Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(71,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.71");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.8 | ||
Root | \(-2.85457 - 0.922735i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.71 |
Dual form | 210.3.e.a.71.16 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 2.85457 | + | 0.922735i | 0.951523 | + | 0.307578i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 1.30494 | − | 4.03697i | 0.217491 | − | 0.672828i | ||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 7.29712 | + | 5.26802i | 0.810791 | + | 0.585335i | ||||
\(10\) | 3.16228 | 0.316228 | ||||||||
\(11\) | − | 4.58314i | − | 0.416649i | −0.978060 | − | 0.208325i | \(-0.933199\pi\) | ||
0.978060 | − | 0.208325i | \(-0.0668010\pi\) | |||||||
\(12\) | −5.70914 | − | 1.84547i | −0.475761 | − | 0.153789i | ||||
\(13\) | 20.4597 | 1.57382 | 0.786910 | − | 0.617068i | \(-0.211680\pi\) | ||||
0.786910 | + | 0.617068i | \(0.211680\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | −2.06330 | + | 6.38301i | −0.137553 | + | 0.425534i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 4.97301i | 0.292530i | 0.989245 | + | 0.146265i | \(0.0467252\pi\) | ||||
−0.989245 | + | 0.146265i | \(0.953275\pi\) | |||||||
\(18\) | 7.45010 | − | 10.3197i | 0.413895 | − | 0.573316i | ||||
\(19\) | 6.22537 | 0.327651 | 0.163826 | − | 0.986489i | \(-0.447617\pi\) | ||||
0.163826 | + | 0.986489i | \(0.447617\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 7.55248 | + | 2.44133i | 0.359642 | + | 0.116254i | ||||
\(22\) | −6.48154 | −0.294615 | ||||||||
\(23\) | 0.140044i | 0.00608889i | 0.999995 | + | 0.00304445i | \(0.000969079\pi\) | ||||
−0.999995 | + | 0.00304445i | \(0.999031\pi\) | |||||||
\(24\) | −2.60989 | + | 8.07394i | −0.108745 | + | 0.336414i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 28.9343i | − | 1.11286i | ||||||
\(27\) | 15.9691 | + | 21.7712i | 0.591450 | + | 0.806342i | ||||
\(28\) | −5.29150 | −0.188982 | ||||||||
\(29\) | 1.76265i | 0.0607812i | 0.999538 | + | 0.0303906i | \(0.00967511\pi\) | ||||
−0.999538 | + | 0.0303906i | \(0.990325\pi\) | |||||||
\(30\) | 9.02694 | + | 2.91794i | 0.300898 | + | 0.0972648i | ||||
\(31\) | −29.7354 | −0.959207 | −0.479603 | − | 0.877485i | \(-0.659219\pi\) | ||||
−0.479603 | + | 0.877485i | \(0.659219\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 4.22902 | − | 13.0829i | 0.128152 | − | 0.396451i | ||||
\(34\) | 7.03290 | 0.206850 | ||||||||
\(35\) | 5.91608i | 0.169031i | ||||||||
\(36\) | −14.5942 | − | 10.5360i | −0.405396 | − | 0.292668i | ||||
\(37\) | −38.8333 | −1.04955 | −0.524774 | − | 0.851242i | \(-0.675850\pi\) | ||||
−0.524774 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(38\) | − | 8.80401i | − | 0.231684i | ||||||
\(39\) | 58.4035 | + | 18.8788i | 1.49753 | + | 0.484073i | ||||
\(40\) | −6.32456 | −0.158114 | ||||||||
\(41\) | − | 68.8223i | − | 1.67859i | −0.543675 | − | 0.839296i | \(-0.682968\pi\) | ||
0.543675 | − | 0.839296i | \(-0.317032\pi\) | |||||||
\(42\) | 3.45256 | − | 10.6808i | 0.0822037 | − | 0.254305i | ||||
\(43\) | −20.3093 | −0.472308 | −0.236154 | − | 0.971716i | \(-0.575887\pi\) | ||||
−0.236154 | + | 0.971716i | \(0.575887\pi\) | |||||||
\(44\) | 9.16628i | 0.208325i | ||||||||
\(45\) | −11.7796 | + | 16.3169i | −0.261770 | + | 0.362597i | ||||
\(46\) | 0.198053 | 0.00430550 | ||||||||
\(47\) | − | 57.3078i | − | 1.21932i | −0.792665 | − | 0.609658i | \(-0.791307\pi\) | ||
0.792665 | − | 0.609658i | \(-0.208693\pi\) | |||||||
\(48\) | 11.4183 | + | 3.69094i | 0.237881 | + | 0.0768946i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 7.07107i | 0.141421i | ||||||||
\(51\) | −4.58877 | + | 14.1958i | −0.0899758 | + | 0.278349i | ||||
\(52\) | −40.9193 | −0.786910 | ||||||||
\(53\) | 41.0342i | 0.774230i | 0.922032 | + | 0.387115i | \(0.126528\pi\) | ||||
−0.922032 | + | 0.387115i | \(0.873472\pi\) | |||||||
\(54\) | 30.7892 | − | 22.5838i | 0.570170 | − | 0.418218i | ||||
\(55\) | 10.2482 | 0.186331 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 17.7708 | + | 5.74437i | 0.311768 | + | 0.100778i | ||||
\(58\) | 2.49277 | 0.0429788 | ||||||||
\(59\) | 79.4508i | 1.34662i | 0.739358 | + | 0.673312i | \(0.235129\pi\) | ||||
−0.739358 | + | 0.673312i | \(0.764871\pi\) | |||||||
\(60\) | 4.12659 | − | 12.7660i | 0.0687766 | − | 0.212767i | ||||
\(61\) | −19.1096 | −0.313273 | −0.156636 | − | 0.987656i | \(-0.550065\pi\) | ||||
−0.156636 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(62\) | 42.0522i | 0.678261i | ||||||||
\(63\) | 19.3064 | + | 13.9379i | 0.306450 | + | 0.221236i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 45.7492i | 0.703834i | ||||||||
\(66\) | −18.5020 | − | 5.98074i | −0.280333 | − | 0.0906173i | ||||
\(67\) | −67.5134 | −1.00766 | −0.503831 | − | 0.863802i | \(-0.668077\pi\) | ||||
−0.503831 | + | 0.863802i | \(0.668077\pi\) | |||||||
\(68\) | − | 9.94602i | − | 0.146265i | ||||||
\(69\) | −0.129224 | + | 0.399767i | −0.00187281 | + | 0.00579372i | ||||
\(70\) | 8.36660 | 0.119523 | ||||||||
\(71\) | 30.8958i | 0.435152i | 0.976043 | + | 0.217576i | \(0.0698150\pi\) | ||||
−0.976043 | + | 0.217576i | \(0.930185\pi\) | |||||||
\(72\) | −14.9002 | + | 20.6394i | −0.206947 | + | 0.286658i | ||||
\(73\) | −111.327 | −1.52502 | −0.762511 | − | 0.646975i | \(-0.776034\pi\) | ||||
−0.762511 | + | 0.646975i | \(0.776034\pi\) | |||||||
\(74\) | 54.9186i | 0.742143i | ||||||||
\(75\) | −14.2728 | − | 4.61367i | −0.190305 | − | 0.0615156i | ||||
\(76\) | −12.4507 | −0.163826 | ||||||||
\(77\) | − | 12.1259i | − | 0.157479i | ||||||
\(78\) | 26.6987 | − | 82.5950i | 0.342291 | − | 1.05891i | ||||
\(79\) | −20.9159 | −0.264759 | −0.132379 | − | 0.991199i | \(-0.542262\pi\) | ||||
−0.132379 | + | 0.991199i | \(0.542262\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 25.4960 | + | 76.8827i | 0.314765 | + | 0.949170i | ||||
\(82\) | −97.3294 | −1.18694 | ||||||||
\(83\) | − | 156.468i | − | 1.88516i | −0.333984 | − | 0.942579i | \(-0.608393\pi\) | ||
0.333984 | − | 0.942579i | \(-0.391607\pi\) | |||||||
\(84\) | −15.1050 | − | 4.88265i | −0.179821 | − | 0.0581268i | ||||
\(85\) | −11.1200 | −0.130823 | ||||||||
\(86\) | 28.7216i | 0.333972i | ||||||||
\(87\) | −1.62646 | + | 5.03162i | −0.0186950 | + | 0.0578347i | ||||
\(88\) | 12.9631 | 0.147308 | ||||||||
\(89\) | 133.632i | 1.50148i | 0.660598 | + | 0.750739i | \(0.270303\pi\) | ||||
−0.660598 | + | 0.750739i | \(0.729697\pi\) | |||||||
\(90\) | 23.0755 | + | 16.6589i | 0.256395 | + | 0.185099i | ||||
\(91\) | 54.1312 | 0.594848 | ||||||||
\(92\) | − | 0.280089i | − | 0.00304445i | ||||||
\(93\) | −84.8817 | − | 27.4379i | −0.912707 | − | 0.295031i | ||||
\(94\) | −81.0455 | −0.862186 | ||||||||
\(95\) | 13.9204i | 0.146530i | ||||||||
\(96\) | 5.21978 | − | 16.1479i | 0.0543727 | − | 0.168207i | ||||
\(97\) | 20.1609 | 0.207845 | 0.103922 | − | 0.994585i | \(-0.466861\pi\) | ||||
0.103922 | + | 0.994585i | \(0.466861\pi\) | |||||||
\(98\) | − | 9.89949i | − | 0.101015i | ||||||
\(99\) | 24.1441 | − | 33.4437i | 0.243880 | − | 0.337816i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 95.9087i | 0.949591i | 0.880096 | + | 0.474796i | \(0.157478\pi\) | ||||
−0.880096 | + | 0.474796i | \(0.842522\pi\) | |||||||
\(102\) | 20.0759 | + | 6.48950i | 0.196822 | + | 0.0636225i | ||||
\(103\) | −136.017 | −1.32056 | −0.660278 | − | 0.751021i | \(-0.729562\pi\) | ||||
−0.660278 | + | 0.751021i | \(0.729562\pi\) | |||||||
\(104\) | 57.8687i | 0.556429i | ||||||||
