Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,5,Mod(5,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.h (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: | \(2.89435896635\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.11337408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 18x^{4} + 81x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(-0.391571i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.17 |
Dual form | 28.5.h.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35901 | − | 0.784623i | −0.151001 | − | 0.0871803i | 0.422596 | − | 0.906318i | \(-0.361119\pi\) |
−0.573597 | + | 0.819138i | \(0.694452\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 38.3327 | − | 22.1314i | 1.53331 | − | 0.885256i | 0.534102 | − | 0.845420i | \(-0.320650\pi\) |
0.999206 | − | 0.0398360i | \(-0.0126836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 42.3967 | + | 24.5667i | 0.865238 | + | 0.501361i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −39.2687 | − | 68.0154i | −0.484799 | − | 0.839697i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.7557 | + | 20.3615i | −0.0971545 | + | 0.168276i | −0.910506 | − | 0.413496i | \(-0.864307\pi\) |
0.813351 | + | 0.581773i | \(0.197641\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 136.269i | 0.806328i | 0.915128 | + | 0.403164i | \(0.132090\pi\) | ||||
−0.915128 | + | 0.403164i | \(0.867910\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −69.4592 | −0.308708 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −227.333 | − | 131.251i | −0.786618 | − | 0.454154i | 0.0521523 | − | 0.998639i | \(-0.483392\pi\) |
−0.838771 | + | 0.544485i | \(0.816725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −387.162 | + | 223.528i | −1.07247 | + | 0.619191i | −0.928855 | − | 0.370442i | \(-0.879206\pi\) |
−0.143615 | + | 0.989634i | \(0.545873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −38.3418 | − | 66.6517i | −0.0869429 | − | 0.151138i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 374.585 | + | 648.800i | 0.708100 | + | 1.22646i | 0.965561 | + | 0.260176i | \(0.0837805\pi\) |
−0.257462 | + | 0.966288i | \(0.582886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 667.098 | − | 1155.45i | 1.06736 | − | 1.84872i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 250.353i | 0.343420i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 406.524 | 0.483382 | 0.241691 | − | 0.970353i | \(-0.422298\pi\) | ||||
0.241691 | + | 0.970353i | \(0.422298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −584.199 | − | 337.287i | −0.607907 | − | 0.350975i | 0.164239 | − | 0.986421i | \(-0.447483\pi\) |
−0.772146 | + | 0.635445i | \(0.780817\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 31.9521 | − | 18.4476i | 0.0293408 | − | 0.0169399i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2168.87 | + | 3.40909i | 1.77051 | + | 0.00278293i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −372.666 | − | 645.476i | −0.272218 | − | 0.471495i | 0.697212 | − | 0.716865i | \(-0.254424\pi\) |
−0.969429 | + | 0.245370i | \(0.921090\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 106.920 | − | 185.191i | 0.0702959 | − | 0.121756i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2476.20i | 1.47305i | 0.676410 | + | 0.736526i | \(0.263535\pi\) | ||||
−0.676410 | + | 0.736526i | \(0.736465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2636.68 | −1.42601 | −0.713003 | − | 0.701161i | \(-0.752665\pi\) | ||||
−0.713003 | + | 0.701161i | \(0.752665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3010.55 | − | 1738.14i | −1.48669 | − | 0.858343i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −579.099 | + | 334.343i | −0.262154 | + | 0.151355i | −0.625317 | − | 0.780371i | \(-0.715030\pi\) |
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1193.96 | + | 2083.09i | 0.497275 | + | 0.867593i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 205.964 | + | 356.741i | 0.0791866 | + | 0.137155i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1014.61 | − | 1757.36i | 0.361200 | − | 0.625617i | −0.626959 | − | 0.779053i | \(-0.715700\pi\) |
0.988159 | + | 0.153436i | \(0.0490338\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1040.68i | 0.344026i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 701.541 | 0.215925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1014.22 | − | 585.561i | −0.291359 | − | 0.168216i | 0.347195 | − | 0.937793i | \(-0.387134\pi\) |
−0.638555 | + | 0.769576i | \(0.720467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2022.05 | + | 1167.43i | −0.543416 | + | 0.313741i | −0.746462 | − | 0.665428i | \(-0.768249\pi\) |
0.203047 | + | 0.979169i | \(0.434916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.04891 | − | 3848.33i | 0.00152404 | − | 0.969597i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3015.83 | + | 5223.58i | 0.713807 | + | 1.23635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3779.79 | − | 6546.78i | 0.842011 | − | 1.45841i | −0.0461815 | − | 0.998933i | \(-0.514705\pi\) |
0.888192 | − | 0.459472i | \(-0.151961\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1175.63i | − | 0.246929i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7575.36 | 1.50275 | 0.751375 | − | 0.659876i | \(-0.229391\pi\) | ||||
0.751375 | + | 0.659876i | \(0.229391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3284.18 | + | 1896.12i | 0.616284 | + | 0.355812i | 0.775421 | − | 0.631445i | \(-0.217538\pi\) |
−0.159137 | + | 0.987257i | \(0.550871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1813.18 | + | 1046.84i | −0.322343 | + | 0.186105i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −998.615 | + | 574.460i | −0.168429 | + | 0.0968898i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3897.33 | − | 6750.37i | −0.624472 | − | 1.08162i | −0.988643 | − | 0.150285i | \(-0.951981\pi\) |
0.364171 | − | 0.931332i | \(-0.381353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2984.33 | + | 5169.02i | −0.454860 | + | 0.787840i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2181.41i | 0.316651i | 0.987387 | + | 0.158326i | \(0.0506096\pi\) | ||||
−0.987387 | + | 0.158326i | \(0.949390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11619.0 | −1.60817 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −552.469 | − | 318.968i | −0.0729910 | − | 0.0421414i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8050.38 | − | 4647.89i | 1.01633 | − | 0.586781i | 0.103294 | − | 0.994651i | \(-0.467062\pi\) |
0.913040 | + | 0.407870i | \(0.133728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3347.69 | + | 5777.37i | −0.404261 | + | 0.697666i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 529.287 | + | 916.751i | 0.0611963 | + | 0.105995i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9893.98 | + | 17136.9i | −1.09629 | + | 1.89882i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9981.90i | − | 1.06089i | −0.847720 | − | 0.530444i | \(-0.822025\pi\) | ||
0.847720 | − | 0.530444i | \(-0.177975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1846.52 | 0.188402 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −675.552 | − | 390.030i | −0.0662241 | − | 0.0382345i | 0.466522 | − | 0.884509i | \(-0.345507\pi\) |
−0.532746 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2383.90 | − | 1376.35i | 0.224706 | − | 0.129734i | −0.383422 | − | 0.923573i | \(-0.625254\pi\) |
0.608127 | + | 0.793840i | \(0.291921\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2944.84 | − | 1706.38i | −0.267106 | − | 0.154774i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7429.46 | − | 12868.2i | −0.648917 | − | 1.12396i | −0.983382 | − | 0.181550i | \(-0.941889\pi\) |
0.334464 | − | 0.942408i | \(-0.391445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1378.33 | + | 2387.33i | −0.116011 | + | 0.200937i | −0.918183 | − | 0.396155i | \(-0.870344\pi\) |
