Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (of order \(2\), degree \(1\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.12 | ||
Root | \(0.854122 + 1.47938i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.c.601.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 6.06258 | − | 3.49930i | 0.866083 | − | 0.499900i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.5400 | −1.59455 | −0.797275 | − | 0.603617i | \(-0.793726\pi\) | ||||
−0.797275 | + | 0.603617i | \(0.793726\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 17.6164i | − | 1.35510i | −0.735475 | − | 0.677552i | \(-0.763041\pi\) | ||
0.735475 | − | 0.677552i | \(-0.236959\pi\) | |||||||
\(14\) | 8.57378 | − | 4.94876i | 0.612413 | − | 0.353483i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 14.0819i | − | 0.828344i | −0.910199 | − | 0.414172i | \(-0.864071\pi\) | ||
0.910199 | − | 0.414172i | \(-0.135929\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | − | 16.6057i | − | 0.873983i | −0.899466 | − | 0.436992i | \(-0.856044\pi\) | ||
0.899466 | − | 0.436992i | \(-0.143956\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.06097 | + | 10.5007i | 0.288618 | + | 0.500033i | ||||
\(22\) | −24.8054 | −1.12752 | ||||||||
\(23\) | 15.5368 | 0.675514 | 0.337757 | − | 0.941233i | \(-0.390332\pi\) | ||||
0.337757 | + | 0.941233i | \(0.390332\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 24.9133i | − | 0.958203i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 12.1252 | − | 6.99861i | 0.433041 | − | 0.249950i | ||||
\(29\) | 36.9225 | 1.27319 | 0.636594 | − | 0.771199i | \(-0.280343\pi\) | ||||
0.636594 | + | 0.771199i | \(0.280343\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 54.2245i | − | 1.74918i | −0.484865 | − | 0.874589i | \(-0.661131\pi\) | ||
0.484865 | − | 0.874589i | \(-0.338869\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 30.3802i | − | 0.920613i | ||||||
\(34\) | − | 19.9147i | − | 0.585728i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −45.0739 | −1.21821 | −0.609107 | − | 0.793088i | \(-0.708472\pi\) | ||||
−0.609107 | + | 0.793088i | \(0.708472\pi\) | |||||||
\(38\) | − | 23.4840i | − | 0.618000i | ||||||
\(39\) | 30.5124 | 0.782370 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.20567i | − | 0.0294067i | −0.999892 | − | 0.0147034i | \(-0.995320\pi\) | ||
0.999892 | − | 0.0147034i | \(-0.00468039\pi\) | |||||||
\(42\) | 8.57151 | + | 14.8502i | 0.204084 | + | 0.353577i | ||||
\(43\) | −50.7479 | −1.18018 | −0.590091 | − | 0.807336i | \(-0.700908\pi\) | ||||
−0.590091 | + | 0.807336i | \(0.700908\pi\) | |||||||
\(44\) | −35.0801 | −0.797275 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.9724 | 0.477661 | ||||||||
\(47\) | 91.7612i | 1.95237i | 0.216949 | + | 0.976183i | \(0.430389\pi\) | ||||
−0.216949 | + | 0.976183i | \(0.569611\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 24.5098 | − | 42.4296i | 0.500199 | − | 0.865910i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.3905 | 0.478245 | ||||||||
\(52\) | − | 35.2327i | − | 0.677552i | ||||||
\(53\) | 51.5658 | 0.972939 | 0.486470 | − | 0.873697i | \(-0.338284\pi\) | ||||
0.486470 | + | 0.873697i | \(0.338284\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17.1476 | − | 9.89752i | 0.306207 | − | 0.176742i | ||||
\(57\) | 28.7619 | 0.504595 | ||||||||
\(58\) | 52.2163 | 0.900281 | ||||||||
\(59\) | − | 14.8313i | − | 0.251378i | −0.992070 | − | 0.125689i | \(-0.959886\pi\) | ||
0.992070 | − | 0.125689i | \(-0.0401142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 91.2041i | 1.49515i | 0.664178 | + | 0.747575i | \(0.268782\pi\) | ||||
−0.664178 | + | 0.747575i | \(0.731218\pi\) | |||||||
\(62\) | − | 76.6850i | − | 1.23686i | ||||||
\(63\) | −18.1877 | + | 10.4979i | −0.288694 | + | 0.166633i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 42.9641i | − | 0.650972i | ||||||
\(67\) | 5.61477 | 0.0838025 | 0.0419013 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0419013 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(68\) | − | 28.1637i | − | 0.414172i | ||||||
\(69\) | 26.9106i | 0.390008i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.8420 | 1.13862 | 0.569310 | − | 0.822123i | \(-0.307210\pi\) | ||||
0.569310 | + | 0.822123i | \(0.307210\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | − | 91.0434i | − | 1.24717i | −0.781756 | − | 0.623585i | \(-0.785676\pi\) | ||
0.781756 | − | 0.623585i | \(-0.214324\pi\) | |||||||
\(74\) | −63.7442 | −0.861408 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 33.2114i | − | 0.436992i | ||||||
\(77\) | −106.338 | + | 61.3779i | −1.38101 | + | 0.797116i | ||||
\(78\) | 43.1511 | 0.553219 | ||||||||
\(79\) | −28.5067 | −0.360845 | −0.180422 | − | 0.983589i | \(-0.557746\pi\) | ||||
−0.180422 | + | 0.983589i | \(0.557746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 1.70508i | − | 0.0207937i | ||||||
\(83\) | − | 50.3930i | − | 0.607145i | −0.952808 | − | 0.303573i | \(-0.901821\pi\) | ||
0.952808 | − | 0.303573i | \(-0.0981795\pi\) | |||||||
\(84\) | 12.1219 | + | 21.0014i | 0.144309 | + | 0.250017i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −71.7683 | −0.834515 | ||||||||
\(87\) | 63.9516i | 0.735076i | ||||||||
\(88\) | −49.6107 | −0.563758 | ||||||||
\(89\) | − | 76.5302i | − | 0.859890i | −0.902855 | − | 0.429945i | \(-0.858533\pi\) | ||
0.902855 | − | 0.429945i | \(-0.141467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61.6450 | − | 106.801i | −0.677417 | − | 1.17363i | ||||
\(92\) | 31.0736 | 0.337757 | ||||||||
\(93\) | 93.9196 | 1.00989 | ||||||||
\(94\) | 129.770i | 1.38053i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 125.356i | 1.29233i | 0.763198 | + | 0.646164i | \(0.223628\pi\) | ||||
−0.763198 | + | 0.646164i | \(0.776372\pi\) | |||||||
\(98\) | 34.6620 | − | 60.0045i | 0.353694 | − | 0.612291i | ||||
\(99\) | 52.6201 | 0.531516 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 133.915i | − | 1.32589i | −0.748667 | − | 0.662946i | \(-0.769306\pi\) | ||
0.748667 | − | 0.662946i | \(-0.230694\pi\) | |||||||
\(102\) | 34.4934 | 0.338170 | ||||||||
\(103\) | − | 71.1180i | − | 0.690466i | −0.938517 | − | 0.345233i | \(-0.887800\pi\) | ||
0.938517 | − | 0.345233i | \(-0.112200\pi\) | |||||||
\(104\) | − | 49.8266i | − | 0.479102i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.9250 | 0.687972 | ||||||||
\(107\) | 9.18582 | 0.0858488 | 0.0429244 | − | 0.999078i | \(-0.486333\pi\) | ||||
0.0429244 | + | 0.999078i | \(0.486333\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 110.684 | 1.01545 | 0.507726 | − | 0.861519i | \(-0.330486\pi\) | ||||
0.507726 | + | 0.861519i | \(0.330486\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 78.0703i | − | 0.703336i | ||||||
\(112\) | 24.2503 | − | 13.9972i | 0.216521 | − | 0.124975i | ||||
\(113\) | 168.521 | 1.49134 | 0.745668 | − | 0.666317i | \(-0.232130\pi\) | ||||
0.745668 | + | 0.666317i | \(0.232130\pi\) | |||||||
\(114\) | 40.6755 | 0.356802 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 73.8450 | 0.636594 | ||||||||
\(117\) | 52.8491i | 0.451701i | ||||||||
\(118\) | − | 20.9747i | − | 0.177751i | ||||||
\(119\) | −49.2767 | − | 85.3723i | −0.414090 | − | 0.717415i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 186.653 | 1.54259 | ||||||||
\(122\) | 128.982i | 1.05723i | ||||||||
\(123\) | 2.08829 | 0.0169780 | ||||||||
