Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(33,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.33");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 33.4 | ||
Root | \(-0.707107 + 0.358323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.33 |
Dual form | 224.3.s.a.129.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.438854 | + | 0.253372i | −0.146285 | + | 0.0844575i | −0.571356 | − | 0.820702i | \(-0.693582\pi\) |
0.425071 | + | 0.905160i | \(0.360249\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.59219 | − | 2.65130i | −0.918439 | − | 0.530261i | −0.0353020 | − | 0.999377i | \(-0.511239\pi\) |
−0.883137 | + | 0.469116i | \(0.844573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.27770 | + | 4.59846i | 0.753957 | + | 0.656923i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.37160 | + | 7.57184i | −0.485734 | + | 0.841316i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.54498 | − | 14.8003i | −0.776817 | − | 1.34549i | −0.933768 | − | 0.357880i | \(-0.883500\pi\) |
0.156951 | − | 0.987606i | \(-0.449833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.4744i | 1.65187i | 0.563762 | + | 0.825937i | \(0.309353\pi\) | ||||
−0.563762 | + | 0.825937i | \(0.690647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68707 | 0.179138 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.7992 | + | 12.0084i | −1.22348 | + | 0.706378i | −0.965659 | − | 0.259814i | \(-0.916339\pi\) |
−0.257824 | + | 0.966192i | \(0.583005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.5831 | + | 6.11016i | 0.557006 | + | 0.321588i | 0.751943 | − | 0.659228i | \(-0.229117\pi\) |
−0.194937 | + | 0.980816i | \(0.562450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.48126 | − | 0.680829i | −0.165775 | − | 0.0324205i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −20.1464 | + | 34.8946i | −0.875932 | + | 1.51716i | −0.0201644 | + | 0.999797i | \(0.506419\pi\) |
−0.855767 | + | 0.517361i | \(0.826914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.55882 | + | 2.69996i | 0.0623530 | + | 0.107998i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 8.99128i | − | 0.333010i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −26.0770 | −0.899209 | −0.449604 | − | 0.893228i | \(-0.648435\pi\) | ||||
−0.449604 | + | 0.893228i | \(0.648435\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21.8789 | − | 12.6318i | 0.705770 | − | 0.407477i | −0.103723 | − | 0.994606i | \(-0.533075\pi\) |
0.809493 | + | 0.587130i | \(0.199742\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 0.227273 | + | 0.131216i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0443 | − | 35.1098i | −0.344123 | − | 1.00314i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.48126 | + | 11.2259i | −0.175169 | + | 0.303402i | −0.940220 | − | 0.340568i | \(-0.889381\pi\) |
0.765051 | + | 0.643970i | \(0.222714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.44101 | − | 9.42411i | −0.139513 | − | 0.241644i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 33.8721i | − | 0.826150i | −0.910697 | − | 0.413075i | \(-0.864455\pi\) | ||
0.910697 | − | 0.413075i | \(-0.135545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.9958 | −0.697576 | −0.348788 | − | 0.937202i | \(-0.613407\pi\) | ||||
−0.348788 | + | 0.937202i | \(0.613407\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 40.1505 | − | 23.1809i | 0.892233 | − | 0.515131i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 48.2788 | + | 27.8738i | 1.02721 | + | 0.593060i | 0.916184 | − | 0.400758i | \(-0.131253\pi\) |
0.111025 | + | 0.993818i | \(0.464587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.70828 | + | 48.5386i | 0.136904 | + | 0.990584i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.08521 | − | 10.5399i | 0.119318 | − | 0.206665i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.36362 | + | 7.55801i | 0.0823324 | + | 0.142604i | 0.904251 | − | 0.427001i | \(-0.140430\pi\) |
−0.821919 | + | 0.569604i | \(0.807096\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 90.6214i | 1.64766i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.19259 | −0.108642 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 43.2893 | − | 24.9931i | 0.733718 | − | 0.423612i | −0.0860631 | − | 0.996290i | \(-0.527429\pi\) |
0.819781 | + | 0.572678i | \(0.194095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40886 | + | 1.96811i | 0.0558829 | + | 0.0322640i | 0.527681 | − | 0.849443i | \(-0.323062\pi\) |
−0.471798 | + | 0.881707i | \(0.656395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −57.8909 | + | 19.8593i | −0.918903 | + | 0.315226i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 56.9351 | − | 98.6144i | 0.875924 | − | 1.51715i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.9426 | − | 91.6994i | −0.790189 | − | 1.36865i | −0.925850 | − | 0.377892i | \(-0.876649\pi\) |
0.135661 | − | 0.990755i | \(-0.456684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 20.4182i | − | 0.295916i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35.0232 | 0.493285 | 0.246642 | − | 0.969107i | \(-0.420673\pi\) | ||||
0.246642 | + | 0.969107i | \(0.420673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.3712 | − | 23.3083i | 0.553030 | − | 0.319292i | −0.197313 | − | 0.980340i | \(-0.563222\pi\) |
0.750343 | + | 0.661049i | \(0.229888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.36819 | − | 0.789926i | −0.0182426 | − | 0.0105323i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.9610 | − | 117.406i | 0.298194 | − | 1.52475i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43.4998 | − | 75.3438i | 0.550630 | − | 0.953719i | −0.447599 | − | 0.894234i | \(-0.647721\pi\) |
0.998229 | − | 0.0594846i | \(-0.0189457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −37.0663 | − | 64.2007i | −0.457609 | − | 0.792601i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64.0079i | 0.771180i | 0.922670 | + | 0.385590i | \(0.126002\pi\) | ||||
−0.922670 | + | 0.385590i | \(0.873998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 127.352 | 1.49826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.4440 | − | 6.60721i | 0.131540 | − | 0.0759449i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 37.2272 | + | 21.4932i | 0.418284 | + | 0.241496i | 0.694343 | − | 0.719645i | \(-0.255695\pi\) |
−0.276059 | + | 0.961141i | \(0.589029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.7491 | + | 113.335i | −1.08515 | + | 1.24544i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.40109 | + | 11.0870i | −0.0688289 | + | 0.119215i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.3998 | − | 56.1181i | −0.341051 | − | 0.590717i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 28.7493i | 0.296384i | 0.988959 | + | 0.148192i | \(0.0473454\pi\) | ||||
−0.988959 | + | 0.148192i | \(0.952655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 149.421 | 1.50930 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −53.2337 | + | 30.7345i | −0.527067 | + | 0.304302i | −0.739821 | − | 0.672804i | \(-0.765090\pi\) |
0.212754 | + | 0.977106i | \(0.431757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51.7263 | − | 29.8642i | −0.502197 | − | 0.289944i | 0.227423 | − | 0.973796i | \(-0.426970\pi\) |
−0.729620 | + | 0.683852i | \(0.760303\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.1816 | + | 12.3564i | 0.135062 | + | 0.117680i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −65.8380 | + | 114.035i | −0.615308 | + | 1.06574i | 0.375022 | + | 0.927016i | \(0.377635\pi\) |
−0.990330 | + | 0.138729i | \(0.955698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9045 | + | 32.7436i | 0.173436 | + | 0.300400i | 0.939619 | − | 0.342222i | \(-0.111180\pi\) |
−0.766183 | + | 0.642623i | \(0.777846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.56870i | − | 0.0591774i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −46.4443 | −0.411012 | −0.205506 | − | 0.978656i | \(-0.565884\pi\) | ||||