0.802172 | + | 0.597092i | \(0.203677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1169.61i | 0.0949281i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6264.79 | 0.490625 | 0.245312 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245312 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28717.7 | + | 16580.2i | 2.17147 | + | 1.25370i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9268.43 | − | 5351.13i | 0.677071 | − | 0.390907i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6413.76 | − | 11149.4i | −0.452917 | − | 0.787331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7044.11 | + | 12200.8i | 0.481122 | + | 0.833328i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1942.88 | − | 3365.17i | 0.128421 | − | 0.222432i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 31391.0i | − | 2.00902i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12855.0 | 0.797010 | 0.398505 | − | 0.917166i | \(-0.369529\pi\) | ||||
0.398505 | + | 0.917166i | \(0.369529\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3583.27 | + | 2068.80i | 0.215328 | + | 0.124320i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21412.5 | + | 12362.5i | −1.24774 | + | 0.720383i | −0.970658 | − | 0.240464i | \(-0.922701\pi\) |
−0.277082 | + | 0.960846i | \(0.589367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21905.7 | − | 34.4320i | −1.23838 | − | 0.00194652i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5540.67 | + | 9596.73i | 0.304015 | + | 0.526569i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −661.078 | + | 1145.02i | −0.0352218 | + | 0.0610059i | −0.883099 | − | 0.469187i | \(-0.844547\pi\) |
0.847877 | + | 0.530193i | \(0.177880\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5119.78i | 0.264985i | 0.991184 | + | 0.132493i | \(0.0422981\pi\) | ||||
−0.991184 | + | 0.132493i | \(0.957702\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1049.33 | 0.0527807 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2774.64 | − | 1601.94i | −0.135686 | − | 0.0783384i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15583.2 | − | 8996.95i | 0.741173 | − | 0.427917i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8445 | − | 3767.74i | 0.000548128 | − | 0.174360i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5104.93 | − | 8842.00i | −0.229942 | − | 0.398270i | 0.727849 | − | 0.685737i | \(-0.240520\pi\) |
−0.957791 | + | 0.287467i | \(0.907187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14672.1 | + | 25412.8i | −0.643483 | + | 1.11455i | 0.341166 | + | 0.940003i | \(0.389178\pi\) |
−0.984650 | + | 0.174543i | \(0.944155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20616.2i | 0.880695i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29858.6 | −1.24281 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −26033.1 | − | 15030.2i | −1.05615 | − | 0.609770i | −0.131787 | − | 0.991278i | \(-0.542072\pi\) |
−0.924366 | + | 0.381508i | \(0.875405\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2757.73 | + | 1592.17i | −0.109083 | + | 0.0629791i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −57.7005 | + | 36709.3i | −0.00222602 | + | 1.41620i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15439.7 | − | 26742.3i | −0.581115 | − | 1.00652i | −0.995348 | − | 0.0963500i | \(-0.969283\pi\) |
0.414232 | − | 0.910171i | \(-0.364050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 816.541 | − | 1414.29i | 0.0299923 | − | 0.0519482i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12858.8i | − | 0.461070i | −0.973064 | − | 0.230535i | \(-0.925952\pi\) | ||
0.973064 | − | 0.230535i | \(-0.0740477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9991.63 | 0.349835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30406.7 | + | 17555.3i | 1.03987 | + | 0.600367i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13588.8 | − | 7845.51i | 0.454035 | − | 0.262137i | −0.255498 | − | 0.966810i | \(-0.582239\pi\) |
0.709533 | + | 0.704672i | \(0.248906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 56668.2 | − | 32598.8i | 1.85039 | − | 1.06445i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 918.890 | + | 1591.56i | 0.0293303 | + | 0.0508016i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15993.2 | − | 27701.0i | 0.499148 | − | 0.864550i | −0.500851 | − | 0.865533i | \(-0.666980\pi\) |
1.00000 | 0.000983488i | \(0.000313054\pi\) | ||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 47967.6i | 1.46417i | 0.681215 | + | 0.732083i | \(0.261452\pi\) | ||||
−0.681215 | + | 0.732083i | \(0.738548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3663.97 | 0.109408 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28570.6 | − | 16495.2i | −0.834787 | − | 0.481965i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5344.91 | − | 3085.88i | 0.152847 | − | 0.0882462i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6150.35 | + | 10614.2i | −0.172177 | + | 0.297141i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2227.93 | − | 3858.88i | −0.0610709 | − | 0.105778i | 0.833873 | − | 0.551956i | \(-0.186118\pi\) |
−0.894944 | + | 0.446178i | \(0.852785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14699.9 | − | 25460.9i | 0.394638 | − | 0.683533i | −0.598417 | − | 0.801185i | \(-0.704203\pi\) |
0.993055 | + | 0.117652i | \(0.0375366\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 9465.17i | − | 0.248920i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23816.0 | 0.613671 | 0.306836 | − | 0.951763i | \(-0.400730\pi\) | ||||
0.306836 | + | 0.951763i | \(0.400730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −42280.9 | − | 24410.9i | −1.06767 | − | 0.616421i | −0.140128 | − | 0.990133i | \(-0.544751\pi\) |
−0.927545 | + | 0.373713i | \(0.878085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10273.5 | + | 5931.41i | −0.254288 | + | 0.146813i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17235.3 | + | 9986.94i | 0.418241 | + | 0.242349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54801.8 | + | 94919.4i | 1.30403 | + | 2.25864i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29418.9 | − | 50955.1i | 0.686572 | − | 1.18918i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10510.9i | − | 0.240629i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9582.07 | −0.215226 | −0.107613 | − | 0.994193i | \(-0.534321\pi\) | ||||
−0.107613 | + | 0.994193i | \(0.534321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10295.0 | − | 5943.80i | −0.226916 | − | 0.131010i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −101071. | + | 58353.5i | −2.18651 | + | 1.26238i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16482.1 | − | 28651.7i | −0.350019 | − | 0.608458i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2975.48 | − | 5153.68i | −0.0620396 | − | 0.107456i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17885.5 | − | 30978.5i | 0.366197 | − | 0.634273i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 54978.9i | 1.10557i | 0.833324 | + | 0.552785i | \(0.186435\pi\) | ||||
−0.833324 | + | 0.552785i | \(0.813565\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −104784. | −2.06981 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7518.24 | − | 4340.66i | −0.145903 | − | 0.0842372i | 0.425271 | − | 0.905066i | \(-0.360179\pi\) |
−0.571174 | + | 0.820829i | \(0.693512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6262.86 | + | 3615.86i | −0.119427 | + | 0.0689511i | −0.558523 | − | 0.829489i | \(-0.688632\pi\) |
0.439097 | + | 0.898440i | \(0.355299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1807.86 | + | 2.84164i | 0.0338798 | + | 5.32531e-5i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4422.96 | − | 7660.79i | −0.0814707 | − | 0.141111i | 0.822411 | − | 0.568894i | \(-0.192628\pi\) |
−0.903882 | + | 0.427782i | \(0.859295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14799.0 | + | 25632.5i | −0.267976 | + | 0.464147i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12231.7i | 0.217767i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 88491.7 | 1.54920 | 0.774599 | − | 0.632453i | \(-0.217952\pi\) | ||||