\(124\) | − | 108.449i | − | 0.874589i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −25.7213 | + | 14.8463i | −0.204138 | + | 0.117828i | ||||
\(127\) | −98.7378 | −0.777463 | −0.388731 | − | 0.921351i | \(-0.627087\pi\) | ||||
−0.388731 | + | 0.921351i | \(0.627087\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 87.8979i | − | 0.681379i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.20765i | − | 0.0397531i | −0.999802 | − | 0.0198765i | \(-0.993673\pi\) | ||
0.999802 | − | 0.0198765i | \(-0.00632732\pi\) | |||||||
\(132\) | − | 60.7605i | − | 0.460307i | ||||||
\(133\) | −58.1083 | − | 100.673i | −0.436905 | − | 0.756942i | ||||
\(134\) | 7.94048 | 0.0592573 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 39.8295i | − | 0.292864i | ||||||
\(137\) | −4.91235 | −0.0358566 | −0.0179283 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179283 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(138\) | 38.0573i | 0.275777i | ||||||||
\(139\) | − | 13.5723i | − | 0.0976424i | −0.998808 | − | 0.0488212i | \(-0.984454\pi\) | ||
0.998808 | − | 0.0488212i | \(-0.0155465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −158.935 | −1.12720 | ||||||||
\(142\) | 114.328 | 0.805126 | ||||||||
\(143\) | 308.992i | 2.16078i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 128.755i | − | 0.881882i | ||||||
\(147\) | 73.4902 | + | 42.4521i | 0.499934 | + | 0.288790i | ||||
\(148\) | −90.1479 | −0.609107 | ||||||||
\(149\) | −154.960 | −1.04000 | −0.520001 | − | 0.854165i | \(-0.674069\pi\) | ||||
−0.520001 | + | 0.854165i | \(0.674069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 197.940 | 1.31086 | 0.655432 | − | 0.755254i | \(-0.272487\pi\) | ||||
0.655432 | + | 0.755254i | \(0.272487\pi\) | |||||||
\(152\) | − | 46.9680i | − | 0.309000i | ||||||
\(153\) | 42.2456i | 0.276115i | ||||||||
\(154\) | −150.384 | + | 86.8015i | −0.976523 | + | 0.563646i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 61.0248 | 0.391185 | ||||||||
\(157\) | 189.082i | 1.20434i | 0.798367 | + | 0.602171i | \(0.205697\pi\) | ||||
−0.798367 | + | 0.602171i | \(0.794303\pi\) | |||||||
\(158\) | −40.3146 | −0.255156 | ||||||||
\(159\) | 89.3146i | 0.561727i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 94.1932 | − | 54.3681i | 0.585051 | − | 0.337690i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −269.128 | −1.65109 | −0.825545 | − | 0.564336i | \(-0.809132\pi\) | ||||
−0.825545 | + | 0.564336i | \(0.809132\pi\) | |||||||
\(164\) | − | 2.41135i | − | 0.0147034i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 71.2665i | − | 0.429316i | ||||||
\(167\) | − | 125.338i | − | 0.750526i | −0.926918 | − | 0.375263i | \(-0.877552\pi\) | ||
0.926918 | − | 0.375263i | \(-0.122448\pi\) | |||||||
\(168\) | 17.1430 | + | 29.7005i | 0.102042 | + | 0.176788i | ||||
\(169\) | −141.336 | −0.836308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 49.8171i | 0.291328i | ||||||||
\(172\) | −101.496 | −0.590091 | ||||||||
\(173\) | 196.074i | 1.13338i | 0.823932 | + | 0.566688i | \(0.191776\pi\) | ||||
−0.823932 | + | 0.566688i | \(0.808224\pi\) | |||||||
\(174\) | 90.4412i | 0.519777i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −70.1602 | −0.398637 | ||||||||
\(177\) | 25.6886 | 0.145133 | ||||||||
\(178\) | − | 108.230i | − | 0.608034i | ||||||
\(179\) | 255.467 | 1.42719 | 0.713596 | − | 0.700557i | \(-0.247065\pi\) | ||||
0.713596 | + | 0.700557i | \(0.247065\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 253.527i | 1.40070i | 0.713799 | + | 0.700351i | \(0.246973\pi\) | ||||
−0.713799 | + | 0.700351i | \(0.753027\pi\) | |||||||
\(182\) | −87.1792 | − | 151.039i | −0.479006 | − | 0.829884i | ||||
\(183\) | −157.970 | −0.863225 | ||||||||
\(184\) | 43.9448 | 0.238830 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 132.822 | 0.714099 | ||||||||
\(187\) | 246.996i | 1.32084i | ||||||||
\(188\) | 183.522i | 0.976183i | ||||||||
\(189\) | −18.1829 | − | 31.5021i | −0.0962059 | − | 0.166678i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −286.274 | −1.49882 | −0.749410 | − | 0.662107i | \(-0.769663\pi\) | ||||
−0.749410 | + | 0.662107i | \(0.769663\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −198.340 | −1.02767 | −0.513834 | − | 0.857889i | \(-0.671775\pi\) | ||||
−0.513834 | + | 0.857889i | \(0.671775\pi\) | |||||||
\(194\) | 177.280i | 0.913814i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.0195 | − | 84.8592i | 0.250099 | − | 0.432955i | ||||
\(197\) | −253.374 | −1.28616 | −0.643080 | − | 0.765799i | \(-0.722344\pi\) | ||||
−0.643080 | + | 0.765799i | \(0.722344\pi\) | |||||||
\(198\) | 74.4161 | 0.375839 | ||||||||
\(199\) | − | 203.091i | − | 1.02056i | −0.860009 | − | 0.510278i | \(-0.829542\pi\) | ||
0.860009 | − | 0.510278i | \(-0.170458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.72507i | 0.0483834i | ||||||||
\(202\) | − | 189.384i | − | 0.937547i | ||||||
\(203\) | 223.845 | − | 129.203i | 1.10269 | − | 0.636468i | ||||
\(204\) | 48.7810 | 0.239122 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 100.576i | − | 0.488233i | ||||||
\(207\) | −46.6105 | −0.225171 | ||||||||
\(208\) | − | 70.4654i | − | 0.338776i | ||||||
\(209\) | 291.264i | 1.39361i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 39.9211 | 0.189200 | 0.0945998 | − | 0.995515i | \(-0.469843\pi\) | ||||
0.0945998 | + | 0.995515i | \(0.469843\pi\) | |||||||
\(212\) | 103.132 | 0.486470 | ||||||||
\(213\) | 140.022i | 0.657382i | ||||||||
\(214\) | 12.9907 | 0.0607043 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −189.748 | − | 328.740i | −0.874415 | − | 1.51493i | ||||
\(218\) | 156.531 | 0.718033 | ||||||||
\(219\) | 157.692 | 0.720054 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −248.071 | −1.12249 | ||||||||
\(222\) | − | 110.408i | − | 0.497334i | ||||||
\(223\) | 220.520i | 0.988880i | 0.869212 | + | 0.494440i | \(0.164627\pi\) | ||||
−0.869212 | + | 0.494440i | \(0.835373\pi\) | |||||||
\(224\) | 34.2951 | − | 19.7950i | 0.153103 | − | 0.0883708i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 238.325 | 1.05453 | ||||||||
\(227\) | 287.672i | 1.26728i | 0.773629 | + | 0.633639i | \(0.218440\pi\) | ||||
−0.773629 | + | 0.633639i | \(0.781560\pi\) | |||||||
\(228\) | 57.5238 | 0.252297 | ||||||||
\(229\) | − | 167.481i | − | 0.731358i | −0.930741 | − | 0.365679i | \(-0.880837\pi\) | ||
0.930741 | − | 0.365679i | \(-0.119163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −106.310 | − | 184.183i | −0.460215 | − | 0.797327i | ||||
\(232\) | 104.433 | 0.450140 | ||||||||
\(233\) | 11.6077 | 0.0498185 | 0.0249092 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249092 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(234\) | 74.7399i | 0.319401i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 29.6626i | − | 0.125689i | ||||||
\(237\) | − | 49.3751i | − | 0.208334i | ||||||
\(238\) | −69.6877 | − | 120.735i | −0.292806 | − | 0.507289i | ||||
\(239\) | −17.5810 | −0.0735608 | −0.0367804 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367804 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 46.5601i | − | 0.193196i | −0.995323 | − | 0.0965978i | \(-0.969204\pi\) | ||
0.995323 | − | 0.0965978i | \(-0.0307960\pi\) | |||||||
\(242\) | 263.967 | 1.09077 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 182.408i | 0.747575i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.95329 | 0.0120052 | ||||||||