−0.205506 | + | 0.978656i | \(0.565884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 185.033 | − | 106.829i | 1.60898 | − | 0.928944i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −162.601 | − | 93.8774i | −1.38975 | − | 0.802371i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −164.992 | − | 32.2675i | −1.38649 | − | 0.271155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.5335 | + | 148.148i | −0.706888 | + | 1.22437i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.58227 | + | 14.8649i | 0.0697745 | + | 0.120853i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 116.034i | 0.928268i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7816 | −0.100642 | −0.0503211 | − | 0.998733i | \(-0.516024\pi\) | ||||
−0.0503211 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.1638 | − | 7.60010i | 0.102045 | − | 0.0589155i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.929338 | − | 0.536554i | −0.00709418 | − | 0.00409583i | 0.496449 | − | 0.868066i | \(-0.334637\pi\) |
−0.503543 | + | 0.863970i | \(0.667970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.7572 | + | 80.9137i | 0.208700 | + | 0.608374i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.8386 | + | 41.2897i | −0.176582 | + | 0.305850i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 33.4330 | + | 57.9076i | 0.244036 | + | 0.422683i | 0.961860 | − | 0.273541i | \(-0.0881951\pi\) |
−0.717824 | + | 0.696225i | \(0.754862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 221.071i | 1.59044i | 0.606322 | + | 0.795219i | \(0.292644\pi\) | ||||
−0.606322 | + | 0.795219i | \(0.707356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.2498 | −0.200353 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 317.828 | − | 183.498i | 2.22257 | − | 1.28320i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 119.751 | + | 69.1382i | 0.825868 | + | 0.476815i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.2423 | − | 19.6017i | −0.103689 | − | 0.133345i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7606 | − | 34.2264i | 0.132621 | − | 0.229707i | −0.792065 | − | 0.610437i | \(-0.790994\pi\) |
0.924686 | + | 0.380730i | \(0.124327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −111.362 | − | 192.885i | −0.737499 | − | 1.27739i | −0.953618 | − | 0.301019i | \(-0.902673\pi\) |
0.216119 | − | 0.976367i | \(-0.430660\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 209.984i | − | 1.37245i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −133.963 | −0.864275 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −175.081 | + | 101.083i | −1.11516 | + | 0.643840i | −0.940162 | − | 0.340728i | \(-0.889327\pi\) |
−0.175002 | + | 0.984568i | \(0.555993\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.82998 | − | 2.21124i | −0.0240879 | − | 0.0139072i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −266.789 | + | 91.5209i | −1.65707 | + | 0.568453i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.31509 | − | 2.27780i | 0.00806802 | − | 0.0139742i | −0.861963 | − | 0.506971i | \(-0.830765\pi\) |
0.870031 | + | 0.492997i | \(0.164099\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.9610 | − | 39.7696i | −0.139157 | − | 0.241028i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 133.004i | 0.796434i | 0.917291 | + | 0.398217i | \(0.130371\pi\) | ||||
−0.917291 | + | 0.398217i | \(0.869629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −292.148 | −1.72869 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −92.5304 | + | 53.4224i | −0.541113 | + | 0.312412i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 84.0786 | + | 48.5428i | 0.486004 | + | 0.280594i | 0.722915 | − | 0.690937i | \(-0.242802\pi\) |
−0.236911 | + | 0.971531i | \(0.576135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.18867 | + | 21.4178i | −0.0239352 | + | 0.122387i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6651 | + | 21.9367i | −0.0715544 | + | 0.123936i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −42.0185 | − | 72.7782i | −0.234740 | − | 0.406582i | 0.724457 | − | 0.689320i | \(-0.242091\pi\) |
−0.959197 | + | 0.282738i | \(0.908757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 214.347i | 1.18424i | 0.805851 | + | 0.592119i | \(0.201708\pi\) | ||||
−0.805851 | + | 0.592119i | \(0.798292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.99466 | −0.0108998 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 59.5264 | − | 34.3676i | 0.321765 | − | 0.185771i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 355.458 | + | 205.224i | 1.90084 | + | 1.09745i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41.3461 | − | 47.4533i | 0.218762 | − | 0.251076i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.3687 | + | 47.4040i | −0.143292 | + | 0.248188i | −0.928734 | − | 0.370746i | \(-0.879102\pi\) |
0.785443 | + | 0.618934i | \(0.212435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 174.150 | + | 301.637i | 0.902332 | + | 1.56289i | 0.824459 | + | 0.565922i | \(0.191480\pi\) |
0.0778732 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 57.7031i | 0.295913i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 161.606 | 0.820337 | 0.410169 | − | 0.912010i | \(-0.365470\pi\) | ||||
0.410169 | + | 0.912010i | \(0.365470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −119.186 | + | 68.8121i | −0.598925 | + | 0.345789i | −0.768618 | − | 0.639707i | \(-0.779056\pi\) |
0.169694 | + | 0.985497i | \(0.445722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 46.4682 | + | 26.8284i | 0.231185 | + | 0.133475i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −137.627 | − | 119.914i | −0.677965 | − | 0.590711i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −89.8053 | + | 155.547i | −0.438075 | + | 0.758768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −176.144 | − | 305.091i | −0.850939 | − | 1.47387i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 208.845i | − | 0.999258i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 101.563 | 0.481341 | 0.240670 | − | 0.970607i | \(-0.422633\pi\) | ||||
0.240670 | + | 0.970607i | \(0.422633\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.3701 | + | 8.87392i | −0.0721600 | + | 0.0416616i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 137.746 | + | 79.5279i | 0.640681 | + | 0.369897i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 173.557 | + | 33.9425i | 0.799802 | + | 0.156417i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.8114 | + | 20.4579i | −0.0539332 | + | 0.0934150i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −257.873 | − | 446.650i | −1.16685 | − | 2.02104i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 180.573i | − | 0.809744i | −0.914373 | − | 0.404872i | \(-0.867316\pi\) | ||
0.914373 | − | 0.404872i | \(-0.132684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.2582 | −0.121148 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 43.9146 | − | 25.3541i | 0.193456 | − | 0.111692i | −0.400143 | − | 0.916453i | \(-0.631040\pi\) |
0.593600 | + | 0.804761i | \(0.297706\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −172.801 | − | 99.7665i | −0.754588 | − | 0.435661i | 0.0727614 | − | 0.997349i | \(-0.476819\pi\) |
−0.827349 | + | 0.561688i | \(0.810152\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.6708 | + | 57.3416i | 0.0851551 | + | 0.248232i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 88.5790 | − | 153.423i | 0.380167 | − | 0.658469i | −0.610919 | − | 0.791693i | \(-0.709200\pi\) |
0.991086 | + | 0.133224i | \(0.0425330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −147.804 | − | 256.004i | −0.628952 | − | 1.08938i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 44.0866i | 0.186019i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 135.694 | 0.567756 | 0.283878 | − | 0.958860i | \(-0.408379\pi\) | ||||
