Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,3,Mod(79,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.79");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.23162107572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 175.1 | ||
Root | \(-1.87459 - 0.697079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.175 |
Dual form | 192.3.l.a.79.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.24354 | + | 5.24354i | −1.04871 | + | 1.04871i | −0.0499563 | + | 0.998751i | \(0.515908\pi\) |
−0.998751 | + | 0.0499563i | \(0.984092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.32796 | 0.761138 | 0.380569 | − | 0.924753i | \(-0.375728\pi\) | ||||
0.380569 | + | 0.924753i | \(0.375728\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.2863 | − | 12.2863i | −1.11693 | − | 1.11693i | −0.992189 | − | 0.124743i | \(-0.960189\pi\) |
−0.124743 | − | 0.992189i | \(-0.539811\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.73657 | − | 5.73657i | −0.441275 | − | 0.441275i | 0.451165 | − | 0.892440i | \(-0.351008\pi\) |
−0.892440 | + | 0.451165i | \(0.851008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 12.8440i | − | 0.856266i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.3997 | −1.37645 | −0.688226 | − | 0.725496i | \(-0.741610\pi\) | ||||
−0.688226 | + | 0.725496i | \(0.741610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.7492 | + | 11.7492i | −0.618380 | + | 0.618380i | −0.945116 | − | 0.326736i | \(-0.894051\pi\) |
0.326736 | + | 0.945116i | \(0.394051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.52540 | + | 6.52540i | −0.310733 | + | 0.310733i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.80841 | −0.252540 | −0.126270 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126270 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 29.9894i | − | 1.19958i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18.3914 | + | 18.3914i | 0.634185 | + | 0.634185i | 0.949115 | − | 0.314930i | \(-0.101981\pi\) |
−0.314930 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.9053i | 0.545332i | 0.962109 | + | 0.272666i | \(0.0879053\pi\) | ||||
−0.962109 | + | 0.272666i | \(0.912095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 30.0951 | 0.911971 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −27.9374 | + | 27.9374i | −0.798211 | + | 0.798211i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.3391 | − | 15.3391i | 0.414571 | − | 0.414571i | −0.468756 | − | 0.883327i | \(-0.655298\pi\) |
0.883327 | + | 0.468756i | \(0.155298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.0517 | 0.360299 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 29.2351i | − | 0.713051i | −0.934286 | − | 0.356526i | \(-0.883961\pi\) | ||
0.934286 | − | 0.356526i | \(-0.116039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.4099 | − | 33.4099i | −0.776975 | − | 0.776975i | 0.202340 | − | 0.979315i | \(-0.435145\pi\) |
−0.979315 | + | 0.202340i | \(0.935145\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.7306 | + | 15.7306i | 0.349569 | + | 0.349569i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18.2125i | 0.387500i | 0.981051 | + | 0.193750i | \(0.0620650\pi\) | ||||
−0.981051 | + | 0.193750i | \(0.937935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −20.6128 | −0.420670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.6586 | − | 28.6586i | 0.561934 | − | 0.561934i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −66.9856 | + | 66.9856i | −1.26388 | + | 1.26388i | −0.314681 | + | 0.949197i | \(0.601898\pi\) |
−0.949197 | + | 0.314681i | \(0.898102\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 128.847 | 2.34267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 28.7796i | − | 0.504905i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27.1523 | + | 27.1523i | 0.460209 | + | 0.460209i | 0.898724 | − | 0.438515i | \(-0.144495\pi\) |
−0.438515 | + | 0.898724i | \(0.644495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 65.2399 | + | 65.2399i | 1.06951 | + | 1.06951i | 0.997397 | + | 0.0721103i | \(0.0229733\pi\) |
0.0721103 | + | 0.997397i | \(0.477027\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 15.9839i | − | 0.253713i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 60.1599 | 0.925537 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 37.6951 | − | 37.6951i | 0.562614 | − | 0.562614i | −0.367435 | − | 0.930049i | \(-0.619764\pi\) |
0.930049 | + | 0.367435i | \(0.119764\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.11382 | − | 7.11382i | 0.103099 | − | 0.103099i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −42.6559 | −0.600788 | −0.300394 | − | 0.953815i | \(-0.597118\pi\) | ||||
−0.300394 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 106.391i | 1.45742i | 0.684825 | + | 0.728708i | \(0.259879\pi\) | ||||
−0.684825 | + | 0.728708i | \(0.740121\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.7294 | + | 36.7294i | 0.489725 | + | 0.489725i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −65.4607 | − | 65.4607i | −0.850139 | − | 0.850139i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21.2821i | 0.269394i | 0.990887 | + | 0.134697i | \(0.0430061\pi\) | ||||
−0.990887 | + | 0.134697i | \(0.956994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −24.1638 | + | 24.1638i | −0.291130 | + | 0.291130i | −0.837527 | − | 0.546396i | \(-0.815999\pi\) |
0.546396 | + | 0.837527i | \(0.315999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 122.697 | − | 122.697i | 1.44350 | − | 1.44350i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −45.0495 | −0.517810 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 52.8029i | 0.593291i | 0.954988 | + | 0.296645i | \(0.0958679\pi\) | ||||
−0.954988 | + | 0.296645i | \(0.904132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.5643 | − | 30.5643i | −0.335871 | − | 0.335871i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.7047 | − | 20.7047i | −0.222631 | − | 0.222631i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 123.215i | − | 1.29700i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −21.0222 | −0.216724 | −0.108362 | − | 0.994112i | \(-0.534560\pi\) | ||||
−0.108362 | + | 0.994112i | \(0.534560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.8588 | + | 36.8588i | −0.372311 | + | 0.372311i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.24960 | + | 3.24960i | −0.0321743 | + | 0.0321743i | −0.723011 | − | 0.690837i | \(-0.757242\pi\) |
0.690837 | + | 0.723011i | \(0.257242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −105.112 | −1.02050 | −0.510252 | − | 0.860025i | \(-0.670448\pi\) | ||||
−0.510252 | + | 0.860025i | \(0.670448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 68.4323i | − | 0.651736i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 99.6160 | + | 99.6160i | 0.930991 | + | 0.930991i | 0.997768 | − | 0.0667770i | \(-0.0212716\pi\) |
−0.0667770 | + | 0.997768i | \(0.521272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −108.050 | − | 108.050i | −0.991282 | − | 0.991282i | 0.00868078 | − | 0.999962i | \(-0.497237\pi\) |
−0.999962 | + | 0.00868078i | \(0.997237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 37.5730i | 0.338496i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −23.2835 | −0.206048 | −0.103024 | − | 0.994679i | \(-0.532852\pi\) | ||||