\(105\) | −5.45897 | + | 16.8879i | −0.0519902 | + | 0.160837i | ||||
\(106\) | 58.0311 | 0.547463 | ||||||||
\(107\) | − | 77.0597i | − | 0.720184i | −0.932917 | − | 0.360092i | \(-0.882745\pi\) | ||
0.932917 | − | 0.360092i | \(-0.117255\pi\) | |||||||
\(108\) | −31.9383 | − | 43.5425i | −0.295725 | − | 0.403171i | ||||
\(109\) | 148.111 | 1.35881 | 0.679406 | − | 0.733762i | \(-0.262237\pi\) | ||||
0.679406 | + | 0.733762i | \(0.262237\pi\) | |||||||
\(110\) | − | 14.4932i | − | 0.131756i | ||||||
\(111\) | −110.852 | − | 35.8328i | −0.998669 | − | 0.322818i | ||||
\(112\) | 10.5830 | 0.0944911 | ||||||||
\(113\) | − | 86.9193i | − | 0.769198i | −0.923084 | − | 0.384599i | \(-0.874340\pi\) | ||
0.923084 | − | 0.384599i | \(-0.125660\pi\) | |||||||
\(114\) | 8.12376 | − | 25.1316i | 0.0712611 | − | 0.220453i | ||||
\(115\) | −0.313149 | −0.00272303 | ||||||||
\(116\) | − | 3.52531i | − | 0.0303906i | ||||||
\(117\) | 149.297 | + | 107.782i | 1.27604 | + | 0.921213i | ||||
\(118\) | 112.360 | 0.952207 | ||||||||
\(119\) | 13.1573i | 0.110566i | ||||||||
\(120\) | −18.0539 | − | 5.83589i | −0.150449 | − | 0.0486324i | ||||
\(121\) | 99.9948 | 0.826403 | ||||||||
\(122\) | 27.0251i | 0.221517i | ||||||||
\(123\) | 63.5047 | − | 196.458i | 0.516298 | − | 1.59722i | ||||
\(124\) | 59.4708 | 0.479603 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 19.7111 | − | 27.3033i | 0.156437 | − | 0.216693i | ||||
\(127\) | 244.384 | 1.92429 | 0.962143 | − | 0.272546i | \(-0.0878658\pi\) | ||||
0.962143 | + | 0.272546i | \(0.0878658\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −57.9742 | − | 18.7401i | −0.449412 | − | 0.145272i | ||||
\(130\) | 64.6991 | 0.497686 | ||||||||
\(131\) | − | 258.568i | − | 1.97380i | −0.161334 | − | 0.986900i | \(-0.551580\pi\) | ||
0.161334 | − | 0.986900i | \(-0.448420\pi\) | |||||||
\(132\) | −8.45805 | + | 26.1658i | −0.0640761 | + | 0.198226i | ||||
\(133\) | 16.4708 | 0.123841 | ||||||||
\(134\) | 95.4784i | 0.712525i | ||||||||
\(135\) | −48.6819 | + | 35.7081i | −0.360607 | + | 0.264504i | ||||
\(136\) | −14.0658 | −0.103425 | ||||||||
\(137\) | − | 217.042i | − | 1.58425i | −0.610361 | − | 0.792123i | \(-0.708976\pi\) | ||
0.610361 | − | 0.792123i | \(-0.291024\pi\) | |||||||
\(138\) | 0.565355 | + | 0.182750i | 0.00409678 | + | 0.00132428i | ||||
\(139\) | −110.593 | −0.795636 | −0.397818 | − | 0.917464i | \(-0.630232\pi\) | ||||
−0.397818 | + | 0.917464i | \(0.630232\pi\) | |||||||
\(140\) | − | 11.8322i | − | 0.0845154i | ||||||
\(141\) | 52.8799 | − | 163.589i | 0.375035 | − | 1.16021i | ||||
\(142\) | 43.6933 | 0.307699 | ||||||||
\(143\) | − | 93.7695i | − | 0.655731i | ||||||
\(144\) | 29.1885 | + | 21.0721i | 0.202698 | + | 0.146334i | ||||
\(145\) | −3.94141 | −0.0271822 | ||||||||
\(146\) | 157.440i | 1.07835i | ||||||||
\(147\) | 19.9820 | + | 6.45914i | 0.135932 | + | 0.0439397i | ||||
\(148\) | 77.6666 | 0.524774 | ||||||||
\(149\) | 42.4042i | 0.284592i | 0.989824 | + | 0.142296i | \(0.0454485\pi\) | ||||
−0.989824 | + | 0.142296i | \(0.954552\pi\) | |||||||
\(150\) | −6.52472 | + | 20.1848i | −0.0434981 | + | 0.134566i | ||||
\(151\) | 106.207 | 0.703357 | 0.351678 | − | 0.936121i | \(-0.385611\pi\) | ||||
0.351678 | + | 0.936121i | \(0.385611\pi\) | |||||||
\(152\) | 17.6080i | 0.115842i | ||||||||
\(153\) | −26.1979 | + | 36.2886i | −0.171228 | + | 0.237181i | ||||
\(154\) | −17.1485 | −0.111354 | ||||||||
\(155\) | − | 66.4904i | − | 0.428970i | ||||||
\(156\) | −116.807 | − | 37.7577i | −0.748763 | − | 0.242036i | ||||
\(157\) | −106.522 | −0.678487 | −0.339244 | − | 0.940699i | \(-0.610171\pi\) | ||||
−0.339244 | + | 0.940699i | \(0.610171\pi\) | |||||||
\(158\) | 29.5796i | 0.187213i | ||||||||
\(159\) | −37.8637 | + | 117.135i | −0.238136 | + | 0.736697i | ||||
\(160\) | 12.6491 | 0.0790569 | ||||||||
\(161\) | 0.370523i | 0.00230138i | ||||||||
\(162\) | 108.729 | − | 36.0567i | 0.671164 | − | 0.222572i | ||||
\(163\) | −143.209 | −0.878584 | −0.439292 | − | 0.898344i | \(-0.644771\pi\) | ||||
−0.439292 | + | 0.898344i | \(0.644771\pi\) | |||||||
\(164\) | 137.645i | 0.839296i | ||||||||
\(165\) | 29.2542 | + | 9.45638i | 0.177298 | + | 0.0573114i | ||||
\(166\) | −221.279 | −1.33301 | ||||||||
\(167\) | − | 134.374i | − | 0.804636i | −0.915500 | − | 0.402318i | \(-0.868205\pi\) | ||
0.915500 | − | 0.402318i | \(-0.131795\pi\) | |||||||
\(168\) | −6.90511 | + | 21.3616i | −0.0411019 | + | 0.127153i | ||||
\(169\) | 249.598 | 1.47691 | ||||||||
\(170\) | 15.7260i | 0.0925061i | ||||||||
\(171\) | 45.4273 | + | 32.7954i | 0.265657 | + | 0.191786i | ||||
\(172\) | 40.6185 | 0.236154 | ||||||||
\(173\) | 271.155i | 1.56737i | 0.621157 | + | 0.783686i | \(0.286663\pi\) | ||||
−0.621157 | + | 0.783686i | \(0.713337\pi\) | |||||||
\(174\) | 7.11578 | + | 2.30016i | 0.0408953 | + | 0.0132193i | ||||
\(175\) | −13.2288 | −0.0755929 | ||||||||
\(176\) | − | 18.3326i | − | 0.104162i | ||||||
\(177\) | −73.3120 | + | 226.798i | −0.414192 | + | 1.28134i | ||||
\(178\) | 188.984 | 1.06171 | ||||||||
\(179\) | − | 101.035i | − | 0.564441i | −0.959350 | − | 0.282221i | \(-0.908929\pi\) | ||
0.959350 | − | 0.282221i | \(-0.0910710\pi\) | |||||||
\(180\) | 23.5593 | − | 32.6337i | 0.130885 | − | 0.181298i | ||||
\(181\) | 245.254 | 1.35499 | 0.677496 | − | 0.735526i | \(-0.263065\pi\) | ||||
0.677496 | + | 0.735526i | \(0.263065\pi\) | |||||||
\(182\) | − | 76.5531i | − | 0.420621i | ||||||
\(183\) | −54.5498 | − | 17.6331i | −0.298086 | − | 0.0963558i | ||||
\(184\) | −0.396106 | −0.00215275 | ||||||||
\(185\) | − | 86.8339i | − | 0.469372i | ||||||
\(186\) | −38.8030 | + | 120.041i | −0.208618 | + | 0.645381i | ||||
\(187\) | 22.7920 | 0.121882 | ||||||||
\(188\) | 114.616i | 0.609658i | ||||||||
\(189\) | 42.2504 | + | 57.6012i | 0.223547 | + | 0.304769i | ||||
\(190\) | 19.6864 | 0.103612 | ||||||||
\(191\) | − | 33.8884i | − | 0.177426i | −0.996057 | − | 0.0887132i | \(-0.971725\pi\) | ||
0.996057 | − | 0.0887132i | \(-0.0282755\pi\) | |||||||
\(192\) | −22.8365 | − | 7.38188i | −0.118940 | − | 0.0384473i | ||||
\(193\) | −304.046 | −1.57537 | −0.787684 | − | 0.616080i | \(-0.788720\pi\) | ||||
−0.787684 | + | 0.616080i | \(0.788720\pi\) | |||||||
\(194\) | − | 28.5119i | − | 0.146968i | ||||||
\(195\) | −42.2144 | + | 130.594i | −0.216484 | + | 0.669714i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 251.710i | 1.27772i | 0.769324 | + | 0.638859i | \(0.220593\pi\) | ||||
−0.769324 | + | 0.638859i | \(0.779407\pi\) | |||||||
\(198\) | −47.2966 | − | 34.1449i | −0.238872 | − | 0.172449i | ||||
\(199\) | −371.292 | −1.86579 | −0.932895 | − | 0.360148i | \(-0.882726\pi\) | ||||
−0.932895 | + | 0.360148i | \(0.882726\pi\) | |||||||
\(200\) | − | 14.1421i | − | 0.0707107i | ||||||
\(201\) | −192.722 | − | 62.2970i | −0.958814 | − | 0.309935i | ||||
\(202\) | 135.635 | 0.671463 | ||||||||
\(203\) | 4.66354i | 0.0229731i | ||||||||
\(204\) | 9.17753 | − | 28.3916i | 0.0449879 | − | 0.139174i | ||||
\(205\) | 153.891 | 0.750689 | ||||||||
\(206\) | 192.358i | 0.933775i | ||||||||
\(207\) | −0.737757 | + | 1.02192i | −0.00356404 | + | 0.00493682i | ||||
\(208\) | 81.8387 | 0.393455 | ||||||||
\(209\) | − | 28.5318i | − | 0.136516i | ||||||
\(210\) | 23.8830 | + | 7.72015i | 0.113729 | + | 0.0367626i | ||||
\(211\) | 219.180 | 1.03877 | 0.519383 | − | 0.854542i | \(-0.326162\pi\) | ||||
0.519383 | + | 0.854542i | \(0.326162\pi\) | |||||||
\(212\) | − | 82.0683i | − | 0.387115i | ||||||
\(213\) | −28.5086 | + | 88.1942i | −0.133843 | + | 0.414057i | ||||