\(247\) | −292.532 | −1.18434 | ||||||||
\(248\) | − | 153.370i | − | 0.618428i | ||||||
\(249\) | 87.2833 | 0.350535 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 227.785i | 0.907510i | 0.891126 | + | 0.453755i | \(0.149916\pi\) | ||||
−0.891126 | + | 0.453755i | \(0.850084\pi\) | |||||||
\(252\) | −36.3755 | + | 20.9958i | −0.144347 | + | 0.0833167i | ||||
\(253\) | −272.516 | −1.07714 | ||||||||
\(254\) | −139.636 | −0.549749 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 91.2755i | − | 0.355158i | −0.984107 | − | 0.177579i | \(-0.943174\pi\) | ||
0.984107 | − | 0.177579i | \(-0.0568265\pi\) | |||||||
\(258\) | − | 124.306i | − | 0.481808i | ||||||
\(259\) | −273.264 | + | 157.727i | −1.05507 | + | 0.608986i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −110.767 | −0.424396 | ||||||||
\(262\) | − | 7.36474i | − | 0.0281097i | ||||||
\(263\) | 108.528 | 0.412653 | 0.206326 | − | 0.978483i | \(-0.433849\pi\) | ||||
0.206326 | + | 0.978483i | \(0.433849\pi\) | |||||||
\(264\) | − | 85.9283i | − | 0.325486i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −82.1776 | − | 142.374i | −0.308938 | − | 0.535239i | ||||
\(267\) | 132.554 | 0.496458 | ||||||||
\(268\) | 11.2295 | 0.0419013 | ||||||||
\(269\) | − | 351.607i | − | 1.30709i | −0.756888 | − | 0.653545i | \(-0.773281\pi\) | ||
0.756888 | − | 0.653545i | \(-0.226719\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 387.665i | 1.43050i | 0.698869 | + | 0.715250i | \(0.253687\pi\) | ||||
−0.698869 | + | 0.715250i | \(0.746313\pi\) | |||||||
\(272\) | − | 56.3274i | − | 0.207086i | ||||||
\(273\) | 184.984 | − | 106.772i | 0.677597 | − | 0.391107i | ||||
\(274\) | −6.94711 | −0.0253544 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 53.8211i | 0.195004i | ||||||||
\(277\) | 503.195 | 1.81659 | 0.908293 | − | 0.418334i | \(-0.137386\pi\) | ||||
0.908293 | + | 0.418334i | \(0.137386\pi\) | |||||||
\(278\) | − | 19.1941i | − | 0.0690436i | ||||||
\(279\) | 162.674i | 0.583059i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 106.871 | 0.380323 | 0.190161 | − | 0.981753i | \(-0.439099\pi\) | ||||
0.190161 | + | 0.981753i | \(0.439099\pi\) | |||||||
\(282\) | −224.768 | −0.797050 | ||||||||
\(283\) | 85.3646i | 0.301642i | 0.988561 | + | 0.150821i | \(0.0481916\pi\) | ||||
−0.988561 | + | 0.150821i | \(0.951808\pi\) | |||||||
\(284\) | 161.684 | 0.569310 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 436.980i | 1.52790i | ||||||||
\(287\) | −4.21902 | − | 7.30950i | −0.0147004 | − | 0.0254686i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 90.7015 | 0.313846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −217.123 | −0.746126 | ||||||||
\(292\) | − | 182.087i | − | 0.623585i | ||||||
\(293\) | 155.961i | 0.532289i | 0.963933 | + | 0.266145i | \(0.0857499\pi\) | ||||
−0.963933 | + | 0.266145i | \(0.914250\pi\) | |||||||
\(294\) | 103.931 | + | 60.0364i | 0.353506 | + | 0.204205i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −127.488 | −0.430704 | ||||||||
\(297\) | 91.1407i | 0.306871i | ||||||||
\(298\) | −219.147 | −0.735393 | ||||||||
\(299\) | − | 273.702i | − | 0.915392i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −307.663 | + | 177.582i | −1.02214 | + | 0.589974i | ||||
\(302\) | 279.930 | 0.926921 | ||||||||
\(303\) | 231.948 | 0.765504 | ||||||||
\(304\) | − | 66.4227i | − | 0.218496i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 59.7442i | 0.195243i | ||||||||
\(307\) | − | 495.927i | − | 1.61540i | −0.589595 | − | 0.807699i | \(-0.700713\pi\) | ||
0.589595 | − | 0.807699i | \(-0.299287\pi\) | |||||||
\(308\) | −212.676 | + | 122.756i | −0.690506 | + | 0.398558i | ||||
\(309\) | 123.180 | 0.398641 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 270.262i | 0.869008i | 0.900670 | + | 0.434504i | \(0.143076\pi\) | ||||
−0.900670 | + | 0.434504i | \(0.856924\pi\) | |||||||
\(312\) | 86.3022 | 0.276610 | ||||||||
\(313\) | 23.6843i | 0.0756688i | 0.999284 | + | 0.0378344i | \(0.0120459\pi\) | ||||
−0.999284 | + | 0.0378344i | \(0.987954\pi\) | |||||||
\(314\) | 267.402i | 0.851598i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −57.0135 | −0.180422 | ||||||||
\(317\) | 3.53825 | 0.0111617 | 0.00558083 | − | 0.999984i | \(-0.498224\pi\) | ||||
0.00558083 | + | 0.999984i | \(0.498224\pi\) | |||||||
\(318\) | 126.310i | 0.397201i | ||||||||
\(319\) | −647.622 | −2.03016 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.9103i | 0.0495648i | ||||||||
\(322\) | 133.209 | − | 76.8880i | 0.413694 | − | 0.238783i | ||||
\(323\) | −233.839 | −0.723959 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −380.604 | −1.16750 | ||||||||
\(327\) | 191.711i | 0.586272i | ||||||||
\(328\) | − | 3.41016i | − | 0.0103968i | ||||||
\(329\) | 321.100 | + | 556.310i | 0.975989 | + | 1.69091i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −341.340 | −1.03124 | −0.515619 | − | 0.856818i | \(-0.672438\pi\) | ||||
−0.515619 | + | 0.856818i | \(0.672438\pi\) | |||||||
\(332\) | − | 100.786i | − | 0.303573i | ||||||
\(333\) | 135.222 | 0.406071 | ||||||||
\(334\) | − | 177.254i | − | 0.530702i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 24.2439 | + | 42.0028i | 0.0721544 | + | 0.125008i | ||||
\(337\) | −92.5173 | −0.274532 | −0.137266 | − | 0.990534i | \(-0.543832\pi\) | ||||
−0.137266 | + | 0.990534i | \(0.543832\pi\) | |||||||
\(338\) | −199.879 | −0.591359 | ||||||||
\(339\) | 291.887i | 0.861024i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 951.100i | 2.78915i | ||||||||
\(342\) | 70.4520i | 0.206000i | ||||||||
\(343\) | 0.118226 | − | 343.000i | 0.000344681 | − | 1.00000i | ||||
\(344\) | −143.537 | −0.417258 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 277.291i | 0.801418i | ||||||||
\(347\) | −354.217 | −1.02080 | −0.510399 | − | 0.859938i | \(-0.670502\pi\) | ||||
−0.510399 | + | 0.859938i | \(0.670502\pi\) | |||||||
\(348\) | 127.903i | 0.367538i | ||||||||
\(349\) | − | 149.606i | − | 0.428670i | −0.976760 | − | 0.214335i | \(-0.931242\pi\) | ||
0.976760 | − | 0.214335i | \(-0.0687584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −91.5373 | −0.260790 | ||||||||
\(352\) | −99.2214 | −0.281879 | ||||||||
\(353\) | − | 326.247i | − | 0.924213i | −0.886824 | − | 0.462107i | \(-0.847094\pi\) | ||
0.886824 | − | 0.462107i | \(-0.152906\pi\) | |||||||
\(354\) | 36.3292 | 0.102625 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 153.060i | − | 0.429945i | ||||||
\(357\) | 147.869 | − | 85.3497i | 0.414200 | − | 0.239075i | ||||
\(358\) | 361.285 | 1.00918 | ||||||||
\(359\) | −296.371 | −0.825545 | −0.412772 | − | 0.910834i | \(-0.635439\pi\) | ||||
−0.412772 | + | 0.910834i | \(0.635439\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 85.2512 | 0.236153 | ||||||||
\(362\) | 358.541i | 0.990445i | ||||||||
\(363\) | 323.292i | 0.890613i | ||||||||
\(364\) | −123.290 | − | 213.601i | −0.338709 | − | 0.586816i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −223.404 | −0.610392 | ||||||||
\(367\) | − | 284.903i | − | 0.776303i | −0.921596 | − | 0.388151i | \(-0.873114\pi\) | ||
0.921596 | − | 0.388151i | \(-0.126886\pi\) | |||||||
\(368\) | 62.1473 | 0.168879 | ||||||||
\(369\) | 3.61702i | 0.00980223i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 312.622 | − | 180.444i | 0.842646 | − | 0.486373i | ||||
\(372\) | 187.839 | 0.504944 | ||||||||
