Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (of order \(4\), 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: | \(28.6104277578\) |
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: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(-0.394902 - 0.394902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.43 |
Dual form | 1050.3.l.h.757.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −1.87083 | + | 1.87083i | −0.267261 | + | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.5078 | −1.04617 | −0.523083 | − | 0.852282i | \(-0.675218\pi\) | ||||
−0.523083 | + | 0.852282i | \(0.675218\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | 7.70521 | + | 7.70521i | 0.592708 | + | 0.592708i | 0.938362 | − | 0.345654i | \(-0.112343\pi\) |
−0.345654 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −21.0749 | + | 21.0749i | −1.23970 | + | 1.23970i | −0.279579 | + | 0.960123i | \(0.590195\pi\) |
−0.960123 | + | 0.279579i | \(0.909805\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | − | 24.1173i | − | 1.26933i | −0.772786 | − | 0.634666i | \(-0.781138\pi\) | ||
0.772786 | − | 0.634666i | \(-0.218862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | −11.5078 | + | 11.5078i | −0.523083 | + | 0.523083i | ||||
\(23\) | −30.1762 | − | 30.1762i | −1.31201 | − | 1.31201i | −0.919934 | − | 0.392073i | \(-0.871758\pi\) |
−0.392073 | − | 0.919934i | \(-0.628242\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.4104 | 0.592708 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 3.74166 | + | 3.74166i | 0.133631 | + | 0.133631i | ||||
\(29\) | − | 51.1392i | − | 1.76342i | −0.471790 | − | 0.881711i | \(-0.656392\pi\) | ||
0.471790 | − | 0.881711i | \(-0.343608\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.9852 | −1.51565 | −0.757826 | − | 0.652457i | \(-0.773738\pi\) | ||||
−0.757826 | + | 0.652457i | \(0.773738\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −14.0941 | − | 14.0941i | −0.427095 | − | 0.427095i | ||||
\(34\) | 42.1499i | 1.23970i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 8.50020 | − | 8.50020i | 0.229735 | − | 0.229735i | −0.582847 | − | 0.812582i | \(-0.698061\pi\) |
0.812582 | + | 0.582847i | \(0.198061\pi\) | |||||||
\(38\) | −24.1173 | − | 24.1173i | −0.634666 | − | 0.634666i | ||||
\(39\) | 18.8738i | 0.483944i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.6089 | 0.453875 | 0.226937 | − | 0.973909i | \(-0.427129\pi\) | ||||
0.226937 | + | 0.973909i | \(0.427129\pi\) | |||||||
\(42\) | −4.58258 | + | 4.58258i | −0.109109 | + | 0.109109i | ||||
\(43\) | 26.1383 | + | 26.1383i | 0.607867 | + | 0.607867i | 0.942388 | − | 0.334522i | \(-0.108575\pi\) |
−0.334522 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(44\) | 23.0156i | 0.523083i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −60.3523 | −1.31201 | ||||||||
\(47\) | −50.1311 | + | 50.1311i | −1.06662 | + | 1.06662i | −0.0690016 | + | 0.997617i | \(0.521981\pi\) |
−0.997617 | + | 0.0690016i | \(0.978019\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −51.6228 | −1.01221 | ||||||||
\(52\) | 15.4104 | − | 15.4104i | 0.296354 | − | 0.296354i | ||||
\(53\) | −7.08527 | − | 7.08527i | −0.133684 | − | 0.133684i | 0.637098 | − | 0.770783i | \(-0.280135\pi\) |
−0.770783 | + | 0.637098i | \(0.780135\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 29.5376 | − | 29.5376i | 0.518203 | − | 0.518203i | ||||
\(58\) | −51.1392 | − | 51.1392i | −0.881711 | − | 0.881711i | ||||
\(59\) | 94.3487i | 1.59913i | 0.600579 | + | 0.799565i | \(0.294937\pi\) | ||||
−0.600579 | + | 0.799565i | \(0.705063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.09003 | 0.132623 | 0.0663117 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663117 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(62\) | −46.9852 | + | 46.9852i | −0.757826 | + | 0.757826i | ||||
\(63\) | −5.61249 | − | 5.61249i | −0.0890871 | − | 0.0890871i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −28.1883 | −0.427095 | ||||||||
\(67\) | 20.6469 | − | 20.6469i | 0.308163 | − | 0.308163i | −0.536034 | − | 0.844197i | \(-0.680078\pi\) |
0.844197 | + | 0.536034i | \(0.180078\pi\) | |||||||
\(68\) | 42.1499 | + | 42.1499i | 0.619851 | + | 0.619851i | ||||
\(69\) | − | 73.9162i | − | 1.07125i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63.7595 | −0.898021 | −0.449011 | − | 0.893526i | \(-0.648223\pi\) | ||||
−0.449011 | + | 0.893526i | \(0.648223\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −50.1883 | − | 50.1883i | −0.687511 | − | 0.687511i | 0.274170 | − | 0.961681i | \(-0.411597\pi\) |
−0.961681 | + | 0.274170i | \(0.911597\pi\) | |||||||
\(74\) | − | 17.0004i | − | 0.229735i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48.2346 | −0.634666 | ||||||||
\(77\) | 21.5292 | − | 21.5292i | 0.279599 | − | 0.279599i | ||||
\(78\) | 18.8738 | + | 18.8738i | 0.241972 | + | 0.241972i | ||||
\(79\) | − | 1.06121i | − | 0.0134331i | −0.999977 | − | 0.00671653i | \(-0.997862\pi\) | ||
0.999977 | − | 0.00671653i | \(-0.00213796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 18.6089 | − | 18.6089i | 0.226937 | − | 0.226937i | ||||
\(83\) | −53.6243 | − | 53.6243i | −0.646075 | − | 0.646075i | 0.305967 | − | 0.952042i | \(-0.401020\pi\) |
−0.952042 | + | 0.305967i | \(0.901020\pi\) | |||||||
\(84\) | 9.16515i | 0.109109i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 52.2765 | 0.607867 | ||||||||
\(87\) | 62.6325 | − | 62.6325i | 0.719914 | − | 0.719914i | ||||
\(88\) | 23.0156 | + | 23.0156i | 0.261541 | + | 0.261541i | ||||
\(89\) | 145.154i | 1.63095i | 0.578794 | + | 0.815473i | \(0.303523\pi\) | ||||
−0.578794 | + | 0.815473i | \(0.696477\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.8303 | −0.316816 | ||||||||
\(92\) | −60.3523 | + | 60.3523i | −0.656003 | + | 0.656003i | ||||
\(93\) | −57.5449 | − | 57.5449i | −0.618762 | − | 0.618762i | ||||
\(94\) | 100.262i | 1.06662i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −23.7872 | + | 23.7872i | −0.245229 | + | 0.245229i | −0.819009 | − | 0.573780i | \(-0.805476\pi\) |
0.573780 | + | 0.819009i | \(0.305476\pi\) | |||||||
\(98\) | −7.00000 | − | 7.00000i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | − | 34.5235i | − | 0.348722i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.1467 | 0.496502 | 0.248251 | − | 0.968696i | \(-0.420144\pi\) | ||||
0.248251 | + | 0.968696i | \(0.420144\pi\) | |||||||
\(102\) | −51.6228 | + | 51.6228i | −0.506106 | + | 0.506106i | ||||
\(103\) | −56.3876 | − | 56.3876i | −0.547453 | − | 0.547453i | 0.378251 | − | 0.925703i | \(-0.376526\pi\) |
−0.925703 | + | 0.378251i | \(0.876526\pi\) | |||||||
\(104\) | − | 30.8208i | − | 0.296354i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1705 | −0.133684 | ||||||||
\(107\) | 135.365 | − | 135.365i | 1.26510 | − | 1.26510i | 0.316506 | − | 0.948590i | \(-0.397490\pi\) |
0.948590 | − | 0.316506i | \(-0.102510\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 100.934i | 0.926001i | 0.886358 | + | 0.463001i | \(0.153227\pi\) | ||||
−0.886358 | + | 0.463001i | \(0.846773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.8211 | 0.187578 | ||||||||
\(112\) | 7.48331 | − | 7.48331i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −25.3174 | − | 25.3174i | −0.224048 | − | 0.224048i | 0.586153 | − | 0.810201i | \(-0.300642\pi\) |
−0.810201 | + | 0.586153i | \(0.800642\pi\) | |||||||
\(114\) | − | 59.0751i | − | 0.518203i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −102.278 | −0.881711 | ||||||||
\(117\) | −23.1156 | + | 23.1156i | −0.197569 | + | 0.197569i | ||||
\(118\) | 94.3487 | + | 94.3487i | 0.799565 | + | 0.799565i | ||||
\(119\) | − | 78.8552i | − | 0.662649i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.4299 | 0.0944623 | ||||||||
\(122\) | 8.09003 | − | 8.09003i | 0.0663117 | − | 0.0663117i | ||||
\(123\) | 22.7911 | + | 22.7911i | 0.185294 | + | 0.185294i | ||||
\(124\) | 93.9704i | 0.757826i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | −116.746 | + | 116.746i | −0.919262 | + | 0.919262i | −0.996976 | − | 0.0777140i | \(-0.975238\pi\) |