\(214\) | −108.979 | −0.509247 | ||||||||
\(215\) | − | 45.4129i | − | 0.211223i | ||||||
\(216\) | −61.5783 | + | 45.1676i | −0.285085 | + | 0.209109i | ||||
\(217\) | −78.6725 | −0.362546 | ||||||||
\(218\) | − | 209.460i | − | 0.960826i | ||||||
\(219\) | −317.789 | − | 102.725i | −1.45109 | − | 0.469064i | ||||
\(220\) | −20.4964 | −0.0931656 | ||||||||
\(221\) | 101.746i | 0.460390i | ||||||||
\(222\) | −50.6753 | + | 156.769i | −0.228267 | + | 0.706166i | ||||
\(223\) | 224.223 | 1.00549 | 0.502743 | − | 0.864436i | \(-0.332324\pi\) | ||||
0.502743 | + | 0.864436i | \(0.332324\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | −36.4856 | − | 26.3401i | −0.162158 | − | 0.117067i | ||||
\(226\) | −122.922 | −0.543905 | ||||||||
\(227\) | − | 386.312i | − | 1.70181i | −0.525317 | − | 0.850907i | \(-0.676053\pi\) | ||
0.525317 | − | 0.850907i | \(-0.323947\pi\) | |||||||
\(228\) | −35.5415 | − | 11.4887i | −0.155884 | − | 0.0503892i | ||||
\(229\) | 159.911 | 0.698300 | 0.349150 | − | 0.937067i | \(-0.386470\pi\) | ||||
0.349150 | + | 0.937067i | \(0.386470\pi\) | |||||||
\(230\) | 0.442860i | 0.00192548i | ||||||||
\(231\) | 11.1889 | − | 34.6141i | 0.0484370 | − | 0.149844i | ||||
\(232\) | −4.98554 | −0.0214894 | ||||||||
\(233\) | 285.263i | 1.22431i | 0.790739 | + | 0.612153i | \(0.209696\pi\) | ||||
−0.790739 | + | 0.612153i | \(0.790304\pi\) | |||||||
\(234\) | 152.427 | − | 211.137i | 0.651396 | − | 0.902296i | ||||
\(235\) | 128.144 | 0.545294 | ||||||||
\(236\) | − | 158.902i | − | 0.673312i | ||||||
\(237\) | −59.7060 | − | 19.2999i | −0.251924 | − | 0.0814340i | ||||
\(238\) | 18.6073 | 0.0781819 | ||||||||
\(239\) | 277.247i | 1.16003i | 0.814606 | + | 0.580015i | \(0.196953\pi\) | ||||
−0.814606 | + | 0.580015i | \(0.803047\pi\) | |||||||
\(240\) | −8.25319 | + | 25.5320i | −0.0343883 | + | 0.106383i | ||||
\(241\) | −66.8596 | −0.277426 | −0.138713 | − | 0.990333i | \(-0.544296\pi\) | ||||
−0.138713 | + | 0.990333i | \(0.544296\pi\) | |||||||
\(242\) | − | 141.414i | − | 0.584355i | ||||||
\(243\) | 1.83761 | + | 242.993i | 0.00756219 | + | 0.999971i | ||||
\(244\) | 38.2193 | 0.156636 | ||||||||
\(245\) | 15.6525i | 0.0638877i | ||||||||
\(246\) | −277.833 | − | 89.8092i | −1.12940 | − | 0.365078i | ||||
\(247\) | 127.369 | 0.515664 | ||||||||
\(248\) | − | 84.1044i | − | 0.339131i | ||||||
\(249\) | 144.379 | − | 446.649i | 0.579833 | − | 1.79377i | ||||
\(250\) | −15.8114 | −0.0632456 | ||||||||
\(251\) | − | 351.334i | − | 1.39974i | −0.714271 | − | 0.699869i | \(-0.753242\pi\) | ||
0.714271 | − | 0.699869i | \(-0.246758\pi\) | |||||||
\(252\) | −38.6127 | − | 27.8757i | −0.153225 | − | 0.110618i | ||||
\(253\) | 0.641844 | 0.00253693 | ||||||||
\(254\) | − | 345.611i | − | 1.36068i | ||||||
\(255\) | −31.7428 | − | 10.2608i | −0.124481 | − | 0.0402384i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 130.747i | 0.508745i | 0.967106 | + | 0.254372i | \(0.0818688\pi\) | ||||
−0.967106 | + | 0.254372i | \(0.918131\pi\) | |||||||
\(258\) | −26.5024 | + | 81.9879i | −0.102723 | + | 0.317782i | ||||
\(259\) | −102.743 | −0.396692 | ||||||||
\(260\) | − | 91.4984i | − | 0.351917i | ||||||
\(261\) | −9.28569 | + | 12.8623i | −0.0355774 | + | 0.0492808i | ||||
\(262\) | −365.670 | −1.39569 | ||||||||
\(263\) | 183.496i | 0.697704i | 0.937178 | + | 0.348852i | \(0.113428\pi\) | ||||
−0.937178 | + | 0.348852i | \(0.886572\pi\) | |||||||
\(264\) | 37.0040 | + | 11.9615i | 0.140167 | + | 0.0453087i | ||||
\(265\) | −91.7552 | −0.346246 | ||||||||
\(266\) | − | 23.2932i | − | 0.0875685i | ||||||
\(267\) | −123.307 | + | 381.461i | −0.461822 | + | 1.42869i | ||||
\(268\) | 135.027 | 0.503831 | ||||||||
\(269\) | 176.353i | 0.655587i | 0.944749 | + | 0.327794i | \(0.106305\pi\) | ||||
−0.944749 | + | 0.327794i | \(0.893695\pi\) | |||||||
\(270\) | 50.4989 | + | 68.8467i | 0.187033 | + | 0.254988i | ||||
\(271\) | −228.813 | −0.844329 | −0.422164 | − | 0.906519i | \(-0.638729\pi\) | ||||
−0.422164 | + | 0.906519i | \(0.638729\pi\) | |||||||
\(272\) | 19.8920i | 0.0731325i | ||||||||
\(273\) | 154.521 | + | 49.9487i | 0.566012 | + | 0.182962i | ||||
\(274\) | −306.943 | −1.12023 | ||||||||
\(275\) | 22.9157i | 0.0833298i | ||||||||
\(276\) | 0.258448 | − | 0.799533i | 0.000936405 | − | 0.00289686i | ||||
\(277\) | 21.1361 | 0.0763035 | 0.0381517 | − | 0.999272i | \(-0.487853\pi\) | ||||
0.0381517 | + | 0.999272i | \(0.487853\pi\) | |||||||
\(278\) | 156.403i | 0.562599i | ||||||||
\(279\) | −216.983 | − | 156.647i | −0.777716 | − | 0.561458i | ||||
\(280\) | −16.7332 | −0.0597614 | ||||||||
\(281\) | 439.326i | 1.56344i | 0.623631 | + | 0.781719i | \(0.285657\pi\) | ||||
−0.623631 | + | 0.781719i | \(0.714343\pi\) | |||||||
\(282\) | −231.350 | − | 74.7835i | −0.820390 | − | 0.265190i | ||||
\(283\) | −76.8388 | −0.271515 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(284\) | − | 61.7916i | − | 0.217576i | ||||||
\(285\) | −12.8448 | + | 39.7366i | −0.0450695 | + | 0.139427i | ||||
\(286\) | −132.610 | −0.463672 | ||||||||
\(287\) | − | 182.087i | − | 0.634448i | ||||||
\(288\) | 29.8004 | − | 41.2788i | 0.103474 | − | 0.143329i | ||||
\(289\) | 264.269 | 0.914426 | ||||||||
\(290\) | 5.57400i | 0.0192207i | ||||||||
\(291\) | 57.5508 | + | 18.6032i | 0.197769 | + | 0.0639285i | ||||
\(292\) | 222.653 | 0.762511 | ||||||||
\(293\) | 255.154i | 0.870834i | 0.900229 | + | 0.435417i | \(0.143399\pi\) | ||||
−0.900229 | + | 0.435417i | \(0.856601\pi\) | |||||||
\(294\) | 9.13461 | − | 28.2588i | 0.0310701 | − | 0.0961183i | ||||
\(295\) | −177.657 | −0.602229 | ||||||||
\(296\) | − | 109.837i | − | 0.371071i | ||||||
\(297\) | 99.7806 | − | 73.1889i | 0.335962 | − | 0.246427i | ||||
\(298\) | 59.9686 | 0.201237 | ||||||||
\(299\) | 2.86526i | 0.00958282i | ||||||||
\(300\) | 28.5457 | + | 9.22735i | 0.0951523 | + | 0.0307578i | ||||
\(301\) | −53.7332 | −0.178516 | ||||||||
\(302\) | − | 150.199i | − | 0.497348i | ||||||
\(303\) | −88.4983 | + | 273.778i | −0.292074 | + | 0.903558i | ||||
\(304\) | 24.9015 | 0.0819128 | ||||||||
\(305\) | − | 42.7304i | − | 0.140100i | ||||||
\(306\) | 51.3199 | + | 37.0494i | 0.167712 | + | 0.121077i | ||||
\(307\) | −162.522 | −0.529389 | −0.264695 | − | 0.964332i | \(-0.585271\pi\) | ||||
−0.264695 | + | 0.964332i | \(0.585271\pi\) | |||||||
\(308\) | 24.2517i | 0.0787393i | ||||||||
\(309\) | −388.271 | − | 125.508i | −1.25654 | − | 0.406174i | ||||
\(310\) | −94.0316 | −0.303328 | ||||||||
\(311\) | 130.962i | 0.421099i | 0.977583 | + | 0.210550i | \(0.0675254\pi\) | ||||
−0.977583 | + | 0.210550i | \(0.932475\pi\) | |||||||
\(312\) | −53.3974 | + | 165.190i | −0.171146 | + | 0.529455i | ||||
\(313\) | 206.265 | 0.658994 | 0.329497 | − | 0.944157i | \(-0.393121\pi\) | ||||
0.329497 | + | 0.944157i | \(0.393121\pi\) | |||||||
\(314\) | 150.646i | 0.479763i | ||||||||
\(315\) | −31.1660 | + | 43.1704i | −0.0989397 | + | 0.137049i | ||||
\(316\) | 41.8319 | 0.132379 | ||||||||
\(317\) | − | 220.246i | − | 0.694783i | −0.937720 | − | 0.347392i | \(-0.887067\pi\) | ||
0.937720 | − | 0.347392i | \(-0.112933\pi\) | |||||||
\(318\) | 165.654 | + | 53.5473i | 0.520924 | + | 0.168388i | ||||
\(319\) | 8.07849 | 0.0253244 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 71.1057 | − | 219.972i | 0.221513 | − | 0.685272i | ||||
\(322\) | 0.523998 | 0.00162732 | ||||||||
\(323\) | 30.9588i | 0.0958478i | ||||||||
\(324\) | −50.9919 | − | 153.765i | −0.157383 | − | 0.474585i | ||||
\(325\) | −102.298 | −0.314764 | ||||||||
