 | 0.709937 | − | 0.704265i | \(-0.248723\pi\) | ||||
0.709937 | + | 0.704265i | \(0.248723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.9083 | − | 5.86150i | −0.509851 | − | 0.200459i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.4595 | 1.34791 | 0.673956 | − | 0.738772i | \(-0.264594\pi\) | ||||
0.673956 | + | 0.738772i | \(0.264594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.5338 | −1.31475 | −0.657377 | − | 0.753561i | \(-0.728334\pi\) | ||||
−0.657377 | + | 0.753561i | \(0.728334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.93957 | − | 10.6307i | −0.168340 | − | 0.362294i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.8874 | −0.881217 | −0.440609 | − | 0.897699i | \(-0.645237\pi\) | ||||
−0.440609 | + | 0.897699i | \(0.645237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 23.3401i | − | 0.793588i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.98393 | + | 10.7262i | 0.169263 | + | 0.364280i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.03511 | −0.136882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.3448 | −0.892661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.69378 | + | 4.80414i | 0.192705 | + | 0.162596i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.2447i | 0.988653i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1823i | 0.478901i | 0.970909 | + | 0.239451i | \(0.0769673\pi\) | ||||
−0.970909 | + | 0.239451i | \(0.923033\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.78370 | + | 21.0560i | 0.329996 | + | 0.710203i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 26.2348i | − | 0.883871i | −0.897047 | − | 0.441936i | \(-0.854292\pi\) | ||
0.897047 | − | 0.441936i | \(-0.145708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.2365 | −0.748317 | −0.374158 | − | 0.927365i | \(-0.622068\pi\) | ||||
−0.374158 | + | 0.927365i | \(0.622068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.00108 | − | 3.25305i | 0.235339 | − | 0.109350i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.4735 | 1.62758 | 0.813790 | − | 0.581159i | \(-0.197400\pi\) | ||||
0.813790 | + | 0.581159i | \(0.197400\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2322i | 0.678566i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.1639 | + | 3.78370i | −0.742517 | + | 0.126759i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.0044 | − | 44.3471i | −0.502103 | − | 1.48402i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.5708i | − | 0.654179i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.578235 | + | 1.24445i | 0.0193067 | + | 0.0415510i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.99230i | 0.0664471i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.6734i | 1.25508i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.861200 | + | 1.85344i | 0.0286589 | + | 0.0616785i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.44023 | 0.214081 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.9850i | 1.39409i | 0.717028 | + | 0.697045i | \(0.245502\pi\) | ||||
−0.717028 | + | 0.697045i | \(0.754498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.5609 | + | 30.8483i | 1.21265 | + | 1.02318i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.8668 | −0.823873 | −0.411937 | − | 0.911213i | \(-0.635147\pi\) | ||||
−0.411937 | + | 0.911213i | \(0.635147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1963 | 0.469827 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.57711 | + | 1.66211i | −0.118256 | + | 0.0549476i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.135521i | − | 0.00447529i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.4355 | −1.20190 | −0.600948 | − | 0.799288i | \(-0.705210\pi\) | ||||
−0.600948 | + | 0.799288i | \(0.705210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.2429 | − | 19.1635i | 1.35900 | − | 0.631459i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.1205i | 0.958513i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 18.0828i | − | 0.594560i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.0225 | − | 34.6129i | −1.34736 | − | 1.13684i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 20.7869i | − | 0.681997i | −0.940064 | − | 0.340999i | \(-0.889235\pi\) | ||
0.940064 | − | 0.340999i | \(-0.110765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.67219 | − | 1.24245i | 0.120351 | − | 0.0407196i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.3770 | + | 7.60960i | −0.536160 | + | 0.249127i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.9394i | 0.488569i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.1210 | 0.951341 | 0.475671 | − | 0.879623i | \(-0.342205\pi\) | ||||
0.475671 | + | 0.879623i | \(0.342205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.07789 | + | 17.3849i | 0.263612 | + | 0.567334i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7848 | −0.677565 | −0.338783 | − | 0.940865i | \(-0.610015\pi\) | ||||
−0.338783 | + | 0.940865i | \(0.610015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.02178i | − | 0.0332737i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.69797 | + | 17.2508i | −0.152825 | + | 0.561168i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.5344i | 0.537294i | 0.963239 | + | 0.268647i | \(0.0865766\pi\) | ||||
−0.963239 | + | 0.268647i | \(0.913423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 22.3934i | − | 0.726921i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.15992 | + | 4.64847i | 0.0700401 | + | 0.150737i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.99710 | −0.0646923 | −0.0323462 | − | 0.999477i | \(-0.510298\pi\) | ||||
−0.0323462 | + | 0.999477i | \(0.510298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.53312 | 0.211407 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.1837 | + | 7.05511i | −0.490819 | + | 0.228059i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.3456i | 1.52887i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7349 | 0.991447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.57729 | − | 3.05455i | 0.0830519 | − | 0.0984316i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.9737 | −0.836122 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0754 | 1.16011 | 0.580053 | − | 0.814579i | \(-0.303032\pi\) | ||||
0.580053 | + | 0.814579i | \(0.303032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.6823 | − | 25.4222i | 0.857157 | − | 0.816679i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.9370 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.5399 | −0.947005 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.2692 | + | 4.77160i | −0.328878 | + | 0.152813i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0411 | −0.641171 | −0.320586 | − | 0.947220i | \(-0.603880\pi\) | ||||
−0.320586 | + | 0.947220i | \(0.603880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.6453i | − | 0.915509i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9802 | − | 32.0459i | −1.21261 | − | 1.02315i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.3031 | −0.519990 | −0.259995 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259995 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.3398 | −0.807395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.3866 | + | 22.0182i | −1.50833 | + | 0.700848i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.178144i | 0.00566465i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5862i | 0.558645i | 0.960197 | + | 0.279322i | \(0.0901098\pi\) | ||||
−0.960197 | + | 0.279322i | \(0.909890\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.15827 | + | 3.32610i | −0.227161 | + | 0.105550i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.78628i | − | 0.120033i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.8255 | 1.41964 | 0.709819 | − | 0.704384i | \(-0.248777\pi\) | ||||
0.709819 | + | 0.704384i | \(0.248777\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.05550 | − | 25.9076i | 0.223226 | − | 0.819680i |
(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 | 912.2.f.i.113.3 | 10 | ||
3.2 | odd | 2 | 912.2.f.h.113.7 | 10 | |||
4.3 | odd | 2 | 456.2.f.a.113.8 | yes | 10 | ||
12.11 | even | 2 | 456.2.f.b.113.4 | yes | 10 | ||
19.18 | odd | 2 | 912.2.f.h.113.8 | 10 | |||
57.56 | even | 2 | inner | 912.2.f.i.113.4 | 10 | ||
76.75 | even | 2 | 456.2.f.b.113.3 | yes | 10 | ||
228.227 | odd | 2 | 456.2.f.a.113.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.f.a.113.7 | ✓ | 10 | 228.227 | odd | 2 | ||
456.2.f.a.113.8 | yes | 10 | 4.3 | odd | 2 | ||
456.2.f.b.113.3 | yes | 10 | 76.75 | even | 2 | ||
456.2.f.b.113.4 | yes | 10 | 12.11 | even | 2 | ||
912.2.f.h.113.7 | 10 | 3.2 | odd | 2 | |||
912.2.f.h.113.8 | 10 | 19.18 | odd | 2 | |||
912.2.f.i.113.3 | 10 | 1.1 | even | 1 | trivial | ||
912.2.f.i.113.4 | 10 | 57.56 | even | 2 | inner |