0.283878 | + | 0.958860i | \(0.408379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273.872 | − | 158.120i | 1.13640 | − | 0.656101i | 0.190863 | − | 0.981617i | \(-0.438871\pi\) |
0.945537 | + | 0.325516i | \(0.105538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 102.613 | + | 59.2439i | 0.422278 | + | 0.243802i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 97.8850 | − | 240.684i | 0.399530 | − | 0.982386i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −131.212 | + | 227.266i | −0.531222 | + | 0.920104i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.2179 | − | 28.0901i | −0.0651319 | − | 0.112812i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 40.1231i | 0.159853i | 0.996801 | + | 0.0799265i | \(0.0254686\pi\) | ||||
−0.996801 | + | 0.0799265i | \(0.974531\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 688.603 | 2.72175 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −55.8889 | + | 32.2675i | −0.219172 | + | 0.126539i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −150.405 | − | 86.8366i | −0.585235 | − | 0.337886i | 0.177976 | − | 0.984035i | \(-0.443045\pi\) |
−0.763211 | + | 0.646149i | \(0.776378\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −85.8280 | + | 29.4430i | −0.331382 | + | 0.113680i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 113.999 | − | 197.451i | 0.436776 | − | 0.756518i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 182.291 | + | 315.737i | 0.693120 | + | 1.20052i | 0.970810 | + | 0.239848i | \(0.0770977\pi\) |
−0.277690 | + | 0.960671i | \(0.589569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 46.2771i | − | 0.174631i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.7831 | −0.0815846 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.0874 | − | 8.71074i | 0.0560871 | − | 0.0323819i | −0.471694 | − | 0.881762i | \(-0.656357\pi\) |
0.527781 | + | 0.849380i | \(0.323024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 112.812 | + | 65.1322i | 0.416281 | + | 0.240340i | 0.693485 | − | 0.720471i | \(-0.256074\pi\) |
−0.277204 | + | 0.960811i | \(0.589408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.6204 | − | 74.7580i | 0.0535545 | − | 0.273839i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.6402 | − | 46.1423i | 0.0968736 | − | 0.167790i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 124.595 | + | 215.804i | 0.449801 | + | 0.779077i | 0.998373 | − | 0.0570258i | \(-0.0181617\pi\) |
−0.548572 | + | 0.836103i | \(0.684828\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 220.885i | 0.791701i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −197.454 | −0.702684 | −0.351342 | − | 0.936247i | \(-0.614275\pi\) | ||||
−0.351342 | + | 0.936247i | \(0.614275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 185.615 | − | 107.165i | 0.655884 | − | 0.378675i | −0.134823 | − | 0.990870i | \(-0.543047\pi\) |
0.790707 | + | 0.612195i | \(0.209713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.4376 | + | 16.4184i | 0.0997809 | + | 0.0576085i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 155.760 | − | 178.767i | 0.542717 | − | 0.622882i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 143.904 | − | 249.250i | 0.497939 | − | 0.862456i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.28427 | − | 12.6167i | −0.0250319 | − | 0.0433565i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71.8385i | 0.245182i | 0.992457 | + | 0.122591i | \(0.0391204\pi\) | ||||
−0.992457 | + | 0.122591i | \(0.960880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −265.057 | −0.898499 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −133.074 | + | 76.8304i | −0.448061 | + | 0.258688i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −749.340 | − | 432.632i | −2.50615 | − | 1.44693i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −158.309 | − | 137.934i | −0.525943 | − | 0.458254i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.5746 | − | 26.9759i | 0.0514012 | − | 0.0890295i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.4361 | − | 18.0758i | −0.0342167 | − | 0.0592651i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 507.046i | − | 1.65162i | −0.563951 | − | 0.825808i | \(-0.690719\pi\) | ||
0.563951 | − | 0.825808i | \(-0.309281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.2671 | 0.0979516 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.089 | − | 155.359i | 0.865239 | − | 0.499546i | −0.000524087 | − | 1.00000i | \(-0.500167\pi\) |
0.865763 | + | 0.500454i | \(0.166833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 475.367 | + | 274.453i | 1.51875 | + | 0.876848i | 0.999756 | + | 0.0220674i | \(0.00702483\pi\) |
0.518989 | + | 0.854781i | \(0.326309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 318.499 | + | 62.2887i | 1.01111 | + | 0.197742i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −70.9651 | + | 122.915i | −0.223865 | + | 0.387745i | −0.955978 | − | 0.293437i | \(-0.905201\pi\) |
0.732113 | + | 0.681183i | \(0.238534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 222.828 | + | 385.949i | 0.698520 | + | 1.20987i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 66.7261i | − | 0.207869i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −293.494 | −0.908649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −57.9800 | + | 33.4748i | −0.178400 | + | 0.102999i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5927 | − | 9.57978i | −0.0507421 | − | 0.0292960i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 126.625 | + | 369.118i | 0.384877 | + | 1.12194i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4325 | − | 31.9260i | 0.0556873 | − | 0.0964533i | −0.836838 | − | 0.547451i | \(-0.815598\pi\) |
0.892525 | + | 0.450997i | \(0.148932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −56.6671 | − | 98.1502i | −0.170171 | − | 0.294745i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 561.468i | 1.67602i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −541.604 | −1.60713 | −0.803567 | − | 0.595214i | \(-0.797067\pi\) | ||||
−0.803567 | + | 0.595214i | \(0.797067\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.3823 | − | 11.7677i | 0.0601247 | − | 0.0347130i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −373.909 | − | 215.877i | −1.09651 | − | 0.633069i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −187.799 | + | 287.020i | −0.547518 | + | 0.836794i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −54.1348 | + | 93.7643i | −0.156913 | + | 0.271781i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 122.201 | + | 211.658i | 0.352164 | + | 0.609966i | 0.986628 | − | 0.162986i | \(-0.0521126\pi\) |
−0.634464 | + | 0.772952i | \(0.718779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 190.205i | 0.545001i | 0.962156 | + | 0.272501i | \(0.0878507\pi\) | ||||
−0.962156 | + | 0.272501i | \(0.912149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 193.082 | 0.550091 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 341.878 | − | 197.383i | 0.968493 | − | 0.559160i | 0.0697166 | − | 0.997567i | \(-0.477791\pi\) |
0.898777 | + | 0.438407i | \(0.144457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −160.833 | − | 92.8572i | −0.453052 | − | 0.261570i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 80.5832 | − | 27.6438i | 0.225723 | − | 0.0774336i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 148.162 | − | 256.625i | 0.412709 | − | 0.714833i | −0.582476 | − | 0.812848i | \(-0.697916\pi\) |
0.995185 | + | 0.0980151i | \(0.0312494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −105.832 | − | 183.306i | −0.293163 | − | 0.507773i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 86.6873i | − | 0.238808i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −247.190 | −0.677232 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −521.865 | + | 301.299i | −1.42198 | + | 0.820978i | −0.996468 | − | 0.0839772i | \(-0.973238\pi\) |