0.774599 | + | 0.632453i | \(0.217952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −53365.8 | − | 30810.7i | −0.918816 | − | 0.530479i | −0.0355589 | − | 0.999368i | \(-0.511321\pi\) |
−0.883257 | + | 0.468889i | \(0.844654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 25673.3 | − | 14822.5i | 0.434779 | − | 0.251020i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 91869.3 | + | 53426.6i | 1.53052 | + | 0.890072i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30460.0 | − | 52758.4i | −0.499271 | − | 0.864763i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1711.59 | − | 2964.55i | 0.0276058 | − | 0.0478146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 57796.3i | 0.917386i | 0.888595 | + | 0.458693i | \(0.151682\pi\) | ||||
−0.888595 | + | 0.458693i | \(0.848318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17614.0 | −0.275180 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15790.3 | + | 9116.56i | 0.242835 | + | 0.140201i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 60734.3 | − | 35065.0i | 0.919534 | − | 0.530893i | 0.0360479 | − | 0.999350i | \(-0.488523\pi\) |
0.883486 | + | 0.468457i | \(0.155190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 57.4050 | − | 36521.2i | 0.000855756 | − | 0.544435i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15963.7 | − | 27649.9i | −0.234343 | − | 0.405894i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11120.9 | + | 19262.0i | −0.160779 | + | 0.278477i | −0.935148 | − | 0.354257i | \(-0.884734\pi\) |
0.774369 | + | 0.632734i | \(0.218067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 89819.0i | − | 1.27902i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14587.4 | −0.204623 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 40332.3 | + | 23285.9i | 0.557376 | + | 0.321801i | 0.752092 | − | 0.659058i | \(-0.229045\pi\) |
−0.194715 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 71958.3 | − | 41545.1i | 0.979811 | − | 0.565694i | 0.0775980 | − | 0.996985i | \(-0.475275\pi\) |
0.902213 | + | 0.431291i | \(0.141942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9082.59 | − | 5224.82i | 0.121866 | − | 0.0701045i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15684.4 | + | 27166.2i | 0.207397 | + | 0.359222i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4514.06 | − | 7818.59i | 0.0588313 | − | 0.101899i | −0.835110 | − | 0.550083i | \(-0.814596\pi\) |
0.893941 | + | 0.448185i | \(0.147929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 52979.4i | 0.680610i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 64188.4 | 0.812912 | 0.406456 | − | 0.913670i | \(-0.366764\pi\) | ||||
0.406456 | + | 0.913670i | \(0.366764\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19563.7 | + | 11295.1i | 0.244274 | + | 0.141032i | 0.617140 | − | 0.786854i | \(-0.288291\pi\) |
−0.372865 | + | 0.927885i | \(0.621625\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26892.0 | − | 15526.1i | 0.331080 | − | 0.191149i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −60832.0 | + | 104983.i | −0.738530 | + | 1.27454i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7307.06 | − | 12656.2i | −0.0874877 | − | 0.151533i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7832.02 | + | 13565.5i | −0.0924885 | + | 0.160195i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 130473.i | − | 1.51980i | −0.650040 | − | 0.759900i | \(-0.725248\pi\) | ||
0.650040 | − | 0.759900i | \(-0.274752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −51837.2 | −0.595658 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5097.56 | − | 2943.08i | −0.0577896 | − | 0.0333648i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −88411.6 | + | 51044.5i | −0.988933 | + | 0.570961i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −111787. | − | 64774.5i | −1.23383 | − | 0.714943i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 612.053 | + | 1060.11i | 0.00666659 | + | 0.0115469i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −51673.7 | + | 89501.6i | −0.555482 | + | 0.962124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 56173.9i | 0.596015i | 0.954563 | + | 0.298008i | \(0.0963221\pi\) | ||||
−0.954563 | + | 0.298008i | \(0.903678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4319.65 | −0.0452410 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 40087.2 | + | 23144.4i | 0.414462 | + | 0.239290i | 0.692705 | − | 0.721221i | \(-0.256419\pi\) |
−0.278243 | + | 0.960511i | \(0.589752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −119814. | + | 69174.4i | −1.22298 | + | 0.706085i | −0.965551 | − | 0.260213i | \(-0.916207\pi\) |
−0.257424 | + | 0.966299i | \(0.582874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −84937.1 | − | 147651.i | −0.856005 | − | 1.48804i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29152.7 | + | 50493.9i | 0.290108 | + | 0.502482i | 0.973835 | − | 0.227256i | \(-0.0729754\pi\) |
−0.683727 | + | 0.729738i | \(0.739642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4778.97 | + | 8277.42i | −0.0469627 | + | 0.0813418i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23317.3i | 0.226291i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 117353. | 1.12483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 157452. | + | 90905.1i | 1.49067 | + | 0.860640i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3746.31 | − | 2162.93i | 0.0350355 | − | 0.0202278i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32765.6 | − | 51.5018i | −0.302709 | − | 0.000475806i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −494.602 | − | 856.675i | −0.00451440 | − | 0.00781916i | 0.863759 | − | 0.503904i | \(-0.168104\pi\) |
−0.868274 | + | 0.496085i | \(0.834770\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −29268.2 | + | 50694.1i | −0.263942 | + | 0.457161i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 334608.i | − | 2.98158i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −55958.7 | −0.492728 | −0.246364 | − | 0.969177i | \(-0.579236\pi\) | ||||
−0.246364 | + | 0.969177i | \(0.579236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8513.89 | − | 4915.49i | −0.0740847 | − | 0.0427728i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13735.3 | − | 7930.09i | 0.118122 | − | 0.0681976i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −554.769 | + | 117648.i | −0.00471546 | + | 0.999989i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26018.3 | − | 45065.1i | −0.218596 | − | 0.378619i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −65322.2 | + | 113141.i | −0.542502 | + | 0.939641i | 0.456257 | + | 0.889848i | \(0.349190\pi\) |
−0.998760 | + | 0.0497936i | \(0.984144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 110948.i | 0.910899i | 0.890262 | + | 0.455450i | \(0.150522\pi\) | ||||
−0.890262 | + | 0.455450i | \(0.849478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34115.5 | −0.276910 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14727.9 | + | 8503.18i | 0.118193 | + | 0.0682389i | 0.557931 | − | 0.829887i | \(-0.311595\pi\) |
−0.439738 | + | 0.898126i | \(0.644929\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 290384. | − | 167653.i | 2.30418 | − | 1.33032i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −31.7265 | + | 20184.5i | −0.000248935 | + | 0.158373i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35732.4 | − | 61890.3i | −0.277251 | − | 0.480212i | 0.693450 | − | 0.720505i | \(-0.256090\pi\) |
−0.970701 | + | 0.240293i | \(0.922757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34769.0 | − | 60221.8i | 0.266795 | − | 0.462103i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 22107.9i | − | 0.167777i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 167855. | 1.25994 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 147543. | + | 85183.8i | 1.09543 | + | 0.632448i | 0.935017 | − | 0.354602i | \(-0.115383\pi\) |