0.0777140 | + | 0.996976i | \(0.475238\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 64.0254i | 0.496321i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 34.8004 | 0.265652 | 0.132826 | − | 0.991139i | \(-0.457595\pi\) | ||||
0.132826 | + | 0.991139i | \(0.457595\pi\) | |||||||
\(132\) | −28.1883 | + | 28.1883i | −0.213548 | + | 0.213548i | ||||
\(133\) | 45.1194 | + | 45.1194i | 0.339243 | + | 0.339243i | ||||
\(134\) | − | 41.2938i | − | 0.308163i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 84.2997 | 0.619851 | ||||||||
\(137\) | −131.552 | + | 131.552i | −0.960235 | + | 0.960235i | −0.999239 | − | 0.0390044i | \(-0.987581\pi\) |
0.0390044 | + | 0.999239i | \(0.487581\pi\) | |||||||
\(138\) | −73.9162 | − | 73.9162i | −0.535625 | − | 0.535625i | ||||
\(139\) | − | 89.4407i | − | 0.643458i | −0.946832 | − | 0.321729i | \(-0.895736\pi\) | ||
0.946832 | − | 0.321729i | \(-0.104264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −122.795 | −0.870890 | ||||||||
\(142\) | −63.7595 | + | 63.7595i | −0.449011 | + | 0.449011i | ||||
\(143\) | −88.6702 | − | 88.6702i | −0.620071 | − | 0.620071i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −100.377 | −0.687511 | ||||||||
\(147\) | 8.57321 | − | 8.57321i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | −17.0004 | − | 17.0004i | −0.114868 | − | 0.114868i | ||||
\(149\) | 55.7399i | 0.374093i | 0.982351 | + | 0.187047i | \(0.0598915\pi\) | ||||
−0.982351 | + | 0.187047i | \(0.940108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.9665 | 0.549447 | 0.274724 | − | 0.961523i | \(-0.411414\pi\) | ||||
0.274724 | + | 0.961523i | \(0.411414\pi\) | |||||||
\(152\) | −48.2346 | + | 48.2346i | −0.317333 | + | 0.317333i | ||||
\(153\) | −63.2248 | − | 63.2248i | −0.413234 | − | 0.413234i | ||||
\(154\) | − | 43.0583i | − | 0.279599i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 37.7477 | 0.241972 | ||||||||
\(157\) | 99.7950 | − | 99.7950i | 0.635637 | − | 0.635637i | −0.313839 | − | 0.949476i | \(-0.601615\pi\) |
0.949476 | + | 0.313839i | \(0.101615\pi\) | |||||||
\(158\) | −1.06121 | − | 1.06121i | −0.00671653 | − | 0.00671653i | ||||
\(159\) | − | 17.3553i | − | 0.109153i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 112.909 | 0.701297 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 45.3884 | + | 45.3884i | 0.278457 | + | 0.278457i | 0.832493 | − | 0.554036i | \(-0.186913\pi\) |
−0.554036 | + | 0.832493i | \(0.686913\pi\) | |||||||
\(164\) | − | 37.2177i | − | 0.226937i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −107.249 | −0.646075 | ||||||||
\(167\) | 99.2501 | − | 99.2501i | 0.594312 | − | 0.594312i | −0.344481 | − | 0.938793i | \(-0.611945\pi\) |
0.938793 | + | 0.344481i | \(0.111945\pi\) | |||||||
\(168\) | 9.16515 | + | 9.16515i | 0.0545545 | + | 0.0545545i | ||||
\(169\) | − | 50.2595i | − | 0.297393i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 72.3520 | 0.423111 | ||||||||
\(172\) | 52.2765 | − | 52.2765i | 0.303933 | − | 0.303933i | ||||
\(173\) | 80.5404 | + | 80.5404i | 0.465551 | + | 0.465551i | 0.900470 | − | 0.434919i | \(-0.143223\pi\) |
−0.434919 | + | 0.900470i | \(0.643223\pi\) | |||||||
\(174\) | − | 125.265i | − | 0.719914i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 46.0313 | 0.261541 | ||||||||
\(177\) | −115.553 | + | 115.553i | −0.652842 | + | 0.652842i | ||||
\(178\) | 145.154 | + | 145.154i | 0.815473 | + | 0.815473i | ||||
\(179\) | − | 154.267i | − | 0.861824i | −0.902394 | − | 0.430912i | \(-0.858192\pi\) | ||
0.902394 | − | 0.430912i | \(-0.141808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.548 | 0.920155 | 0.460078 | − | 0.887879i | \(-0.347822\pi\) | ||||
0.460078 | + | 0.887879i | \(0.347822\pi\) | |||||||
\(182\) | −28.8303 | + | 28.8303i | −0.158408 | + | 0.158408i | ||||
\(183\) | 9.90822 | + | 9.90822i | 0.0541433 | + | 0.0541433i | ||||
\(184\) | 120.705i | 0.656003i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −115.090 | −0.618762 | ||||||||
\(187\) | 242.527 | − | 242.527i | 1.29693 | − | 1.29693i | ||||
\(188\) | 100.262 | + | 100.262i | 0.533309 | + | 0.533309i | ||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −235.646 | −1.23375 | −0.616873 | − | 0.787063i | \(-0.711601\pi\) | ||||
−0.616873 | + | 0.787063i | \(0.711601\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 16.2211 | + | 16.2211i | 0.0840471 | + | 0.0840471i | 0.747880 | − | 0.663833i | \(-0.231072\pi\) |
−0.663833 | + | 0.747880i | \(0.731072\pi\) | |||||||
\(194\) | 47.5744i | 0.245229i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 6.68134 | − | 6.68134i | 0.0339154 | − | 0.0339154i | −0.689946 | − | 0.723861i | \(-0.742366\pi\) |
0.723861 | + | 0.689946i | \(0.242366\pi\) | |||||||
\(198\) | −34.5235 | − | 34.5235i | −0.174361 | − | 0.174361i | ||||
\(199\) | 32.0712i | 0.161162i | 0.996748 | + | 0.0805808i | \(0.0256775\pi\) | ||||
−0.996748 | + | 0.0805808i | \(0.974322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 50.5744 | 0.251614 | ||||||||
\(202\) | 50.1467 | − | 50.1467i | 0.248251 | − | 0.248251i | ||||
\(203\) | 95.6728 | + | 95.6728i | 0.471294 | + | 0.471294i | ||||
\(204\) | 103.246i | 0.506106i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −112.775 | −0.547453 | ||||||||
\(207\) | 90.5285 | − | 90.5285i | 0.437336 | − | 0.437336i | ||||
\(208\) | −30.8208 | − | 30.8208i | −0.148177 | − | 0.148177i | ||||
\(209\) | 277.538i | 1.32793i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 123.531 | 0.585457 | 0.292728 | − | 0.956196i | \(-0.405437\pi\) | ||||
0.292728 | + | 0.956196i | \(0.405437\pi\) | |||||||
\(212\) | −14.1705 | + | 14.1705i | −0.0668422 | + | 0.0668422i | ||||
\(213\) | −78.0891 | − | 78.0891i | −0.366616 | − | 0.366616i | ||||
\(214\) | − | 270.731i | − | 1.26510i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 87.9013 | − | 87.9013i | 0.405075 | − | 0.405075i | ||||
\(218\) | 100.934 | + | 100.934i | 0.463001 | + | 0.463001i | ||||
\(219\) | − | 122.936i | − | 0.561350i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −324.774 | −1.46956 | ||||||||
\(222\) | 20.8211 | − | 20.8211i | 0.0937890 | − | 0.0937890i | ||||
\(223\) | 81.9590 | + | 81.9590i | 0.367529 | + | 0.367529i | 0.866575 | − | 0.499046i | \(-0.166316\pi\) |
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.6348 | −0.224048 | ||||||||
\(227\) | −93.6089 | + | 93.6089i | −0.412374 | + | 0.412374i | −0.882565 | − | 0.470191i | \(-0.844185\pi\) |
0.470191 | + | 0.882565i | \(0.344185\pi\) | |||||||
\(228\) | −59.0751 | − | 59.0751i | −0.259101 | − | 0.259101i | ||||
\(229\) | 348.973i | 1.52390i | 0.647635 | + | 0.761950i | \(0.275758\pi\) | ||||
−0.647635 | + | 0.761950i | \(0.724242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 52.7355 | 0.228292 | ||||||||
\(232\) | −102.278 | + | 102.278i | −0.440856 | + | 0.440856i | ||||
\(233\) | −208.319 | − | 208.319i | −0.894074 | − | 0.894074i | 0.100829 | − | 0.994904i | \(-0.467850\pi\) |
−0.994904 | + | 0.100829i | \(0.967850\pi\) | |||||||
\(234\) | 46.2313i | 0.197569i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 188.697 | 0.799565 | ||||||||
\(237\) | 1.29971 | − | 1.29971i | 0.00548403 | − | 0.00548403i | ||||
\(238\) | −78.8552 | − | 78.8552i | −0.331324 | − | 0.331324i | ||||
\(239\) | 330.793i | 1.38407i | 0.721864 | + | 0.692035i | \(0.243285\pi\) | ||||
−0.721864 | + | 0.692035i | \(0.756715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 375.584 | 1.55844 | 0.779221 | − | 0.626749i | \(-0.215615\pi\) | ||||
0.779221 | + | 0.626749i | \(0.215615\pi\) | |||||||
\(242\) | 11.4299 | − | 11.4299i | 0.0472312 | − | 0.0472312i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 16.1801i | − | 0.0663117i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 45.5822 | 0.185294 | ||||||||
\(247\) | 185.829 | − | 185.829i | 0.752344 | − | 0.752344i | ||||
\(248\) | 93.9704 | + | 93.9704i | 0.378913 | + | 0.378913i | ||||
\(249\) | − | 131.352i | − | 0.527518i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 41.2876 | 0.164493 | 0.0822463 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822463 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(252\) | −11.2250 | + | 11.2250i | −0.0445435 | + | 0.0445435i | ||||