−0.103024 | + | 0.994679i | \(0.532852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.4566 | − | 30.4566i | 0.264840 | − | 0.264840i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.2097 | + | 17.2097i | −0.147092 | + | 0.147092i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −124.673 | −1.04767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 180.904i | 1.49508i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.8055 | + | 35.8055i | 0.291102 | + | 0.291102i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 26.1621 | + | 26.1621i | 0.209297 | + | 0.209297i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.180i | 0.930550i | 0.885166 | + | 0.465275i | \(0.154045\pi\) | ||||
−0.885166 | + | 0.465275i | \(0.845955\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 81.8373 | 0.634398 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 69.2067 | − | 69.2067i | 0.528296 | − | 0.528296i | −0.391768 | − | 0.920064i | \(-0.628137\pi\) |
0.920064 | + | 0.391768i | \(0.128137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −62.5994 | + | 62.5994i | −0.470672 | + | 0.470672i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −38.5320 | −0.285422 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 124.474i | − | 0.908572i | −0.890856 | − | 0.454286i | \(-0.849894\pi\) | ||
0.890856 | − | 0.454286i | \(-0.150106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −169.014 | − | 169.014i | −1.21593 | − | 1.21593i | −0.969046 | − | 0.246881i | \(-0.920594\pi\) |
−0.246881 | − | 0.969046i | \(-0.579406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.3057 | − | 22.3057i | −0.158196 | − | 0.158196i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 140.962i | 0.985749i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −192.872 | −1.33015 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25.2454 | − | 25.2454i | 0.171738 | − | 0.171738i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 146.988 | − | 146.988i | 0.986495 | − | 0.986495i | −0.0134145 | − | 0.999910i | \(-0.504270\pi\) |
0.999910 | + | 0.0134145i | \(0.00427011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −75.5456 | −0.500302 | −0.250151 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250151 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 70.1991i | 0.458817i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −88.6435 | − | 88.6435i | −0.571893 | − | 0.571893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −81.5356 | − | 81.5356i | −0.519335 | − | 0.519335i | 0.398035 | − | 0.917370i | \(-0.369692\pi\) |
−0.917370 | + | 0.398035i | \(0.869692\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 164.080i | − | 1.03195i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.9470 | −0.192217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −55.8065 | + | 55.8065i | −0.342371 | + | 0.342371i | −0.857258 | − | 0.514887i | \(-0.827834\pi\) |
0.514887 | + | 0.857258i | \(0.327834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −157.805 | + | 157.805i | −0.956391 | + | 0.956391i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.6339 | 0.147508 | 0.0737540 | − | 0.997276i | \(-0.476502\pi\) | ||||
0.0737540 | + | 0.997276i | \(0.476502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 103.183i | − | 0.610553i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 35.2476 | + | 35.2476i | 0.206127 | + | 0.206127i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.88551 | + | 4.88551i | 0.0282399 | + | 0.0282399i | 0.721086 | − | 0.692846i | \(-0.243643\pi\) |
−0.692846 | + | 0.721086i | \(0.743643\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 159.782i | − | 0.913042i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −66.5094 | −0.375759 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 229.504 | − | 229.504i | 1.28215 | − | 1.28215i | 0.342702 | − | 0.939444i | \(-0.388658\pi\) |
0.939444 | − | 0.342702i | \(-0.111342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 116.607 | − | 116.607i | 0.644238 | − | 0.644238i | −0.307356 | − | 0.951595i | \(-0.599444\pi\) |
0.951595 | + | 0.307356i | \(0.0994443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −159.805 | −0.873249 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 160.863i | 0.869528i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 287.495 | + | 287.495i | 1.53740 | + | 1.53740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.5762 | + | 19.5762i | 0.103578 | + | 0.103578i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 94.2316i | − | 0.493359i | −0.969097 | − | 0.246680i | \(-0.920660\pi\) | ||
0.969097 | − | 0.246680i | \(-0.0793395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 84.2667 | 0.436615 | 0.218308 | − | 0.975880i | \(-0.429946\pi\) | ||||
0.218308 | + | 0.975880i | \(0.429946\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −73.6805 | + | 73.6805i | −0.377849 | + | 0.377849i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −56.9578 | + | 56.9578i | −0.289126 | + | 0.289126i | −0.836734 | − | 0.547609i | \(-0.815538\pi\) |
0.547609 | + | 0.836734i | \(0.315538\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 196.179 | 0.985827 | 0.492913 | − | 0.870078i | \(-0.335932\pi\) | ||||
0.492913 | + | 0.870078i | \(0.335932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 92.3338i | 0.459372i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 97.9886 | + | 97.9886i | 0.482702 | + | 0.482702i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 153.295 | + | 153.295i | 0.747782 | + | 0.747782i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.4252i | 0.0841799i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 288.708 | 1.38138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −177.340 | + | 177.340i | −0.840475 | + | 0.840475i | −0.988921 | − | 0.148445i | \(-0.952573\pi\) |
0.148445 | + | 0.988921i | \(0.452573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 52.2426 | − | 52.2426i | 0.245271 | − | 0.245271i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 350.373 | 1.62964 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 90.0707i | 0.415072i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −130.302 | − | 130.302i | −0.594987 | − | 0.594987i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 134.234 | + | 134.234i | 0.607394 | + | 0.607394i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 377.924i | 1.69473i | 0.531012 | + | 0.847364i | \(0.321812\pi\) | ||||
−0.531012 | + | 0.847364i | \(0.678188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −89.9682 | −0.399859 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −103.909 | + | 103.909i | −0.457750 | + | 0.457750i | −0.897916 | − | 0.440166i | \(-0.854920\pi\) |
0.440166 | + | 0.897916i | \(0.354920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −101.055 | + | 101.055i | −0.441290 | + | 0.441290i | −0.892445 | − | 0.451156i | \(-0.851012\pi\) |
0.451156 | + | 0.892445i | \(0.351012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 160.345 | 0.694136 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 287.259i | − | 1.23287i | −0.787405 | − | 0.616436i | \(-0.788576\pi\) | ||
0.787405 | − | 0.616436i | \(-0.211424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −95.4979 | − | 95.4979i | −0.406374 | − | 0.406374i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.0651 | − | 26.0651i | −0.109980 | − | 0.109980i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 150.941i | − | 0.631554i | −0.948833 | − | 0.315777i | \(-0.897735\pi\) | ||
0.948833 | − | 0.315777i | \(-0.102265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37.7817 | 0.156771 | 0.0783853 | − | 0.996923i | \(-0.475024\pi\) | ||||