\(373\) | 163.961 | 0.439573 | 0.219787 | − | 0.975548i | \(-0.429464\pi\) | ||||
0.219787 | + | 0.975548i | \(0.429464\pi\) | |||||||
\(374\) | 349.305i | 0.933972i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 259.540i | 0.690266i | ||||||||
\(377\) | − | 650.440i | − | 1.72530i | ||||||
\(378\) | −25.7145 | − | 44.5507i | −0.0680278 | − | 0.117859i | ||||
\(379\) | −178.496 | −0.470966 | −0.235483 | − | 0.971878i | \(-0.575667\pi\) | ||||
−0.235483 | + | 0.971878i | \(0.575667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 171.019i | − | 0.448868i | ||||||
\(382\) | −404.853 | −1.05983 | ||||||||
\(383\) | 522.144i | 1.36330i | 0.731678 | + | 0.681650i | \(0.238737\pi\) | ||||
−0.731678 | + | 0.681650i | \(0.761263\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −280.495 | −0.726672 | ||||||||
\(387\) | 152.244 | 0.393394 | ||||||||
\(388\) | 250.712i | 0.646164i | ||||||||
\(389\) | 582.959 | 1.49861 | 0.749305 | − | 0.662225i | \(-0.230388\pi\) | ||||
0.749305 | + | 0.662225i | \(0.230388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 218.787i | − | 0.559558i | ||||||
\(392\) | 69.3240 | − | 120.009i | 0.176847 | − | 0.306146i | ||||
\(393\) | 9.01992 | 0.0229515 | ||||||||
\(394\) | −358.324 | −0.909453 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 105.240 | 0.265758 | ||||||||
\(397\) | 431.754i | 1.08754i | 0.839234 | + | 0.543770i | \(0.183004\pi\) | ||||
−0.839234 | + | 0.543770i | \(0.816996\pi\) | |||||||
\(398\) | − | 287.214i | − | 0.721643i | ||||||
\(399\) | 174.371 | − | 100.647i | 0.437021 | − | 0.252247i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 261.939 | 0.653216 | 0.326608 | − | 0.945160i | \(-0.394094\pi\) | ||||
0.326608 | + | 0.945160i | \(0.394094\pi\) | |||||||
\(402\) | 13.7533i | 0.0342122i | ||||||||
\(403\) | −955.238 | −2.37032 | ||||||||
\(404\) | − | 267.830i | − | 0.662946i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 316.565 | − | 182.721i | 0.779718 | − | 0.450051i | ||||
\(407\) | 790.598 | 1.94250 | ||||||||
\(408\) | 68.9867 | 0.169085 | ||||||||
\(409\) | − | 443.220i | − | 1.08367i | −0.840485 | − | 0.541834i | \(-0.817730\pi\) | ||
0.840485 | − | 0.541834i | \(-0.182270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8.50844i | − | 0.0207018i | ||||||
\(412\) | − | 142.236i | − | 0.345233i | ||||||
\(413\) | −51.8993 | − | 89.9161i | −0.125664 | − | 0.217714i | ||||
\(414\) | −65.9172 | −0.159220 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 99.6532i | − | 0.239551i | ||||||
\(417\) | 23.5079 | 0.0563739 | ||||||||
\(418\) | 411.910i | 0.985431i | ||||||||
\(419\) | 255.406i | 0.609561i | 0.952423 | + | 0.304781i | \(0.0985832\pi\) | ||||
−0.952423 | + | 0.304781i | \(0.901417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 317.879 | 0.755057 | 0.377529 | − | 0.925998i | \(-0.376774\pi\) | ||||
0.377529 | + | 0.925998i | \(0.376774\pi\) | |||||||
\(422\) | 56.4570 | 0.133784 | ||||||||
\(423\) | − | 275.284i | − | 0.650789i | ||||||
\(424\) | 145.850 | 0.343986 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 198.022i | 0.464840i | ||||||||
\(427\) | 319.151 | + | 552.932i | 0.747426 | + | 1.29492i | ||||
\(428\) | 18.3716 | 0.0429244 | ||||||||
\(429\) | −535.189 | −1.24753 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 83.1442 | 0.192910 | 0.0964550 | − | 0.995337i | \(-0.469250\pi\) | ||||
0.0964550 | + | 0.995337i | \(0.469250\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | − | 501.302i | − | 1.15774i | −0.815419 | − | 0.578871i | \(-0.803494\pi\) | ||
0.815419 | − | 0.578871i | \(-0.196506\pi\) | |||||||
\(434\) | −268.344 | − | 464.909i | −0.618305 | − | 1.07122i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 221.369 | 0.507726 | ||||||||
\(437\) | − | 258.000i | − | 0.590388i | ||||||
\(438\) | 223.010 | 0.509155 | ||||||||
\(439\) | 10.1601i | 0.0231438i | 0.999933 | + | 0.0115719i | \(0.00368354\pi\) | ||||
−0.999933 | + | 0.0115719i | \(0.996316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −73.5293 | + | 127.289i | −0.166733 | + | 0.288637i | ||||
\(442\) | −350.825 | −0.793722 | ||||||||
\(443\) | 201.289 | 0.454377 | 0.227189 | − | 0.973851i | \(-0.427047\pi\) | ||||
0.227189 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(444\) | − | 156.141i | − | 0.351668i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 311.863i | 0.699244i | ||||||||
\(447\) | − | 268.399i | − | 0.600446i | ||||||
\(448\) | 48.5006 | − | 27.9944i | 0.108260 | − | 0.0624876i | ||||
\(449\) | 602.966 | 1.34291 | 0.671454 | − | 0.741046i | \(-0.265670\pi\) | ||||
0.671454 | + | 0.741046i | \(0.265670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.1476i | 0.0468904i | ||||||||
\(452\) | 337.042 | 0.745668 | ||||||||
\(453\) | 342.843i | 0.756828i | ||||||||
\(454\) | 406.830i | 0.896101i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 81.3509 | 0.178401 | ||||||||
\(457\) | 233.942 | 0.511909 | 0.255955 | − | 0.966689i | \(-0.417610\pi\) | ||||
0.255955 | + | 0.966689i | \(0.417610\pi\) | |||||||
\(458\) | − | 236.854i | − | 0.517148i | ||||||
\(459\) | −73.1714 | −0.159415 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 536.813i | 1.16445i | 0.813027 | + | 0.582226i | \(0.197818\pi\) | ||||
−0.813027 | + | 0.582226i | \(0.802182\pi\) | |||||||
\(462\) | −150.345 | − | 260.474i | −0.325421 | − | 0.563796i | ||||
\(463\) | 23.5707 | 0.0509087 | 0.0254543 | − | 0.999676i | \(-0.491897\pi\) | ||||
0.0254543 | + | 0.999676i | \(0.491897\pi\) | |||||||
\(464\) | 147.690 | 0.318297 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.4158 | 0.0352270 | ||||||||
\(467\) | 716.108i | 1.53342i | 0.641993 | + | 0.766711i | \(0.278108\pi\) | ||||
−0.641993 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(468\) | 105.698i | 0.225851i | ||||||||
\(469\) | 34.0400 | − | 19.6478i | 0.0725799 | − | 0.0418929i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −327.499 | −0.695327 | ||||||||
\(472\) | − | 41.9493i | − | 0.0888757i | ||||||
\(473\) | 890.119 | 1.88186 | ||||||||
\(474\) | − | 69.8270i | − | 0.147314i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −98.5533 | − | 170.745i | −0.207045 | − | 0.358707i | ||||
\(477\) | −154.697 | −0.324313 | ||||||||
\(478\) | −24.8633 | −0.0520153 | ||||||||
\(479\) | 484.826i | 1.01216i | 0.862486 | + | 0.506082i | \(0.168907\pi\) | ||||
−0.862486 | + | 0.506082i | \(0.831093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 794.038i | 1.65081i | ||||||||
\(482\) | − | 65.8460i | − | 0.136610i | ||||||
\(483\) | 94.1682 | + | 163.147i | 0.194965 | + | 0.337779i | ||||
\(484\) | 373.306 | 0.771293 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 104.620 | 0.214825 | 0.107413 | − | 0.994215i | \(-0.465743\pi\) | ||||
0.107413 | + | 0.994215i | \(0.465743\pi\) | |||||||
\(488\) | 257.964i | 0.528615i | ||||||||
\(489\) | − | 466.143i | − | 0.953257i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.7002 | 0.0645624 | 0.0322812 | − | 0.999479i | \(-0.489723\pi\) | ||||
0.0322812 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(492\) | 4.17658 | 0.00848898 | ||||||||
\(493\) | − | 519.937i | − | 1.05464i | ||||||
\(494\) | −413.702 | −0.837454 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 216.898i | − | 0.437294i | ||||||
\(497\) | 490.111 | − | 282.891i | 0.986139 | − | 0.569197i | ||||
\(498\) | 123.437 | 0.247866 | ||||||||