\(253\) | 347.262 | + | 347.262i | 1.37258 | + | 1.37258i | ||||
\(254\) | 233.492i | 0.919262i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 101.370 | − | 101.370i | 0.394437 | − | 0.394437i | −0.481828 | − | 0.876266i | \(-0.660027\pi\) |
0.876266 | + | 0.481828i | \(0.160027\pi\) | |||||||
\(258\) | 64.0254 | + | 64.0254i | 0.248161 | + | 0.248161i | ||||
\(259\) | 31.8048i | 0.122799i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 153.418 | 0.587807 | ||||||||
\(262\) | 34.8004 | − | 34.8004i | 0.132826 | − | 0.132826i | ||||
\(263\) | −164.594 | − | 164.594i | −0.625833 | − | 0.625833i | 0.321184 | − | 0.947017i | \(-0.395919\pi\) |
−0.947017 | + | 0.321184i | \(0.895919\pi\) | |||||||
\(264\) | 56.3766i | 0.213548i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 90.2387 | 0.339243 | ||||||||
\(267\) | −177.777 | + | 177.777i | −0.665831 | + | 0.665831i | ||||
\(268\) | −41.2938 | − | 41.2938i | −0.154081 | − | 0.154081i | ||||
\(269\) | − | 254.148i | − | 0.944788i | −0.881387 | − | 0.472394i | \(-0.843390\pi\) | ||
0.881387 | − | 0.472394i | \(-0.156610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4723 | 0.0829237 | 0.0414619 | − | 0.999140i | \(-0.486798\pi\) | ||||
0.0414619 | + | 0.999140i | \(0.486798\pi\) | |||||||
\(272\) | 84.2997 | − | 84.2997i | 0.309925 | − | 0.309925i | ||||
\(273\) | −35.3097 | − | 35.3097i | −0.129340 | − | 0.129340i | ||||
\(274\) | 263.104i | 0.960235i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −147.832 | −0.535625 | ||||||||
\(277\) | −47.3949 | + | 47.3949i | −0.171101 | + | 0.171101i | −0.787463 | − | 0.616362i | \(-0.788606\pi\) |
0.616362 | + | 0.787463i | \(0.288606\pi\) | |||||||
\(278\) | −89.4407 | − | 89.4407i | −0.321729 | − | 0.321729i | ||||
\(279\) | − | 140.956i | − | 0.505217i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8810 | −0.0671920 | −0.0335960 | − | 0.999435i | \(-0.510696\pi\) | ||||
−0.0335960 | + | 0.999435i | \(0.510696\pi\) | |||||||
\(282\) | −122.795 | + | 122.795i | −0.435445 | + | 0.435445i | ||||
\(283\) | 115.825 | + | 115.825i | 0.409277 | + | 0.409277i | 0.881486 | − | 0.472209i | \(-0.156543\pi\) |
−0.472209 | + | 0.881486i | \(0.656543\pi\) | |||||||
\(284\) | 127.519i | 0.449011i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −177.340 | −0.620071 | ||||||||
\(287\) | −34.8140 | + | 34.8140i | −0.121303 | + | 0.121303i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 599.306i | − | 2.07372i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −58.2665 | −0.200228 | ||||||||
\(292\) | −100.377 | + | 100.377i | −0.343756 | + | 0.343756i | ||||
\(293\) | −224.451 | − | 224.451i | −0.766043 | − | 0.766043i | 0.211364 | − | 0.977407i | \(-0.432209\pi\) |
−0.977407 | + | 0.211364i | \(0.932209\pi\) | |||||||
\(294\) | − | 17.1464i | − | 0.0583212i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −34.0008 | −0.114868 | ||||||||
\(297\) | 42.2824 | − | 42.2824i | 0.142365 | − | 0.142365i | ||||
\(298\) | 55.7399 | + | 55.7399i | 0.187047 | + | 0.187047i | ||||
\(299\) | − | 465.027i | − | 1.55528i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −97.8004 | −0.324918 | ||||||||
\(302\) | 82.9665 | − | 82.9665i | 0.274724 | − | 0.274724i | ||||
\(303\) | 61.4169 | + | 61.4169i | 0.202696 | + | 0.202696i | ||||
\(304\) | 96.4693i | 0.317333i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −126.450 | −0.413234 | ||||||||
\(307\) | 42.5120 | − | 42.5120i | 0.138476 | − | 0.138476i | −0.634471 | − | 0.772947i | \(-0.718782\pi\) |
0.772947 | + | 0.634471i | \(0.218782\pi\) | |||||||
\(308\) | −43.0583 | − | 43.0583i | −0.139800 | − | 0.139800i | ||||
\(309\) | − | 138.121i | − | 0.446993i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −97.1353 | −0.312332 | −0.156166 | − | 0.987731i | \(-0.549914\pi\) | ||||
−0.156166 | + | 0.987731i | \(0.549914\pi\) | |||||||
\(312\) | 37.7477 | − | 37.7477i | 0.120986 | − | 0.120986i | ||||
\(313\) | 94.4913 | + | 94.4913i | 0.301889 | + | 0.301889i | 0.841753 | − | 0.539863i | \(-0.181524\pi\) |
−0.539863 | + | 0.841753i | \(0.681524\pi\) | |||||||
\(314\) | − | 199.590i | − | 0.635637i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.12242 | −0.00671653 | ||||||||
\(317\) | −146.150 | + | 146.150i | −0.461040 | + | 0.461040i | −0.898996 | − | 0.437956i | \(-0.855703\pi\) |
0.437956 | + | 0.898996i | \(0.355703\pi\) | |||||||
\(318\) | −17.3553 | − | 17.3553i | −0.0545764 | − | 0.0545764i | ||||
\(319\) | 588.501i | 1.84483i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 331.576 | 1.03295 | ||||||||
\(322\) | 112.909 | − | 112.909i | 0.350649 | − | 0.350649i | ||||
\(323\) | 508.271 | + | 508.271i | 1.57359 | + | 1.57359i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 90.7768 | 0.278457 | ||||||||
\(327\) | −123.619 | + | 123.619i | −0.378039 | + | 0.378039i | ||||
\(328\) | −37.2177 | − | 37.2177i | −0.113469 | − | 0.113469i | ||||
\(329\) | − | 187.573i | − | 0.570131i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 223.981 | 0.676679 | 0.338339 | − | 0.941024i | \(-0.390135\pi\) | ||||
0.338339 | + | 0.941024i | \(0.390135\pi\) | |||||||
\(332\) | −107.249 | + | 107.249i | −0.323038 | + | 0.323038i | ||||
\(333\) | 25.5006 | + | 25.5006i | 0.0765784 | + | 0.0765784i | ||||
\(334\) | − | 198.500i | − | 0.594312i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | 41.7444 | − | 41.7444i | 0.123871 | − | 0.123871i | −0.642454 | − | 0.766324i | \(-0.722084\pi\) |
0.766324 | + | 0.642454i | \(0.222084\pi\) | |||||||
\(338\) | −50.2595 | − | 50.2595i | −0.148697 | − | 0.148697i | ||||
\(339\) | − | 62.0147i | − | 0.182934i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 540.697 | 1.58562 | ||||||||
\(342\) | 72.3520 | − | 72.3520i | 0.211555 | − | 0.211555i | ||||
\(343\) | 13.0958 | + | 13.0958i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 104.553i | − | 0.303933i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 161.081 | 0.465551 | ||||||||
\(347\) | −283.163 | + | 283.163i | −0.816031 | + | 0.816031i | −0.985530 | − | 0.169500i | \(-0.945785\pi\) |
0.169500 | + | 0.985530i | \(0.445785\pi\) | |||||||
\(348\) | −125.265 | − | 125.265i | −0.359957 | − | 0.359957i | ||||
\(349\) | − | 73.8529i | − | 0.211613i | −0.994387 | − | 0.105807i | \(-0.966258\pi\) | ||
0.994387 | − | 0.105807i | \(-0.0337424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −56.6215 | −0.161315 | ||||||||
\(352\) | 46.0313 | − | 46.0313i | 0.130771 | − | 0.130771i | ||||
\(353\) | 221.700 | + | 221.700i | 0.628047 | + | 0.628047i | 0.947576 | − | 0.319530i | \(-0.103525\pi\) |
−0.319530 | + | 0.947576i | \(0.603525\pi\) | |||||||
\(354\) | 231.106i | 0.652842i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 290.309 | 0.815473 | ||||||||
\(357\) | 96.5775 | − | 96.5775i | 0.270525 | − | 0.270525i | ||||
\(358\) | −154.267 | − | 154.267i | −0.430912 | − | 0.430912i | ||||
\(359\) | − | 351.735i | − | 0.979764i | −0.871789 | − | 0.489882i | \(-0.837040\pi\) | ||
0.871789 | − | 0.489882i | \(-0.162960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −220.645 | −0.611205 | ||||||||
\(362\) | 166.548 | − | 166.548i | 0.460078 | − | 0.460078i | ||||
\(363\) | 13.9988 | + | 13.9988i | 0.0385641 | + | 0.0385641i | ||||
\(364\) | 57.6605i | 0.158408i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19.8164 | 0.0541433 | ||||||||
\(367\) | −9.03767 | + | 9.03767i | −0.0246258 | + | 0.0246258i | −0.719312 | − | 0.694687i | \(-0.755543\pi\) |
0.694687 | + | 0.719312i | \(0.255543\pi\) | |||||||
\(368\) | 120.705 | + | 120.705i | 0.328002 | + | 0.328002i | ||||
\(369\) | 55.8266i | 0.151292i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.5107 | 0.0714573 | ||||||||
\(372\) | −115.090 | + | 115.090i | −0.309381 | + | 0.309381i | ||||
\(373\) | 151.095 | + | 151.095i | 0.405079 | + | 0.405079i | 0.880019 | − | 0.474939i | \(-0.157530\pi\) |
−0.474939 | + | 0.880019i | \(0.657530\pi\) | |||||||
\(374\) | − | 485.053i | − | 1.29693i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 200.524 | 0.533309 | ||||||||
\(377\) | 394.039 | − | 394.039i | 1.04520 | − | 1.04520i | ||||