0.0783853 | + | 0.996923i | \(0.475024\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108.084 | − | 108.084i | 0.441159 | − | 0.441159i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 134.800 | 0.545751 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 59.1890i | − | 0.237707i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −100.915 | − | 100.915i | −0.402050 | − | 0.402050i | 0.476905 | − | 0.878955i | \(-0.341759\pi\) |
−0.878955 | + | 0.476905i | \(0.841759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 71.3637 | + | 71.3637i | 0.282070 | + | 0.282070i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 300.545i | 1.17861i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 241.295 | 0.938891 | 0.469446 | − | 0.882961i | \(-0.344454\pi\) | ||||
0.469446 | + | 0.882961i | \(0.344454\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 81.7263 | − | 81.7263i | 0.315546 | − | 0.315546i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 55.1741 | − | 55.1741i | 0.211395 | − | 0.211395i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 118.747 | 0.451509 | 0.225754 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225754 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 702.483i | − | 2.65088i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −64.6700 | − | 64.6700i | −0.242210 | − | 0.242210i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.74853 | + | 7.74853i | 0.0288050 | + | 0.0288050i | 0.721363 | − | 0.692558i | \(-0.243516\pi\) |
−0.692558 | + | 0.721363i | \(0.743516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 131.899i | − | 0.486712i | −0.969937 | − | 0.243356i | \(-0.921752\pi\) | ||
0.969937 | − | 0.243356i | \(-0.0782484\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 74.8668 | 0.274237 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −368.457 | + | 368.457i | −1.33984 | + | 1.33984i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −202.352 | + | 202.352i | −0.730513 | + | 0.730513i | −0.970721 | − | 0.240208i | \(-0.922784\pi\) |
0.240208 | + | 0.970721i | \(0.422784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 50.7158 | 0.181777 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 68.8493i | 0.245015i | 0.992468 | + | 0.122508i | \(0.0390936\pi\) | ||||
−0.992468 | + | 0.122508i | \(0.960906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −206.773 | − | 206.773i | −0.730646 | − | 0.730646i | 0.240102 | − | 0.970748i | \(-0.422819\pi\) |
−0.970748 | + | 0.240102i | \(0.922819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 150.907 | + | 150.907i | 0.529498 | + | 0.529498i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 155.764i | − | 0.542730i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 258.545 | 0.894620 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.7468 | − | 25.7468i | 0.0884770 | − | 0.0884770i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −361.237 | + | 361.237i | −1.23289 | + | 1.23289i | −0.270043 | + | 0.962848i | \(0.587038\pi\) |
−0.962848 | + | 0.270043i | \(0.912962\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −284.749 | −0.965250 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 90.2852i | − | 0.303990i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.3204 | + | 33.3204i | 0.111439 | + | 0.111439i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −178.007 | − | 178.007i | −0.591385 | − | 0.591385i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 7.95987i | − | 0.0262702i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −684.176 | −2.24320 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9073 | − | 10.9073i | 0.0355286 | − | 0.0355286i | −0.689119 | − | 0.724648i | \(-0.742002\pi\) |
0.724648 | + | 0.689119i | \(0.242002\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 128.735 | − | 128.735i | 0.416619 | − | 0.416619i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160.251 | 0.515278 | 0.257639 | − | 0.966241i | \(-0.417055\pi\) | ||||
0.257639 | + | 0.966241i | \(0.417055\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 355.500i | 1.13578i | 0.823103 | + | 0.567892i | \(0.192241\pi\) | ||||
−0.823103 | + | 0.567892i | \(0.807759\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 83.8121 | + | 83.8121i | 0.266070 | + | 0.266070i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 72.5192 | + | 72.5192i | 0.228767 | + | 0.228767i | 0.812178 | − | 0.583410i | \(-0.198282\pi\) |
−0.583410 | + | 0.812178i | \(0.698282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 451.922i | − | 1.41668i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −244.008 | −0.760151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 274.928 | − | 274.928i | 0.851170 | − | 0.851170i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −172.036 | + | 172.036i | −0.529343 | + | 0.529343i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 264.667 | 0.809378 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 97.0355i | 0.294941i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 248.096 | + | 248.096i | 0.749536 | + | 0.749536i | 0.974392 | − | 0.224856i | \(-0.0721912\pi\) |
−0.224856 | + | 0.974392i | \(0.572191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −46.0174 | − | 46.0174i | −0.138190 | − | 0.138190i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 395.312i | 1.18003i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −467.271 | −1.38656 | −0.693280 | − | 0.720668i | \(-0.743835\pi\) | ||||
−0.693280 | + | 0.720668i | \(0.743835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.5163 | − | 28.5163i | 0.0841189 | − | 0.0841189i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 207.703 | − | 207.703i | 0.609098 | − | 0.609098i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −370.894 | −1.08133 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 74.6032i | 0.216241i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −292.821 | − | 292.821i | −0.843863 | − | 0.843863i | 0.145496 | − | 0.989359i | \(-0.453522\pi\) |
−0.989359 | + | 0.145496i | \(0.953522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 346.260 | + | 346.260i | 0.992150 | + | 0.992150i | 0.999969 | − | 0.00781941i | \(-0.00248902\pi\) |
−0.00781941 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 42.1550i | − | 0.120100i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.01816 | 0.0227143 | 0.0113572 | − | 0.999936i | \(-0.496385\pi\) | ||||
0.0113572 | + | 0.999936i | \(0.496385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 223.668 | − | 223.668i | 0.630051 | − | 0.630051i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 152.692 | − | 152.692i | 0.427709 | − | 0.427709i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −590.403 | −1.64458 | −0.822289 | − | 0.569071i | \(-0.807303\pi\) | ||||
−0.822289 | + | 0.569071i | \(0.807303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 84.9121i | 0.235213i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −221.561 | − | 221.561i | −0.610362 | − | 0.610362i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −557.867 | − | 557.867i | −1.52840 | − | 1.52840i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 397.100i | − | 1.08202i | −0.841017 | − | 0.541008i | \(-0.818043\pi\) | ||
0.841017 | − | 0.541008i | \(-0.181957\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −87.7053 | −0.237684 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −356.897 | + | 356.897i | −0.961986 | + | 0.961986i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −165.010 | + | 165.010i | −0.442387 | + | 0.442387i | −0.892814 | − | 0.450427i | \(-0.851272\pi\) |