−0.425507 | + | 0.904955i | \(0.639904\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 256.474 | + | 148.076i | 0.695053 | + | 0.401289i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.7253 | + | 59.9548i | −0.0316047 | + | 0.161603i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −53.4998 | + | 92.6644i | −0.143431 | + | 0.248430i | −0.928787 | − | 0.370615i | \(-0.879147\pi\) |
0.785355 | + | 0.619045i | \(0.212480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.3997 | − | 50.9218i | −0.0783992 | − | 0.135791i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 559.988i | − | 1.48538i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 539.901 | 1.42454 | 0.712270 | − | 0.701906i | \(-0.247667\pi\) | ||||
0.712270 | + | 0.701906i | \(0.247667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.60924 | − | 3.23849i | 0.0147224 | − | 0.00849998i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −115.719 | − | 66.8102i | −0.302137 | − | 0.174439i | 0.341265 | − | 0.939967i | \(-0.389145\pi\) |
−0.643403 | + | 0.765528i | \(0.722478\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −416.719 | + | 478.273i | −1.08239 | + | 1.24227i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 131.130 | − | 227.123i | 0.338836 | − | 0.586882i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 285.627 | + | 494.721i | 0.734260 | + | 1.27178i | 0.955047 | + | 0.296454i | \(0.0958043\pi\) |
−0.220787 | + | 0.975322i | \(0.570862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 967.707i | − | 2.47495i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.543792 | 0.00138369 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −399.518 | + | 230.662i | −1.01144 | + | 0.583955i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −172.662 | − | 99.6863i | −0.434916 | − | 0.251099i | 0.266523 | − | 0.963829i | \(-0.414125\pi\) |
−0.701439 | + | 0.712730i | \(0.747459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.6826 | − | 28.4764i | −0.0819114 | − | 0.0713694i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −317.211 | + | 549.426i | −0.791050 | + | 1.37014i | 0.134267 | + | 0.990945i | \(0.457132\pi\) |
−0.925317 | + | 0.379194i | \(0.876201\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 271.259 | + | 469.835i | 0.673100 | + | 1.16584i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 393.096i | 0.970608i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 221.529 | 0.544298 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −597.403 | + | 344.911i | −1.46064 | + | 0.843303i | −0.999041 | − | 0.0437846i | \(-0.986058\pi\) |
−0.461602 | + | 0.887087i | \(0.652725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.3444 | − | 16.9420i | −0.0713975 | − | 0.0412214i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 343.398 | + | 67.1582i | 0.831472 | + | 0.162611i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 169.704 | − | 293.937i | 0.408926 | − | 0.708281i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.0133 | − | 97.0179i | −0.134324 | − | 0.232657i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 43.8224i | − | 0.104588i | −0.998632 | − | 0.0522940i | \(-0.983347\pi\) | ||
0.998632 | − | 0.0522940i | \(-0.0166533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −357.611 | −0.849433 | −0.424717 | − | 0.905326i | \(-0.639626\pi\) | ||||
−0.424717 | + | 0.905326i | \(0.639626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −422.112 | + | 243.706i | −0.997901 | + | 0.576138i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −64.8446 | − | 37.4380i | −0.152575 | − | 0.0880895i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.94068 | + | 26.0626i | 0.0209384 | + | 0.0610365i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −92.9867 | + | 161.058i | −0.216752 | + | 0.375426i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 143.259 | + | 248.131i | 0.332387 | + | 0.575711i | 0.982979 | − | 0.183716i | \(-0.0588127\pi\) |
−0.650592 | + | 0.759427i | \(0.725479\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 407.880i | 0.941986i | 0.882137 | + | 0.470993i | \(0.156104\pi\) | ||||
−0.882137 | + | 0.470993i | \(0.843896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −70.0708 | −0.161082 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −426.424 | + | 246.196i | −0.975798 | + | 0.563377i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 46.8249 | + | 27.0344i | 0.106663 | + | 0.0615817i | 0.552382 | − | 0.833591i | \(-0.313719\pi\) |
−0.445720 | + | 0.895173i | \(0.647052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −396.853 | − | 161.398i | −0.899893 | − | 0.365981i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 158.497 | − | 274.526i | 0.357782 | − | 0.619697i | −0.629808 | − | 0.776751i | \(-0.716866\pi\) |
0.987590 | + | 0.157054i | \(0.0501997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −113.970 | − | 197.401i | −0.256112 | − | 0.443599i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.0272i | 0.0448035i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 544.261 | 1.21216 | 0.606081 | − | 0.795403i | \(-0.292741\pi\) | ||||
0.606081 | + | 0.795403i | \(0.292741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −501.319 | + | 289.437i | −1.11157 | + | 0.641767i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 97.7437 | + | 56.4323i | 0.215770 | + | 0.124575i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 753.961 | − | 258.644i | 1.65706 | − | 0.568448i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 343.708 | − | 595.320i | 0.752096 | − | 1.30267i | −0.194709 | − | 0.980861i | \(-0.562376\pi\) |
0.946805 | − | 0.321808i | \(-0.104291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 107.971 | + | 187.011i | 0.235231 | + | 0.407432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 676.260i | 1.46694i | 0.679721 | + | 0.733470i | \(0.262101\pi\) | ||||
−0.679721 | + | 0.733470i | \(0.737899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −559.738 | −1.20894 | −0.604469 | − | 0.796629i | \(-0.706615\pi\) | ||||
−0.604469 | + | 0.796629i | \(0.706615\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 58.7901 | − | 33.9425i | 0.126430 | − | 0.0729945i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 319.886 | + | 184.686i | 0.684981 | + | 0.395474i | 0.801729 | − | 0.597687i | \(-0.203914\pi\) |
−0.116748 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 142.261 | − | 727.417i | 0.303327 | − | 1.55100i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 51.2233 | − | 88.7213i | 0.108754 | − | 0.188368i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 256.313 | + | 443.948i | 0.541889 | + | 0.938579i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.0987i | 0.0802077i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −76.3040 | −0.159967 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −270.362 | + | 156.094i | −0.564430 | + | 0.325874i | −0.754922 | − | 0.655815i | \(-0.772325\pi\) |
0.190492 | + | 0.981689i | \(0.438992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −241.069 | − | 139.181i | −0.501182 | − | 0.289358i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 93.8923 | − | 107.761i | 0.194394 | − | 0.223108i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 76.2231 | − | 132.022i | 0.157161 | − | 0.272211i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 140.195 | + | 242.824i | 0.287874 | + | 0.498613i | 0.973302 | − | 0.229528i | \(-0.0737182\pi\) |
−0.685428 | + | 0.728140i | \(0.740385\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33283i | 0.00272562i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −423.804 | −0.863145 | −0.431573 | − | 0.902078i | \(-0.642041\pi\) | ||||