0.160415 | + | 0.987050i | \(0.448717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 168420. | − | 97237.2i | 1.23692 | − | 0.714134i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 86188.6 | − | 49580.5i | 0.626184 | − | 0.360216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −75346.0 | − | 130503.i | −0.541555 | − | 0.938001i | −0.998815 | − | 0.0486680i | \(-0.984502\pi\) |
0.457260 | − | 0.889333i | \(-0.348831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24630.1 | + | 42660.5i | −0.175147 | + | 0.303364i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 55396.8i | 0.389764i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −211477. | −1.47226 | −0.736129 | − | 0.676841i | \(-0.763348\pi\) | ||||
−0.736129 | + | 0.676841i | \(0.763348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17470.0 | − | 10086.3i | −0.120349 | − | 0.0694836i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −102769. | + | 59333.6i | −0.700590 | + | 0.404486i | −0.807567 | − | 0.589776i | \(-0.799216\pi\) |
0.106977 | + | 0.994261i | \(0.465883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25566.0 | + | 44121.4i | −0.172481 | + | 0.297665i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 103539. | + | 179335.i | 0.691326 | + | 1.19741i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −107858. | + | 186816.i | −0.712778 | + | 1.23457i | 0.251033 | + | 0.967979i | \(0.419230\pi\) |
−0.963810 | + | 0.266588i | \(0.914104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 196658.i | − | 1.28635i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38799.6 | 0.251213 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −298790. | − | 172507.i | −1.91502 | − | 1.10564i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −134011. | + | 77371.1i | −0.850273 | + | 0.490905i | −0.860743 | − | 0.509040i | \(-0.830001\pi\) |
0.0104699 | + | 0.999945i | \(0.496667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29743.0 | + | 17234.5i | 0.186827 | + | 0.108256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −100029. | − | 173255.i | −0.622067 | − | 1.07745i | −0.989100 | − | 0.147244i | \(-0.952960\pi\) |
0.367033 | − | 0.930208i | \(-0.380374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45962.0 | − | 79608.5i | 0.283001 | − | 0.490173i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 264190.i | 1.61067i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17523.8 | 0.105789 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 190382. | + | 109917.i | 1.13810 | + | 0.657080i | 0.945958 | − | 0.324288i | \(-0.105125\pi\) |
0.192137 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1796.82 | − | 1037.39i | 0.0106370 | − | 0.00614129i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28614.4 | − | 49741.9i | −0.167758 | − | 0.291623i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48277.7 | + | 83619.4i | 0.280318 | + | 0.485524i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4017.10 | − | 6957.81i | 0.0231015 | − | 0.0400130i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31359.8i | 0.178626i | 0.996004 | + | 0.0893132i | \(0.0284672\pi\) | ||||
−0.996004 | + | 0.0893132i | \(0.971533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −73690.7 | −0.415766 | −0.207883 | − | 0.978154i | \(-0.566657\pi\) | ||||
−0.207883 | + | 0.978154i | \(0.566657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45481.0 | + | 26258.5i | 0.254184 | + | 0.146753i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −303306. | + | 175114.i | −1.67920 | + | 0.969489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −114408. | − | 179.830i | −0.627481 | − | 0.000986291i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2513.84 | + | 4354.10i | 0.0136591 | + | 0.0236583i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 132586. | − | 229646.i | 0.713746 | − | 1.23624i | −0.249695 | − | 0.968325i | \(-0.580330\pi\) |
0.963441 | − | 0.267920i | \(-0.0863364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 124873.i | 0.666027i | 0.942922 | + | 0.333014i | \(0.108066\pi\) | ||||
−0.942922 | + | 0.333014i | \(0.891934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28236.8 | −0.149224 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −290050. | − | 167460.i | −1.51883 | − | 0.876898i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −120989. | + | 69852.8i | −0.627792 | + | 0.362456i | −0.779896 | − | 0.625909i | \(-0.784728\pi\) |
0.152105 | + | 0.988364i | \(0.451395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 94797.1 | − | 163008.i | 0.487437 | − | 0.838169i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 110595. | + | 191556.i | 0.563544 | + | 0.976087i | 0.997183 | + | 0.0750005i | \(0.0238959\pi\) |
−0.433639 | + | 0.901087i | \(0.642771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 205729. | − | 356332.i | 1.03890 | − | 1.79943i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16021.8i | 0.0801855i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 255878. | 1.26923 | 0.634615 | − | 0.772828i | \(-0.281159\pi\) | ||||
0.634615 | + | 0.772828i | \(0.281159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50419.0 | − | 29109.4i | −0.247880 | − | 0.143114i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 39878.9 | − | 23024.1i | 0.194333 | − | 0.112198i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −464.555 | + | 295551.i | −0.00224396 | + | 1.42761i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 159964. | + | 277065.i | 0.765929 | + | 1.32663i | 0.939754 | + | 0.341852i | \(0.111054\pi\) |
−0.173825 | + | 0.984777i | \(0.555613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32859.0 | − | 56913.5i | 0.155966 | − | 0.270141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 369557.i | − | 1.73892i | −0.494002 | − | 0.869461i | \(-0.664466\pi\) | ||
0.494002 | − | 0.869461i | \(-0.335534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32715.0 | 0.152611 | 0.0763053 | − | 0.997084i | \(-0.475688\pi\) | ||||
0.0763053 | + | 0.997084i | \(0.475688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 40578.0 | + | 23427.7i | 0.187666 | + | 0.108349i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 265325. | − | 153186.i | 1.21659 | − | 0.702400i | 0.252405 | − | 0.967622i | \(-0.418779\pi\) |
0.964187 | + | 0.265222i | \(0.0854452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 321083. | − | 184705.i | 1.45973 | − | 0.839717i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23586.1 | + | 40852.3i | 0.106320 | + | 0.184151i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30996.0 | − | 53686.7i | 0.138543 | − | 0.239963i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 596460.i | 2.64359i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −159370. | −0.700438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −226801. | − | 130944.i | −0.988493 | − | 0.570707i | −0.0836697 | − | 0.996494i | \(-0.526664\pi\) |
−0.904824 | + | 0.425787i | \(0.859997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 87958.7 | − | 50783.0i | 0.380180 | − | 0.219497i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28881.3 | − | 49842.8i | 0.123801 | − | 0.213653i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −220913. | − | 382633.i | −0.939158 | − | 1.62667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41127.7 | + | 71235.3i | −0.173411 | + | 0.300357i | −0.939610 | − | 0.342246i | \(-0.888812\pi\) |
0.766199 | + | 0.642603i | \(0.222146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48457.2i | 0.202647i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −102923. | −0.426924 | −0.213462 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213462 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −92416.2 | − | 53356.5i | −0.380237 | − | 0.219530i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 70782.3 | − | 40866.2i | 0.288878 | − | 0.166784i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 321170. | + | 186101.i | 1.30024 | + | 0.753420i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −75028.2 | − | 129953.i | −0.301317 | − | 0.521896i | 0.675118 | − | 0.737710i | \(-0.264093\pi\) |