0.450427 | + | 0.892814i | \(0.351272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −64.0837 | −0.170890 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 211.007i | − | 0.559700i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 206.669 | + | 206.669i | 0.545300 | + | 0.545300i | 0.925078 | − | 0.379778i | \(-0.124000\pi\) |
−0.379778 | + | 0.925078i | \(0.624000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −144.740 | − | 144.740i | −0.379895 | − | 0.379895i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 598.414i | 1.56244i | 0.624257 | + | 0.781219i | \(0.285402\pi\) | ||||
−0.624257 | + | 0.781219i | \(0.714598\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 686.492 | 1.78310 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −100.230 | + | 100.230i | −0.258992 | + | 0.258992i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 186.696 | − | 186.696i | 0.479939 | − | 0.479939i | −0.425173 | − | 0.905112i | \(-0.639787\pi\) |
0.905112 | + | 0.425173i | \(0.139787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 135.915 | 0.347609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 169.521i | 0.431352i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −111.594 | − | 111.594i | −0.282515 | − | 0.282515i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −57.3727 | − | 57.3727i | −0.144516 | − | 0.144516i | 0.631147 | − | 0.775663i | \(-0.282584\pi\) |
−0.775663 | + | 0.631147i | \(0.782584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 153.337i | − | 0.384302i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −466.082 | −1.16230 | −0.581149 | − | 0.813797i | \(-0.697397\pi\) | ||||
−0.581149 | + | 0.813797i | \(0.697397\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 96.9784 | − | 96.9784i | 0.240641 | − | 0.240641i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 47.1918 | − | 47.1918i | 0.116523 | − | 0.116523i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −376.921 | −0.926096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 597.952i | − | 1.46198i | −0.682386 | − | 0.730992i | \(-0.739058\pi\) | ||
0.682386 | − | 0.730992i | \(-0.260942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 152.449 | + | 152.449i | 0.370923 | + | 0.370923i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 144.667 | + | 144.667i | 0.350282 | + | 0.350282i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 253.408i | − | 0.610621i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 413.998 | 0.992800 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.65301 | − | 4.65301i | 0.0111050 | − | 0.0111050i | −0.701532 | − | 0.712638i | \(-0.747500\pi\) |
0.712638 | + | 0.701532i | \(0.247500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3754 | − | 34.3754i | 0.0816519 | − | 0.0816519i | −0.665101 | − | 0.746753i | \(-0.731612\pi\) |
0.746753 | + | 0.665101i | \(0.231612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 54.6375 | 0.129167 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 701.742i | 1.65116i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 347.596 | + | 347.596i | 0.814042 | + | 0.814042i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −172.643 | − | 172.643i | −0.402430 | − | 0.402430i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 423.823i | 0.983347i | 0.870780 | + | 0.491674i | \(0.163615\pi\) | ||||
−0.870780 | + | 0.491674i | \(0.836385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 833.377 | 1.92466 | 0.962330 | − | 0.271885i | \(-0.0876472\pi\) | ||||
0.962330 | + | 0.271885i | \(0.0876472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 236.219 | − | 236.219i | 0.543031 | − | 0.543031i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 68.2443 | − | 68.2443i | 0.156165 | − | 0.156165i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3193 | −0.0736203 | −0.0368102 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368102 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 61.8384i | 0.140223i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −119.527 | − | 119.527i | −0.269813 | − | 0.269813i | 0.559212 | − | 0.829025i | \(-0.311104\pi\) |
−0.829025 | + | 0.559212i | \(0.811104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −276.874 | − | 276.874i | −0.622189 | − | 0.622189i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 360.045i | 0.805470i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −182.359 | −0.406146 | −0.203073 | − | 0.979164i | \(-0.565093\pi\) | ||||
−0.203073 | + | 0.979164i | \(0.565093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −359.190 | + | 359.190i | −0.796430 | + | 0.796430i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 92.5241 | − | 92.5241i | 0.204248 | − | 0.204248i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 320.530 | 0.704461 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 272.942i | 0.597246i | 0.954371 | + | 0.298623i | \(0.0965274\pi\) | ||||
−0.954371 | + | 0.298623i | \(0.903473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −85.9759 | − | 85.9759i | −0.187311 | − | 0.187311i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 188.323 | + | 188.323i | 0.408510 | + | 0.408510i | 0.881219 | − | 0.472709i | \(-0.156724\pi\) |
−0.472709 | + | 0.881219i | \(0.656724\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 116.023i | 0.250590i | 0.992120 | + | 0.125295i | \(0.0399877\pi\) | ||||
−0.992120 | + | 0.125295i | \(0.960012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 217.131 | 0.466949 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 271.914 | − | 271.914i | 0.582257 | − | 0.582257i | −0.353266 | − | 0.935523i | \(-0.614929\pi\) |
0.935523 | + | 0.353266i | \(0.114929\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 200.838 | − | 200.838i | 0.428227 | − | 0.428227i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 199.721 | 0.424035 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 820.966i | 1.73566i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 352.352 | + | 352.352i | 0.741793 | + | 0.741793i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 200.957 | + | 200.957i | 0.421293 | + | 0.421293i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 775.808i | − | 1.61964i | −0.586678 | − | 0.809820i | \(-0.699565\pi\) | ||
0.586678 | − | 0.809820i | \(-0.300435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −175.988 | −0.365880 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.9022 | − | 37.9022i | 0.0784725 | − | 0.0784725i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 110.231 | − | 110.231i | 0.227280 | − | 0.227280i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −174.891 | −0.359118 | −0.179559 | − | 0.983747i | \(-0.557467\pi\) | ||||
−0.179559 | + | 0.983747i | \(0.557467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 136.697i | − | 0.279545i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 348.578 | + | 348.578i | 0.709934 | + | 0.709934i | 0.966521 | − | 0.256587i | \(-0.0825980\pi\) |
−0.256587 | + | 0.966521i | \(0.582598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −430.352 | − | 430.352i | −0.872926 | − | 0.872926i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 386.541i | − | 0.780890i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −227.269 | −0.457282 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 607.544 | − | 607.544i | 1.21752 | − | 1.21752i | 0.249027 | − | 0.968496i | \(-0.419889\pi\) |