\(499\) | 527.582 | 1.05728 | 0.528639 | − | 0.848847i | \(-0.322702\pi\) | ||||
0.528639 | + | 0.848847i | \(0.322702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 217.091 | 0.433316 | ||||||||
\(502\) | 322.137i | 0.641706i | ||||||||
\(503\) | 635.097i | 1.26262i | 0.775531 | + | 0.631309i | \(0.217482\pi\) | ||||
−0.775531 | + | 0.631309i | \(0.782518\pi\) | |||||||
\(504\) | −51.4427 | + | 29.6926i | −0.102069 | + | 0.0589138i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −385.397 | −0.761653 | ||||||||
\(507\) | − | 244.801i | − | 0.482843i | ||||||
\(508\) | −197.476 | −0.388731 | ||||||||
\(509\) | − | 376.147i | − | 0.738992i | −0.929232 | − | 0.369496i | \(-0.879530\pi\) | ||
0.929232 | − | 0.369496i | \(-0.120470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −318.588 | − | 551.958i | −0.623461 | − | 1.08015i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −86.2857 | −0.168198 | ||||||||
\(514\) | − | 129.083i | − | 0.251134i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 175.796i | − | 0.340689i | ||||||
\(517\) | − | 1609.49i | − | 3.11314i | ||||||
\(518\) | −386.454 | + | 223.060i | −0.746050 | + | 0.430618i | ||||
\(519\) | −339.610 | −0.654355 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 375.330i | − | 0.720403i | −0.932875 | − | 0.360201i | \(-0.882708\pi\) | ||
0.932875 | − | 0.360201i | \(-0.117292\pi\) | |||||||
\(522\) | −156.649 | −0.300094 | ||||||||
\(523\) | 375.647i | 0.718255i | 0.933288 | + | 0.359128i | \(0.116926\pi\) | ||||
−0.933288 | + | 0.359128i | \(0.883074\pi\) | |||||||
\(524\) | − | 10.4153i | − | 0.0198765i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 153.481 | 0.291790 | ||||||||
\(527\) | −763.582 | −1.44892 | ||||||||
\(528\) | − | 121.521i | − | 0.230153i | ||||||
\(529\) | −287.607 | −0.543681 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44.4940i | 0.0837928i | ||||||||
\(532\) | −116.217 | − | 201.347i | −0.218452 | − | 0.378471i | ||||
\(533\) | −21.2396 | −0.0398492 | ||||||||
\(534\) | 187.460 | 0.351049 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.8810 | 0.0296287 | ||||||||
\(537\) | 442.482i | 0.823990i | ||||||||
\(538\) | − | 497.247i | − | 0.924252i | ||||||
\(539\) | −429.902 | + | 744.217i | −0.797592 | + | 1.38074i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −252.515 | −0.466755 | −0.233378 | − | 0.972386i | \(-0.574978\pi\) | ||||
−0.233378 | + | 0.972386i | \(0.574978\pi\) | |||||||
\(542\) | 548.241i | 1.01152i | ||||||||
\(543\) | −439.122 | −0.808695 | ||||||||
\(544\) | − | 79.6590i | − | 0.146432i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 261.607 | − | 150.999i | 0.479134 | − | 0.276554i | ||||
\(547\) | −619.645 | −1.13281 | −0.566403 | − | 0.824129i | \(-0.691665\pi\) | ||||
−0.566403 | + | 0.824129i | \(0.691665\pi\) | |||||||
\(548\) | −9.82470 | −0.0179283 | ||||||||
\(549\) | − | 273.612i | − | 0.498383i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 613.123i | − | 1.11275i | ||||||
\(552\) | 76.1146i | 0.137889i | ||||||||
\(553\) | −172.824 | + | 99.7538i | −0.312522 | + | 0.180387i | ||||
\(554\) | 711.625 | 1.28452 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 27.1446i | − | 0.0488212i | ||||||
\(557\) | 243.944 | 0.437960 | 0.218980 | − | 0.975729i | \(-0.429727\pi\) | ||||
0.218980 | + | 0.975729i | \(0.429727\pi\) | |||||||
\(558\) | 230.055i | 0.412285i | ||||||||
\(559\) | 893.992i | 1.59927i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −427.810 | −0.762585 | ||||||||
\(562\) | 151.138 | 0.268929 | ||||||||
\(563\) | 754.322i | 1.33983i | 0.742440 | + | 0.669913i | \(0.233668\pi\) | ||||
−0.742440 | + | 0.669913i | \(0.766332\pi\) | |||||||
\(564\) | −317.870 | −0.563599 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 120.724i | 0.213293i | ||||||||
\(567\) | 54.5632 | − | 31.4937i | 0.0962314 | − | 0.0555445i | ||||
\(568\) | 228.656 | 0.402563 | ||||||||
\(569\) | 755.833 | 1.32835 | 0.664176 | − | 0.747576i | \(-0.268782\pi\) | ||||
0.664176 | + | 0.747576i | \(0.268782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −517.669 | −0.906601 | −0.453300 | − | 0.891358i | \(-0.649753\pi\) | ||||
−0.453300 | + | 0.891358i | \(0.649753\pi\) | |||||||
\(572\) | 617.983i | 1.08039i | ||||||||
\(573\) | − | 495.842i | − | 0.865344i | ||||||
\(574\) | −5.96660 | − | 10.3372i | −0.0103948 | − | 0.0180090i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 451.476i | 0.782455i | 0.920294 | + | 0.391227i | \(0.127949\pi\) | ||||
−0.920294 | + | 0.391227i | \(0.872051\pi\) | |||||||
\(578\) | 128.271 | 0.221923 | ||||||||
\(579\) | − | 343.535i | − | 0.593325i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −176.341 | − | 305.512i | −0.303512 | − | 0.525838i | ||||
\(582\) | −307.058 | −0.527591 | ||||||||
\(583\) | −904.466 | −1.55140 | ||||||||
\(584\) | − | 257.510i | − | 0.440941i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 220.562i | 0.376385i | ||||||||
\(587\) | − | 145.909i | − | 0.248568i | −0.992247 | − | 0.124284i | \(-0.960337\pi\) | ||
0.992247 | − | 0.124284i | \(-0.0396634\pi\) | |||||||
\(588\) | 146.980 | + | 84.9043i | 0.249967 | + | 0.144395i | ||||
\(589\) | −900.435 | −1.52875 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 438.856i | − | 0.742565i | ||||||
\(592\) | −180.296 | −0.304554 | ||||||||
\(593\) | − | 920.404i | − | 1.55211i | −0.630663 | − | 0.776057i | \(-0.717217\pi\) | ||
0.630663 | − | 0.776057i | \(-0.282783\pi\) | |||||||
\(594\) | 128.892i | 0.216991i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −309.921 | −0.520001 | ||||||||
\(597\) | 351.764 | 0.589219 | ||||||||
\(598\) | − | 387.073i | − | 0.647280i | ||||||
\(599\) | 458.821 | 0.765979 | 0.382989 | − | 0.923753i | \(-0.374895\pi\) | ||||
0.382989 | + | 0.923753i | \(0.374895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 936.167i | − | 1.55768i | −0.627222 | − | 0.778841i | \(-0.715808\pi\) | ||
0.627222 | − | 0.778841i | \(-0.284192\pi\) | |||||||
\(602\) | −435.101 | + | 251.139i | −0.722759 | + | 0.417175i | ||||
\(603\) | −16.8443 | −0.0279342 | ||||||||
\(604\) | 395.881 | 0.655432 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 328.024 | 0.541293 | ||||||||
\(607\) | 851.306i | 1.40248i | 0.712925 | + | 0.701240i | \(0.247370\pi\) | ||||
−0.712925 | + | 0.701240i | \(0.752630\pi\) | |||||||
\(608\) | − | 93.9359i | − | 0.154500i | ||||||
\(609\) | 223.786 | + | 387.712i | 0.367465 | + | 0.636637i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1616.50 | 2.64566 | ||||||||
\(612\) | 84.4911i | 0.138057i | ||||||||
\(613\) | 769.065 | 1.25459 | 0.627296 | − | 0.778781i | \(-0.284162\pi\) | ||||
0.627296 | + | 0.778781i | \(0.284162\pi\) | |||||||
\(614\) | − | 701.347i | − | 1.14226i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −300.769 | + | 173.603i | −0.488261 | + | 0.281823i | ||||
\(617\) | 326.419 | 0.529042 | 0.264521 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264521 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(618\) | 174.203 | 0.281882 | ||||||||
\(619\) | − | 256.214i | − | 0.413917i | −0.978350 | − | 0.206958i | \(-0.933644\pi\) | ||
0.978350 | − | 0.206958i | \(-0.0663564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 80.7317i | − | 0.130003i | ||||||
\(622\) | 382.208i | 0.614482i | ||||||||
\(623\) | −267.802 | − | 463.970i | −0.429859 | − | 0.744736i | ||||