\(378\) | −13.7477 | − | 13.7477i | −0.0363696 | − | 0.0363696i | ||||
\(379\) | − | 268.787i | − | 0.709201i | −0.935018 | − | 0.354601i | \(-0.884617\pi\) | ||
0.935018 | − | 0.354601i | \(-0.115383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −285.969 | −0.750574 | ||||||||
\(382\) | −235.646 | + | 235.646i | −0.616873 | + | 0.616873i | ||||
\(383\) | −304.341 | − | 304.341i | −0.794625 | − | 0.794625i | 0.187618 | − | 0.982242i | \(-0.439923\pi\) |
−0.982242 | + | 0.187618i | \(0.939923\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.4422 | 0.0840471 | ||||||||
\(387\) | −78.4148 | + | 78.4148i | −0.202622 | + | 0.202622i | ||||
\(388\) | 47.5744 | + | 47.5744i | 0.122614 | + | 0.122614i | ||||
\(389\) | 50.0127i | 0.128567i | 0.997932 | + | 0.0642837i | \(0.0204763\pi\) | ||||
−0.997932 | + | 0.0642837i | \(0.979524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1271.92 | 3.25299 | ||||||||
\(392\) | −14.0000 | + | 14.0000i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 42.6216 | + | 42.6216i | 0.108452 | + | 0.108452i | ||||
\(394\) | − | 13.3627i | − | 0.0339154i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −69.0469 | −0.174361 | ||||||||
\(397\) | 325.002 | − | 325.002i | 0.818644 | − | 0.818644i | −0.167268 | − | 0.985912i | \(-0.553494\pi\) |
0.985912 | + | 0.167268i | \(0.0534944\pi\) | |||||||
\(398\) | 32.0712 | + | 32.0712i | 0.0805808 | + | 0.0805808i | ||||
\(399\) | 110.519i | 0.276991i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −462.981 | −1.15457 | −0.577283 | − | 0.816544i | \(-0.695887\pi\) | ||||
−0.577283 | + | 0.816544i | \(0.695887\pi\) | |||||||
\(402\) | 50.5744 | − | 50.5744i | 0.125807 | − | 0.125807i | ||||
\(403\) | −362.031 | − | 362.031i | −0.898340 | − | 0.898340i | ||||
\(404\) | − | 100.293i | − | 0.248251i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 191.346 | 0.471294 | ||||||||
\(407\) | −97.8188 | + | 97.8188i | −0.240341 | + | 0.240341i | ||||
\(408\) | 103.246 | + | 103.246i | 0.253053 | + | 0.253053i | ||||
\(409\) | − | 131.630i | − | 0.321834i | −0.986968 | − | 0.160917i | \(-0.948555\pi\) | ||
0.986968 | − | 0.160917i | \(-0.0514451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −322.236 | −0.784028 | ||||||||
\(412\) | −112.775 | + | 112.775i | −0.273726 | + | 0.273726i | ||||
\(413\) | −176.510 | − | 176.510i | −0.427386 | − | 0.427386i | ||||
\(414\) | − | 181.057i | − | 0.437336i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −61.6417 | −0.148177 | ||||||||
\(417\) | 109.542 | − | 109.542i | 0.262691 | − | 0.262691i | ||||
\(418\) | 277.538 | + | 277.538i | 0.663966 | + | 0.663966i | ||||
\(419\) | − | 536.418i | − | 1.28023i | −0.768277 | − | 0.640117i | \(-0.778886\pi\) | ||
0.768277 | − | 0.640117i | \(-0.221114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −508.770 | −1.20848 | −0.604240 | − | 0.796803i | \(-0.706523\pi\) | ||||
−0.604240 | + | 0.796803i | \(0.706523\pi\) | |||||||
\(422\) | 123.531 | − | 123.531i | 0.292728 | − | 0.292728i | ||||
\(423\) | −150.393 | − | 150.393i | −0.355539 | − | 0.355539i | ||||
\(424\) | 28.3411i | 0.0668422i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −156.178 | −0.366616 | ||||||||
\(427\) | −15.1351 | + | 15.1351i | −0.0354451 | + | 0.0354451i | ||||
\(428\) | −270.731 | − | 270.731i | −0.632548 | − | 0.632548i | ||||
\(429\) | − | 217.197i | − | 0.506286i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 467.561 | 1.08483 | 0.542414 | − | 0.840111i | \(-0.317510\pi\) | ||||
0.542414 | + | 0.840111i | \(0.317510\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 129.391 | + | 129.391i | 0.298825 | + | 0.298825i | 0.840554 | − | 0.541729i | \(-0.182230\pi\) |
−0.541729 | + | 0.840554i | \(0.682230\pi\) | |||||||
\(434\) | − | 175.803i | − | 0.405075i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 201.868 | 0.463001 | ||||||||
\(437\) | −727.768 | + | 727.768i | −1.66537 | + | 1.66537i | ||||
\(438\) | −122.936 | − | 122.936i | −0.280675 | − | 0.280675i | ||||
\(439\) | 51.7818i | 0.117954i | 0.998259 | + | 0.0589770i | \(0.0187839\pi\) | ||||
−0.998259 | + | 0.0589770i | \(0.981216\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −324.774 | + | 324.774i | −0.734782 | + | 0.734782i | ||||
\(443\) | −357.514 | − | 357.514i | −0.807029 | − | 0.807029i | 0.177154 | − | 0.984183i | \(-0.443311\pi\) |
−0.984183 | + | 0.177154i | \(0.943311\pi\) | |||||||
\(444\) | − | 41.6423i | − | 0.0937890i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 163.918 | 0.367529 | ||||||||
\(447\) | −68.2671 | + | 68.2671i | −0.152723 | + | 0.152723i | ||||
\(448\) | −14.9666 | − | 14.9666i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 615.742i | 1.37136i | 0.727902 | + | 0.685681i | \(0.240496\pi\) | ||||
−0.727902 | + | 0.685681i | \(0.759504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −214.148 | −0.474828 | ||||||||
\(452\) | −50.6348 | + | 50.6348i | −0.112024 | + | 0.112024i | ||||
\(453\) | 101.613 | + | 101.613i | 0.224311 | + | 0.224311i | ||||
\(454\) | 187.218i | 0.412374i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −118.150 | −0.259101 | ||||||||
\(457\) | 502.144 | − | 502.144i | 1.09878 | − | 1.09878i | 0.104230 | − | 0.994553i | \(-0.466762\pi\) |
0.994553 | − | 0.104230i | \(-0.0332379\pi\) | |||||||
\(458\) | 348.973 | + | 348.973i | 0.761950 | + | 0.761950i | ||||
\(459\) | − | 154.868i | − | 0.337404i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 100.965 | 0.219012 | 0.109506 | − | 0.993986i | \(-0.465073\pi\) | ||||
0.109506 | + | 0.993986i | \(0.465073\pi\) | |||||||
\(462\) | 52.7355 | − | 52.7355i | 0.114146 | − | 0.114146i | ||||
\(463\) | −312.235 | − | 312.235i | −0.674374 | − | 0.674374i | 0.284347 | − | 0.958721i | \(-0.408223\pi\) |
−0.958721 | + | 0.284347i | \(0.908223\pi\) | |||||||
\(464\) | 204.557i | 0.440856i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −416.639 | −0.894074 | ||||||||
\(467\) | −502.571 | + | 502.571i | −1.07617 | + | 1.07617i | −0.0793198 | + | 0.996849i | \(0.525275\pi\) |
−0.996849 | + | 0.0793198i | \(0.974725\pi\) | |||||||
\(468\) | 46.2313 | + | 46.2313i | 0.0987847 | + | 0.0987847i | ||||
\(469\) | 77.2537i | 0.164720i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 244.447 | 0.518995 | ||||||||
\(472\) | 188.697 | − | 188.697i | 0.399783 | − | 0.399783i | ||||
\(473\) | −300.794 | − | 300.794i | −0.635929 | − | 0.635929i | ||||
\(474\) | − | 2.59943i | − | 0.00548403i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −157.710 | −0.331324 | ||||||||
\(477\) | 21.2558 | − | 21.2558i | 0.0445614 | − | 0.0445614i | ||||
\(478\) | 330.793 | + | 330.793i | 0.692035 | + | 0.692035i | ||||
\(479\) | − | 270.133i | − | 0.563952i | −0.959421 | − | 0.281976i | \(-0.909010\pi\) | ||
0.959421 | − | 0.281976i | \(-0.0909899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 130.992 | 0.272332 | ||||||||
\(482\) | 375.584 | − | 375.584i | 0.779221 | − | 0.779221i | ||||
\(483\) | 138.285 | + | 138.285i | 0.286303 | + | 0.286303i | ||||
\(484\) | − | 22.8599i | − | 0.0472312i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 227.632 | − | 227.632i | 0.467417 | − | 0.467417i | −0.433660 | − | 0.901077i | \(-0.642778\pi\) |
0.901077 | + | 0.433660i | \(0.142778\pi\) | |||||||
\(488\) | −16.1801 | − | 16.1801i | −0.0331559 | − | 0.0331559i | ||||
\(489\) | 111.178i | 0.227359i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.2563 | −0.0473652 | −0.0236826 | − | 0.999720i | \(-0.507539\pi\) | ||||
−0.0236826 | + | 0.999720i | \(0.507539\pi\) | |||||||
\(492\) | 45.5822 | − | 45.5822i | 0.0926468 | − | 0.0926468i | ||||
\(493\) | 1077.76 | + | 1077.76i | 2.18612 | + | 2.18612i | ||||
\(494\) | − | 371.658i | − | 0.752344i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 187.941 | 0.378913 | ||||||||
\(497\) | 119.283 | − | 119.283i | 0.240006 | − | 0.240006i | ||||
\(498\) | −131.352 | − | 131.352i | −0.263759 | − | 0.263759i | ||||
\(499\) | − | 319.077i | − | 0.639433i | −0.947513 | − | 0.319717i | \(-0.896412\pi\) | ||
0.947513 | − | 0.319717i | \(-0.103588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 243.112 | 0.485254 | ||||||||