0.968496 | − | 0.249027i | \(-0.0801109\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.1702 | + | 30.1702i | −0.0602199 | + | 0.0602199i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 130.935 | 0.260309 | 0.130154 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130154 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 34.0789i | − | 0.0674829i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 126.373 | + | 126.373i | 0.249257 | + | 0.249257i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −61.5539 | − | 61.5539i | −0.120931 | − | 0.120931i | 0.644051 | − | 0.764982i | \(-0.277252\pi\) |
−0.764982 | + | 0.644051i | \(0.777252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 566.849i | 1.10929i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −86.3387 | −0.168302 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 551.159 | − | 551.159i | 1.07021 | − | 1.07021i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 223.763 | − | 223.763i | 0.432811 | − | 0.432811i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.9670 | −0.0230578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.5929i | 0.0625584i | 0.999511 | + | 0.0312792i | \(0.00995810\pi\) | ||||
−0.999511 | + | 0.0312792i | \(0.990042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 226.407 | + | 226.407i | 0.432900 | + | 0.432900i | 0.889614 | − | 0.456713i | \(-0.150974\pi\) |
−0.456713 | + | 0.889614i | \(0.650974\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 195.693 | + | 195.693i | 0.372748 | + | 0.372748i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 395.578i | − | 0.750623i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −495.262 | −0.936224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 81.4570 | − | 81.4570i | 0.153403 | − | 0.153403i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −167.709 | + | 167.709i | −0.314652 | + | 0.314652i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1044.68 | −1.95267 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 562.168i | 1.04687i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 253.254 | + | 253.254i | 0.469859 | + | 0.469859i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 510.912 | + | 510.912i | 0.944385 | + | 0.944385i | 0.998533 | − | 0.0541480i | \(-0.0172443\pi\) |
−0.0541480 | + | 0.998533i | \(0.517244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 285.628i | 0.526018i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1133.13 | 2.07913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −512.889 | + | 512.889i | −0.937639 | + | 0.937639i | −0.998167 | − | 0.0605271i | \(-0.980722\pi\) |
0.0605271 | + | 0.998167i | \(0.480722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 195.720 | − | 195.720i | 0.356502 | − | 0.356502i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −432.168 | −0.784334 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 113.390i | 0.205046i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −197.016 | − | 197.016i | −0.354983 | − | 0.354983i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 566.691 | + | 566.691i | 1.01740 | + | 1.01740i | 0.999846 | + | 0.0175529i | \(0.00558754\pi\) |
0.0175529 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 383.317i | 0.685720i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −704.215 | −1.25529 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −548.653 | + | 548.653i | −0.974517 | + | 0.974517i | −0.999683 | − | 0.0251665i | \(-0.991988\pi\) |
0.0251665 | + | 0.999683i | \(0.491988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 122.088 | − | 122.088i | 0.216085 | − | 0.216085i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.9517 | −0.0845708 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 551.224i | − | 0.968760i | −0.874858 | − | 0.484380i | \(-0.839045\pi\) | ||
0.874858 | − | 0.484380i | \(-0.160955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −458.387 | − | 458.387i | −0.802780 | − | 0.802780i | 0.180749 | − | 0.983529i | \(-0.442148\pi\) |
−0.983529 | + | 0.180749i | \(0.942148\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 115.410 | + | 115.410i | 0.201413 | + | 0.201413i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 174.191i | 0.302941i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −718.488 | −1.24521 | −0.622607 | − | 0.782535i | \(-0.713926\pi\) | ||||
−0.622607 | + | 0.782535i | \(0.713926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −103.205 | + | 103.205i | −0.178247 | + | 0.178247i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −128.744 | + | 128.744i | −0.221590 | + | 0.221590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1646.00 | 2.82333 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 180.480i | − | 0.308512i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.02450 | − | 3.02450i | −0.00515247 | − | 0.00515247i | 0.704526 | − | 0.709678i | \(-0.251160\pi\) |
−0.709678 | + | 0.704526i | \(0.751160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −198.624 | − | 198.624i | −0.337222 | − | 0.337222i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 139.517i | − | 0.236070i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 576.193 | 0.971657 | 0.485829 | − | 0.874054i | \(-0.338518\pi\) | ||||
0.485829 | + | 0.874054i | \(0.338518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 653.726 | − | 653.726i | 1.09870 | − | 1.09870i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −240.270 | + | 240.270i | −0.402462 | + | 0.402462i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1101.40 | 1.83873 | 0.919365 | − | 0.393406i | \(-0.128703\pi\) | ||||
0.919365 | + | 0.393406i | \(0.128703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.11053i | − | 0.0118312i | −0.999983 | − | 0.00591558i | \(-0.998117\pi\) | ||
0.999983 | − | 0.00591558i | \(-0.00188300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −113.085 | − | 113.085i | −0.187538 | − | 0.187538i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −948.578 | − | 948.578i | −1.56790 | − | 1.56790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 528.384i | − | 0.870485i | −0.900313 | − | 0.435242i | \(-0.856663\pi\) | ||
0.900313 | − | 0.435242i | \(-0.143337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −240.022 | −0.394125 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 104.477 | − | 104.477i | 0.170994 | − | 0.170994i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −642.364 | + | 642.364i | −1.04790 | + | 1.04790i | −0.0491093 | + | 0.998793i | \(0.515638\pi\) |
−0.998793 | + | 0.0491093i | \(0.984362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −375.496 | −0.610562 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1068.16i | − | 1.73122i | −0.500717 | − | 0.865611i | \(-0.666930\pi\) | ||
0.500717 | − | 0.865611i | \(-0.333070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −691.136 | − | 691.136i | −1.11654 | − | 1.11654i | −0.992246 | − | 0.124290i | \(-0.960335\pi\) |
−0.124290 | − | 0.992246i | \(-0.539665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.3415 | − | 21.3415i | −0.0343663 | − | 0.0343663i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 281.332i | 0.451576i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 475.371 | 0.760594 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −353.593 | + | 353.593i | −0.563945 | + | 0.563945i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −358.931 | + | 358.931i | −0.570637 | + | 0.570637i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −486.622 | −0.771191 | −0.385596 | − | 0.922668i | \(-0.626004\pi\) | ||||