\(326\) | 202.528i | 0.621253i | ||||||||
\(327\) | 422.792 | + | 136.667i | 1.29294 | + | 0.417941i | ||||
\(328\) | 194.659 | 0.593472 | ||||||||
\(329\) | − | 151.622i | − | 0.460858i | ||||||
\(330\) | 13.3733 | − | 41.3717i | 0.0405253 | − | 0.125369i | ||||
\(331\) | 533.158 | 1.61075 | 0.805375 | − | 0.592765i | \(-0.201964\pi\) | ||||
0.805375 | + | 0.592765i | \(0.201964\pi\) | |||||||
\(332\) | 312.936i | 0.942579i | ||||||||
\(333\) | −283.371 | − | 204.574i | −0.850965 | − | 0.614338i | ||||
\(334\) | −190.034 | −0.568963 | ||||||||
\(335\) | − | 150.965i | − | 0.450641i | ||||||
\(336\) | 30.2099 | + | 9.76531i | 0.0899105 | + | 0.0290634i | ||||
\(337\) | −507.809 | −1.50685 | −0.753425 | − | 0.657533i | \(-0.771600\pi\) | ||||
−0.753425 | + | 0.657533i | \(0.771600\pi\) | |||||||
\(338\) | − | 352.985i | − | 1.04433i | ||||||
\(339\) | 80.2035 | − | 248.117i | 0.236588 | − | 0.731909i | ||||
\(340\) | 22.2400 | 0.0654117 | ||||||||
\(341\) | 136.282i | 0.399653i | ||||||||
\(342\) | 46.3797 | − | 64.2439i | 0.135613 | − | 0.187848i | ||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | − | 57.4433i | − | 0.166986i | ||||||
\(345\) | −0.893905 | − | 0.288953i | −0.00259103 | − | 0.000837546i | ||||
\(346\) | 383.472 | 1.10830 | ||||||||
\(347\) | 361.202i | 1.04093i | 0.853883 | + | 0.520464i | \(0.174241\pi\) | ||||
−0.853883 | + | 0.520464i | \(0.825759\pi\) | |||||||
\(348\) | 3.25292 | − | 10.0632i | 0.00934748 | − | 0.0289173i | ||||
\(349\) | 283.631 | 0.812698 | 0.406349 | − | 0.913718i | \(-0.366802\pi\) | ||||
0.406349 | + | 0.913718i | \(0.366802\pi\) | |||||||
\(350\) | 18.7083i | 0.0534522i | ||||||||
\(351\) | 326.723 | + | 445.432i | 0.930836 | + | 1.26904i | ||||
\(352\) | −25.9262 | −0.0736539 | ||||||||
\(353\) | − | 54.6557i | − | 0.154832i | −0.996999 | − | 0.0774161i | \(-0.975333\pi\) | ||
0.996999 | − | 0.0774161i | \(-0.0246670\pi\) | |||||||
\(354\) | 320.741 | + | 103.679i | 0.906047 | + | 0.292878i | ||||
\(355\) | −69.0851 | −0.194606 | ||||||||
\(356\) | − | 267.263i | − | 0.750739i | ||||||
\(357\) | −12.1407 | + | 37.5585i | −0.0340077 | + | 0.105206i | ||||
\(358\) | −142.885 | −0.399120 | ||||||||
\(359\) | 74.6193i | 0.207853i | 0.994585 | + | 0.103927i | \(0.0331407\pi\) | ||||
−0.994585 | + | 0.103927i | \(0.966859\pi\) | |||||||
\(360\) | −46.1510 | − | 33.3179i | −0.128197 | − | 0.0925496i | ||||
\(361\) | −322.245 | −0.892645 | ||||||||
\(362\) | − | 346.841i | − | 0.958124i | ||||||
\(363\) | 285.442 | + | 92.2687i | 0.786342 | + | 0.254184i | ||||
\(364\) | −108.262 | −0.297424 | ||||||||
\(365\) | − | 248.934i | − | 0.682011i | ||||||
\(366\) | −24.9370 | + | 77.1450i | −0.0681339 | + | 0.210779i | ||||
\(367\) | 592.999 | 1.61580 | 0.807901 | − | 0.589318i | \(-0.200603\pi\) | ||||
0.807901 | + | 0.589318i | \(0.200603\pi\) | |||||||
\(368\) | 0.560178i | 0.00152222i | ||||||||
\(369\) | 362.557 | − | 502.204i | 0.982539 | − | 1.36099i | ||||
\(370\) | −122.802 | −0.331896 | ||||||||
\(371\) | 108.566i | 0.292631i | ||||||||
\(372\) | 169.763 | + | 54.8758i | 0.456353 | + | 0.147516i | ||||
\(373\) | 477.906 | 1.28125 | 0.640624 | − | 0.767855i | \(-0.278676\pi\) | ||||
0.640624 | + | 0.767855i | \(0.278676\pi\) | |||||||
\(374\) | − | 32.2328i | − | 0.0861838i | ||||||
\(375\) | 10.3165 | − | 31.9150i | 0.0275106 | − | 0.0851068i | ||||
\(376\) | 162.091 | 0.431093 | ||||||||
\(377\) | 36.0633i | 0.0956586i | ||||||||
\(378\) | 81.4605 | − | 59.7511i | 0.215504 | − | 0.158072i | ||||
\(379\) | 155.751 | 0.410952 | 0.205476 | − | 0.978662i | \(-0.434126\pi\) | ||||
0.205476 | + | 0.978662i | \(0.434126\pi\) | |||||||
\(380\) | − | 27.8407i | − | 0.0732650i | ||||||
\(381\) | 697.612 | + | 225.502i | 1.83100 | + | 0.591868i | ||||
\(382\) | −47.9255 | −0.125459 | ||||||||
\(383\) | 204.995i | 0.535235i | 0.963525 | + | 0.267618i | \(0.0862364\pi\) | ||||
−0.963525 | + | 0.267618i | \(0.913764\pi\) | |||||||
\(384\) | −10.4396 | + | 32.2958i | −0.0271863 | + | 0.0841035i | ||||
\(385\) | 27.1142 | 0.0704266 | ||||||||
\(386\) | 429.986i | 1.11395i | ||||||||
\(387\) | −148.199 | − | 106.990i | −0.382943 | − | 0.276459i | ||||
\(388\) | −40.3219 | −0.103922 | ||||||||
\(389\) | − | 161.706i | − | 0.415696i | −0.978161 | − | 0.207848i | \(-0.933354\pi\) | ||
0.978161 | − | 0.207848i | \(-0.0666460\pi\) | |||||||
\(390\) | 184.688 | + | 59.7001i | 0.473559 | + | 0.153077i | ||||
\(391\) | −0.696442 | −0.00178118 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | 238.589 | − | 738.099i | 0.607098 | − | 1.87812i | ||||
\(394\) | 355.972 | 0.903483 | ||||||||
\(395\) | − | 46.7695i | − | 0.118404i | ||||||
\(396\) | −48.2881 | + | 66.8875i | −0.121940 | + | 0.168908i | ||||
\(397\) | −487.130 | −1.22703 | −0.613514 | − | 0.789684i | \(-0.710244\pi\) | ||||
−0.613514 | + | 0.789684i | \(0.710244\pi\) | |||||||
\(398\) | 525.087i | 1.31931i | ||||||||
\(399\) | 47.0170 | + | 15.1982i | 0.117837 | + | 0.0380906i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 504.622i | 1.25841i | 0.777240 | + | 0.629205i | \(0.216619\pi\) | ||||
−0.777240 | + | 0.629205i | \(0.783381\pi\) | |||||||
\(402\) | −88.1012 | + | 272.550i | −0.219157 | + | 0.677984i | ||||
\(403\) | −608.376 | −1.50962 | ||||||||
\(404\) | − | 191.817i | − | 0.474796i | ||||||
\(405\) | −171.915 | + | 57.0107i | −0.424482 | + | 0.140767i | ||||
\(406\) | 6.59525 | 0.0162444 | ||||||||
\(407\) | 177.978i | 0.437293i | ||||||||
\(408\) | −40.1518 | − | 12.9790i | −0.0984112 | − | 0.0318113i | ||||
\(409\) | −93.2305 | −0.227947 | −0.113974 | − | 0.993484i | \(-0.536358\pi\) | ||||
−0.113974 | + | 0.993484i | \(0.536358\pi\) | |||||||
\(410\) | − | 217.635i | − | 0.530817i | ||||||
\(411\) | 200.272 | − | 619.560i | 0.487280 | − | 1.50745i | ||||
\(412\) | 272.035 | 0.660278 | ||||||||
\(413\) | 210.207i | 0.508976i | ||||||||
\(414\) | 1.44522 | + | 1.04335i | 0.00349086 | + | 0.00252016i | ||||
\(415\) | 349.873 | 0.843068 | ||||||||
\(416\) | − | 115.737i | − | 0.278215i | ||||||
\(417\) | −315.696 | − | 102.048i | −0.757066 | − | 0.244720i | ||||
\(418\) | −40.3500 | −0.0965311 | ||||||||
\(419\) | − | 213.512i | − | 0.509575i | −0.966997 | − | 0.254787i | \(-0.917995\pi\) | ||
0.966997 | − | 0.254787i | \(-0.0820055\pi\) | |||||||
\(420\) | 10.9179 | − | 33.7757i | 0.0259951 | − | 0.0804184i | ||||
\(421\) | −415.349 | −0.986578 | −0.493289 | − | 0.869866i | \(-0.664205\pi\) | ||||
−0.493289 | + | 0.869866i | \(0.664205\pi\) | |||||||
\(422\) | − | 309.967i | − | 0.734518i | ||||||
\(423\) | 301.899 | − | 418.182i | 0.713708 | − | 0.988610i | ||||
\(424\) | −116.062 | −0.273732 | ||||||||
\(425\) | − | 24.8650i | − | 0.0585060i | ||||||
\(426\) | 124.725 | + | 40.3173i | 0.292783 | + | 0.0946415i | ||||
\(427\) | −50.5593 | −0.118406 | ||||||||
\(428\) | 154.119i | 0.360092i | ||||||||
\(429\) | 86.5244 | − | 267.672i | 0.201689 | − | 0.623943i | ||||
\(430\) | −64.2235 | −0.149357 | ||||||||
\(431\) | 375.874i | 0.872098i | 0.899923 | + | 0.436049i | \(0.143623\pi\) | ||||
−0.899923 | + | 0.436049i | \(0.856377\pi\) | |||||||
\(432\) | 63.8766 | + | 87.0849i | 0.147862 | + | 0.201585i | ||||
\(433\) | −448.441 | −1.03566 | −0.517830 | − | 0.855483i | \(-0.673260\pi\) | ||||
−0.517830 | + | 0.855483i | \(0.673260\pi\) | |||||||
\(434\) | 111.260i | 0.256359i | ||||||||
\(435\) | −11.2510 | − | 3.63688i | −0.0258644 | − | 0.00836064i | ||||
\(436\) | −296.221 | −0.679406 | ||||||||
\(437\) | 0.871829i | 0.00199503i | ||||||||
\(438\) | −145.275 | + | 449.422i | −0.331678 | + | 1.02608i | ||||