\(502\) | 41.2876 | − | 41.2876i | 0.0822463 | − | 0.0822463i | ||||
\(503\) | −585.731 | − | 585.731i | −1.16448 | − | 1.16448i | −0.983485 | − | 0.180990i | \(-0.942070\pi\) |
−0.180990 | − | 0.983485i | \(-0.557930\pi\) | |||||||
\(504\) | 22.4499i | 0.0445435i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 694.524 | 1.37258 | ||||||||
\(507\) | 61.5551 | − | 61.5551i | 0.121410 | − | 0.121410i | ||||
\(508\) | 233.492 | + | 233.492i | 0.459631 | + | 0.459631i | ||||
\(509\) | − | 266.157i | − | 0.522902i | −0.965217 | − | 0.261451i | \(-0.915799\pi\) | ||
0.965217 | − | 0.261451i | \(-0.0842009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 187.787 | 0.367490 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 88.6127 | + | 88.6127i | 0.172734 | + | 0.172734i | ||||
\(514\) | − | 202.741i | − | 0.394437i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 128.051 | 0.248161 | ||||||||
\(517\) | 576.899 | − | 576.899i | 1.11586 | − | 1.11586i | ||||
\(518\) | 31.8048 | + | 31.8048i | 0.0613993 | + | 0.0613993i | ||||
\(519\) | 197.283i | 0.380121i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.52542 | −0.00292786 | −0.00146393 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146393 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(522\) | 153.418 | − | 153.418i | 0.293904 | − | 0.293904i | ||||
\(523\) | −260.120 | − | 260.120i | −0.497362 | − | 0.497362i | 0.413254 | − | 0.910616i | \(-0.364392\pi\) |
−0.910616 | + | 0.413254i | \(0.864392\pi\) | |||||||
\(524\) | − | 69.6007i | − | 0.132826i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −329.188 | −0.625833 | ||||||||
\(527\) | 990.210 | − | 990.210i | 1.87896 | − | 1.87896i | ||||
\(528\) | 56.3766 | + | 56.3766i | 0.106774 | + | 0.106774i | ||||
\(529\) | 1292.20i | 2.44272i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −283.046 | −0.533044 | ||||||||
\(532\) | 90.2387 | − | 90.2387i | 0.169622 | − | 0.169622i | ||||
\(533\) | 143.385 | + | 143.385i | 0.269015 | + | 0.269015i | ||||
\(534\) | 355.554i | 0.665831i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −82.5877 | −0.154081 | ||||||||
\(537\) | 188.937 | − | 188.937i | 0.351838 | − | 0.351838i | ||||
\(538\) | −254.148 | − | 254.148i | −0.472394 | − | 0.472394i | ||||
\(539\) | 80.5547i | 0.149452i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −273.648 | −0.505820 | −0.252910 | − | 0.967490i | \(-0.581388\pi\) | ||||
−0.252910 | + | 0.967490i | \(0.581388\pi\) | |||||||
\(542\) | 22.4723 | − | 22.4723i | 0.0414619 | − | 0.0414619i | ||||
\(543\) | 203.979 | + | 203.979i | 0.375652 | + | 0.375652i | ||||
\(544\) | − | 168.599i | − | 0.309925i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −70.6194 | −0.129340 | ||||||||
\(547\) | −355.490 | + | 355.490i | −0.649890 | + | 0.649890i | −0.952966 | − | 0.303077i | \(-0.901986\pi\) |
0.303077 | + | 0.952966i | \(0.401986\pi\) | |||||||
\(548\) | 263.104 | + | 263.104i | 0.480117 | + | 0.480117i | ||||
\(549\) | 24.2701i | 0.0442078i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1233.34 | −2.23837 | ||||||||
\(552\) | −147.832 | + | 147.832i | −0.267812 | + | 0.267812i | ||||
\(553\) | 1.98535 | + | 1.98535i | 0.00359014 | + | 0.00359014i | ||||
\(554\) | 94.7898i | 0.171101i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −178.881 | −0.321729 | ||||||||
\(557\) | 270.897 | − | 270.897i | 0.486350 | − | 0.486350i | −0.420802 | − | 0.907152i | \(-0.638251\pi\) |
0.907152 | + | 0.420802i | \(0.138251\pi\) | |||||||
\(558\) | −140.956 | − | 140.956i | −0.252609 | − | 0.252609i | ||||
\(559\) | 402.802i | 0.720575i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 594.066 | 1.05894 | ||||||||
\(562\) | −18.8810 | + | 18.8810i | −0.0335960 | + | 0.0335960i | ||||
\(563\) | −73.1143 | − | 73.1143i | −0.129866 | − | 0.129866i | 0.639186 | − | 0.769052i | \(-0.279271\pi\) |
−0.769052 | + | 0.639186i | \(0.779271\pi\) | |||||||
\(564\) | 245.591i | 0.435445i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 231.651 | 0.409277 | ||||||||
\(567\) | 16.8375 | − | 16.8375i | 0.0296957 | − | 0.0296957i | ||||
\(568\) | 127.519 | + | 127.519i | 0.224505 | + | 0.224505i | ||||
\(569\) | 1018.55i | 1.79007i | 0.445992 | + | 0.895037i | \(0.352851\pi\) | ||||
−0.445992 | + | 0.895037i | \(0.647149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −621.517 | −1.08847 | −0.544236 | − | 0.838932i | \(-0.683180\pi\) | ||||
−0.544236 | + | 0.838932i | \(0.683180\pi\) | |||||||
\(572\) | −177.340 | + | 177.340i | −0.310036 | + | 0.310036i | ||||
\(573\) | −288.606 | − | 288.606i | −0.503675 | − | 0.503675i | ||||
\(574\) | 69.6280i | 0.121303i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −760.301 | + | 760.301i | −1.31768 | + | 1.31768i | −0.402071 | + | 0.915608i | \(0.631710\pi\) |
−0.915608 | + | 0.402071i | \(0.868290\pi\) | |||||||
\(578\) | −599.306 | − | 599.306i | −1.03686 | − | 1.03686i | ||||
\(579\) | 39.7334i | 0.0686242i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 200.644 | 0.345342 | ||||||||
\(582\) | −58.2665 | + | 58.2665i | −0.100114 | + | 0.100114i | ||||
\(583\) | 81.5360 | + | 81.5360i | 0.139856 | + | 0.139856i | ||||
\(584\) | 200.753i | 0.343756i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −448.901 | −0.766043 | ||||||||
\(587\) | −5.94607 | + | 5.94607i | −0.0101296 | + | 0.0101296i | −0.712153 | − | 0.702024i | \(-0.752280\pi\) |
0.702024 | + | 0.712153i | \(0.252280\pi\) | |||||||
\(588\) | −17.1464 | − | 17.1464i | −0.0291606 | − | 0.0291606i | ||||
\(589\) | 1133.16i | 1.92387i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.3659 | 0.0276918 | ||||||||
\(592\) | −34.0008 | + | 34.0008i | −0.0574338 | + | 0.0574338i | ||||
\(593\) | 463.916 | + | 463.916i | 0.782320 | + | 0.782320i | 0.980222 | − | 0.197902i | \(-0.0634127\pi\) |
−0.197902 | + | 0.980222i | \(0.563413\pi\) | |||||||
\(594\) | − | 84.5649i | − | 0.142365i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 111.480 | 0.187047 | ||||||||
\(597\) | −39.2790 | + | 39.2790i | −0.0657940 | + | 0.0657940i | ||||
\(598\) | −465.027 | − | 465.027i | −0.777638 | − | 0.777638i | ||||
\(599\) | − | 660.745i | − | 1.10308i | −0.834148 | − | 0.551540i | \(-0.814040\pi\) | ||
0.834148 | − | 0.551540i | \(-0.185960\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −905.439 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(602\) | −97.8004 | + | 97.8004i | −0.162459 | + | 0.162459i | ||||
\(603\) | 61.9407 | + | 61.9407i | 0.102721 | + | 0.102721i | ||||
\(604\) | − | 165.933i | − | 0.274724i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 122.834 | 0.202696 | ||||||||
\(607\) | −518.514 | + | 518.514i | −0.854224 | + | 0.854224i | −0.990650 | − | 0.136426i | \(-0.956438\pi\) |
0.136426 | + | 0.990650i | \(0.456438\pi\) | |||||||
\(608\) | 96.4693 | + | 96.4693i | 0.158667 | + | 0.158667i | ||||
\(609\) | 234.349i | 0.384810i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −772.541 | −1.26439 | ||||||||
\(612\) | −126.450 | + | 126.450i | −0.206617 | + | 0.206617i | ||||
\(613\) | 500.739 | + | 500.739i | 0.816867 | + | 0.816867i | 0.985653 | − | 0.168786i | \(-0.0539847\pi\) |
−0.168786 | + | 0.985653i | \(0.553985\pi\) | |||||||
\(614\) | − | 85.0240i | − | 0.138476i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −86.1166 | −0.139800 | ||||||||
\(617\) | −122.242 | + | 122.242i | −0.198123 | + | 0.198123i | −0.799195 | − | 0.601072i | \(-0.794740\pi\) |
0.601072 | + | 0.799195i | \(0.294740\pi\) | |||||||
\(618\) | −138.121 | − | 138.121i | −0.223497 | − | 0.223497i | ||||
\(619\) | 320.914i | 0.518440i | 0.965818 | + | 0.259220i | \(0.0834655\pi\) | ||||
−0.965818 | + | 0.259220i | \(0.916534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 221.749 | 0.357083 | ||||||||
\(622\) | −97.1353 | + | 97.1353i | −0.156166 | + | 0.156166i | ||||
\(623\) | −271.559 | − | 271.559i | −0.435889 | − | 0.435889i | ||||
\(624\) | − | 75.4953i | − | 0.120986i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 188.983 | 0.301889 | ||||||||
\(627\) | −339.913 | + | 339.913i | −0.542126 | + | 0.542126i | ||||