\(624\) | 122.050 | 0.195592 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.4947i | 0.0535059i | ||||||||
\(627\) | −504.485 | −0.804601 | ||||||||
\(628\) | 378.163i | 0.602171i | ||||||||
\(629\) | 634.724i | 1.00910i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1195.94 | 1.89531 | 0.947655 | − | 0.319297i | \(-0.103447\pi\) | ||||
0.947655 | + | 0.319297i | \(0.103447\pi\) | |||||||
\(632\) | −80.6293 | −0.127578 | ||||||||
\(633\) | 69.1454i | 0.109234i | ||||||||
\(634\) | 5.00384 | 0.00789249 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 178.629i | 0.280863i | ||||||||
\(637\) | −747.455 | − | 431.773i | −1.17340 | − | 0.677822i | ||||
\(638\) | −915.875 | −1.43554 | ||||||||
\(639\) | −242.526 | −0.379540 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 922.133 | 1.43858 | 0.719292 | − | 0.694707i | \(-0.244466\pi\) | ||||
0.719292 | + | 0.694707i | \(0.244466\pi\) | |||||||
\(642\) | 22.5006i | 0.0350476i | ||||||||
\(643\) | − | 113.572i | − | 0.176628i | −0.996093 | − | 0.0883140i | \(-0.971852\pi\) | ||
0.996093 | − | 0.0883140i | \(-0.0281479\pi\) | |||||||
\(644\) | 188.386 | − | 108.736i | 0.292526 | − | 0.168845i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −330.698 | −0.511916 | ||||||||
\(647\) | − | 345.510i | − | 0.534019i | −0.963694 | − | 0.267010i | \(-0.913964\pi\) | ||
0.963694 | − | 0.267010i | \(-0.0860355\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 260.142i | 0.400835i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 569.395 | − | 328.653i | 0.874647 | − | 0.504844i | ||||
\(652\) | −538.255 | −0.825545 | ||||||||
\(653\) | −584.964 | −0.895810 | −0.447905 | − | 0.894081i | \(-0.647830\pi\) | ||||
−0.447905 | + | 0.894081i | \(0.647830\pi\) | |||||||
\(654\) | 271.120i | 0.414557i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 4.82270i | − | 0.00735168i | ||||||
\(657\) | 273.130i | 0.415723i | ||||||||
\(658\) | 454.104 | + | 786.740i | 0.690128 | + | 1.19565i | ||||
\(659\) | −1144.54 | −1.73678 | −0.868389 | − | 0.495884i | \(-0.834844\pi\) | ||||
−0.868389 | + | 0.495884i | \(0.834844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 462.966i | − | 0.700402i | −0.936674 | − | 0.350201i | \(-0.886113\pi\) | ||
0.936674 | − | 0.350201i | \(-0.113887\pi\) | |||||||
\(662\) | −482.728 | −0.729196 | ||||||||
\(663\) | − | 429.671i | − | 0.648072i | ||||||
\(664\) | − | 142.533i | − | 0.214658i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 191.232 | 0.287136 | ||||||||
\(667\) | 573.658 | 0.860057 | ||||||||
\(668\) | − | 250.676i | − | 0.375263i | ||||||
\(669\) | −381.952 | −0.570930 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1599.72i | − | 2.38409i | ||||||
\(672\) | 34.2860 | + | 59.4009i | 0.0510209 | + | 0.0883942i | ||||
\(673\) | 529.399 | 0.786625 | 0.393312 | − | 0.919405i | \(-0.371329\pi\) | ||||
0.393312 | + | 0.919405i | \(0.371329\pi\) | |||||||
\(674\) | −130.839 | −0.194124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −282.672 | −0.418154 | ||||||||
\(677\) | 1079.35i | 1.59431i | 0.603776 | + | 0.797154i | \(0.293662\pi\) | ||||
−0.603776 | + | 0.797154i | \(0.706338\pi\) | |||||||
\(678\) | 412.791i | 0.608836i | ||||||||
\(679\) | 438.658 | + | 759.980i | 0.646036 | + | 1.11926i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −498.263 | −0.731664 | ||||||||
\(682\) | 1345.06i | 1.97223i | ||||||||
\(683\) | 661.804 | 0.968966 | 0.484483 | − | 0.874801i | \(-0.339008\pi\) | ||||
0.484483 | + | 0.874801i | \(0.339008\pi\) | |||||||
\(684\) | 99.6341i | 0.145664i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.167196 | − | 485.075i | 0.000243726 | − | 0.707107i | ||||
\(687\) | 290.085 | 0.422250 | ||||||||
\(688\) | −202.991 | −0.295046 | ||||||||
\(689\) | − | 908.401i | − | 1.31843i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 987.850i | − | 1.42959i | −0.699332 | − | 0.714797i | \(-0.746519\pi\) | ||
0.699332 | − | 0.714797i | \(-0.253481\pi\) | |||||||
\(692\) | 392.148i | 0.566688i | ||||||||
\(693\) | 319.014 | − | 184.134i | 0.460337 | − | 0.265705i | ||||
\(694\) | −500.938 | −0.721813 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 180.882i | 0.259889i | ||||||||
\(697\) | −16.9781 | −0.0243589 | ||||||||
\(698\) | − | 211.574i | − | 0.303115i | ||||||
\(699\) | 20.1051i | 0.0287627i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −747.087 | −1.06574 | −0.532872 | − | 0.846196i | \(-0.678887\pi\) | ||||
−0.532872 | + | 0.846196i | \(0.678887\pi\) | |||||||
\(702\) | −129.453 | −0.184406 | ||||||||
\(703\) | 748.483i | 1.06470i | ||||||||
\(704\) | −140.320 | −0.199319 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 461.383i | − | 0.653517i | ||||||
\(707\) | −468.609 | − | 811.871i | −0.662814 | − | 1.14833i | ||||
\(708\) | 51.3772 | 0.0725667 | ||||||||
\(709\) | 169.799 | 0.239491 | 0.119746 | − | 0.992805i | \(-0.461792\pi\) | ||||
0.119746 | + | 0.992805i | \(0.461792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 85.5202 | 0.120282 | ||||||||
\(712\) | − | 216.460i | − | 0.304017i | ||||||
\(713\) | − | 842.477i | − | 1.18159i | ||||||
\(714\) | 209.119 | − | 120.703i | 0.292883 | − | 0.169051i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 510.935 | 0.713596 | ||||||||
\(717\) | − | 30.4512i | − | 0.0424704i | ||||||
\(718\) | −419.131 | −0.583748 | ||||||||
\(719\) | 1213.73i | 1.68808i | 0.536277 | + | 0.844042i | \(0.319830\pi\) | ||||
−0.536277 | + | 0.844042i | \(0.680170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −248.863 | − | 431.159i | −0.345164 | − | 0.598001i | ||||
\(722\) | 120.563 | 0.166985 | ||||||||
\(723\) | 80.6445 | 0.111542 | ||||||||
\(724\) | 507.054i | 0.700351i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 457.205i | 0.629758i | ||||||||
\(727\) | − | 372.922i | − | 0.512960i | −0.966550 | − | 0.256480i | \(-0.917437\pi\) | ||
0.966550 | − | 0.256480i | \(-0.0825628\pi\) | |||||||
\(728\) | −174.358 | − | 302.078i | −0.239503 | − | 0.414942i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 714.624i | 0.977597i | ||||||||
\(732\) | −315.940 | −0.431613 | ||||||||
\(733\) | − | 421.740i | − | 0.575362i | −0.957726 | − | 0.287681i | \(-0.907116\pi\) | ||
0.957726 | − | 0.287681i | \(-0.0928843\pi\) | |||||||
\(734\) | − | 402.914i | − | 0.548929i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 87.8895 | 0.119415 | ||||||||
\(737\) | −98.4833 | −0.133627 | ||||||||
\(738\) | 5.11525i | 0.00693123i | ||||||||
\(739\) | 271.839 | 0.367847 | 0.183923 | − | 0.982941i | \(-0.441120\pi\) | ||||
0.183923 | + | 0.982941i | \(0.441120\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 506.680i | − | 0.683778i | ||||||
\(742\) | 442.114 | − | 255.187i | 0.595841 | − | 0.343918i | ||||
\(743\) | −68.6075 | −0.0923385 | −0.0461693 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461693 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(744\) | 265.645 | 0.357049 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 231.876 | 0.310825 | ||||||||
\(747\) | 151.179i | 0.202382i | ||||||||
\(748\) | 493.992i | 0.660418i | ||||||||
\(749\) | 55.6898 | − | 32.1440i | 0.0743522 | − | 0.0429159i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1404.74 | 1.87049 | 0.935246 | − | 0.353999i | \(-0.115179\pi\) | ||||
0.935246 | + | 0.353999i | \(0.115179\pi\) | |||||||
\(752\) | 367.045i | 0.488091i | ||||||||
\(753\) | −394.535 | −0.523951 | ||||||||