−0.431573 | + | 0.902078i | \(0.642041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 542.382 | − | 313.144i | 1.10017 | − | 0.635181i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −686.171 | − | 396.161i | −1.38620 | − | 0.800325i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 184.842 | + | 161.053i | 0.371916 | + | 0.324050i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −83.0243 | + | 143.802i | −0.166381 | + | 0.288181i | −0.937145 | − | 0.348940i | \(-0.886542\pi\) |
0.770764 | + | 0.637121i | \(0.219875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.6997 | − | 58.3695i | −0.0672648 | − | 0.116506i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 632.164i | − | 1.25679i | −0.777896 | − | 0.628393i | \(-0.783713\pi\) | ||
0.777896 | − | 0.628393i | \(-0.216287\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 325.946 | 0.645438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 128.211 | − | 74.0224i | 0.252881 | − | 0.146001i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −269.053 | − | 155.338i | −0.528592 | − | 0.305183i | 0.211851 | − | 0.977302i | \(-0.432051\pi\) |
−0.740443 | + | 0.672119i | \(0.765384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 320.249 | + | 62.6310i | 0.626711 | + | 0.122566i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 54.9382 | − | 95.1558i | 0.107092 | − | 0.185489i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 158.358 | + | 274.284i | 0.307491 | + | 0.532591i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 952.725i | − | 1.84279i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.1977 | −0.0947932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 58.0568 | − | 33.5191i | 0.111433 | − | 0.0643361i | −0.443247 | − | 0.896399i | \(-0.646174\pi\) |
0.554681 | + | 0.832063i | \(0.312840\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 462.718 | + | 267.150i | 0.884738 | + | 0.510804i | 0.872218 | − | 0.489118i | \(-0.162681\pi\) |
0.0125204 | + | 0.999922i | \(0.496015\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.58846 | − | 10.4606i | −0.00683517 | − | 0.0199249i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −303.375 | + | 525.462i | −0.575665 | + | 0.997081i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −547.257 | − | 947.877i | −1.03451 | − | 1.79183i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 437.040i | 0.823051i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 727.383 | 1.36470 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 604.681 | − | 349.113i | 1.13025 | − | 0.652547i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.8800 | + | 21.2927i | 0.0686778 | + | 0.0396512i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 661.066 | − | 514.047i | 1.22647 | − | 0.953704i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −75.6707 | + | 131.065i | −0.139872 | + | 0.242265i | −0.927448 | − | 0.373952i | \(-0.878002\pi\) |
0.787576 | + | 0.616217i | \(0.211336\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −54.3096 | − | 94.0670i | −0.100018 | − | 0.173236i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 200.487i | − | 0.367865i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −775.543 | −1.41781 | −0.708906 | − | 0.705303i | \(-0.750811\pi\) | ||||
−0.708906 | + | 0.705303i | \(0.750811\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.8044 | + | 17.2076i | −0.0542885 | + | 0.0313435i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −275.976 | − | 159.335i | −0.500865 | − | 0.289174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 576.044 | − | 197.610i | 1.04167 | − | 0.357342i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.4156 | + | 30.1647i | −0.0313795 | + | 0.0543508i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.2200 | − | 55.8066i | −0.0578455 | − | 0.100191i | 0.835653 | − | 0.549258i | \(-0.185090\pi\) |
−0.893498 | + | 0.449067i | \(0.851756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 644.140i | − | 1.15231i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −207.992 | −0.370752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −789.688 | + | 455.927i | −1.40264 | + | 0.809816i | −0.994663 | − | 0.103175i | \(-0.967100\pi\) |
−0.407980 | + | 0.912991i | \(0.633767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 213.281 | + | 123.138i | 0.377489 | + | 0.217943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 99.5997 | − | 509.280i | 0.175661 | − | 0.898201i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −118.002 | + | 204.386i | −0.207385 | + | 0.359201i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) |
0.743505 | + | 0.668730i | \(0.233162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 414.770 | + | 718.403i | 0.726392 | + | 1.25815i | 0.958398 | + | 0.285434i | \(0.0921377\pi\) |
−0.232006 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.7379i | − | 0.0484082i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −125.619 | −0.218468 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 380.226 | − | 219.524i | 0.658971 | − | 0.380457i | −0.132914 | − | 0.991128i | \(-0.542433\pi\) |
0.791885 | + | 0.610671i | \(0.209100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −152.853 | − | 88.2497i | −0.263995 | − | 0.152417i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −294.338 | + | 337.815i | −0.506606 | + | 0.581437i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 74.5741 | − | 129.166i | 0.127914 | − | 0.221554i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 497.795 | + | 862.207i | 0.850932 | + | 1.47386i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 871.738i | − | 1.48507i | −0.669805 | − | 0.742537i | \(-0.733622\pi\) | ||
0.669805 | − | 0.742537i | \(-0.266378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 308.729 | 0.524158 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −70.9216 | + | 40.9466i | −0.120003 | + | 0.0692836i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 662.637 | + | 382.574i | 1.11743 | + | 0.645149i | 0.940744 | − | 0.339117i | \(-0.110128\pi\) |
0.176688 | + | 0.984267i | \(0.443462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 672.125 | + | 585.623i | 1.12962 | + | 0.984240i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.8702 | − | 60.3969i | 0.0584090 | − | 0.101167i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −146.400 | − | 253.571i | −0.244407 | − | 0.423325i | 0.717558 | − | 0.696499i | \(-0.245260\pi\) |
−0.961965 | + | 0.273174i | \(0.911926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 748.440i | − | 1.24532i | −0.782491 | − | 0.622662i | \(-0.786051\pi\) | ||
0.782491 | − | 0.622662i | \(-0.213949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 925.777 | 1.53529 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 785.572 | − | 453.550i | 1.29847 | − | 0.749670i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 53.7404 | + | 31.0270i | 0.0885344 | + | 0.0511154i | 0.543614 | − | 0.839336i | \(-0.317056\pi\) |
−0.455079 | + | 0.890451i | \(0.650389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 90.7811 | + | 17.7540i | 0.149066 | + | 0.0291527i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −598.572 | + | 1036.76i | −0.979660 | + | 1.69682i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.3280 | − | 38.6732i | −0.0364241 | − | 0.0630884i | 0.847239 | − | 0.531212i | \(-0.178263\pi\) |
−0.883663 | + | 0.468124i | \(0.844930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 91.0168i | − | 0.147995i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −832.160 | −1.34872 | −0.674360 | − | 0.738403i | \(-0.735580\pi\) | ||||
−0.674360 | + | 0.738403i | \(0.735580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −216.394 | + | 124.935i | −0.349586 | + | 0.201834i | −0.664503 | − | 0.747285i | \(-0.731357\pi\) |