\(628\) | −199.590 | − | 199.590i | −0.317818 | − | 0.317818i | ||||
\(629\) | 358.282i | 0.569606i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −636.141 | −1.00815 | −0.504074 | − | 0.863661i | \(-0.668166\pi\) | ||||
−0.504074 | + | 0.863661i | \(0.668166\pi\) | |||||||
\(632\) | −2.12242 | + | 2.12242i | −0.00335827 | + | 0.00335827i | ||||
\(633\) | 151.294 | + | 151.294i | 0.239012 | + | 0.239012i | ||||
\(634\) | 292.300i | 0.461040i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −34.7106 | −0.0545764 | ||||||||
\(637\) | 53.9365 | − | 53.9365i | 0.0846726 | − | 0.0846726i | ||||
\(638\) | 588.501 | + | 588.501i | 0.922416 | + | 0.922416i | ||||
\(639\) | − | 191.278i | − | 0.299340i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −682.051 | −1.06404 | −0.532021 | − | 0.846731i | \(-0.678567\pi\) | ||||
−0.532021 | + | 0.846731i | \(0.678567\pi\) | |||||||
\(642\) | 331.576 | − | 331.576i | 0.516474 | − | 0.516474i | ||||
\(643\) | 5.33298 | + | 5.33298i | 0.00829390 | + | 0.00829390i | 0.711242 | − | 0.702948i | \(-0.248133\pi\) |
−0.702948 | + | 0.711242i | \(0.748133\pi\) | |||||||
\(644\) | − | 225.818i | − | 0.350649i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1016.54 | 1.57359 | ||||||||
\(647\) | −285.931 | + | 285.931i | −0.441933 | + | 0.441933i | −0.892661 | − | 0.450728i | \(-0.851164\pi\) |
0.450728 | + | 0.892661i | \(0.351164\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 1085.75i | − | 1.67296i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 215.313 | 0.330742 | ||||||||
\(652\) | 90.7768 | − | 90.7768i | 0.139228 | − | 0.139228i | ||||
\(653\) | −199.462 | − | 199.462i | −0.305455 | − | 0.305455i | 0.537689 | − | 0.843144i | \(-0.319298\pi\) |
−0.843144 | + | 0.537689i | \(0.819298\pi\) | |||||||
\(654\) | 247.237i | 0.378039i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −74.4355 | −0.113469 | ||||||||
\(657\) | 150.565 | − | 150.565i | 0.229170 | − | 0.229170i | ||||
\(658\) | −187.573 | − | 187.573i | −0.285066 | − | 0.285066i | ||||
\(659\) | 204.685i | 0.310599i | 0.987867 | + | 0.155300i | \(0.0496343\pi\) | ||||
−0.987867 | + | 0.155300i | \(0.950366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 143.044 | 0.216406 | 0.108203 | − | 0.994129i | \(-0.465490\pi\) | ||||
0.108203 | + | 0.994129i | \(0.465490\pi\) | |||||||
\(662\) | 223.981 | − | 223.981i | 0.338339 | − | 0.338339i | ||||
\(663\) | −397.765 | − | 397.765i | −0.599947 | − | 0.599947i | ||||
\(664\) | 214.497i | 0.323038i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 51.0012 | 0.0765784 | ||||||||
\(667\) | −1543.19 | + | 1543.19i | −2.31362 | + | 2.31362i | ||||
\(668\) | −198.500 | − | 198.500i | −0.297156 | − | 0.297156i | ||||
\(669\) | 200.758i | 0.300086i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −93.0986 | −0.138746 | ||||||||
\(672\) | 18.3303 | − | 18.3303i | 0.0272772 | − | 0.0272772i | ||||
\(673\) | 317.527 | + | 317.527i | 0.471808 | + | 0.471808i | 0.902499 | − | 0.430691i | \(-0.141730\pi\) |
−0.430691 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(674\) | − | 83.4888i | − | 0.123871i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −100.519 | −0.148697 | ||||||||
\(677\) | 272.663 | − | 272.663i | 0.402752 | − | 0.402752i | −0.476450 | − | 0.879202i | \(-0.658077\pi\) |
0.879202 | + | 0.476450i | \(0.158077\pi\) | |||||||
\(678\) | −62.0147 | − | 62.0147i | −0.0914671 | − | 0.0914671i | ||||
\(679\) | − | 89.0035i | − | 0.131080i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −229.294 | −0.336702 | ||||||||
\(682\) | 540.697 | − | 540.697i | 0.792812 | − | 0.792812i | ||||
\(683\) | 449.231 | + | 449.231i | 0.657732 | + | 0.657732i | 0.954843 | − | 0.297111i | \(-0.0960232\pi\) |
−0.297111 | + | 0.954843i | \(0.596023\pi\) | |||||||
\(684\) | − | 144.704i | − | 0.211555i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | −427.403 | + | 427.403i | −0.622130 | + | 0.622130i | ||||
\(688\) | −104.553 | − | 104.553i | −0.151967 | − | 0.151967i | ||||
\(689\) | − | 109.187i | − | 0.158472i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1004.13 | 1.45316 | 0.726578 | − | 0.687084i | \(-0.241109\pi\) | ||||
0.726578 | + | 0.687084i | \(0.241109\pi\) | |||||||
\(692\) | 161.081 | − | 161.081i | 0.232776 | − | 0.232776i | ||||
\(693\) | 64.5875 | + | 64.5875i | 0.0931998 | + | 0.0931998i | ||||
\(694\) | 566.325i | 0.816031i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −250.530 | −0.359957 | ||||||||
\(697\) | −392.181 | + | 392.181i | −0.562669 | + | 0.562669i | ||||
\(698\) | −73.8529 | − | 73.8529i | −0.105807 | − | 0.105807i | ||||
\(699\) | − | 510.276i | − | 0.730009i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −869.248 | −1.24001 | −0.620006 | − | 0.784597i | \(-0.712870\pi\) | ||||
−0.620006 | + | 0.784597i | \(0.712870\pi\) | |||||||
\(702\) | −56.6215 | + | 56.6215i | −0.0806574 | + | 0.0806574i | ||||
\(703\) | −205.002 | − | 205.002i | −0.291610 | − | 0.291610i | ||||
\(704\) | − | 92.0626i | − | 0.130771i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 443.401 | 0.628047 | ||||||||
\(707\) | −93.8159 | + | 93.8159i | −0.132696 | + | 0.132696i | ||||
\(708\) | 231.106 | + | 231.106i | 0.326421 | + | 0.326421i | ||||
\(709\) | 79.6980i | 0.112409i | 0.998419 | + | 0.0562045i | \(0.0178999\pi\) | ||||
−0.998419 | + | 0.0562045i | \(0.982100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.18364 | 0.00447769 | ||||||||
\(712\) | 290.309 | − | 290.309i | 0.407737 | − | 0.407737i | ||||
\(713\) | 1417.83 | + | 1417.83i | 1.98855 | + | 1.98855i | ||||
\(714\) | − | 193.155i | − | 0.270525i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −308.533 | −0.430912 | ||||||||
\(717\) | −405.136 | + | 405.136i | −0.565044 | + | 0.565044i | ||||
\(718\) | −351.735 | − | 351.735i | −0.489882 | − | 0.489882i | ||||
\(719\) | 1081.03i | 1.50351i | 0.659440 | + | 0.751757i | \(0.270793\pi\) | ||||
−0.659440 | + | 0.751757i | \(0.729207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 210.983 | 0.292626 | ||||||||
\(722\) | −220.645 | + | 220.645i | −0.305603 | + | 0.305603i | ||||
\(723\) | 459.995 | + | 459.995i | 0.636231 | + | 0.636231i | ||||
\(724\) | − | 333.096i | − | 0.460078i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 27.9975 | 0.0385641 | ||||||||
\(727\) | −281.701 | + | 281.701i | −0.387484 | + | 0.387484i | −0.873789 | − | 0.486305i | \(-0.838344\pi\) |
0.486305 | + | 0.873789i | \(0.338344\pi\) | |||||||
\(728\) | 57.6605 | + | 57.6605i | 0.0792040 | + | 0.0792040i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1101.72 | −1.50715 | ||||||||
\(732\) | 19.8164 | − | 19.8164i | 0.0270716 | − | 0.0270716i | ||||
\(733\) | −1016.28 | − | 1016.28i | −1.38647 | − | 1.38647i | −0.832611 | − | 0.553858i | \(-0.813155\pi\) |
−0.553858 | − | 0.832611i | \(-0.686845\pi\) | |||||||
\(734\) | 18.0753i | 0.0246258i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 241.409 | 0.328002 | ||||||||
\(737\) | −237.601 | + | 237.601i | −0.322389 | + | 0.322389i | ||||
\(738\) | 55.8266 | + | 55.8266i | 0.0756458 | + | 0.0756458i | ||||
\(739\) | 289.140i | 0.391258i | 0.980678 | + | 0.195629i | \(0.0626749\pi\) | ||||
−0.980678 | + | 0.195629i | \(0.937325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 455.186 | 0.614286 | ||||||||
\(742\) | 26.5107 | − | 26.5107i | 0.0357286 | − | 0.0357286i | ||||
\(743\) | −290.501 | − | 290.501i | −0.390984 | − | 0.390984i | 0.484054 | − | 0.875038i | \(-0.339164\pi\) |
−0.875038 | + | 0.484054i | \(0.839164\pi\) | |||||||
\(744\) | 230.180i | 0.309381i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 302.189 | 0.405079 | ||||||||
\(747\) | 160.873 | − | 160.873i | 0.215358 | − | 0.215358i | ||||
\(748\) | −485.053 | − | 485.053i | −0.648467 | − | 0.648467i | ||||
\(749\) | 506.491i | 0.676223i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 688.089 | 0.916231 | 0.458115 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458115 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(752\) | 200.524 | − | 200.524i | 0.266655 | − | 0.266655i | ||||
\(753\) | 50.5668 | + | 50.5668i | 0.0671538 | + | 0.0671538i | ||||