\(439\) | 409.075 | 0.931833 | 0.465916 | − | 0.884829i | \(-0.345725\pi\) | ||||
0.465916 | + | 0.884829i | \(0.345725\pi\) | |||||||
\(440\) | 28.9863i | 0.0658780i | ||||||||
\(441\) | 51.0799 | + | 36.8761i | 0.115827 | + | 0.0836193i | ||||
\(442\) | 143.891 | 0.325545 | ||||||||
\(443\) | 142.814i | 0.322380i | 0.986923 | + | 0.161190i | \(0.0515332\pi\) | ||||
−0.986923 | + | 0.161190i | \(0.948467\pi\) | |||||||
\(444\) | 221.705 | + | 71.6656i | 0.499335 | + | 0.161409i | ||||
\(445\) | −298.809 | −0.671482 | ||||||||
\(446\) | − | 317.100i | − | 0.710986i | ||||||
\(447\) | −39.1278 | + | 121.046i | −0.0875343 | + | 0.270796i | ||||
\(448\) | −21.1660 | −0.0472456 | ||||||||
\(449\) | − | 435.581i | − | 0.970114i | −0.874483 | − | 0.485057i | \(-0.838799\pi\) | ||
0.874483 | − | 0.485057i | \(-0.161201\pi\) | |||||||
\(450\) | −37.2505 | + | 51.5984i | −0.0827789 | + | 0.114663i | ||||
\(451\) | −315.422 | −0.699384 | ||||||||
\(452\) | 173.839i | 0.384599i | ||||||||
\(453\) | 303.175 | + | 98.0008i | 0.669260 | + | 0.216337i | ||||
\(454\) | −546.327 | −1.20336 | ||||||||
\(455\) | 121.041i | 0.266024i | ||||||||
\(456\) | −16.2475 | + | 50.2633i | −0.0356305 | + | 0.110226i | ||||
\(457\) | 403.048 | 0.881943 | 0.440972 | − | 0.897521i | \(-0.354634\pi\) | ||||
0.440972 | + | 0.897521i | \(0.354634\pi\) | |||||||
\(458\) | − | 226.148i | − | 0.493773i | ||||||
\(459\) | −108.268 | + | 79.4147i | −0.235879 | + | 0.173017i | ||||
\(460\) | 0.626298 | 0.00136152 | ||||||||
\(461\) | − | 862.233i | − | 1.87035i | −0.354181 | − | 0.935177i | \(-0.615240\pi\) | ||
0.354181 | − | 0.935177i | \(-0.384760\pi\) | |||||||
\(462\) | −48.9517 | − | 15.8236i | −0.105956 | − | 0.0342501i | ||||
\(463\) | −85.0507 | −0.183695 | −0.0918474 | − | 0.995773i | \(-0.529277\pi\) | ||||
−0.0918474 | + | 0.995773i | \(0.529277\pi\) | |||||||
\(464\) | 7.05061i | 0.0151953i | ||||||||
\(465\) | 61.3530 | − | 189.801i | 0.131942 | − | 0.408175i | ||||
\(466\) | 403.423 | 0.865715 | ||||||||
\(467\) | − | 509.615i | − | 1.09125i | −0.838028 | − | 0.545627i | \(-0.816292\pi\) | ||
0.838028 | − | 0.545627i | \(-0.183708\pi\) | |||||||
\(468\) | −298.593 | − | 215.564i | −0.638020 | − | 0.460606i | ||||
\(469\) | −178.624 | −0.380861 | ||||||||
\(470\) | − | 181.223i | − | 0.385581i | ||||||
\(471\) | −304.076 | − | 98.2920i | −0.645596 | − | 0.208688i | ||||
\(472\) | −224.721 | −0.476104 | ||||||||
\(473\) | 93.0802i | 0.196787i | ||||||||
\(474\) | −27.2941 | + | 84.4370i | −0.0575826 | + | 0.178137i | ||||
\(475\) | −31.1269 | −0.0655302 | ||||||||
\(476\) | − | 26.3147i | − | 0.0552830i | ||||||
\(477\) | −216.169 | + | 299.431i | −0.453184 | + | 0.627739i | ||||
\(478\) | 392.087 | 0.820266 | ||||||||
\(479\) | 207.378i | 0.432940i | 0.976289 | + | 0.216470i | \(0.0694543\pi\) | ||||
−0.976289 | + | 0.216470i | \(0.930546\pi\) | |||||||
\(480\) | 36.1078 | + | 11.6718i | 0.0752245 | + | 0.0243162i | ||||
\(481\) | −794.516 | −1.65180 | ||||||||
\(482\) | 94.5537i | 0.196170i | ||||||||
\(483\) | −0.341894 | + | 1.05768i | −0.000707856 | + | 0.00218982i | ||||
\(484\) | −199.990 | −0.413202 | ||||||||
\(485\) | 45.0812i | 0.0929509i | ||||||||
\(486\) | 343.644 | − | 2.59878i | 0.707087 | − | 0.00534728i | ||||
\(487\) | −28.4608 | −0.0584411 | −0.0292206 | − | 0.999573i | \(-0.509303\pi\) | ||||
−0.0292206 | + | 0.999573i | \(0.509303\pi\) | |||||||
\(488\) | − | 54.0502i | − | 0.110759i | ||||||
\(489\) | −408.801 | − | 132.144i | −0.835993 | − | 0.270233i | ||||
\(490\) | 22.1359 | 0.0451754 | ||||||||
\(491\) | 757.575i | 1.54292i | 0.636277 | + | 0.771461i | \(0.280474\pi\) | ||||
−0.636277 | + | 0.771461i | \(0.719526\pi\) | |||||||
\(492\) | −127.009 | + | 392.916i | −0.258149 | + | 0.798609i | ||||
\(493\) | −8.76569 | −0.0177803 | ||||||||
\(494\) | − | 180.127i | − | 0.364630i | ||||||
\(495\) | 74.7825 | + | 53.9878i | 0.151076 | + | 0.109066i | ||||
\(496\) | −118.942 | −0.239802 | ||||||||
\(497\) | 81.7426i | 0.164472i | ||||||||
\(498\) | −631.657 | − | 204.182i | −1.26839 | − | 0.410004i | ||||
\(499\) | −165.989 | −0.332643 | −0.166322 | − | 0.986072i | \(-0.553189\pi\) | ||||
−0.166322 | + | 0.986072i | \(0.553189\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 123.992 | − | 383.580i | 0.247488 | − | 0.765629i | ||||
\(502\) | −496.861 | −0.989764 | ||||||||
\(503\) | 842.529i | 1.67501i | 0.546431 | + | 0.837504i | \(0.315986\pi\) | ||||
−0.546431 | + | 0.837504i | \(0.684014\pi\) | |||||||
\(504\) | −39.4222 | + | 54.6067i | −0.0782187 | + | 0.108347i | ||||
\(505\) | −214.458 | −0.424670 | ||||||||
\(506\) | − | 0.907704i | − | 0.00179388i | ||||||
\(507\) | 712.494 | + | 230.313i | 1.40531 | + | 0.454265i | ||||
\(508\) | −488.768 | −0.962143 | ||||||||
\(509\) | − | 119.739i | − | 0.235244i | −0.993058 | − | 0.117622i | \(-0.962473\pi\) | ||
0.993058 | − | 0.117622i | \(-0.0375271\pi\) | |||||||
\(510\) | −14.5110 | + | 44.8910i | −0.0284529 | + | 0.0880216i | ||||
\(511\) | −294.543 | −0.576404 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 99.4139 | + | 135.534i | 0.193789 | + | 0.264199i | ||||
\(514\) | 184.905 | 0.359737 | ||||||||
\(515\) | − | 304.144i | − | 0.590571i | ||||||
\(516\) | 115.948 | + | 37.4801i | 0.224706 | + | 0.0726359i | ||||
\(517\) | −262.650 | −0.508027 | ||||||||
\(518\) | 145.301i | 0.280504i | ||||||||
\(519\) | −250.205 | + | 774.032i | −0.482090 | + | 1.49139i | ||||
\(520\) | −129.398 | −0.248843 | ||||||||
\(521\) | − | 320.580i | − | 0.615316i | −0.951497 | − | 0.307658i | \(-0.900455\pi\) | ||
0.951497 | − | 0.307658i | \(-0.0995452\pi\) | |||||||
\(522\) | 18.1900 | + | 13.1320i | 0.0348468 | + | 0.0251570i | ||||
\(523\) | −341.396 | −0.652764 | −0.326382 | − | 0.945238i | \(-0.605830\pi\) | ||||
−0.326382 | + | 0.945238i | \(0.605830\pi\) | |||||||
\(524\) | 517.136i | 0.986900i | ||||||||
\(525\) | −37.7624 | − | 12.2066i | −0.0719284 | − | 0.0232507i | ||||
\(526\) | 259.503 | 0.493351 | ||||||||
\(527\) | − | 147.874i | − | 0.280597i | ||||||
\(528\) | 16.9161 | − | 52.3316i | 0.0320381 | − | 0.0991128i | ||||
\(529\) | 528.980 | 0.999963 | ||||||||
\(530\) | 129.761i | 0.244833i | ||||||||
\(531\) | −418.548 | + | 579.762i | −0.788227 | + | 1.09183i | ||||
\(532\) | −32.9416 | −0.0619203 | ||||||||
\(533\) | − | 1408.08i | − | 2.64180i | ||||||
\(534\) | 539.467 | + | 174.382i | 1.01024 | + | 0.326558i | ||||
\(535\) | 172.311 | 0.322076 | ||||||||
\(536\) | − | 190.957i | − | 0.356263i | ||||||
\(537\) | 93.2284 | − | 288.411i | 0.173610 | − | 0.537079i | ||||
\(538\) | 249.401 | 0.463570 | ||||||||
\(539\) | − | 32.0820i | − | 0.0595213i | ||||||
\(540\) | 97.3639 | − | 71.4162i | 0.180303 | − | 0.132252i | ||||
\(541\) | −158.832 | −0.293590 | −0.146795 | − | 0.989167i | \(-0.546896\pi\) | ||||
−0.146795 | + | 0.989167i | \(0.546896\pi\) | |||||||
\(542\) | 323.591i | 0.597031i | ||||||||
\(543\) | 700.093 | + | 226.304i | 1.28931 | + | 0.416766i | ||||
\(544\) | 28.1316 | 0.0517125 | ||||||||
\(545\) | 331.185i | 0.607680i | ||||||||
\(546\) | 70.6382 | − | 218.526i | 0.129374 | − | 0.400231i | ||||
\(547\) | 350.423 | 0.640628 | 0.320314 | − | 0.947312i | \(-0.396212\pi\) | ||||
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(548\) | 434.083i | 0.792123i | ||||||||
\(549\) | −139.445 | − | 100.670i | −0.253999 | − | 0.183370i | ||||
\(550\) | 32.4077 | 0.0589231 | ||||||||
\(551\) | 10.9732i | 0.0199150i | ||||||||
\(552\) | −1.13071 | − | 0.365500i | −0.00204839 | − | 0.000662138i | ||||