−0.976434 | + | 0.215814i | \(0.930759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10089.3 | + | 17475.2i | −0.0401962 | + | 0.0696219i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 91806.6i | 0.362859i | 0.983404 | + | 0.181430i | \(0.0580725\pi\) | ||||
−0.983404 | + | 0.181430i | \(0.941928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34527.6 | −0.135389 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13578.7 | − | 7839.66i | −0.0528253 | − | 0.0304987i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −412600. | + | 238215.i | −1.59255 | + | 0.919460i | −0.599684 | + | 0.800237i | \(0.704707\pi\) |
−0.992867 | + | 0.119224i | \(0.961959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 92656.9 | + | 161071.i | 0.354843 | + | 0.616843i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −55961.0 | − | 96927.3i | −0.212643 | − | 0.368308i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 60921.0 | − | 105518.i | 0.229696 | − | 0.397844i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15721.7i | − | 0.0588192i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24623.1 | −0.0914128 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 147768. | + | 85314.0i | 0.544384 | + | 0.314300i | 0.746854 | − | 0.664988i | \(-0.231563\pi\) |
−0.202470 | + | 0.979289i | \(0.564897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 85040.5 | − | 49098.2i | 0.310901 | − | 0.179499i | −0.336428 | − | 0.941709i | \(-0.609219\pi\) |
0.647330 | + | 0.762210i | \(0.275886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −102590. | − | 161.254i | −0.372209 | − | 0.000585048i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 88538.3 | + | 153353.i | 0.318794 | + | 0.552167i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −140707. | + | 243711.i | −0.502810 | + | 0.870892i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 91977.0i | 0.326205i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −337430. | −1.18776 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −569582. | − | 328849.i | −1.98998 | − | 1.14892i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −43469.7 | + | 25097.3i | −0.150743 | + | 0.0870318i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −56450.5 | − | 177.461i | −0.194308 | − | 0.000610838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 52833.7 | + | 91510.6i | 0.180516 | + | 0.312663i | 0.942056 | − | 0.335454i | \(-0.108890\pi\) |
−0.761540 | + | 0.648118i | \(0.775557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37636.4 | − | 65188.2i | 0.127646 | − | 0.221090i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 122017.i | 0.410798i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −127121. | −0.424855 | −0.212428 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212428 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 158807. | + | 91687.0i | 0.526895 | + | 0.304203i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −157391. | + | 90869.5i | −0.518413 | + | 0.299306i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 600.340 | − | 381938.i | 0.00196312 | − | 1.24894i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25885.1 | + | 44834.3i | 0.0840356 | + | 0.145554i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15246.5 | + | 26407.6i | −0.0491427 | + | 0.0851176i | −0.889550 | − | 0.456837i | \(-0.848982\pi\) |
0.840408 | + | 0.541955i | \(0.182316\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 359300.i | − | 1.14983i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9685.01 | −0.0307733 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 459404. | + | 265237.i | 1.44936 | + | 0.836791i | 0.998444 | − | 0.0557725i | \(-0.0177622\pi\) |
0.450921 | + | 0.892564i | \(0.351095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 240146. | − | 138649.i | 0.752279 | − | 0.434329i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −253511. | + | 145834.i | −0.788554 | + | 0.453621i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 169366. | + | 293351.i | 0.523121 | + | 0.906072i | 0.999638 | + | 0.0269067i | \(0.00856571\pi\) |
−0.476517 | + | 0.879165i | \(0.658101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 53455.6 | − | 92587.8i | 0.163954 | − | 0.283976i | −0.772330 | − | 0.635222i | \(-0.780909\pi\) |
0.936283 | + | 0.351246i | \(0.114242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6992.33i | 0.0212967i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 999538. | 3.02318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −104337. | − | 60238.8i | −0.313390 | − | 0.180936i | 0.335052 | − | 0.942200i | \(-0.391246\pi\) |
−0.648443 | + | 0.761264i | \(0.724579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39954.4 | + | 23067.7i | −0.119181 | + | 0.0688093i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53590.0 | + | 92484.6i | −0.158757 | + | 0.273979i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23854.9 | + | 41317.9i | 0.0701844 | + | 0.121563i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 236856. | − | 410247.i | 0.692106 | − | 1.19876i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 525818.i | − | 1.52602i | −0.646389 | − | 0.763008i | \(-0.723722\pi\) | ||
0.646389 | − | 0.763008i | \(-0.276278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 301573. | 0.869283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32366.0 | − | 18686.5i | −0.0926648 | − | 0.0535000i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −64283.0 | + | 37113.8i | −0.182804 | + | 0.105542i | −0.588610 | − | 0.808417i | \(-0.700324\pi\) |
0.405805 | + | 0.913960i | \(0.366991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −492609. | − | 285441.i | −1.39145 | − | 0.806274i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38306.7 | + | 66349.1i | 0.107480 | + | 0.186160i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10990.7 | + | 19036.5i | −0.0306318 | + | 0.0530558i | −0.880935 | − | 0.473237i | \(-0.843085\pi\) |
0.850303 | + | 0.526293i | \(0.176419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 77418.2i | 0.214336i | 0.994241 | + | 0.107168i | \(0.0341782\pi\) | ||||
−0.994241 | + | 0.107168i | \(0.965822\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −593710. | −1.63282 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 540039. | + | 311792.i | 1.47542 | + | 0.851832i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 155765. | − | 89931.2i | 0.422760 | − | 0.244081i | −0.273498 | − | 0.961873i | \(-0.588181\pi\) |
0.696257 | + | 0.717792i | \(0.254847\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15586.9 | − | 27095.5i | −0.0420266 | − | 0.0730572i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45560.7 | − | 78913.5i | −0.122042 | − | 0.211382i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −314637. | + | 544968.i | −0.837316 | + | 1.45027i | 0.0548147 | + | 0.998497i | \(0.482543\pi\) |
−0.892131 | + | 0.451777i | \(0.850790\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 171995.i | − | 0.454742i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −52877.1 | −0.138899 | −0.0694493 | − | 0.997585i | \(-0.522124\pi\) | ||||
−0.0694493 | + | 0.997585i | \(0.522124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 447040. | + | 258099.i | 1.16672 | + | 0.673603i | 0.952904 | − | 0.303271i | \(-0.0980789\pi\) |
0.213811 | + | 0.976875i | \(0.431412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −162429. | + | 93778.6i | −0.421193 | + | 0.243176i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 455493. | + | 715.955i | 1.17356 | + | 0.00184463i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −277790. | − | 481147.i | −0.711143 | − | 1.23174i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8247.09 | + | 14284.4i | −0.0209781 | + | 0.0363351i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 195651.i | 0.494515i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 193439. | 0.485831 | 0.242915 | − | 0.970047i | \(-0.421896\pi\) | ||||