−0.385596 | + | 0.922668i | \(0.626004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 434.393i | − | 0.686245i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −619.681 | − | 619.681i | −0.975875 | − | 0.975875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 118.247 | + | 118.247i | 0.185631 | + | 0.185631i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 127.968i | 0.200263i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −691.017 | −1.07803 | −0.539015 | − | 0.842296i | \(-0.681203\pi\) | ||||
−0.539015 | + | 0.842296i | \(0.681203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −652.605 | + | 652.605i | −1.01494 | + | 1.01494i | −0.0150512 | + | 0.999887i | \(0.504791\pi\) |
−0.999887 | + | 0.0150512i | \(0.995209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −429.117 | + | 429.117i | −0.665298 | + | 0.665298i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1156.72 | −1.78782 | −0.893911 | − | 0.448245i | \(-0.852049\pi\) | ||||
−0.893911 | + | 0.448245i | \(0.852049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 667.201i | − | 1.02804i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −110.314 | − | 110.314i | −0.169453 | − | 0.169453i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −209.105 | − | 209.105i | −0.320222 | − | 0.320222i | 0.528630 | − | 0.848852i | \(-0.322706\pi\) |
−0.848852 | + | 0.528630i | \(0.822706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 725.776i | 1.10806i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 319.174 | 0.485805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −533.902 | + | 533.902i | −0.810170 | + | 0.810170i | −0.984659 | − | 0.174489i | \(-0.944173\pi\) |
0.174489 | + | 0.984659i | \(0.444173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 283.120 | − | 283.120i | 0.428320 | − | 0.428320i | −0.459736 | − | 0.888056i | \(-0.652056\pi\) |
0.888056 | + | 0.459736i | \(0.152056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −328.805 | −0.495935 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 656.484i | − | 0.987195i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −106.825 | − | 106.825i | −0.160157 | − | 0.160157i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −462.861 | − | 462.861i | −0.691870 | − | 0.691870i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1603.11i | − | 2.38913i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −397.854 | −0.591164 | −0.295582 | − | 0.955317i | \(-0.595514\pi\) | ||||
−0.295582 | + | 0.955317i | \(0.595514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 110.188 | − | 110.188i | 0.163242 | − | 0.163242i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 289.959 | − | 289.959i | 0.428299 | − | 0.428299i | −0.459749 | − | 0.888049i | \(-0.652061\pi\) |
0.888049 | + | 0.459749i | \(0.152061\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −112.005 | −0.164956 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 254.525i | − | 0.373751i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 150.197 | + | 150.197i | 0.219908 | + | 0.219908i | 0.808460 | − | 0.588551i | \(-0.200302\pi\) |
−0.588551 | + | 0.808460i | \(0.700302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 652.686 | + | 652.686i | 0.952826 | + | 0.952826i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 247.534i | − | 0.360312i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 768.535 | 1.11544 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −791.212 | + | 791.212i | −1.14502 | + | 1.14502i | −0.157506 | + | 0.987518i | \(0.550345\pi\) |
−0.987518 | + | 0.157506i | \(0.949655\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −196.382 | + | 196.382i | −0.283380 | + | 0.283380i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1772.46 | 2.55030 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 684.092i | 0.981481i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 351.819 | + | 351.819i | 0.503318 | + | 0.503318i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 900.201 | + | 900.201i | 1.28417 | + | 1.28417i | 0.938274 | + | 0.345893i | \(0.112424\pi\) |
0.345893 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 360.445i | 0.512724i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 233.921 | 0.331803 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.3138 | + | 17.3138i | −0.0244891 | + | 0.0244891i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 128.490 | − | 128.490i | 0.181227 | − | 0.181227i | −0.610663 | − | 0.791891i | \(-0.709097\pi\) |
0.791891 | + | 0.610663i | \(0.209097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 63.8463 | 0.0897979 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 98.1928i | − | 0.137718i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −739.140 | − | 739.140i | −1.03376 | − | 1.03376i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 184.865 | + | 184.865i | 0.257831 | + | 0.257831i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1246.14i | 1.73315i | 0.499045 | + | 0.866576i | \(0.333684\pi\) | ||||
−0.499045 | + | 0.866576i | \(0.666316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −560.033 | −0.776745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.2730 | + | 46.2730i | −0.0640014 | + | 0.0640014i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 551.546 | − | 551.546i | 0.760753 | − | 0.760753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1130.07 | 1.55443 | 0.777216 | − | 0.629234i | \(-0.216631\pi\) | ||||
0.777216 | + | 0.629234i | \(0.216631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 781.782 | + | 781.782i | 1.06947 | + | 1.06947i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −708.087 | − | 708.087i | −0.966012 | − | 0.966012i | 0.0334292 | − | 0.999441i | \(-0.489357\pi\) |
−0.999441 | + | 0.0334292i | \(0.989357\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 264.751i | 0.360205i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −926.264 | −1.25680 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.7516 | − | 32.7516i | 0.0443188 | − | 0.0443188i | −0.684600 | − | 0.728919i | \(-0.740023\pi\) |
0.728919 | + | 0.684600i | \(0.240023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −165.096 | + | 165.096i | −0.222802 | + | 0.222802i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −708.128 | −0.953066 | −0.476533 | − | 0.879157i | \(-0.658107\pi\) | ||||
−0.476533 | + | 0.879157i | \(0.658107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1541.47i | 2.06909i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 72.4914 | + | 72.4914i | 0.0970434 | + | 0.0970434i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 530.751 | + | 530.751i | 0.708612 | + | 0.708612i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1242.37i | − | 1.65429i | −0.561990 | − | 0.827144i | \(-0.689964\pi\) | ||
0.561990 | − | 0.827144i | \(-0.310036\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 247.189 | 0.328272 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 396.127 | − | 396.127i | 0.524671 | − | 0.524671i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −311.304 | + | 311.304i | −0.411233 | + | 0.411233i | −0.882168 | − | 0.470935i | \(-0.843917\pi\) |
0.470935 | + | 0.882168i | \(0.343917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −174.805 | −0.230309 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 179.137i | 0.235397i | 0.993049 | + | 0.117699i | \(0.0375517\pi\) | ||||