\(553\) | −55.3384 | −0.100069 | ||||||||
\(554\) | − | 29.8909i | − | 0.0539547i | ||||||
\(555\) | 80.1246 | − | 247.873i | 0.144369 | − | 0.446618i | ||||
\(556\) | 221.187 | 0.397818 | ||||||||
\(557\) | 206.230i | 0.370251i | 0.982715 | + | 0.185125i | \(0.0592691\pi\) | ||||
−0.982715 | + | 0.185125i | \(0.940731\pi\) | |||||||
\(558\) | −221.532 | + | 306.860i | −0.397010 | + | 0.549928i | ||||
\(559\) | −415.521 | −0.743328 | ||||||||
\(560\) | 23.6643i | 0.0422577i | ||||||||
\(561\) | 65.0613 | + | 21.0310i | 0.115974 | + | 0.0374884i | ||||
\(562\) | 621.301 | 1.10552 | ||||||||
\(563\) | − | 1075.62i | − | 1.91051i | −0.295789 | − | 0.955253i | \(-0.595583\pi\) | ||
0.295789 | − | 0.955253i | \(-0.404417\pi\) | |||||||
\(564\) | −105.760 | + | 327.178i | −0.187517 | + | 0.580103i | ||||
\(565\) | 194.358 | 0.343996 | ||||||||
\(566\) | 108.666i | 0.191990i | ||||||||
\(567\) | 67.4560 | + | 203.413i | 0.118970 | + | 0.358752i | ||||
\(568\) | −87.3865 | −0.153849 | ||||||||
\(569\) | 969.357i | 1.70362i | 0.523854 | + | 0.851808i | \(0.324494\pi\) | ||||
−0.523854 | + | 0.851808i | \(0.675506\pi\) | |||||||
\(570\) | 56.1960 | + | 18.1653i | 0.0985896 | + | 0.0318689i | ||||
\(571\) | −961.564 | −1.68400 | −0.842000 | − | 0.539477i | \(-0.818622\pi\) | ||||
−0.842000 | + | 0.539477i | \(0.818622\pi\) | |||||||
\(572\) | 187.539i | 0.327865i | ||||||||
\(573\) | 31.2700 | − | 96.7369i | 0.0545725 | − | 0.168825i | ||||
\(574\) | −257.509 | −0.448623 | ||||||||
\(575\) | − | 0.700222i | − | 0.00121778i | ||||||
\(576\) | −58.3770 | − | 42.1441i | −0.101349 | − | 0.0731669i | ||||
\(577\) | 985.988 | 1.70882 | 0.854409 | − | 0.519601i | \(-0.173920\pi\) | ||||
0.854409 | + | 0.519601i | \(0.173920\pi\) | |||||||
\(578\) | − | 373.733i | − | 0.646597i | ||||||
\(579\) | −867.920 | − | 280.554i | −1.49900 | − | 0.484549i | ||||
\(580\) | 7.88283 | 0.0135911 | ||||||||
\(581\) | − | 413.976i | − | 0.712523i | ||||||
\(582\) | 26.3089 | − | 81.3891i | 0.0452043 | − | 0.139844i | ||||
\(583\) | 188.065 | 0.322582 | ||||||||
\(584\) | − | 314.879i | − | 0.539177i | ||||||
\(585\) | −241.008 | + | 333.837i | −0.411979 | + | 0.570662i | ||||
\(586\) | 360.843 | 0.615772 | ||||||||
\(587\) | − | 665.664i | − | 1.13401i | −0.823714 | − | 0.567005i | \(-0.808102\pi\) | ||
0.823714 | − | 0.567005i | \(-0.191898\pi\) | |||||||
\(588\) | −39.9640 | − | 12.9183i | −0.0679659 | − | 0.0219699i | ||||
\(589\) | −185.114 | −0.314285 | ||||||||
\(590\) | 251.246i | 0.425840i | ||||||||
\(591\) | −232.262 | + | 718.525i | −0.392998 | + | 1.21578i | ||||
\(592\) | −155.333 | −0.262387 | ||||||||
\(593\) | 485.553i | 0.818808i | 0.912353 | + | 0.409404i | \(0.134263\pi\) | ||||
−0.912353 | + | 0.409404i | \(0.865737\pi\) | |||||||
\(594\) | −103.505 | − | 141.111i | −0.174250 | − | 0.237561i | ||||
\(595\) | −29.4207 | −0.0494466 | ||||||||
\(596\) | − | 84.8084i | − | 0.142296i | ||||||
\(597\) | −1059.88 | − | 342.604i | −1.77534 | − | 0.573876i | ||||
\(598\) | 4.05209 | 0.00677608 | ||||||||
\(599\) | 701.599i | 1.17128i | 0.810570 | + | 0.585642i | \(0.199158\pi\) | ||||
−0.810570 | + | 0.585642i | \(0.800842\pi\) | |||||||
\(600\) | 13.0494 | − | 40.3697i | 0.0217491 | − | 0.0672828i | ||||
\(601\) | 63.1246 | 0.105033 | 0.0525163 | − | 0.998620i | \(-0.483276\pi\) | ||||
0.0525163 | + | 0.998620i | \(0.483276\pi\) | |||||||
\(602\) | 75.9903i | 0.126230i | ||||||||
\(603\) | −492.654 | − | 355.662i | −0.817004 | − | 0.589821i | ||||
\(604\) | −212.414 | −0.351678 | ||||||||
\(605\) | 223.595i | 0.369579i | ||||||||
\(606\) | 387.181 | + | 125.156i | 0.638912 | + | 0.206527i | ||||
\(607\) | −234.302 | −0.386001 | −0.193000 | − | 0.981199i | \(-0.561822\pi\) | ||||
−0.193000 | + | 0.981199i | \(0.561822\pi\) | |||||||
\(608\) | − | 35.2160i | − | 0.0579211i | ||||||
\(609\) | −4.30321 | + | 13.3124i | −0.00706603 | + | 0.0218594i | ||||
\(610\) | −60.4300 | −0.0990655 | ||||||||
\(611\) | − | 1172.50i | − | 1.91898i | ||||||
\(612\) | 52.3958 | − | 72.5773i | 0.0856141 | − | 0.118590i | ||||
\(613\) | −15.8710 | −0.0258908 | −0.0129454 | − | 0.999916i | \(-0.504121\pi\) | ||||
−0.0129454 | + | 0.999916i | \(0.504121\pi\) | |||||||
\(614\) | 229.842i | 0.374335i | ||||||||
\(615\) | 439.293 | + | 142.001i | 0.714298 | + | 0.230896i | ||||
\(616\) | 34.2971 | 0.0556771 | ||||||||
\(617\) | − | 307.663i | − | 0.498644i | −0.968421 | − | 0.249322i | \(-0.919792\pi\) | ||
0.968421 | − | 0.249322i | \(-0.0802077\pi\) | |||||||
\(618\) | −177.495 | + | 549.098i | −0.287209 | + | 0.888508i | ||||
\(619\) | 0.497116 | 0.000803095 | 0.000401548 | − | 1.00000i | \(-0.499872\pi\) | ||||
0.000401548 | 1.00000i | \(0.499872\pi\) | ||||||||
\(620\) | 132.981i | 0.214485i | ||||||||
\(621\) | −3.04894 | + | 2.23639i | −0.00490973 | + | 0.00360127i | ||||
\(622\) | 185.208 | 0.297762 | ||||||||
\(623\) | 353.556i | 0.567506i | ||||||||
\(624\) | 233.614 | + | 75.5154i | 0.374381 | + | 0.121018i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 291.703i | − | 0.465979i | ||||||
\(627\) | 26.3272 | − | 81.4459i | 0.0419892 | − | 0.129898i | ||||
\(628\) | 213.045 | 0.339244 | ||||||||
\(629\) | − | 193.118i | − | 0.307024i | ||||||
\(630\) | 61.0521 | + | 44.0754i | 0.0969081 | + | 0.0699610i | ||||
\(631\) | 414.758 | 0.657302 | 0.328651 | − | 0.944451i | \(-0.393406\pi\) | ||||
0.328651 | + | 0.944451i | \(0.393406\pi\) | |||||||
\(632\) | − | 59.1592i | − | 0.0936064i | ||||||
\(633\) | 625.663 | + | 202.245i | 0.988409 | + | 0.319502i | ||||
\(634\) | −311.475 | −0.491286 | ||||||||
\(635\) | 546.460i | 0.860567i | ||||||||
\(636\) | 75.7273 | − | 234.270i | 0.119068 | − | 0.368349i | ||||
\(637\) | 143.218 | 0.224831 | ||||||||
\(638\) | − | 11.4247i | − | 0.0179071i | ||||||
\(639\) | −162.760 | + | 225.450i | −0.254710 | + | 0.352818i | ||||
\(640\) | −25.2982 | −0.0395285 | ||||||||
\(641\) | 636.221i | 0.992544i | 0.868167 | + | 0.496272i | \(0.165298\pi\) | ||||
−0.868167 | + | 0.496272i | \(0.834702\pi\) | |||||||
\(642\) | −311.088 | − | 100.559i | −0.484560 | − | 0.156633i | ||||
\(643\) | 556.821 | 0.865974 | 0.432987 | − | 0.901400i | \(-0.357460\pi\) | ||||
0.432987 | + | 0.901400i | \(0.357460\pi\) | |||||||
\(644\) | − | 0.741046i | − | 0.00115069i | ||||||
\(645\) | 41.9040 | − | 129.634i | 0.0649675 | − | 0.200983i | ||||
\(646\) | 43.7824 | 0.0677746 | ||||||||
\(647\) | − | 528.501i | − | 0.816848i | −0.912792 | − | 0.408424i | \(-0.866078\pi\) | ||
0.912792 | − | 0.408424i | \(-0.133922\pi\) | |||||||
\(648\) | −217.457 | + | 72.1135i | −0.335582 | + | 0.111286i | ||||
\(649\) | 364.134 | 0.561070 | ||||||||
\(650\) | 144.672i | 0.222572i | ||||||||
\(651\) | −224.576 | − | 72.5938i | −0.344971 | − | 0.111511i | ||||
\(652\) | 286.418 | 0.439292 | ||||||||
\(653\) | 476.577i | 0.729826i | 0.931042 | + | 0.364913i | \(0.118901\pi\) | ||||
−0.931042 | + | 0.364913i | \(0.881099\pi\) | |||||||
\(654\) | 193.276 | − | 597.918i | 0.295529 | − | 0.914248i | ||||
\(655\) | 578.175 | 0.882710 | ||||||||
\(656\) | − | 275.289i | − | 0.419648i | ||||||
\(657\) | −812.364 | − | 586.471i | −1.23647 | − | 0.892649i | ||||
\(658\) | −214.426 | −0.325876 | ||||||||
\(659\) | − | 247.290i | − | 0.375250i | −0.982241 | − | 0.187625i | \(-0.939921\pi\) | ||
0.982241 | − | 0.187625i | \(-0.0600790\pi\) | |||||||
\(660\) | −58.5085 | − | 18.9128i | −0.0886492 | − | 0.0286557i | ||||
\(661\) | 72.2288 | 0.109272 | 0.0546360 | − | 0.998506i | \(-0.482600\pi\) | ||||