0.314917 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 313.747 | + | 181.142i | 0.505229 | + | 0.291694i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 97.6388 | + | 284.623i | 0.156724 | + | 0.456858i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 346.611 | − | 600.347i | 0.554577 | − | 0.960556i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 52.9156 | + | 91.6525i | 0.0843948 | + | 0.146176i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 311.319i | − | 0.494943i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0372 | −0.0412634 | −0.0206317 | − | 0.999787i | \(-0.506568\pi\) | ||||
−0.0206317 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.5713 | + | 25.7332i | −0.0704128 | + | 0.0406528i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.6954 | + | 33.8878i | 0.0924336 | + | 0.0533666i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1042.34 | + | 144.056i | −1.63632 | + | 0.226148i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −153.108 | + | 265.190i | −0.239605 | + | 0.415008i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −235.195 | − | 407.370i | −0.366920 | − | 0.635523i | 0.622163 | − | 0.782888i | \(-0.286254\pi\) |
−0.989082 | + | 0.147365i | \(0.952921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 668.123i | − | 1.03907i | −0.854449 | − | 0.519536i | \(-0.826105\pi\) | ||
0.854449 | − | 0.519536i | \(-0.173895\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −80.6007 | −0.124962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −925.107 | + | 534.111i | −1.42984 | + | 0.825519i | −0.997108 | − | 0.0760031i | \(-0.975784\pi\) |
−0.432733 | + | 0.901522i | \(0.642451\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −739.813 | − | 427.131i | −1.13993 | − | 0.658138i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −84.7662 | + | 29.0788i | −0.130209 | + | 0.0446678i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 389.917 | − | 675.357i | 0.597117 | − | 1.03424i | −0.396128 | − | 0.918195i | \(-0.629646\pi\) |
0.993244 | − | 0.116041i | \(-0.0370204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.84513 | + | 4.92792i | 0.00434371 | + | 0.00752353i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 407.579i | 0.620363i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1017.20 | 1.54355 | 0.771774 | − | 0.635897i | \(-0.219370\pi\) | ||||
0.771774 | + | 0.635897i | \(0.219370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −819.200 | + | 472.966i | −1.23934 | + | 0.715530i | −0.968958 | − | 0.247224i | \(-0.920482\pi\) |
−0.270377 | + | 0.962755i | \(0.587148\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 226.337 | + | 130.676i | 0.341384 | + | 0.197098i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 87.0605 | − | 445.164i | 0.130918 | − | 0.669419i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 525.359 | − | 909.949i | 0.787645 | − | 1.36424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.7522 | + | 79.2452i | 0.0683890 | + | 0.118453i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 67.2697i | − | 0.100253i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −76.8911 | −0.114251 | −0.0571256 | − | 0.998367i | \(-0.518194\pi\) | ||||
−0.0571256 | + | 0.998367i | \(0.518194\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.2761 | − | 14.0158i | 0.0359646 | − | 0.0207642i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 555.161 | + | 320.523i | 0.820031 | + | 0.473445i | 0.850427 | − | 0.526093i | \(-0.176343\pi\) |
−0.0303959 | + | 0.999538i | \(0.509677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −132.202 | + | 151.730i | −0.194702 | + | 0.223461i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.8481 | + | 22.2535i | −0.0188665 | + | 0.0326777i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −511.461 | − | 885.877i | −0.748845 | − | 1.29704i | −0.948377 | − | 0.317147i | \(-0.897275\pi\) |
0.199531 | − | 0.979891i | \(-0.436058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 354.564i | − | 0.517611i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 101.112 | 0.147180 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −162.303 | + | 93.7059i | −0.235564 | + | 0.136003i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −597.595 | − | 345.021i | −0.864826 | − | 0.499307i | 0.000799666 | − | 1.00000i | \(-0.499745\pi\) |
−0.865625 | + | 0.500692i | \(0.833079\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 788.600 | + | 687.108i | 1.13795 | + | 0.991497i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 586.126 | − | 1015.20i | 0.843347 | − | 1.46072i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 406.751 | + | 704.513i | 0.583574 | + | 1.01078i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 89.7739i | 0.128432i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −361.922 | −0.516294 | −0.258147 | − | 0.966106i | \(-0.583112\pi\) | ||||
−0.258147 | + | 0.966106i | \(0.583112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −137.184 | + | 79.2032i | −0.195141 | + | 0.112665i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 129.729 | + | 74.8988i | 0.184012 | + | 0.106239i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −422.283 | − | 82.5858i | −0.597289 | − | 0.116812i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −260.952 | + | 451.982i | −0.368056 | + | 0.637492i | −0.989262 | − | 0.146156i | \(-0.953310\pi\) |
0.621205 | + | 0.783648i | \(0.286643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 380.327 | + | 658.746i | 0.534919 | + | 0.926507i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1017.94i | 1.42769i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1946.04 | −2.72173 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −59.5497 | + | 34.3810i | −0.0830540 | + | 0.0479513i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 573.144 | + | 330.905i | 0.797141 | + | 0.460230i | 0.842470 | − | 0.538743i | \(-0.181100\pi\) |
−0.0453294 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −135.667 | − | 395.476i | −0.188164 | − | 0.548510i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −80.1267 | + | 138.783i | −0.110825 | + | 0.191955i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.6495 | − | 70.4070i | −0.0560683 | − | 0.0971132i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1169.62i | 1.60882i | 0.594071 | + | 0.804412i | \(0.297520\pi\) | ||||
−0.594071 | + | 0.804412i | \(0.702480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 607.150 | 0.832854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 623.888 | − | 360.202i | 0.853472 | − | 0.492752i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −391.800 | − | 226.206i | −0.534516 | − | 0.308603i | 0.208338 | − | 0.978057i | \(-0.433195\pi\) |
−0.742853 | + | 0.669454i | \(0.766528\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.0256 | + | 130.427i | 0.0245246 | + | 0.177451i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −904.788 | + | 1567.14i | −1.22766 | + | 2.12638i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.75378 | − | 4.76968i | −0.00372636 | − | 0.00645424i | 0.864156 | − | 0.503224i | \(-0.167853\pi\) |
−0.867883 | + | 0.496769i | \(0.834519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 132.982i | − | 0.179463i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 866.020 | 1.16557 | 0.582786 | − | 0.812626i | \(-0.301963\pi\) | ||||
0.582786 | + | 0.812626i | \(0.301963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −181.489 | + | 104.783i | −0.243609 | + | 0.140648i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −484.658 | − | 279.817i | −0.648806 | − | 0.374588i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −871.857 | + | 299.088i | −1.16403 | + | 0.399316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 230.421 | − | 399.101i | 0.306819 | − | 0.531426i | −0.670846 | − | 0.741597i | \(-0.734069\pi\) |
0.977665 | + | 0.210171i | \(0.0674020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.1661 | − | 17.6082i | −0.0135008 | − | 0.0233840i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1181.02i | 1.56427i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −547.987 | −0.723893 | −0.361946 | − | 0.932199i | \(-0.617888\pi\) | ||||