−0.993049 | + | 0.117699i | \(0.962448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −575.685 | − | 575.685i | −0.754502 | − | 0.754502i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −368.091 | − | 368.091i | −0.481165 | − | 0.481165i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 311.523i | − | 0.406158i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −967.409 | −1.25801 | −0.629005 | − | 0.777402i | \(-0.716537\pi\) | ||||
−0.629005 | + | 0.777402i | \(0.716537\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −295.525 | + | 295.525i | −0.383301 | + | 0.383301i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −96.7342 | + | 96.7342i | −0.125141 | + | 0.125141i | −0.766904 | − | 0.641762i | \(-0.778204\pi\) |
0.641762 | + | 0.766904i | \(0.278204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 506.979 | 0.654166 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 200.188i | 0.257642i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 343.489 | + | 343.489i | 0.440936 | + | 0.440936i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 524.082 | + | 524.082i | 0.671039 | + | 0.671039i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 135.148i | 0.172603i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 855.070 | 1.08926 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 381.038 | − | 381.038i | 0.484166 | − | 0.484166i | −0.422293 | − | 0.906459i | \(-0.638775\pi\) |
0.906459 | + | 0.422293i | \(0.138775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −145.435 | + | 145.435i | −0.184328 | + | 0.184328i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −124.054 | −0.156831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 748.507i | − | 0.943893i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 860.362 | + | 860.362i | 1.08222 | + | 1.08222i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −371.148 | − | 371.148i | −0.465681 | − | 0.465681i | 0.434831 | − | 0.900512i | \(-0.356808\pi\) |
−0.900512 | + | 0.434831i | \(0.856808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 426.167i | − | 0.533375i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 158.409 | 0.197764 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1307.15 | − | 1307.15i | 1.62783 | − | 1.62783i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 162.272 | − | 162.272i | 0.201580 | − | 0.201580i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.9799 | −0.0235191 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 309.566i | − | 0.382653i | −0.981526 | − | 0.191326i | \(-0.938721\pi\) | ||
0.981526 | − | 0.191326i | \(-0.0612789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.2916 | + | 27.2916i | 0.0336517 | + | 0.0336517i | 0.723732 | − | 0.690081i | \(-0.242425\pi\) |
−0.690081 | + | 0.723732i | \(0.742425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 161.543 | + | 161.543i | 0.198699 | + | 0.198699i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 585.247i | − | 0.718095i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 785.081 | 0.960931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −91.6928 | + | 91.6928i | −0.111957 | + | 0.111957i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −879.903 | + | 879.903i | −1.07175 | + | 1.07175i | −0.0745264 | + | 0.997219i | \(0.523745\pi\) |
−0.997219 | + | 0.0745264i | \(0.976255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −68.6842 | −0.0834559 | −0.0417280 | − | 0.999129i | \(-0.513286\pi\) | ||||
−0.0417280 | + | 0.999129i | \(0.513286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 902.533i | − | 1.09398i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −942.097 | − | 942.097i | −1.13917 | − | 1.13917i | −0.988599 | − | 0.150575i | \(-0.951887\pi\) |
−0.150575 | − | 0.988599i | \(-0.548113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −568.532 | − | 568.532i | −0.685805 | − | 0.685805i | 0.275497 | − | 0.961302i | \(-0.411158\pi\) |
−0.961302 | + | 0.275497i | \(0.911158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 495.660i | − | 0.596462i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 482.333 | 0.579031 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −129.169 | + | 129.169i | −0.154693 | + | 0.154693i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.1140 | + | 62.1140i | −0.0742102 | + | 0.0742102i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1346.87 | 1.60533 | 0.802666 | − | 0.596429i | \(-0.203414\pi\) | ||||
0.802666 | + | 0.596429i | \(0.203414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 164.515i | − | 0.195618i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −84.3228 | − | 84.3228i | −0.100027 | − | 0.100027i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 541.046 | + | 541.046i | 0.640291 | + | 0.640291i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 963.851i | 1.13796i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 506.488 | 0.596570 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −89.0960 | + | 89.0960i | −0.104696 | + | 0.104696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 74.4816 | − | 74.4816i | 0.0873172 | − | 0.0873172i | −0.662099 | − | 0.749416i | \(-0.730334\pi\) |
0.749416 | + | 0.662099i | \(0.230334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −369.645 | −0.432333 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.7221i | 0.0626862i | 0.999509 | + | 0.0313431i | \(0.00997845\pi\) | ||||
−0.999509 | + | 0.0313431i | \(0.990022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 537.704 | + | 537.704i | 0.625965 | + | 0.625965i | 0.947050 | − | 0.321085i | \(-0.104048\pi\) |
−0.321085 | + | 0.947050i | \(0.604048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 190.771 | + | 190.771i | 0.221569 | + | 0.221569i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1390.97i | 1.61178i | 0.592064 | + | 0.805891i | \(0.298313\pi\) | ||||
−0.592064 | + | 0.805891i | \(0.701687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −51.2347 | −0.0592309 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −316.652 | + | 316.652i | −0.365227 | + | 0.365227i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 261.477 | − | 261.477i | 0.300895 | − | 0.300895i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −432.482 | −0.496535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 63.0666i | 0.0722412i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 139.391 | + | 139.391i | 0.159303 | + | 0.159303i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 940.115 | + | 940.115i | 1.07197 | + | 1.07197i | 0.997201 | + | 0.0747652i | \(0.0238207\pi\) |
0.0747652 | + | 0.997201i | \(0.476179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 884.847i | − | 1.00665i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −140.985 | −0.160029 | −0.0800143 | − | 0.996794i | \(-0.525497\pi\) | ||||
−0.0800143 | + | 0.996794i | \(0.525497\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 482.231 | − | 482.231i | 0.546127 | − | 0.546127i | −0.379191 | − | 0.925318i | \(-0.623798\pi\) |
0.925318 | + | 0.379191i | \(0.123798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 348.744 | − | 348.744i | 0.394062 | − | 0.394062i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −266.180 | −0.300091 | −0.150045 | − | 0.988679i | \(-0.547942\pi\) | ||||