0.0546360 | + | 0.998506i | \(0.482600\pi\) | |||||||
\(662\) | − | 754.000i | − | 1.13897i | ||||||
\(663\) | −93.8846 | + | 290.441i | −0.141606 | + | 0.438071i | ||||
\(664\) | 442.559 | 0.666504 | ||||||||
\(665\) | 36.8298i | 0.0553832i | ||||||||
\(666\) | −289.312 | + | 400.747i | −0.434402 | + | 0.601723i | ||||
\(667\) | −0.246850 | −0.000370090 | ||||||||
\(668\) | 268.748i | 0.402318i | ||||||||
\(669\) | 640.061 | + | 206.899i | 0.956743 | + | 0.309266i | ||||
\(670\) | −213.496 | −0.318651 | ||||||||
\(671\) | 87.5821i | 0.130525i | ||||||||
\(672\) | 13.8102 | − | 42.7233i | 0.0205509 | − | 0.0635763i | ||||
\(673\) | 309.647 | 0.460099 | 0.230050 | − | 0.973179i | \(-0.426111\pi\) | ||||
0.230050 | + | 0.973179i | \(0.426111\pi\) | |||||||
\(674\) | 718.150i | 1.06550i | ||||||||
\(675\) | −79.8457 | − | 108.856i | −0.118290 | − | 0.161268i | ||||
\(676\) | −499.196 | −0.738455 | ||||||||
\(677\) | − | 155.619i | − | 0.229866i | −0.993373 | − | 0.114933i | \(-0.963335\pi\) | ||
0.993373 | − | 0.114933i | \(-0.0366653\pi\) | |||||||
\(678\) | −350.891 | − | 113.425i | −0.517538 | − | 0.167293i | ||||
\(679\) | 53.3408 | 0.0785579 | ||||||||
\(680\) | − | 31.4521i | − | 0.0462530i | ||||||
\(681\) | 356.463 | − | 1102.75i | 0.523441 | − | 1.61931i | ||||
\(682\) | 192.731 | 0.282597 | ||||||||
\(683\) | − | 625.573i | − | 0.915919i | −0.888973 | − | 0.457960i | \(-0.848580\pi\) | ||
0.888973 | − | 0.457960i | \(-0.151420\pi\) | |||||||
\(684\) | −90.8546 | − | 65.5908i | −0.132828 | − | 0.0958929i | ||||
\(685\) | 485.320 | 0.708496 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 456.476 | + | 147.555i | 0.664448 | + | 0.214782i | ||||
\(688\) | −81.2370 | −0.118077 | ||||||||
\(689\) | 839.545i | 1.21850i | ||||||||
\(690\) | −0.408642 | + | 1.26417i | −0.000592235 | + | 0.00183213i | ||||
\(691\) | 186.932 | 0.270523 | 0.135262 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135262 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(692\) | − | 542.311i | − | 0.783686i | ||||||
\(693\) | 63.8792 | − | 88.4838i | 0.0921778 | − | 0.127682i | ||||
\(694\) | 510.817 | 0.736048 | ||||||||
\(695\) | − | 247.294i | − | 0.355819i | ||||||
\(696\) | −14.2316 | − | 4.60033i | −0.0204476 | − | 0.00660967i | ||||
\(697\) | 342.254 | 0.491038 | ||||||||
\(698\) | − | 401.115i | − | 0.574664i | ||||||
\(699\) | −263.222 | + | 814.304i | −0.376570 | + | 1.16496i | ||||
\(700\) | 26.4575 | 0.0377964 | ||||||||
\(701\) | 20.0020i | 0.0285336i | 0.999898 | + | 0.0142668i | \(0.00454141\pi\) | ||||
−0.999898 | + | 0.0142668i | \(0.995459\pi\) | |||||||
\(702\) | 629.936 | − | 462.057i | 0.897345 | − | 0.658200i | ||||
\(703\) | −241.752 | −0.343886 | ||||||||
\(704\) | 36.6651i | 0.0520811i | ||||||||
\(705\) | 365.796 | + | 118.243i | 0.518860 | + | 0.167721i | ||||
\(706\) | −77.2949 | −0.109483 | ||||||||
\(707\) | 253.751i | 0.358912i | ||||||||
\(708\) | 146.624 | − | 453.596i | 0.207096 | − | 0.640672i | ||||
\(709\) | 168.823 | 0.238114 | 0.119057 | − | 0.992887i | \(-0.462013\pi\) | ||||
0.119057 | + | 0.992887i | \(0.462013\pi\) | |||||||
\(710\) | 97.7011i | 0.137607i | ||||||||
\(711\) | −152.626 | − | 110.186i | −0.214664 | − | 0.154973i | ||||
\(712\) | −377.967 | −0.530853 | ||||||||
\(713\) | − | 4.16428i | − | 0.00584050i | ||||||
\(714\) | 53.1158 | + | 17.1696i | 0.0743919 | + | 0.0240471i | ||||
\(715\) | 209.675 | 0.293252 | ||||||||
\(716\) | 202.070i | 0.282221i | ||||||||
\(717\) | −255.826 | + | 791.422i | −0.356800 | + | 1.10380i | ||||
\(718\) | 105.528 | 0.146974 | ||||||||
\(719\) | 244.215i | 0.339659i | 0.985473 | + | 0.169830i | \(0.0543217\pi\) | ||||
−0.985473 | + | 0.169830i | \(0.945678\pi\) | |||||||
\(720\) | −47.1186 | + | 65.2674i | −0.0654425 | + | 0.0906492i | ||||
\(721\) | −359.868 | −0.499124 | ||||||||
\(722\) | 455.723i | 0.631195i | ||||||||
\(723\) | −190.855 | − | 61.6936i | −0.263977 | − | 0.0853301i | ||||
\(724\) | −490.507 | −0.677496 | ||||||||
\(725\) | − | 8.81327i | − | 0.0121562i | ||||||
\(726\) | 130.488 | − | 403.676i | 0.179735 | − | 0.556028i | ||||
\(727\) | −187.393 | −0.257762 | −0.128881 | − | 0.991660i | \(-0.541139\pi\) | ||||
−0.128881 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(728\) | 153.106i | 0.210311i | ||||||||
\(729\) | −218.973 | + | 695.336i | −0.300374 | + | 0.953822i | ||||
\(730\) | −352.046 | −0.482254 | ||||||||
\(731\) | − | 100.998i | − | 0.138164i | ||||||
\(732\) | 109.100 | + | 35.2662i | 0.149043 | + | 0.0481779i | ||||
\(733\) | 771.777 | 1.05290 | 0.526451 | − | 0.850206i | \(-0.323522\pi\) | ||||
0.526451 | + | 0.850206i | \(0.323522\pi\) | |||||||
\(734\) | − | 838.628i | − | 1.14254i | ||||||
\(735\) | −14.4431 | + | 44.6811i | −0.0196505 | + | 0.0607906i | ||||
\(736\) | 0.792211 | 0.00107637 | ||||||||
\(737\) | 309.423i | 0.419842i | ||||||||
\(738\) | −710.224 | − | 512.733i | −0.962364 | − | 0.694760i | ||||
\(739\) | 534.142 | 0.722791 | 0.361395 | − | 0.932413i | \(-0.382301\pi\) | ||||
0.361395 | + | 0.932413i | \(0.382301\pi\) | |||||||
\(740\) | 173.668i | 0.234686i | ||||||||
\(741\) | 363.584 | + | 117.528i | 0.490666 | + | 0.158607i | ||||
\(742\) | 153.536 | 0.206922 | ||||||||
\(743\) | − | 983.813i | − | 1.32411i | −0.749456 | − | 0.662054i | \(-0.769685\pi\) | ||
0.749456 | − | 0.662054i | \(-0.230315\pi\) | |||||||
\(744\) | 77.6061 | − | 240.082i | 0.104309 | − | 0.322691i | ||||
\(745\) | −94.8187 | −0.127273 | ||||||||
\(746\) | − | 675.860i | − | 0.905979i | ||||||
\(747\) | 824.277 | − | 1141.77i | 1.10345 | − | 1.52847i | ||||
\(748\) | −45.5840 | −0.0609412 | ||||||||
\(749\) | − | 203.881i | − | 0.272204i | ||||||
\(750\) | −45.1347 | − | 14.5897i | −0.0601796 | − | 0.0194530i | ||||
\(751\) | 261.058 | 0.347614 | 0.173807 | − | 0.984780i | \(-0.444393\pi\) | ||||
0.173807 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(752\) | − | 229.231i | − | 0.304829i | ||||||
\(753\) | 324.188 | − | 1002.91i | 0.430529 | − | 1.33188i | ||||
\(754\) | 51.0012 | 0.0676409 | ||||||||
\(755\) | 237.486i | 0.314551i | ||||||||
\(756\) | −84.5008 | − | 115.202i | −0.111774 | − | 0.152384i | ||||
\(757\) | −870.719 | −1.15022 | −0.575111 | − | 0.818075i | \(-0.695041\pi\) | ||||
−0.575111 | + | 0.818075i | \(0.695041\pi\) | |||||||
\(758\) | − | 220.265i | − | 0.290587i | ||||||
\(759\) | 1.83219 | + | 0.592251i | 0.00241395 | + | 0.000780305i | ||||
\(760\) | −39.3727 | −0.0518062 | ||||||||
\(761\) | 497.495i | 0.653739i | 0.945070 | + | 0.326869i | \(0.105994\pi\) | ||||
−0.945070 | + | 0.326869i | \(0.894006\pi\) | |||||||
\(762\) | 318.908 | − | 986.572i | 0.418514 | − | 1.29471i | ||||
\(763\) | 391.864 | 0.513583 | ||||||||
\(764\) | 67.7769i | 0.0887132i | ||||||||
\(765\) | −81.1439 | − | 58.5803i | −0.106070 | − | 0.0765755i | ||||
\(766\) | 289.907 | 0.378469 | ||||||||
\(767\) | 1625.54i | 2.11934i | ||||||||
\(768\) | 45.6731 | + | 14.7638i | 0.0594702 | + | 0.0192236i | ||||
\(769\) | 1119.67 | 1.45601 | 0.728003 | − | 0.685574i | \(-0.240449\pi\) | ||||
0.728003 | + | 0.685574i | \(0.240449\pi\) | |||||||
\(770\) | − | 38.3453i | − | 0.0497991i | ||||||
\(771\) | −120.645 | + | 373.227i | −0.156479 | + | 0.484082i | ||||
\(772\) | 608.092 | 0.787684 | ||||||||
\(773\) | − | 1029.28i | − | 1.33154i | −0.746159 | − | 0.665768i | \(-0.768104\pi\) | ||
0.746159 | − | 0.665768i | \(-0.231896\pi\) | |||||||
\(774\) | −151.306 | + | 209.585i | −0.195486 | + | 0.270782i | ||||
\(775\) | 148.677 | 0.191841 | ||||||||
\(776\) | 57.0237i | 0.0734842i | ||||||||