0.242915 | + | 0.970047i | \(0.421896\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13022.1 | + | 7518.31i | 0.0324993 | + | 0.0187635i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 492766. | − | 284499.i | 1.22206 | − | 0.705558i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −283862. | + | 162700.i | −0.699565 | + | 0.400967i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −297475. | − | 515242.i | −0.728532 | − | 1.26185i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −376563. | + | 652226.i | −0.916477 | + | 1.58738i | −0.111751 | + | 0.993736i | \(0.535646\pi\) |
−0.804725 | + | 0.593648i | \(0.797687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7110.23i | − | 0.0171974i | −0.999963 | − | 0.00859868i | \(-0.997263\pi\) | ||
0.999963 | − | 0.00859868i | \(-0.00273708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 183142. | 0.440219 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −341808. | − | 197343.i | −0.816534 | − | 0.471426i | 0.0326859 | − | 0.999466i | \(-0.489594\pi\) |
−0.849220 | + | 0.528040i | \(0.822927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23845.8 | − | 13767.4i | 0.0566137 | − | 0.0326860i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −81.5306 | + | 51870.0i | −0.000192380 | + | 0.122392i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −115578. | − | 200186.i | −0.271049 | − | 0.469470i | 0.698082 | − | 0.716018i | \(-0.254037\pi\) |
−0.969131 | + | 0.246548i | \(0.920704\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −547198. | + | 947775.i | −1.27545 | + | 2.20914i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 297833.i | − | 0.689989i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −772498. | −1.77880 | −0.889399 | − | 0.457131i | \(-0.848877\pi\) | ||||
−0.889399 | + | 0.457131i | \(0.848877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −195287. | − | 112749.i | −0.446962 | − | 0.258053i | 0.259584 | − | 0.965720i | \(-0.416414\pi\) |
−0.706546 | + | 0.707667i | \(0.749748\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48612.9 | + | 28066.7i | −0.110592 | + | 0.0638504i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −840468. | + | 483484.i | −1.90054 | + | 1.09330i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 152278. | + | 263753.i | 0.342282 | + | 0.592851i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43137.7 | − | 74716.6i | 0.0963839 | − | 0.166942i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 54895.8i | − | 0.121925i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 59564.6 | 0.131510 | 0.0657549 | − | 0.997836i | \(-0.479054\pi\) | ||||
0.0657549 | + | 0.997836i | \(0.479054\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 289270. | + | 167010.i | 0.634887 | + | 0.366552i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 687131. | − | 396715.i | 1.49921 | − | 0.865569i | 0.499210 | − | 0.866481i | \(-0.333624\pi\) |
1.00000 | 0.000912440i | \(0.000290439\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 245222. | − | 423199.i | 0.531888 | − | 0.917921i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6811.56 | + | 11798.0i | 0.0146876 | + | 0.0254397i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46304.3 | − | 80201.3i | 0.0992612 | − | 0.171925i | −0.812118 | − | 0.583493i | \(-0.801685\pi\) |
0.911379 | + | 0.411568i | \(0.135019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 58522.3i | 0.124721i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11348.4 | 0.0240447 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 239474. | + | 138261.i | 0.504453 | + | 0.291246i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −162273. | + | 93688.2i | −0.339852 | + | 0.196213i | −0.660206 | − | 0.751084i | \(-0.729531\pi\) |
0.320355 | + | 0.947298i | \(0.396198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 78286.5 | + | 45362.9i | 0.163012 | + | 0.0944571i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 113308. | + | 196255.i | 0.234580 | + | 0.406304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 325003. | − | 562921.i | 0.668993 | − | 1.15873i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13881.4i | 0.0284105i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 326056. | 0.663522 | 0.331761 | − | 0.943363i | \(-0.392357\pi\) | ||||
0.331761 | + | 0.943363i | \(0.392357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 288564. | + | 166603.i | 0.583891 | + | 0.337110i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40223.8 | − | 23223.2i | 0.0809290 | − | 0.0467244i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19059.4 | − | 33132.0i | −0.0381303 | − | 0.0662841i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32372.6 | − | 56070.9i | −0.0643998 | − | 0.111544i | 0.832028 | − | 0.554734i | \(-0.187180\pi\) |
−0.896428 | + | 0.443190i | \(0.853847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −306086. | + | 530157.i | −0.605487 | + | 1.04873i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 505371.i | − | 0.994102i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −141813. | −0.277398 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −120261. | − | 69432.6i | −0.233930 | − | 0.135060i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −616355. | + | 355853.i | −1.19227 | + | 0.688355i | −0.958820 | − | 0.284014i | \(-0.908334\pi\) |
−0.233446 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 134882. | + | 212.011i | 0.259468 | + | 0.000407838i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48349.6 | + | 83744.0i | 0.0924946 | + | 0.160205i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 271191. | − | 469717.i | 0.515941 | − | 0.893635i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 763134.i | − | 1.44388i | −0.691954 | − | 0.721941i | \(-0.743250\pi\) | ||
0.691954 | − | 0.721941i | \(-0.256750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 436942. | 0.822183 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 599404. | + | 346066.i | 1.12172 | + | 0.647626i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17848.0 | + | 10304.6i | −0.0332187 | + | 0.0191788i | −0.516517 | − | 0.856277i | \(-0.672772\pi\) |
0.483299 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −82931.3 | − | 144690.i | −0.153513 | − | 0.267832i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 88868.0 | + | 153924.i | 0.163610 | + | 0.283381i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 393194. | − | 681032.i | 0.719976 | − | 1.24703i | −0.241033 | − | 0.970517i | \(-0.577486\pi\) |
0.961009 | − | 0.276518i | \(-0.0891805\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 95598.6i | 0.174107i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 740479. | 1.34133 | 0.670664 | − | 0.741761i | \(-0.266009\pi\) | ||||
0.670664 | + | 0.741761i | \(0.266009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −391372. | − | 225959.i | −0.705143 | − | 0.407114i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 148370. | − | 85661.3i | 0.265891 | − | 0.153512i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1144.42 | − | 728086.i | 0.00203997 | − | 1.29783i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 247292. | + | 428322.i | 0.438460 | + | 0.759436i | 0.997571 | − | 0.0696574i | \(-0.0221906\pi\) |
−0.559111 | + | 0.829093i | \(0.688857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45348.3 | − | 78545.5i | 0.0799780 | − | 0.138526i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.29885e6i | 2.27859i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −139399. | −0.243258 | −0.121629 | − | 0.992576i | \(-0.538812\pi\) | ||||
−0.121629 | + | 0.992576i | \(0.538812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23937.5 | + | 13820.3i | 0.0415524 | + | 0.0239903i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −207340. | + | 119708.i | −0.358025 | + | 0.206706i | −0.668214 | − | 0.743969i | \(-0.732941\pi\) |