−0.361946 | + | 0.932199i | \(0.617888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −302.196 | + | 174.473i | −0.398151 | + | 0.229872i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1129.20 | − | 651.942i | −1.48383 | − | 0.856691i | −0.484002 | − | 0.875067i | \(-0.660817\pi\) |
−0.999831 | + | 0.0183760i | \(0.994150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.7978 | + | 259.743i | −0.0665764 | + | 0.340423i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −556.732 | + | 964.289i | −0.727755 | + | 1.26051i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 536.711 | + | 929.611i | 0.699754 | + | 1.21201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 771.004i | 1.00261i | 0.865272 | + | 0.501303i | \(0.167146\pi\) | ||||
−0.865272 | + | 0.501303i | \(0.832854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 88.0080 | 0.114148 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −922.592 | + | 532.659i | −1.19352 | + | 0.689080i | −0.959104 | − | 0.283056i | \(-0.908652\pi\) |
−0.234418 | + | 0.972136i | \(0.575319\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 68.2106 | + | 39.3814i | 0.0880137 | + | 0.0508147i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.2059 | − | 34.6676i | 0.0388750 | − | 0.0446173i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 206.964 | − | 358.473i | 0.265679 | − | 0.460170i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −299.273 | − | 518.356i | −0.383192 | − | 0.663708i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 234.466i | 0.299446i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1072.01 | 1.36561 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 818.075 | − | 472.316i | 1.03948 | − | 0.600147i | 0.119798 | − | 0.992798i | \(-0.461775\pi\) |
0.919687 | + | 0.392651i | \(0.128442\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −159.998 | − | 92.3748i | −0.202786 | − | 0.117078i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −245.119 | − | 213.572i | −0.309885 | − | 0.270003i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.2638 | + | 73.2031i | −0.0532961 | + | 0.0923116i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.7253 | + | 20.3089i | 0.0147489 | + | 0.0255458i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1245.89i | 1.56322i | 0.623765 | + | 0.781612i | \(0.285602\pi\) | ||||
−0.623765 | + | 0.781612i | \(0.714398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1338.88 | −1.67570 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −325.486 | + | 187.919i | −0.406349 | + | 0.234606i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −689.942 | − | 398.338i | −0.859205 | − | 0.496062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1467.79 | + | 287.056i | 1.82335 | + | 0.356591i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.41412 | + | 7.64548i | −0.00546979 | + | 0.00947396i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 88.6536 | + | 153.553i | 0.109584 | + | 0.189805i | 0.915602 | − | 0.402086i | \(-0.131715\pi\) |
−0.806018 | + | 0.591891i | \(0.798381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1212.71i | − | 1.49532i | −0.664079 | − | 0.747662i | \(-0.731176\pi\) | ||
0.664079 | − | 0.747662i | \(-0.268824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −66.0108 | −0.0811941 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0783 | + | 6.97339i | −0.0148200 | + | 0.00855631i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −317.449 | − | 183.279i | −0.388554 | − | 0.224332i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −426.465 | − | 1243.17i | −0.520714 | − | 1.51791i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 532.253 | − | 921.889i | 0.648298 | − | 1.12289i | −0.335231 | − | 0.942136i | \(-0.608814\pi\) |
0.983529 | − | 0.180749i | \(-0.0578523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 142.824 | + | 247.378i | 0.173540 | + | 0.300581i | 0.939655 | − | 0.342123i | \(-0.111146\pi\) |
−0.766115 | + | 0.642704i | \(0.777813\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.9996i | 0.0327268i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1182.30 | 1.42962 | 0.714811 | − | 0.699317i | \(-0.246513\pi\) | ||||
0.714811 | + | 0.699317i | \(0.246513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 624.399 | − | 360.497i | 0.753195 | − | 0.434857i | −0.0736521 | − | 0.997284i | \(-0.523465\pi\) |
0.826847 | + | 0.562427i | \(0.190132\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −109.358 | − | 63.1378i | −0.131598 | − | 0.0759781i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −722.399 | − | 929.009i | −0.867226 | − | 1.11526i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 352.635 | − | 610.782i | 0.422317 | − | 0.731475i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −113.576 | − | 196.719i | −0.135694 | − | 0.235029i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 548.052i | 0.653221i | 0.945159 | + | 0.326610i | \(0.105906\pi\) | ||||
−0.945159 | + | 0.326610i | \(0.894094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −160.988 | −0.191424 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 86.6536 | − | 50.0295i | 0.102792 | − | 0.0593469i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1341.60 | + | 774.574i | 1.58769 | + | 0.916656i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1132.67 | + | 388.560i | −1.33728 | + | 0.458749i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.3053 | + | 94.0596i | −0.0639639 | + | 0.110789i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −261.149 | − | 452.323i | −0.306873 | − | 0.531519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1110.62i | − | 1.30201i | −0.759072 | − | 0.651007i | \(-0.774347\pi\) | ||
0.759072 | − | 0.651007i | \(-0.225653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 566.556 | 0.662639 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −125.717 | + | 72.5826i | −0.146694 | + | 0.0846939i | −0.571551 | − | 0.820567i | \(-0.693658\pi\) |
0.424856 | + | 0.905261i | \(0.360325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1156.42 | + | 667.660i | 1.34624 | + | 0.777252i | 0.987715 | − | 0.156268i | \(-0.0499462\pi\) |
0.358526 | + | 0.933520i | \(0.383280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.0612 | + | 117.918i | −0.0267841 | + | 0.136955i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −281.425 | + | 487.443i | −0.326101 | + | 0.564824i | −0.981735 | − | 0.190255i | \(-0.939068\pi\) |
0.655633 | + | 0.755079i | \(0.272402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −257.404 | − | 445.836i | −0.297576 | − | 0.515417i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 145.846i | 0.168219i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1486.82 | −1.71095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1969.19 | − | 1136.91i | 2.26083 | − | 1.30529i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −217.685 | − | 125.680i | −0.249353 | − | 0.143964i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −533.576 | + | 612.390i | −0.609801 | + | 0.699875i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 453.268 | − | 785.084i | 0.516840 | − | 0.895193i | −0.482969 | − | 0.875637i | \(-0.660442\pi\) |
0.999809 | − | 0.0195553i | \(-0.00622505\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.2019 | − | 31.5266i | −0.0207075 | − | 0.0358664i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 422.614i | 0.479698i | 0.970810 | + | 0.239849i | \(0.0770979\pi\) | ||||
−0.970810 | + | 0.239849i | \(0.922902\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −310.036 | −0.351116 | −0.175558 | − | 0.984469i | \(-0.556173\pi\) | ||||
−0.175558 | + | 0.984469i | \(0.556173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 116.321 | − | 67.1582i | 0.131437 | − | 0.0758850i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −983.657 | − | 567.915i | −1.10897 | − | 0.640265i | −0.170408 | − | 0.985374i | \(-0.554509\pi\) |