−0.150045 | + | 0.988679i | \(0.547942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 629.658i | 0.708277i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 110.576 | + | 110.576i | 0.124104 | + | 0.124104i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −213.982 | − | 213.982i | −0.239622 | − | 0.239622i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2406.83i | 2.68919i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −81.6180 | −0.0909899 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −310.911 | + | 310.911i | −0.345841 | + | 0.345841i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1567.44 | − | 1567.44i | 1.73967 | − | 1.73967i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 436.026 | 0.482864 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1222.87i | 1.35124i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 303.117 | + | 303.117i | 0.334197 | + | 0.334197i | 0.854178 | − | 0.519981i | \(-0.174061\pi\) |
−0.519981 | + | 0.854178i | \(0.674061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.74881 | + | 9.74881i | 0.0107248 | + | 0.0107248i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 296.228i | 0.325168i | 0.986695 | + | 0.162584i | \(0.0519829\pi\) | ||||
−0.986695 | + | 0.162584i | \(0.948017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 593.765 | 0.650346 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 837.941 | − | 837.941i | 0.915783 | − | 0.915783i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 368.731 | − | 368.731i | 0.402106 | − | 0.402106i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 228.052 | 0.248153 | 0.124076 | − | 0.992273i | \(-0.460403\pi\) | ||||
0.124076 | + | 0.992273i | \(0.460403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.7172i | 0.0290090i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 244.699 | + | 244.699i | 0.265113 | + | 0.265113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −460.011 | − | 460.011i | −0.497309 | − | 0.497309i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 315.336i | 0.340168i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −574.026 | −0.617897 | −0.308948 | − | 0.951079i | \(-0.599977\pi\) | ||||
−0.308948 | + | 0.951079i | \(0.599977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 242.184 | − | 242.184i | 0.260133 | − | 0.260133i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −196.267 | + | 196.267i | −0.210361 | + | 0.210361i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3014.98 | −3.22457 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1098.22i | 1.17206i | 0.810291 | + | 0.586028i | \(0.199309\pi\) | ||||
−0.810291 | + | 0.586028i | \(0.800691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −435.397 | − | 435.397i | −0.463682 | − | 0.463682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −857.669 | − | 857.669i | −0.911444 | − | 0.911444i | 0.0849418 | − | 0.996386i | \(-0.472930\pi\) |
−0.996386 | + | 0.0849418i | \(0.972930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 169.810i | 0.180074i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −205.297 | −0.217245 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1041.67 | + | 1041.67i | −1.09997 | + | 1.09997i | −0.105556 | + | 0.994413i | \(0.533662\pi\) |
−0.994413 | + | 0.105556i | \(0.966338\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 610.322 | − | 610.322i | 0.643121 | − | 0.643121i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −177.635 | −0.186788 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 910.089i | − | 0.954973i | −0.878639 | − | 0.477486i | \(-0.841548\pi\) | ||
0.878639 | − | 0.477486i | \(-0.158452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 494.107 | + | 494.107i | 0.517389 | + | 0.517389i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 553.489 | + | 553.489i | 0.578359 | + | 0.578359i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 663.195i | − | 0.691548i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 675.212 | 0.702614 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 298.848 | − | 298.848i | 0.310330 | − | 0.310330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −441.856 | + | 441.856i | −0.457882 | + | 0.457882i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 695.071 | 0.718791 | 0.359396 | − | 0.933185i | \(-0.382983\pi\) | ||||
0.359396 | + | 0.933185i | \(0.382983\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 673.433i | 0.694977i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1208.40 | + | 1208.40i | 1.24449 | + | 1.24449i | 0.958120 | + | 0.286366i | \(0.0924472\pi\) |
0.286366 | + | 0.958120i | \(0.407553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −900.500 | − | 900.500i | −0.925488 | − | 0.925488i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 421.401i | − | 0.432206i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 141.036 | 0.144356 | 0.0721780 | − | 0.997392i | \(-0.477005\pi\) | ||||
0.0721780 | + | 0.997392i | \(0.477005\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 648.750 | − | 648.750i | 0.662666 | − | 0.662666i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −324.149 | + | 324.149i | −0.330427 | + | 0.330427i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1692.71 | −1.72199 | −0.860994 | − | 0.508616i | \(-0.830157\pi\) | ||||
−0.860994 | + | 0.508616i | \(0.830157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 597.320i | − | 0.606417i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −118.844 | − | 118.844i | −0.120409 | − | 0.120409i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 194.059 | + | 194.059i | 0.196217 | + | 0.196217i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1532.62i | − | 1.54654i | −0.634079 | − | 0.773268i | \(-0.718621\pi\) | ||
0.634079 | − | 0.773268i | \(-0.281379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −607.710 | −0.611994 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1028.67 | + | 1028.67i | −1.03384 | + | 1.03384i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1131.91 | − | 1131.91i | 1.13532 | − | 1.13532i | 0.146039 | − | 0.989279i | \(-0.453348\pi\) |
0.989279 | − | 0.146039i | \(-0.0466524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 112.719 | 0.112832 |
(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 | 192.3.l.a.175.1 | 16 | ||
3.2 | odd | 2 | 576.3.m.c.559.8 | 16 | |||
4.3 | odd | 2 | 48.3.l.a.19.7 | ✓ | 16 | ||
8.3 | odd | 2 | 384.3.l.a.223.4 | 16 | |||
8.5 | even | 2 | 384.3.l.b.223.8 | 16 | |||
12.11 | even | 2 | 144.3.m.c.19.2 | 16 | |||
16.3 | odd | 4 | 384.3.l.b.31.8 | 16 | |||
16.5 | even | 4 | 48.3.l.a.43.7 | yes | 16 | ||
16.11 | odd | 4 | inner | 192.3.l.a.79.1 | 16 | ||
16.13 | even | 4 | 384.3.l.a.31.4 | 16 | |||
24.5 | odd | 2 | 1152.3.m.c.991.1 | 16 | |||
24.11 | even | 2 | 1152.3.m.f.991.1 | 16 | |||
48.5 | odd | 4 | 144.3.m.c.91.2 | 16 | |||
48.11 | even | 4 | 576.3.m.c.271.8 | 16 | |||
48.29 | odd | 4 | 1152.3.m.f.415.1 | 16 | |||
48.35 | even | 4 | 1152.3.m.c.415.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.7 | ✓ | 16 | 4.3 | odd | 2 | ||
48.3.l.a.43.7 | yes | 16 | 16.5 | even | 4 | ||
144.3.m.c.19.2 | 16 | 12.11 | even | 2 | |||
144.3.m.c.91.2 | 16 | 48.5 | odd | 4 | |||
192.3.l.a.79.1 | 16 | 16.11 | odd | 4 | inner | ||
192.3.l.a.175.1 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.a.31.4 | 16 | 16.13 | even | 4 | |||
384.3.l.a.223.4 | 16 | 8.3 | odd | 2 | |||
384.3.l.b.31.8 | 16 | 16.3 | odd | 4 | |||
384.3.l.b.223.8 | 16 | 8.5 | even | 2 | |||
576.3.m.c.271.8 | 16 | 48.11 | even | 4 | |||
576.3.m.c.559.8 | 16 | 3.2 | odd | 2 | |||
1152.3.m.c.415.1 | 16 | 48.35 | even | 4 | |||
1152.3.m.c.991.1 | 16 | 24.5 | odd | 2 | |||
1152.3.m.f.415.1 | 16 | 48.29 | odd | 4 | |||
1152.3.m.f.991.1 | 16 | 24.11 | even | 2 |