\(754\) | − | 919.860i | − | 1.21997i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −36.3658 | − | 63.0042i | −0.0481029 | − | 0.0833389i | ||||
\(757\) | −551.876 | −0.729031 | −0.364515 | − | 0.931197i | \(-0.618765\pi\) | ||||
−0.364515 | + | 0.931197i | \(0.618765\pi\) | |||||||
\(758\) | −252.432 | −0.333023 | ||||||||
\(759\) | − | 472.012i | − | 0.621887i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 664.607i | 0.873334i | 0.899623 | + | 0.436667i | \(0.143841\pi\) | ||||
−0.899623 | + | 0.436667i | \(0.856159\pi\) | |||||||
\(762\) | − | 241.857i | − | 0.317398i | ||||||
\(763\) | 671.032 | − | 387.318i | 0.879466 | − | 0.507625i | ||||
\(764\) | −572.549 | −0.749410 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 738.423i | 0.963999i | ||||||||
\(767\) | −261.274 | −0.340644 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 428.695i | − | 0.557471i | −0.960368 | − | 0.278735i | \(-0.910085\pi\) | ||
0.960368 | − | 0.278735i | \(-0.0899152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 158.094 | 0.205050 | ||||||||
\(772\) | −396.680 | −0.513834 | ||||||||
\(773\) | − | 1082.57i | − | 1.40047i | −0.713910 | − | 0.700237i | \(-0.753078\pi\) | ||
0.713910 | − | 0.700237i | \(-0.246922\pi\) | |||||||
\(774\) | 215.305 | 0.278172 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 354.560i | 0.456907i | ||||||||
\(777\) | −273.192 | − | 473.308i | −0.351598 | − | 0.609148i | ||||
\(778\) | 824.429 | 1.05968 | ||||||||
\(779\) | −20.0211 | −0.0257010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1417.97 | −1.81558 | ||||||||
\(782\) | − | 309.412i | − | 0.395667i | ||||||
\(783\) | − | 191.855i | − | 0.245025i | ||||||
\(784\) | 98.0390 | − | 169.718i | 0.125050 | − | 0.216478i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.7561 | 0.0162291 | ||||||||
\(787\) | 391.950i | 0.498030i | 0.968500 | + | 0.249015i | \(0.0801069\pi\) | ||||
−0.968500 | + | 0.249015i | \(0.919893\pi\) | |||||||
\(788\) | −506.747 | −0.643080 | ||||||||
\(789\) | 187.976i | 0.238245i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1021.67 | − | 589.706i | 1.29162 | − | 0.745520i | ||||
\(792\) | 148.832 | 0.187919 | ||||||||
\(793\) | 1606.68 | 2.02608 | ||||||||
\(794\) | 610.592i | 0.769007i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 406.182i | − | 0.510278i | ||||||
\(797\) | − | 518.451i | − | 0.650504i | −0.945627 | − | 0.325252i | \(-0.894551\pi\) | ||
0.945627 | − | 0.325252i | \(-0.105449\pi\) | |||||||
\(798\) | 246.598 | − | 142.336i | 0.309020 | − | 0.178366i | ||||
\(799\) | 1292.17 | 1.61723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 229.591i | 0.286630i | ||||||||
\(802\) | 370.438 | 0.461893 | ||||||||
\(803\) | 1596.90i | 1.98867i | ||||||||
\(804\) | 19.4501i | 0.0241917i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1350.91 | −1.67607 | ||||||||
\(807\) | 609.001 | 0.754648 | ||||||||
\(808\) | − | 378.769i | − | 0.468773i | ||||||
\(809\) | −244.444 | −0.302155 | −0.151078 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 179.191i | − | 0.220951i | −0.993879 | − | 0.110476i | \(-0.964763\pi\) | ||
0.993879 | − | 0.110476i | \(-0.0352374\pi\) | |||||||
\(812\) | 447.691 | − | 258.406i | 0.551344 | − | 0.318234i | ||||
\(813\) | −671.456 | −0.825899 | ||||||||
\(814\) | 1118.08 | 1.37356 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 97.5619 | 0.119561 | ||||||||
\(817\) | 842.703i | 1.03146i | ||||||||
\(818\) | − | 626.808i | − | 0.766269i | ||||||
\(819\) | 184.935 | + | 320.402i | 0.225806 | + | 0.391211i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 907.336 | 1.10516 | 0.552579 | − | 0.833460i | \(-0.313644\pi\) | ||||
0.552579 | + | 0.833460i | \(0.313644\pi\) | |||||||
\(822\) | − | 12.0328i | − | 0.0146384i | ||||||
\(823\) | 946.853 | 1.15049 | 0.575245 | − | 0.817981i | \(-0.304907\pi\) | ||||
0.575245 | + | 0.817981i | \(0.304907\pi\) | |||||||
\(824\) | − | 201.152i | − | 0.244117i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −73.3967 | − | 127.161i | −0.0888580 | − | 0.153947i | ||||
\(827\) | −1016.38 | −1.22899 | −0.614497 | − | 0.788919i | \(-0.710641\pi\) | ||||
−0.614497 | + | 0.788919i | \(0.710641\pi\) | |||||||
\(828\) | −93.2209 | −0.112586 | ||||||||
\(829\) | − | 1222.70i | − | 1.47491i | −0.675394 | − | 0.737457i | \(-0.736027\pi\) | ||
0.675394 | − | 0.737457i | \(-0.263973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 871.558i | 1.04881i | ||||||||
\(832\) | − | 140.931i | − | 0.169388i | ||||||
\(833\) | −597.488 | − | 345.143i | −0.717272 | − | 0.414337i | ||||
\(834\) | 33.2452 | 0.0398624 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 582.529i | 0.696805i | ||||||||
\(837\) | −281.759 | −0.336629 | ||||||||
\(838\) | 361.199i | 0.431025i | ||||||||
\(839\) | − | 1149.98i | − | 1.37066i | −0.728235 | − | 0.685328i | \(-0.759659\pi\) | ||
0.728235 | − | 0.685328i | \(-0.240341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 522.269 | 0.621010 | ||||||||
\(842\) | 449.549 | 0.533906 | ||||||||
\(843\) | 185.105i | 0.219579i | ||||||||
\(844\) | 79.8422 | 0.0945998 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 389.310i | − | 0.460177i | ||||||
\(847\) | 1131.60 | − | 653.155i | 1.33601 | − | 0.771140i | ||||
\(848\) | 206.263 | 0.243235 | ||||||||
\(849\) | −147.856 | −0.174153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −700.306 | −0.822921 | ||||||||
\(852\) | 280.045i | 0.328691i | ||||||||
\(853\) | − | 340.841i | − | 0.399579i | −0.979839 | − | 0.199789i | \(-0.935974\pi\) | ||
0.979839 | − | 0.199789i | \(-0.0640258\pi\) | |||||||
\(854\) | 451.348 | + | 781.964i | 0.528510 | + | 0.915649i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9814 | 0.0303521 | ||||||||
\(857\) | 154.862i | 0.180702i | 0.995910 | + | 0.0903511i | \(0.0287989\pi\) | ||||
−0.995910 | + | 0.0903511i | \(0.971201\pi\) | |||||||
\(858\) | −756.872 | −0.882135 | ||||||||
\(859\) | − | 1186.43i | − | 1.38118i | −0.723246 | − | 0.690590i | \(-0.757351\pi\) | ||
0.723246 | − | 0.690590i | \(-0.242649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6604 | − | 7.30756i | 0.0147043 | − | 0.00848729i | ||||
\(862\) | 117.584 | 0.136408 | ||||||||
\(863\) | 25.3901 | 0.0294207 | 0.0147104 | − | 0.999892i | \(-0.495317\pi\) | ||||
0.0147104 | + | 0.999892i | \(0.495317\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 708.948i | − | 0.818647i | ||||||
\(867\) | 157.100i | 0.181199i | ||||||||
\(868\) | −379.496 | − | 657.481i | −0.437207 | − | 0.757466i | ||||
\(869\) | 500.009 | 0.575385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 98.9118i | − | 0.113561i | ||||||
\(872\) | 313.062 | 0.359017 | ||||||||
\(873\) | − | 376.068i | − | 0.430776i | ||||||
\(874\) | − | 364.867i | − | 0.417467i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 315.384 | 0.360027 | ||||||||
\(877\) | 1270.43 | 1.44861 | 0.724304 | − | 0.689481i | \(-0.242161\pi\) | ||||
0.724304 | + | 0.689481i | \(0.242161\pi\) | |||||||
\(878\) | 14.3686i | 0.0163652i | ||||||||
\(879\) | −270.132 | −0.307317 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.8647i | − | 0.0236830i | −0.999930 | − | 0.0118415i | \(-0.996231\pi\) | ||
0.999930 | − | 0.0118415i | \(-0.00376935\pi\) | |||||||
\(882\) | −103.986 | + | 180.014i | −0.117898 | + | 0.204097i | ||||
\(883\) | 850.321 | 0.962990 | 0.481495 | − | 0.876449i | \(-0.340094\pi\) | ||||