−0.938563 | + | 0.345109i | \(0.887842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −67.4572 | − | 58.7755i | −0.0758799 | − | 0.0661142i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −633.462 | + | 1097.19i | −0.710956 | + | 1.23141i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 340.627 | + | 589.983i | 0.381441 | + | 0.660676i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 445.616i | 0.497895i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 438.468 | 0.488816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −570.536 | + | 329.399i | −0.634635 | + | 0.366406i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −181.519 | − | 104.800i | −0.201464 | − | 0.116316i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 104.423 | + | 20.4220i | 0.115640 | + | 0.0226157i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 568.299 | − | 984.323i | 0.627955 | − | 1.08765i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.4633 | + | 70.0846i | 0.0446123 | + | 0.0772707i | 0.887469 | − | 0.460867i | \(-0.152461\pi\) |
−0.842857 | + | 0.538138i | \(0.819128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 537.436i | − | 0.591239i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1285.92 | 1.41155 | 0.705774 | − | 0.708437i | \(-0.250599\pi\) | ||||
0.705774 | + | 0.708437i | \(0.250599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 947.340 | − | 546.947i | 1.03761 | − | 0.599065i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.15984 | + | 5.28844i | 0.0100108 | + | 0.00577971i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.43745 | − | 7.10530i | −0.00265807 | − | 0.00774842i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −856.410 | + | 1483.35i | −0.931894 | + | 1.61409i | −0.151812 | + | 0.988409i | \(0.548511\pi\) |
−0.780082 | + | 0.625678i | \(0.784823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 128.472 | + | 222.519i | 0.139491 | + | 0.241606i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 752.101i | 0.814845i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.4126 | −0.0436893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 452.254 | − | 261.109i | 0.487868 | − | 0.281671i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1178.70 | + | 680.522i | 1.26878 | + | 0.732531i | 0.974757 | − | 0.223267i | \(-0.0716720\pi\) |
0.294024 | + | 0.955798i | \(0.405005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −225.585 | + | 554.679i | −0.242303 | + | 0.595788i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −78.7273 | + | 136.360i | −0.0843808 | + | 0.146152i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1088.22 | − | 1884.85i | −1.16387 | − | 2.01588i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 314.858i | 0.336028i | 0.985785 | + | 0.168014i | \(0.0537354\pi\) | ||||
−0.985785 | + | 0.168014i | \(0.946265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −278.156 | −0.296226 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −261.326 | + | 150.877i | −0.277711 | + | 0.160336i | −0.632387 | − | 0.774653i | \(-0.717925\pi\) |
0.354676 | + | 0.934989i | \(0.384591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1181.96 | + | 682.403i | 1.25340 | + | 0.723651i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −315.682 | + | 108.294i | −0.334055 | + | 0.114597i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 726.588 | − | 1258.49i | 0.767252 | − | 1.32892i | −0.171796 | − | 0.985133i | \(-0.554957\pi\) |
0.939048 | − | 0.343787i | \(-0.111710\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 500.531 | + | 866.945i | 0.527430 | + | 0.913536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 71.9225i | − | 0.0756282i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 977.784 | 1.02601 | 0.513003 | − | 0.858387i | \(-0.328533\pi\) | ||||
0.513003 | + | 0.858387i | \(0.328533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 251.365 | − | 145.126i | 0.263209 | − | 0.151964i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −195.578 | − | 112.917i | −0.204366 | − | 0.117991i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −89.8367 | + | 459.359i | −0.0936775 | + | 0.478998i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −161.377 | + | 279.512i | −0.167926 | + | 0.290856i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −575.635 | − | 997.029i | −0.597752 | − | 1.03534i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1846.90i | − | 1.91389i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −181.044 | −0.187222 | −0.0936109 | − | 0.995609i | \(-0.529841\pi\) | ||||
−0.0936109 | + | 0.995609i | \(0.529841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 128.801 | − | 74.3632i | 0.132921 | − | 0.0767422i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −210.470 | − | 121.515i | −0.216756 | − | 0.125144i | 0.387691 | − | 0.921789i | \(-0.373273\pi\) |
−0.604447 | + | 0.796645i | \(0.706606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1016.59 | + | 1166.75i | −1.04480 | + | 1.19912i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.9632 | − | 29.3811i | 0.0173981 | − | 0.0301344i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −715.865 | − | 1239.91i | −0.732717 | − | 1.26910i | −0.955718 | − | 0.294285i | \(-0.904918\pi\) |
0.223000 | − | 0.974818i | \(-0.428415\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 734.635i | − | 0.750393i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −330.573 | −0.336975 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −384.934 | + | 222.241i | −0.391591 | + | 0.226085i | −0.682849 | − | 0.730559i | \(-0.739259\pi\) |
0.291259 | + | 0.956644i | \(0.405926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −742.128 | − | 428.468i | −0.753429 | − | 0.434993i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −149.094 | − | 129.906i | −0.151058 | − | 0.131617i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 604.308 | − | 1046.69i | 0.611029 | − | 1.05833i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −902.358 | − | 1562.93i | −0.910553 | − | 1.57712i | −0.813284 | − | 0.581867i | \(-0.802323\pi\) |
−0.0972693 | − | 0.995258i | \(-0.531011\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6812i | 0.0188128i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 729.767 | 0.733434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1649.18 | − | 952.153i | 1.65414 | − | 0.955018i | 0.678796 | − | 0.734327i | \(-0.262502\pi\) |
0.975344 | − | 0.220691i | \(-0.0708312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 100.935 | + | 58.2749i | 0.101036 | + | 0.0583332i |
(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 | 224.3.s.a.33.4 | ✓ | 16 | |
4.3 | odd | 2 | inner | 224.3.s.a.33.5 | yes | 16 | |
7.2 | even | 3 | 1568.3.c.h.97.8 | 16 | |||
7.3 | odd | 6 | inner | 224.3.s.a.129.4 | yes | 16 | |
7.5 | odd | 6 | 1568.3.c.h.97.9 | 16 | |||
8.3 | odd | 2 | 448.3.s.g.257.4 | 16 | |||
8.5 | even | 2 | 448.3.s.g.257.5 | 16 | |||
28.3 | even | 6 | inner | 224.3.s.a.129.5 | yes | 16 | |
28.19 | even | 6 | 1568.3.c.h.97.7 | 16 | |||
28.23 | odd | 6 | 1568.3.c.h.97.10 | 16 | |||
56.3 | even | 6 | 448.3.s.g.129.4 | 16 | |||
56.45 | odd | 6 | 448.3.s.g.129.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
224.3.s.a.33.5 | yes | 16 | 4.3 | odd | 2 | inner | |
224.3.s.a.129.4 | yes | 16 | 7.3 | odd | 6 | inner | |
224.3.s.a.129.5 | yes | 16 | 28.3 | even | 6 | inner | |
448.3.s.g.129.4 | 16 | 56.3 | even | 6 | |||
448.3.s.g.129.5 | 16 | 56.45 | odd | 6 | |||
448.3.s.g.257.4 | 16 | 8.3 | odd | 2 | |||
448.3.s.g.257.5 | 16 | 8.5 | even | 2 | |||
1568.3.c.h.97.7 | 16 | 28.19 | even | 6 | |||
1568.3.c.h.97.8 | 16 | 7.2 | even | 3 | |||
1568.3.c.h.97.9 | 16 | 7.5 | odd | 6 | |||
1568.3.c.h.97.10 | 16 | 28.23 | odd | 6 |