0.310189 | + | 0.950675i | \(0.399608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −117085. | + | 67354.1i | −0.201119 | + | 0.115695i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 456265. | + | 790274.i | 0.779640 | + | 1.35038i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 79794.1 | − | 138208.i | 0.135638 | − | 0.234931i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 98701.5i | − | 0.166906i | −0.996512 | − | 0.0834528i | \(-0.973405\pi\) | ||
0.996512 | − | 0.0834528i | \(-0.0265948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −110051. | −0.185134 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −507921. | − | 293248.i | −0.850036 | − | 0.490769i | 0.0106268 | − | 0.999944i | \(-0.496617\pi\) |
−0.860663 | + | 0.509175i | \(0.829951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −779435. | + | 450007.i | −1.29771 | + | 0.749232i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28733.4 | + | 49587.5i | −0.0475932 | + | 0.0821354i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −553500. | − | 958690.i | −0.912100 | − | 1.57980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −89053.6 | + | 154245.i | −0.145999 | + | 0.252877i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 101775.i | 0.166003i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.33056e6 | −2.15921 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −129536. | − | 74787.4i | −0.209141 | − | 0.120748i | 0.391771 | − | 0.920063i | \(-0.371863\pi\) |
−0.600912 | + | 0.799315i | \(0.705196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30226.8 | − | 17451.4i | 0.0485554 | − | 0.0280335i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 265606. | + | 153905.i | 0.424507 | + | 0.245980i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −159085. | − | 275544.i | −0.252978 | − | 0.438171i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −70474.1 | + | 122065.i | −0.111505 | + | 0.193133i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 241092.i | − | 0.379547i | −0.981828 | − | 0.189774i | \(-0.939225\pi\) | ||
0.981828 | − | 0.189774i | \(-0.0607754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 175531. | 0.274954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −632256. | − | 365033.i | −0.985436 | − | 0.568941i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −77215.6 | + | 44580.4i | −0.119750 | + | 0.0691374i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 810215. | + | 1.40844e6i | 1.25028 | + | 2.17344i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36541.3 | − | 63291.3i | −0.0561095 | − | 0.0971845i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −100933. | + | 174820.i | −0.154218 | + | 0.267113i | −0.932774 | − | 0.360462i | \(-0.882619\pi\) |
0.778556 | + | 0.627575i | \(0.215952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16747e6i | 1.77503i | 0.460779 | + | 0.887515i | \(0.347570\pi\) | ||||
−0.460779 | + | 0.887515i | \(0.652430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −130389. | −0.197270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.18369e6 | − | 683402.i | −1.78206 | − | 1.02887i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.02082e6 | − | 589373.i | 1.52935 | − | 0.882970i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 524410. | + | 824.281i | 0.781814 | + | 0.00122887i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 324585. | + | 562198.i | 0.481551 | + | 0.834071i | 0.999776 | − | 0.0211734i | \(-0.00674022\pi\) |
−0.518225 | + | 0.855245i | \(0.673407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 245486. | − | 425193.i | 0.362432 | − | 0.627750i | −0.625929 | − | 0.779880i | \(-0.715280\pi\) |
0.988360 | + | 0.152130i | \(0.0486133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 49225.3i | − | 0.0723237i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −709017. | −1.03668 | −0.518341 | − | 0.855174i | \(-0.673450\pi\) | ||||
−0.518341 | + | 0.855174i | \(0.673450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 534645. | + | 308677.i | 0.777958 | + | 0.449154i | 0.835706 | − | 0.549177i | \(-0.185059\pi\) |
−0.0577480 | + | 0.998331i | \(0.518392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12269.3 | + | 7083.68i | −0.0177671 | + | 0.0102579i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1981.33 | − | 630262.i | 0.00285540 | − | 0.908304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −284583. | − | 492912.i | −0.408165 | − | 0.706963i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 84441.0 | − | 146256.i | 0.120532 | − | 0.208768i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 493961.i | 0.701728i | 0.936426 | + | 0.350864i | \(0.114112\pi\) | ||||
−0.936426 | + | 0.350864i | \(0.885888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −542019. | −0.766342 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −87232.4 | − | 50363.7i | −0.122750 | − | 0.0708699i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 383006. | − | 221129.i | 0.536404 | − | 0.309693i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1085.07 | + | 690322.i | −0.00151248 | + | 0.962243i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17724.8 | − | 30700.2i | −0.0245904 | − | 0.0425918i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 279190. | − | 483571.i | 0.385514 | − | 0.667730i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 505142.i | 0.694249i | 0.937819 | + | 0.347124i | \(0.112842\pi\) | ||||
−0.937819 | + | 0.347124i | \(0.887158\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.55410e6 | 2.12591 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −969980. | − | 560018.i | −1.32069 | − | 0.762501i | −0.336852 | − | 0.941557i | \(-0.609362\pi\) |
−0.983839 | + | 0.179056i | \(0.942696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −605141. | + | 349379.i | −0.820107 | + | 0.473489i | −0.850453 | − | 0.526050i | \(-0.823672\pi\) |
0.0303463 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 165043. | − | 94941.9i | 0.222633 | − | 0.128071i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −479533. | − | 830576.i | −0.643868 | − | 1.11521i | −0.984562 | − | 0.175038i | \(-0.943995\pi\) |
0.340693 | − | 0.940175i | \(-0.389338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 347264. | − | 601479.i | 0.464117 | − | 0.803875i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22933.1i | 0.0305088i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 183263. | 0.242681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 892127. | + | 515069.i | 1.17595 | + | 0.678937i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −678923. | + | 391976.i | −0.890824 | + | 0.514318i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 771172. | − | 1.33087e6i | 1.00724 | − | 1.73828i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 498442. | + | 863326.i | 0.648060 | + | 1.12247i | 0.983586 | + | 0.180442i | \(0.0577527\pi\) |
−0.335526 | + | 0.942031i | \(0.608914\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −102372. | + | 177314.i | −0.132497 | + | 0.229491i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 494568.i | 0.637198i | 0.947890 | + | 0.318599i | \(0.103212\pi\) | ||||
−0.947890 | + | 0.318599i | \(0.896788\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 887278. | 1.13799 | 0.568995 | − | 0.822341i | \(-0.307333\pi\) | ||||
0.568995 | + | 0.822341i | \(0.307333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 70447.1 | + | 40672.6i | 0.0899448 | + | 0.0519297i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 542062. | − | 312960.i | 0.688973 | − | 0.397779i | −0.114254 | − | 0.993452i | \(-0.536448\pi\) |