\(754\) | − | 788.077i | − | 1.04520i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | −180.960 | + | 180.960i | −0.239049 | + | 0.239049i | −0.816456 | − | 0.577408i | \(-0.804064\pi\) |
0.577408 | + | 0.816456i | \(0.304064\pi\) | |||||||
\(758\) | −268.787 | − | 268.787i | −0.354601 | − | 0.354601i | ||||
\(759\) | 850.614i | 1.12070i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1096.09 | 1.44033 | 0.720163 | − | 0.693805i | \(-0.244067\pi\) | ||||
0.720163 | + | 0.693805i | \(0.244067\pi\) | |||||||
\(762\) | −285.969 | + | 285.969i | −0.375287 | + | 0.375287i | ||||
\(763\) | −188.831 | − | 188.831i | −0.247484 | − | 0.247484i | ||||
\(764\) | 471.291i | 0.616873i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −608.682 | −0.794625 | ||||||||
\(767\) | −726.977 | + | 726.977i | −0.947818 | + | 0.947818i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 892.540i | − | 1.16065i | −0.814385 | − | 0.580325i | \(-0.802925\pi\) | ||
0.814385 | − | 0.580325i | \(-0.197075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 248.306 | 0.322057 | ||||||||
\(772\) | 32.4422 | − | 32.4422i | 0.0420235 | − | 0.0420235i | ||||
\(773\) | −836.773 | − | 836.773i | −1.08250 | − | 1.08250i | −0.996276 | − | 0.0862244i | \(-0.972520\pi\) |
−0.0862244 | − | 0.996276i | \(-0.527480\pi\) | |||||||
\(774\) | 156.830i | 0.202622i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 95.1487 | 0.122614 | ||||||||
\(777\) | −38.9528 | + | 38.9528i | −0.0501323 | + | 0.0501323i | ||||
\(778\) | 50.0127 | + | 50.0127i | 0.0642837 | + | 0.0642837i | ||||
\(779\) | − | 448.796i | − | 0.576118i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 733.733 | 0.939479 | ||||||||
\(782\) | 1271.92 | − | 1271.92i | 1.62650 | − | 1.62650i | ||||
\(783\) | 187.898 | + | 187.898i | 0.239971 | + | 0.239971i | ||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 85.2431 | 0.108452 | ||||||||
\(787\) | 226.485 | − | 226.485i | 0.287782 | − | 0.287782i | −0.548420 | − | 0.836203i | \(-0.684771\pi\) |
0.836203 | + | 0.548420i | \(0.184771\pi\) | |||||||
\(788\) | −13.3627 | − | 13.3627i | −0.0169577 | − | 0.0169577i | ||||
\(789\) | − | 403.171i | − | 0.510990i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 94.7290 | 0.119759 | ||||||||
\(792\) | −69.0469 | + | 69.0469i | −0.0871805 | + | 0.0871805i | ||||
\(793\) | 62.3354 | + | 62.3354i | 0.0786070 | + | 0.0786070i | ||||
\(794\) | − | 650.003i | − | 0.818644i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 64.1423 | 0.0805808 | ||||||||
\(797\) | 728.914 | − | 728.914i | 0.914572 | − | 0.914572i | −0.0820555 | − | 0.996628i | \(-0.526148\pi\) |
0.996628 | + | 0.0820555i | \(0.0261485\pi\) | |||||||
\(798\) | 110.519 | + | 110.519i | 0.138496 | + | 0.138496i | ||||
\(799\) | − | 2113.02i | − | 2.64458i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −435.463 | −0.543649 | ||||||||
\(802\) | −462.981 | + | 462.981i | −0.577283 | + | 0.577283i | ||||
\(803\) | 577.558 | + | 577.558i | 0.719250 | + | 0.719250i | ||||
\(804\) | − | 101.149i | − | 0.125807i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −724.062 | −0.898340 | ||||||||
\(807\) | 311.267 | − | 311.267i | 0.385708 | − | 0.385708i | ||||
\(808\) | −100.293 | − | 100.293i | −0.124126 | − | 0.124126i | ||||
\(809\) | 1196.38i | 1.47884i | 0.673247 | + | 0.739418i | \(0.264899\pi\) | ||||
−0.673247 | + | 0.739418i | \(0.735101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1180.03 | −1.45503 | −0.727513 | − | 0.686094i | \(-0.759324\pi\) | ||||
−0.727513 | + | 0.686094i | \(0.759324\pi\) | |||||||
\(812\) | 191.346 | − | 191.346i | 0.235647 | − | 0.235647i | ||||
\(813\) | 27.5229 | + | 27.5229i | 0.0338535 | + | 0.0338535i | ||||
\(814\) | 195.638i | 0.240341i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 206.491 | 0.253053 | ||||||||
\(817\) | 630.385 | − | 630.385i | 0.771585 | − | 0.771585i | ||||
\(818\) | −131.630 | − | 131.630i | −0.160917 | − | 0.160917i | ||||
\(819\) | − | 86.4908i | − | 0.105605i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.8305 | 0.0436425 | 0.0218212 | − | 0.999762i | \(-0.493054\pi\) | ||||
0.0218212 | + | 0.999762i | \(0.493054\pi\) | |||||||
\(822\) | −322.236 | + | 322.236i | −0.392014 | + | 0.392014i | ||||
\(823\) | −448.829 | − | 448.829i | −0.545357 | − | 0.545357i | 0.379737 | − | 0.925094i | \(-0.376014\pi\) |
−0.925094 | + | 0.379737i | \(0.876014\pi\) | |||||||
\(824\) | 225.550i | 0.273726i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −353.021 | −0.427386 | ||||||||
\(827\) | −874.926 | + | 874.926i | −1.05795 | + | 1.05795i | −0.0597373 | + | 0.998214i | \(0.519026\pi\) |
−0.998214 | + | 0.0597373i | \(0.980974\pi\) | |||||||
\(828\) | −181.057 | − | 181.057i | −0.218668 | − | 0.218668i | ||||
\(829\) | − | 934.022i | − | 1.12669i | −0.826223 | − | 0.563343i | \(-0.809515\pi\) | ||
0.826223 | − | 0.563343i | \(-0.190485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −116.093 | −0.139703 | ||||||||
\(832\) | −61.6417 | + | 61.6417i | −0.0740886 | + | 0.0740886i | ||||
\(833\) | 147.525 | + | 147.525i | 0.177100 | + | 0.177100i | ||||
\(834\) | − | 219.084i | − | 0.262691i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 555.076 | 0.663966 | ||||||||
\(837\) | 172.635 | − | 172.635i | 0.206254 | − | 0.206254i | ||||
\(838\) | −536.418 | − | 536.418i | −0.640117 | − | 0.640117i | ||||
\(839\) | 10.5147i | 0.0125324i | 0.999980 | + | 0.00626621i | \(0.00199461\pi\) | ||||
−0.999980 | + | 0.00626621i | \(0.998005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1774.22 | −2.10966 | ||||||||
\(842\) | −508.770 | + | 508.770i | −0.604240 | + | 0.604240i | ||||
\(843\) | −23.1244 | − | 23.1244i | −0.0274310 | − | 0.0274310i | ||||
\(844\) | − | 247.063i | − | 0.292728i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −300.786 | −0.355539 | ||||||||
\(847\) | −21.3835 | + | 21.3835i | −0.0252461 | + | 0.0252461i | ||||
\(848\) | 28.3411 | + | 28.3411i | 0.0334211 | + | 0.0334211i | ||||
\(849\) | 283.713i | 0.334173i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −513.007 | −0.602828 | ||||||||
\(852\) | −156.178 | + | 156.178i | −0.183308 | + | 0.183308i | ||||
\(853\) | −1082.57 | − | 1082.57i | −1.26914 | − | 1.26914i | −0.946534 | − | 0.322603i | \(-0.895442\pi\) |
−0.322603 | − | 0.946534i | \(-0.604558\pi\) | |||||||
\(854\) | 30.2701i | 0.0354451i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −541.461 | −0.632548 | ||||||||
\(857\) | −506.843 | + | 506.843i | −0.591416 | + | 0.591416i | −0.938014 | − | 0.346598i | \(-0.887337\pi\) |
0.346598 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(858\) | −217.197 | − | 217.197i | −0.253143 | − | 0.253143i | ||||
\(859\) | 471.172i | 0.548512i | 0.961657 | + | 0.274256i | \(0.0884315\pi\) | ||||
−0.961657 | + | 0.274256i | \(0.911568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85.2765 | −0.0990436 | ||||||||
\(862\) | 467.561 | − | 467.561i | 0.542414 | − | 0.542414i | ||||
\(863\) | −352.570 | − | 352.570i | −0.408540 | − | 0.408540i | 0.472689 | − | 0.881229i | \(-0.343283\pi\) |
−0.881229 | + | 0.472689i | \(0.843283\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 258.782 | 0.298825 | ||||||||
\(867\) | 733.996 | − | 733.996i | 0.846593 | − | 0.846593i | ||||
\(868\) | −175.803 | − | 175.803i | −0.202538 | − | 0.202538i | ||||
\(869\) | 12.2122i | 0.0140532i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 318.178 | 0.365301 | ||||||||
\(872\) | 201.868 | − | 201.868i | 0.231500 | − | 0.231500i | ||||
\(873\) | −71.3616 | − | 71.3616i | −0.0817429 | − | 0.0817429i | ||||
\(874\) | 1455.54i | 1.66537i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −245.872 | −0.280675 | ||||||||
\(877\) | 1223.94 | − | 1223.94i | 1.39560 | − | 1.39560i | 0.583467 | − | 0.812137i | \(-0.301696\pi\) |
0.812137 | − | 0.583467i | \(-0.198304\pi\) | |||||||
\(878\) | 51.7818 | + | 51.7818i | 0.0589770 | + | 0.0589770i | ||||
\(879\) | − | 549.790i | − | 0.625472i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −635.103 | −0.720889 | −0.360444 | − | 0.932781i | \(-0.617375\pi\) | ||||
−0.360444 | + | 0.932781i | \(0.617375\pi\) | |||||||