0.481495 | + | 0.876449i | \(0.340094\pi\) | |||||||
\(884\) | −496.142 | −0.561246 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 284.666 | 0.321293 | ||||||||
\(887\) | 347.058i | 0.391272i | 0.980677 | + | 0.195636i | \(0.0626771\pi\) | ||||
−0.980677 | + | 0.195636i | \(0.937323\pi\) | |||||||
\(888\) | − | 220.816i | − | 0.248667i | ||||||
\(889\) | −598.606 | + | 345.513i | −0.673347 | + | 0.388654i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −157.860 | −0.177172 | ||||||||
\(892\) | 441.040i | 0.494440i | ||||||||
\(893\) | 1523.76 | 1.70634 | ||||||||
\(894\) | − | 379.574i | − | 0.424579i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 68.5903 | − | 39.5901i | 0.0765516 | − | 0.0441854i | ||||
\(897\) | 474.066 | 0.528502 | ||||||||
\(898\) | 852.722 | 0.949579 | ||||||||
\(899\) | − | 2002.10i | − | 2.22703i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 726.142i | − | 0.805929i | ||||||
\(902\) | 29.9072i | 0.0331565i | ||||||||
\(903\) | −307.581 | − | 532.888i | −0.340622 | − | 0.590130i | ||||
\(904\) | 476.650 | 0.527267 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 484.853i | 0.535158i | ||||||||
\(907\) | 808.517 | 0.891419 | 0.445710 | − | 0.895178i | \(-0.352951\pi\) | ||||
0.445710 | + | 0.895178i | \(0.352951\pi\) | |||||||
\(908\) | 575.344i | 0.633639i | ||||||||
\(909\) | 401.745i | 0.441964i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 290.542 | 0.318926 | 0.159463 | − | 0.987204i | \(-0.449024\pi\) | ||||
0.159463 | + | 0.987204i | \(0.449024\pi\) | |||||||
\(912\) | 115.048 | 0.126149 | ||||||||
\(913\) | 883.896i | 0.968123i | ||||||||
\(914\) | 330.845 | 0.361974 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 334.962i | − | 0.365679i | ||||||
\(917\) | −18.2232 | − | 31.5718i | −0.0198726 | − | 0.0344295i | ||||
\(918\) | −103.480 | −0.112723 | ||||||||
\(919\) | −632.051 | −0.687759 | −0.343880 | − | 0.939014i | \(-0.611741\pi\) | ||||
−0.343880 | + | 0.939014i | \(0.611741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 858.971 | 0.932651 | ||||||||
\(922\) | 759.168i | 0.823392i | ||||||||
\(923\) | − | 1424.14i | − | 1.54295i | ||||||
\(924\) | −212.619 | − | 368.365i | −0.230108 | − | 0.398664i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33.3340 | 0.0359979 | ||||||||
\(927\) | 213.354i | 0.230155i | ||||||||
\(928\) | 208.865 | 0.225070 | ||||||||
\(929\) | − | 39.3251i | − | 0.0423306i | −0.999776 | − | 0.0211653i | \(-0.993262\pi\) | ||
0.999776 | − | 0.0211653i | \(-0.00673762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −704.573 | − | 407.001i | −0.756791 | − | 0.437166i | ||||
\(932\) | 23.2154 | 0.0249092 | ||||||||
\(933\) | −468.107 | −0.501722 | ||||||||
\(934\) | 1012.73i | 1.08429i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 149.480i | 0.159701i | ||||||||
\(937\) | 1178.92i | 1.25818i | 0.777331 | + | 0.629092i | \(0.216573\pi\) | ||||
−0.777331 | + | 0.629092i | \(0.783427\pi\) | |||||||
\(938\) | 48.1398 | − | 27.7862i | 0.0513218 | − | 0.0296228i | ||||
\(939\) | −41.0225 | −0.0436874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 818.442i | − | 0.869758i | −0.900489 | − | 0.434879i | \(-0.856791\pi\) | ||
0.900489 | − | 0.434879i | \(-0.143209\pi\) | |||||||
\(942\) | −463.154 | −0.491671 | ||||||||
\(943\) | − | 18.7324i | − | 0.0198646i | ||||||
\(944\) | − | 59.3253i | − | 0.0628446i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1258.82 | 1.33068 | ||||||||
\(947\) | −1154.06 | −1.21865 | −0.609324 | − | 0.792921i | \(-0.708559\pi\) | ||||
−0.609324 | + | 0.792921i | \(0.708559\pi\) | |||||||
\(948\) | − | 98.7503i | − | 0.104167i | ||||||
\(949\) | −1603.85 | −1.69005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.12843i | 0.00644419i | ||||||||
\(952\) | −139.375 | − | 241.469i | −0.146403 | − | 0.253644i | ||||
\(953\) | 534.547 | 0.560910 | 0.280455 | − | 0.959867i | \(-0.409515\pi\) | ||||
0.280455 | + | 0.959867i | \(0.409515\pi\) | |||||||
\(954\) | −218.775 | −0.229324 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.1621 | −0.0367804 | ||||||||
\(957\) | − | 1121.71i | − | 1.17211i | ||||||
\(958\) | 685.648i | 0.715708i | ||||||||
\(959\) | −29.7815 | + | 17.1898i | −0.0310548 | + | 0.0179247i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1979.30 | −2.05962 | ||||||||
\(962\) | 1122.94i | 1.16730i | ||||||||
\(963\) | −27.5575 | −0.0286163 | ||||||||
\(964\) | − | 93.1203i | − | 0.0965978i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 133.174 | + | 230.725i | 0.137861 | + | 0.238846i | ||||
\(967\) | 88.4962 | 0.0915163 | 0.0457581 | − | 0.998953i | \(-0.485430\pi\) | ||||
0.0457581 | + | 0.998953i | \(0.485430\pi\) | |||||||
\(968\) | 527.934 | 0.545387 | ||||||||
\(969\) | − | 405.021i | − | 0.417978i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1732.09i | 1.78382i | 0.452216 | + | 0.891908i | \(0.350634\pi\) | ||||
−0.452216 | + | 0.891908i | \(0.649366\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −47.4936 | − | 82.2831i | −0.0488115 | − | 0.0845664i | ||||
\(974\) | 147.955 | 0.151904 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 364.817i | 0.373787i | ||||||||
\(977\) | 83.2486 | 0.0852084 | 0.0426042 | − | 0.999092i | \(-0.486435\pi\) | ||||
0.0426042 | + | 0.999092i | \(0.486435\pi\) | |||||||
\(978\) | − | 659.225i | − | 0.674055i | ||||||
\(979\) | 1342.34i | 1.37114i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −332.053 | −0.338484 | ||||||||
\(982\) | 44.8308 | 0.0456525 | ||||||||
\(983\) | 1409.80i | 1.43418i | 0.696978 | + | 0.717092i | \(0.254527\pi\) | ||||
−0.696978 | + | 0.717092i | \(0.745473\pi\) | |||||||
\(984\) | 5.90658 | 0.00600262 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 735.302i | − | 0.745742i | ||||||
\(987\) | −963.556 | + | 556.162i | −0.976248 | + | 0.563487i | ||||
\(988\) | −585.063 | −0.592169 | ||||||||
\(989\) | −788.460 | −0.797230 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 480.699 | 0.485064 | 0.242532 | − | 0.970143i | \(-0.422022\pi\) | ||||
0.242532 | + | 0.970143i | \(0.422022\pi\) | |||||||
\(992\) | − | 306.740i | − | 0.309214i | ||||||
\(993\) | − | 591.218i | − | 0.595386i | ||||||
\(994\) | 693.122 | − | 400.068i | 0.697306 | − | 0.402483i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 174.567 | 0.175268 | ||||||||
\(997\) | − | 1588.98i | − | 1.59376i | −0.604136 | − | 0.796881i | \(-0.706482\pi\) | ||
0.604136 | − | 0.796881i | \(-0.293518\pi\) | |||||||
\(998\) | 746.114 | 0.747609 | ||||||||
\(999\) | 234.211i | 0.234445i |
(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 | 1050.3.f.c.601.12 | yes | 12 | |
5.2 | odd | 4 | 1050.3.h.c.349.22 | 24 | |||
5.3 | odd | 4 | 1050.3.h.c.349.5 | 24 | |||
5.4 | even | 2 | 1050.3.f.d.601.1 | yes | 12 | ||
7.6 | odd | 2 | inner | 1050.3.f.c.601.9 | ✓ | 12 | |
35.13 | even | 4 | 1050.3.h.c.349.21 | 24 | |||
35.27 | even | 4 | 1050.3.h.c.349.6 | 24 | |||
35.34 | odd | 2 | 1050.3.f.d.601.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.f.c.601.9 | ✓ | 12 | 7.6 | odd | 2 | inner | |
1050.3.f.c.601.12 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.f.d.601.1 | yes | 12 | 5.4 | even | 2 | ||
1050.3.f.d.601.4 | yes | 12 | 35.34 | odd | 2 | ||
1050.3.h.c.349.5 | 24 | 5.3 | odd | 4 | |||
1050.3.h.c.349.6 | 24 | 35.27 | even | 4 | |||
1050.3.h.c.349.21 | 24 | 35.13 | even | 4 | |||
1050.3.h.c.349.22 | 24 | 5.2 | odd | 4 |