0.803227 | + | 0.595673i | \(0.203115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 545008. | + | 315804.i | 0.689604 | + | 0.399589i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −70165.8 | − | 121531.i | −0.0883833 | − | 0.153084i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 149470. | − | 258890.i | 0.187435 | − | 0.324647i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.41581e6i | − | 1.76750i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 160203. | 0.199106 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −237491. | − | 137115.i | −0.293851 | − | 0.169655i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −461309. | + | 266337.i | −0.568253 | + | 0.328081i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 101095. | + | 175739.i | 0.123981 | + | 0.215523i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.06159e6 | + | 1.83873e6i | 1.29616 | + | 2.24502i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 634131. | − | 1.09835e6i | 0.770840 | − | 1.33513i | −0.166263 | − | 0.986081i | \(-0.553170\pi\) |
0.937103 | − | 0.349052i | \(-0.113496\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 61263.9i | 0.0741442i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.09985e6 | −1.32525 | −0.662625 | − | 0.748951i | \(-0.730558\pi\) | ||||
−0.662625 | + | 0.748951i | \(0.730558\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44416.7 | − | 25644.0i | −0.0532850 | − | 0.0307641i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 140450. | − | 81088.8i | 0.167756 | − | 0.0968542i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.21152e6 | − | 1904.30i | −1.44076 | − | 0.00226463i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −430660. | − | 745925.i | −0.509922 | − | 0.883211i | −0.999934 | − | 0.0114950i | \(-0.996341\pi\) |
0.490012 | − | 0.871716i | \(-0.336992\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44075.3 | − | 76340.6i | 0.0519608 | − | 0.0899987i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.03229e6i | 1.21171i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −994418. | −1.16221 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −187226. | − | 108095.i | −0.217874 | − | 0.125790i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −326247. | + | 188359.i | −0.378021 | + | 0.218250i | −0.676957 | − | 0.736023i | \(-0.736702\pi\) |
0.298936 | + | 0.954273i | \(0.403368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −927884. | − | 539610.i | −1.07052 | − | 0.622560i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36319.2 | − | 62906.7i | −0.0417227 | − | 0.0722659i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 136590. | − | 236580.i | 0.156241 | − | 0.270617i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 417813.i | − | 0.475885i | −0.971279 | − | 0.237943i | \(-0.923527\pi\) | ||
0.971279 | − | 0.237943i | \(-0.0764731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 217103. | 0.246227 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 213031. | + | 122994.i | 0.240582 | + | 0.138900i | 0.615444 | − | 0.788180i | \(-0.288977\pi\) |
−0.374862 | + | 0.927081i | \(0.622310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60656e6 | + | 927546.i | −1.80665 | + | 1.04307i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −853.478 | + | 542985.i | −0.000955716 | + | 0.608029i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 722964. | + | 1.25221e6i | 0.806152 | + | 1.39630i | 0.915511 | + | 0.402294i | \(0.131787\pi\) |
−0.109359 | + | 0.994002i | \(0.534880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −258384. | + | 447533.i | −0.286901 | + | 0.496928i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 91495.4i | − | 0.101167i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 907377. | 0.999084 | 0.499542 | − | 0.866290i | \(-0.333502\pi\) | ||||
0.499542 | + | 0.866290i | \(0.333502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −170805. | − | 98614.2i | −0.187281 | − | 0.108127i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12989.3 | − | 7499.38i | 0.0141828 | − | 0.00818845i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56156.9 | + | 32304.6i | −0.0610612 | + | 0.0351259i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −234235. | − | 405707.i | −0.253633 | − | 0.439305i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −583491. | + | 1.01064e6i | −0.629189 | + | 1.08979i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.30132e6i | − | 1.39742i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50286.2 | −0.0537770 | −0.0268885 | − | 0.999638i | \(-0.508560\pi\) | ||||
−0.0268885 | + | 0.999638i | \(0.508560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −159483. | − | 92077.6i | −0.169851 | − | 0.0980633i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 677500. | − | 391155.i | 0.718573 | − | 0.414868i | −0.0956544 | − | 0.995415i | \(-0.530494\pi\) |
0.814227 | + | 0.580546i | \(0.197161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −125776. | + | 217062.i | −0.132853 | + | 0.229275i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −142652. | − | 247081.i | −0.150062 | − | 0.259914i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −638714. | + | 1.10629e6i | −0.669141 | + | 1.15899i | 0.309004 | + | 0.951061i | \(0.400004\pi\) |
−0.978145 | + | 0.207925i | \(0.933329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 218557.i | 0.228033i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 216501. | 0.224968 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.36250e6 | + | 786638.i | 1.41003 | + | 0.814081i | 0.995391 | − | 0.0959049i | \(-0.0305745\pi\) |
0.414639 | + | 0.909986i | \(0.363908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 912930. | − | 527080.i | 0.940947 | − | 0.543256i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 44488.2 | + | 25778.6i | 0.0456679 | + | 0.0264621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −987661. | − | 1.71068e6i | −1.00975 | − | 1.74894i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −162173. | + | 280892.i | −0.165132 | + | 0.286017i | −0.936702 | − | 0.350127i | \(-0.886138\pi\) |
0.771570 | + | 0.636144i | \(0.219472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1552.30i | 0.00157427i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.16099e6 | −2.18276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.57129e6 | − | 907185.i | −1.58076 | − | 0.912652i | −0.994748 | − | 0.102350i | \(-0.967364\pi\) |
−0.586012 | − | 0.810303i | \(-0.699303\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 161597. | − | 93298.2i | 0.161921 | − | 0.0934851i |
(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 | 28.5.h.a.17.2 | yes | 6 | |
3.2 | odd | 2 | 252.5.z.f.73.1 | 6 | |||
4.3 | odd | 2 | 112.5.s.c.17.2 | 6 | |||
5.2 | odd | 4 | 700.5.o.a.549.3 | 12 | |||
5.3 | odd | 4 | 700.5.o.a.549.4 | 12 | |||
5.4 | even | 2 | 700.5.s.a.101.2 | 6 | |||
7.2 | even | 3 | 196.5.h.c.117.2 | 6 | |||
7.3 | odd | 6 | 196.5.b.a.97.3 | 6 | |||
7.4 | even | 3 | 196.5.b.a.97.4 | 6 | |||
7.5 | odd | 6 | inner | 28.5.h.a.5.2 | ✓ | 6 | |
7.6 | odd | 2 | 196.5.h.c.129.2 | 6 | |||
21.5 | even | 6 | 252.5.z.f.145.1 | 6 | |||
28.3 | even | 6 | 784.5.c.e.97.4 | 6 | |||
28.11 | odd | 6 | 784.5.c.e.97.3 | 6 | |||
28.19 | even | 6 | 112.5.s.c.33.2 | 6 | |||
35.12 | even | 12 | 700.5.o.a.649.4 | 12 | |||
35.19 | odd | 6 | 700.5.s.a.201.2 | 6 | |||
35.33 | even | 12 | 700.5.o.a.649.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.5.h.a.5.2 | ✓ | 6 | 7.5 | odd | 6 | inner | |
28.5.h.a.17.2 | yes | 6 | 1.1 | even | 1 | trivial | |
112.5.s.c.17.2 | 6 | 4.3 | odd | 2 | |||
112.5.s.c.33.2 | 6 | 28.19 | even | 6 | |||
196.5.b.a.97.3 | 6 | 7.3 | odd | 6 | |||
196.5.b.a.97.4 | 6 | 7.4 | even | 3 | |||
196.5.h.c.117.2 | 6 | 7.2 | even | 3 | |||
196.5.h.c.129.2 | 6 | 7.6 | odd | 2 | |||
252.5.z.f.73.1 | 6 | 3.2 | odd | 2 | |||
252.5.z.f.145.1 | 6 | 21.5 | even | 6 | |||
700.5.o.a.549.3 | 12 | 5.2 | odd | 4 | |||
700.5.o.a.549.4 | 12 | 5.3 | odd | 4 | |||
700.5.o.a.649.3 | 12 | 35.33 | even | 12 | |||
700.5.o.a.649.4 | 12 | 35.12 | even | 12 | |||
700.5.s.a.101.2 | 6 | 5.4 | even | 2 | |||
700.5.s.a.201.2 | 6 | 35.19 | odd | 6 | |||
784.5.c.e.97.3 | 6 | 28.11 | odd | 6 | |||
784.5.c.e.97.4 | 6 | 28.3 | even | 6 |