\(882\) | 21.0000 | − | 21.0000i | 0.0238095 | − | 0.0238095i | ||||
\(883\) | 230.546 | + | 230.546i | 0.261094 | + | 0.261094i | 0.825498 | − | 0.564405i | \(-0.190894\pi\) |
−0.564405 | + | 0.825498i | \(0.690894\pi\) | |||||||
\(884\) | 649.547i | 0.734782i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −715.028 | −0.807029 | ||||||||
\(887\) | 1224.61 | − | 1224.61i | 1.38062 | − | 1.38062i | 0.537101 | − | 0.843518i | \(-0.319520\pi\) |
0.843518 | − | 0.537101i | \(-0.180480\pi\) | |||||||
\(888\) | −41.6423 | − | 41.6423i | −0.0468945 | − | 0.0468945i | ||||
\(889\) | − | 436.824i | − | 0.491366i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 103.570 | 0.116241 | ||||||||
\(892\) | 163.918 | − | 163.918i | 0.183765 | − | 0.183765i | ||||
\(893\) | 1209.03 | + | 1209.03i | 1.35389 | + | 1.35389i | ||||
\(894\) | 136.534i | 0.152723i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 569.540 | − | 569.540i | 0.634938 | − | 0.634938i | ||||
\(898\) | 615.742 | + | 615.742i | 0.685681 | + | 0.685681i | ||||
\(899\) | 2402.79i | 2.67273i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 298.643 | 0.331457 | ||||||||
\(902\) | −214.148 | + | 214.148i | −0.237414 | + | 0.237414i | ||||
\(903\) | −119.781 | − | 119.781i | −0.132647 | − | 0.132647i | ||||
\(904\) | 101.270i | 0.112024i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 203.226 | 0.224311 | ||||||||
\(907\) | −766.713 | + | 766.713i | −0.845329 | + | 0.845329i | −0.989546 | − | 0.144217i | \(-0.953934\pi\) |
0.144217 | + | 0.989546i | \(0.453934\pi\) | |||||||
\(908\) | 187.218 | + | 187.218i | 0.206187 | + | 0.206187i | ||||
\(909\) | 150.440i | 0.165501i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −754.441 | −0.828146 | −0.414073 | − | 0.910244i | \(-0.635894\pi\) | ||||
−0.414073 | + | 0.910244i | \(0.635894\pi\) | |||||||
\(912\) | −118.150 | + | 118.150i | −0.129551 | + | 0.129551i | ||||
\(913\) | 617.098 | + | 617.098i | 0.675902 | + | 0.675902i | ||||
\(914\) | − | 1004.29i | − | 1.09878i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 697.947 | 0.761950 | ||||||||
\(917\) | −65.1055 | + | 65.1055i | −0.0709984 | + | 0.0709984i | ||||
\(918\) | −154.868 | − | 154.868i | −0.168702 | − | 0.168702i | ||||
\(919\) | 858.117i | 0.933750i | 0.884323 | + | 0.466875i | \(0.154620\pi\) | ||||
−0.884323 | + | 0.466875i | \(0.845380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 104.133 | 0.113065 | ||||||||
\(922\) | 100.965 | − | 100.965i | 0.109506 | − | 0.109506i | ||||
\(923\) | −491.280 | − | 491.280i | −0.532265 | − | 0.532265i | ||||
\(924\) | − | 105.471i | − | 0.114146i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −624.471 | −0.674374 | ||||||||
\(927\) | 169.163 | − | 169.163i | 0.182484 | − | 0.182484i | ||||
\(928\) | 204.557 | + | 204.557i | 0.220428 | + | 0.220428i | ||||
\(929\) | 631.542i | 0.679809i | 0.940460 | + | 0.339904i | \(0.110395\pi\) | ||||
−0.940460 | + | 0.339904i | \(0.889605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −168.821 | −0.181333 | ||||||||
\(932\) | −416.639 | + | 416.639i | −0.447037 | + | 0.447037i | ||||
\(933\) | −118.966 | − | 118.966i | −0.127509 | − | 0.127509i | ||||
\(934\) | 1005.14i | 1.07617i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 92.4625 | 0.0987847 | ||||||||
\(937\) | −1167.50 | + | 1167.50i | −1.24599 | + | 1.24599i | −0.288519 | + | 0.957474i | \(0.593163\pi\) |
−0.957474 | + | 0.288519i | \(0.906837\pi\) | |||||||
\(938\) | 77.2537 | + | 77.2537i | 0.0823600 | + | 0.0823600i | ||||
\(939\) | 231.455i | 0.246491i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −614.550 | −0.653082 | −0.326541 | − | 0.945183i | \(-0.605883\pi\) | ||||
−0.326541 | + | 0.945183i | \(0.605883\pi\) | |||||||
\(942\) | 244.447 | − | 244.447i | 0.259498 | − | 0.259498i | ||||
\(943\) | −561.544 | − | 561.544i | −0.595487 | − | 0.595487i | ||||
\(944\) | − | 377.395i | − | 0.399783i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −601.589 | −0.635929 | ||||||||
\(947\) | 635.282 | − | 635.282i | 0.670837 | − | 0.670837i | −0.287072 | − | 0.957909i | \(-0.592682\pi\) |
0.957909 | + | 0.287072i | \(0.0926820\pi\) | |||||||
\(948\) | −2.59943 | − | 2.59943i | −0.00274201 | − | 0.00274201i | ||||
\(949\) | − | 773.423i | − | 0.814987i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −357.992 | −0.376438 | ||||||||
\(952\) | −157.710 | + | 157.710i | −0.165662 | + | 0.165662i | ||||
\(953\) | −350.517 | − | 350.517i | −0.367803 | − | 0.367803i | 0.498872 | − | 0.866676i | \(-0.333748\pi\) |
−0.866676 | + | 0.498872i | \(0.833748\pi\) | |||||||
\(954\) | − | 42.5116i | − | 0.0445614i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 661.585 | 0.692035 | ||||||||
\(957\) | −720.764 | + | 720.764i | −0.753149 | + | 0.753149i | ||||
\(958\) | −270.133 | − | 270.133i | −0.281976 | − | 0.281976i | ||||
\(959\) | − | 492.223i | − | 0.513267i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1246.61 | 1.29720 | ||||||||
\(962\) | 130.992 | − | 130.992i | 0.136166 | − | 0.136166i | ||||
\(963\) | 406.096 | + | 406.096i | 0.421699 | + | 0.421699i | ||||
\(964\) | − | 751.169i | − | 0.779221i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 276.569 | 0.286303 | ||||||||
\(967\) | −435.204 | + | 435.204i | −0.450056 | + | 0.450056i | −0.895373 | − | 0.445317i | \(-0.853091\pi\) |
0.445317 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(968\) | −22.8599 | − | 22.8599i | −0.0236156 | − | 0.0236156i | ||||
\(969\) | 1245.00i | 1.28483i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 218.866 | 0.225403 | 0.112701 | − | 0.993629i | \(-0.464050\pi\) | ||||
0.112701 | + | 0.993629i | \(0.464050\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 167.328 | + | 167.328i | 0.171971 | + | 0.171971i | ||||
\(974\) | − | 455.264i | − | 0.467417i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.3601 | −0.0331559 | ||||||||
\(977\) | −1000.73 | + | 1000.73i | −1.02429 | + | 1.02429i | −0.0245886 | + | 0.999698i | \(0.507828\pi\) |
−0.999698 | + | 0.0245886i | \(0.992172\pi\) | |||||||
\(978\) | 111.178 | + | 111.178i | 0.113679 | + | 0.113679i | ||||
\(979\) | − | 1670.41i | − | 1.70624i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −302.802 | −0.308667 | ||||||||
\(982\) | −23.2563 | + | 23.2563i | −0.0236826 | + | 0.0236826i | ||||
\(983\) | −915.596 | − | 915.596i | −0.931431 | − | 0.931431i | 0.0663648 | − | 0.997795i | \(-0.478860\pi\) |
−0.997795 | + | 0.0663648i | \(0.978860\pi\) | |||||||
\(984\) | − | 91.1645i | − | 0.0926468i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2155.51 | 2.18612 | ||||||||
\(987\) | 229.729 | − | 229.729i | 0.232755 | − | 0.232755i | ||||
\(988\) | −371.658 | − | 371.658i | −0.376172 | − | 0.376172i | ||||
\(989\) | − | 1577.50i | − | 1.59505i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −437.633 | −0.441608 | −0.220804 | − | 0.975318i | \(-0.570868\pi\) | ||||
−0.220804 | + | 0.975318i | \(0.570868\pi\) | |||||||
\(992\) | 187.941 | − | 187.941i | 0.189457 | − | 0.189457i | ||||
\(993\) | 274.319 | + | 274.319i | 0.276253 | + | 0.276253i | ||||
\(994\) | − | 238.566i | − | 0.240006i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −262.704 | −0.263759 | ||||||||
\(997\) | −180.748 | + | 180.748i | −0.181292 | + | 0.181292i | −0.791919 | − | 0.610627i | \(-0.790918\pi\) |
0.610627 | + | 0.791919i | \(0.290918\pi\) | |||||||
\(998\) | −319.077 | − | 319.077i | −0.319717 | − | 0.319717i | ||||
\(999\) | 62.4634i | 0.0625260i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.l.h.43.5 | 16 | ||
5.2 | odd | 4 | inner | 1050.3.l.h.757.5 | 16 | ||
5.3 | odd | 4 | 210.3.l.b.127.4 | yes | 16 | ||
5.4 | even | 2 | 210.3.l.b.43.4 | ✓ | 16 | ||
15.8 | even | 4 | 630.3.o.f.127.1 | 16 | |||
15.14 | odd | 2 | 630.3.o.f.253.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.4 | ✓ | 16 | 5.4 | even | 2 | ||
210.3.l.b.127.4 | yes | 16 | 5.3 | odd | 4 | ||
630.3.o.f.127.1 | 16 | 15.8 | even | 4 | |||
630.3.o.f.253.1 | 16 | 15.14 | odd | 2 | |||
1050.3.l.h.43.5 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.l.h.757.5 | 16 | 5.2 | odd | 4 | inner |