\(777\) | −293.288 | − | 94.8047i | −0.377461 | − | 0.122014i | ||||
\(778\) | −228.687 | −0.293942 | ||||||||
\(779\) | − | 428.444i | − | 0.549993i | ||||||
\(780\) | 84.4287 | − | 261.188i | 0.108242 | − | 0.334857i | ||||
\(781\) | 141.600 | 0.181306 | ||||||||
\(782\) | 0.984918i | 0.00125949i | ||||||||
\(783\) | −38.3751 | + | 28.1481i | −0.0490104 | + | 0.0359490i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | − | 238.192i | − | 0.303429i | ||||||
\(786\) | −1043.83 | − | 337.416i | −1.32803 | − | 0.429283i | ||||
\(787\) | 180.973 | 0.229953 | 0.114977 | − | 0.993368i | \(-0.463321\pi\) | ||||
0.114977 | + | 0.993368i | \(0.463321\pi\) | |||||||
\(788\) | − | 503.421i | − | 0.638859i | ||||||
\(789\) | −169.318 | + | 523.802i | −0.214599 | + | 0.663881i | ||||
\(790\) | −66.1420 | −0.0837241 | ||||||||
\(791\) | − | 229.967i | − | 0.290729i | ||||||
\(792\) | 94.5932 | + | 68.2897i | 0.119436 | + | 0.0862244i | ||||
\(793\) | −390.977 | −0.493035 | ||||||||
\(794\) | 688.906i | 0.867639i | ||||||||
\(795\) | −261.921 | − | 84.6657i | −0.329461 | − | 0.106498i | ||||
\(796\) | 742.584 | 0.932895 | ||||||||
\(797\) | 1063.75i | 1.33469i | 0.744750 | + | 0.667343i | \(0.232569\pi\) | ||||
−0.744750 | + | 0.667343i | \(0.767431\pi\) | |||||||
\(798\) | 21.4935 | − | 66.4921i | 0.0269342 | − | 0.0833234i | ||||
\(799\) | 284.992 | 0.356686 | ||||||||
\(800\) | 28.2843i | 0.0353553i | ||||||||
\(801\) | −703.974 | + | 975.126i | −0.878869 | + | 1.21739i | ||||
\(802\) | 713.643 | 0.889830 | ||||||||
\(803\) | 510.226i | 0.635399i | ||||||||
\(804\) | 385.443 | + | 124.594i | 0.479407 | + | 0.154968i | ||||
\(805\) | −0.828514 | −0.00102921 | ||||||||
\(806\) | 860.374i | 1.06746i | ||||||||
\(807\) | −162.727 | + | 503.412i | −0.201644 | + | 0.623806i | ||||
\(808\) | −271.271 | −0.335731 | ||||||||
\(809\) | − | 652.710i | − | 0.806811i | −0.915021 | − | 0.403406i | \(-0.867826\pi\) | ||
0.915021 | − | 0.403406i | \(-0.132174\pi\) | |||||||
\(810\) | 80.6253 | + | 243.125i | 0.0995374 | + | 0.300154i | ||||
\(811\) | 188.572 | 0.232518 | 0.116259 | − | 0.993219i | \(-0.462910\pi\) | ||||
0.116259 | + | 0.993219i | \(0.462910\pi\) | |||||||
\(812\) | − | 9.32709i | − | 0.0114866i | ||||||
\(813\) | −653.163 | − | 211.134i | −0.803398 | − | 0.259697i | ||||
\(814\) | 251.700 | 0.309213 | ||||||||
\(815\) | − | 320.226i | − | 0.392915i | ||||||
\(816\) | −18.3551 | + | 56.7832i | −0.0224940 | + | 0.0695872i | ||||
\(817\) | −126.433 | −0.154752 | ||||||||
\(818\) | 131.848i | 0.161183i | ||||||||
\(819\) | 395.002 | + | 285.164i | 0.482298 | + | 0.348186i | ||||
\(820\) | −307.783 | −0.375345 | ||||||||
\(821\) | − | 1051.42i | − | 1.28066i | −0.768099 | − | 0.640332i | \(-0.778797\pi\) | ||
0.768099 | − | 0.640332i | \(-0.221203\pi\) | |||||||
\(822\) | −876.191 | − | 283.227i | −1.06593 | − | 0.344559i | ||||
\(823\) | 296.725 | 0.360541 | 0.180271 | − | 0.983617i | \(-0.442303\pi\) | ||||
0.180271 | + | 0.983617i | \(0.442303\pi\) | |||||||
\(824\) | − | 384.715i | − | 0.466887i | ||||||
\(825\) | −21.1451 | + | 65.4145i | −0.0256304 | + | 0.0792902i | ||||
\(826\) | 297.278 | 0.359900 | ||||||||
\(827\) | 483.556i | 0.584711i | 0.956310 | + | 0.292355i | \(0.0944390\pi\) | ||||
−0.956310 | + | 0.292355i | \(0.905561\pi\) | |||||||
\(828\) | 1.47551 | − | 2.04384i | 0.00178202 | − | 0.00246841i | ||||
\(829\) | 1009.43 | 1.21765 | 0.608826 | − | 0.793303i | \(-0.291641\pi\) | ||||
0.608826 | + | 0.793303i | \(0.291641\pi\) | |||||||
\(830\) | − | 494.796i | − | 0.596139i | ||||||
\(831\) | 60.3343 | + | 19.5030i | 0.0726045 | + | 0.0234693i | ||||
\(832\) | −163.677 | −0.196728 | ||||||||
\(833\) | 34.8111i | 0.0417900i | ||||||||
\(834\) | −144.318 | + | 446.462i | −0.173043 | + | 0.535326i | ||||
\(835\) | 300.470 | 0.359844 | ||||||||
\(836\) | 57.0635i | 0.0682578i | ||||||||
\(837\) | −474.849 | − | 647.376i | −0.567323 | − | 0.773448i | ||||
\(838\) | −301.951 | −0.360324 | ||||||||
\(839\) | 402.644i | 0.479909i | 0.970784 | + | 0.239954i | \(0.0771325\pi\) | ||||
−0.970784 | + | 0.239954i | \(0.922868\pi\) | |||||||
\(840\) | −47.7661 | − | 15.4403i | −0.0568644 | − | 0.0183813i | ||||
\(841\) | 837.893 | 0.996306 | ||||||||
\(842\) | 587.393i | 0.697616i | ||||||||
\(843\) | −405.381 | + | 1254.09i | −0.480879 | + | 1.48765i | ||||
\(844\) | −438.359 | −0.519383 | ||||||||
\(845\) | 558.118i | 0.660494i | ||||||||
\(846\) | −591.399 | − | 426.949i | −0.699053 | − | 0.504668i | ||||
\(847\) | 264.561 | 0.312351 | ||||||||
\(848\) | 164.137i | 0.193557i | ||||||||
\(849\) | −219.342 | − | 70.9018i | −0.258353 | − | 0.0835121i | ||||
\(850\) | −35.1645 | −0.0413700 | ||||||||
\(851\) | − | 5.43839i | − | 0.00639058i | ||||||
\(852\) | 57.0172 | − | 176.388i | 0.0669217 | − | 0.207029i | ||||
\(853\) | 544.670 | 0.638534 | 0.319267 | − | 0.947665i | \(-0.396563\pi\) | ||||
0.319267 | + | 0.947665i | \(0.396563\pi\) | |||||||
\(854\) | 71.5017i | 0.0837256i | ||||||||
\(855\) | −73.3327 | + | 101.579i | −0.0857692 | + | 0.118805i | ||||
\(856\) | 217.958 | 0.254624 | ||||||||
\(857\) | 1535.83i | 1.79210i | 0.443951 | + | 0.896051i | \(0.353577\pi\) | ||||
−0.443951 | + | 0.896051i | \(0.646423\pi\) | |||||||
\(858\) | −378.545 | − | 122.364i | −0.441194 | − | 0.142615i | ||||
\(859\) | −710.763 | −0.827430 | −0.413715 | − | 0.910406i | \(-0.635769\pi\) | ||||
−0.413715 | + | 0.910406i | \(0.635769\pi\) | |||||||
\(860\) | 90.8258i | 0.105611i | ||||||||
\(861\) | 168.018 | − | 519.779i | 0.195142 | − | 0.603692i | ||||
\(862\) | 531.566 | 0.616666 | ||||||||
\(863\) | − | 746.122i | − | 0.864568i | −0.901738 | − | 0.432284i | \(-0.857708\pi\) | ||
0.901738 | − | 0.432284i | \(-0.142292\pi\) | |||||||
\(864\) | 123.157 | − | 90.3352i | 0.142542 | − | 0.104555i | ||||
\(865\) | −606.322 | −0.700950 | ||||||||
\(866\) | 634.191i | 0.732322i | ||||||||
\(867\) | 754.374 | + | 243.850i | 0.870097 | + | 0.281258i | ||||
\(868\) | 157.345 | 0.181273 | ||||||||
\(869\) | 95.8607i | 0.110312i | ||||||||
\(870\) | −5.14332 | + | 15.9114i | −0.00591187 | + | 0.0182889i | ||||
\(871\) | −1381.30 | −1.58588 | ||||||||
\(872\) | 418.920i | 0.480413i | ||||||||
\(873\) | 147.117 | + | 106.208i | 0.168519 | + | 0.121659i | ||||
\(874\) | 1.23295 | 0.00141070 | ||||||||
\(875\) | − | 29.5804i | − | 0.0338062i | ||||||
\(876\) | 635.579 | + | 205.450i | 0.725547 | + | 0.234532i | ||||
\(877\) | −1221.75 | −1.39310 | −0.696552 | − | 0.717506i | \(-0.745284\pi\) | ||||
−0.696552 | + | 0.717506i | \(0.745284\pi\) | |||||||
\(878\) | − | 578.519i | − | 0.658905i | ||||||
\(879\) | −235.440 | + | 728.355i | −0.267849 | + | 0.828618i | ||||
\(880\) | 40.9929 | 0.0465828 | ||||||||
\(881\) | − | 213.476i | − | 0.242311i | −0.992634 | − | 0.121155i | \(-0.961340\pi\) | ||
0.992634 | − | 0.121155i | \(-0.0386599\pi\) | |||||||
\(882\) | 52.1507 | − | 72.2378i | 0.0591278 | − | 0.0819023i | ||||
\(883\) | −1084.76 | −1.22850 | −0.614249 | − | 0.789112i | \(-0.710541\pi\) | ||||
−0.614249 | + | 0.789112i | \(0.710541\pi\) | |||||||
\(884\) | − | 203.492i | − | 0.230195i | ||||||
\(885\) | −507.135 | − | 163.931i | −0.573034 | − | 0.185232i | ||||
\(886\) | 201.970 | 0.227957 | ||||||||
\(887\) | 167.255i | 0.188563i | 0.995546 | + | 0.0942813i | \(0.0300553\pi\) | ||||
−0.995546 | + | 0.0942813i | \(0.969945\pi\) | |||||||
\(888\) | 101.351 | − | 313.538i | 0.114133 | − | 0.353083i | ||||
\(889\) | 646.580 | 0.727311 | ||||||||
\(890\) | 422.580i | 0.474809i | ||||||||
\(891\) | 352.364 | − | 116.852i | 0.395471 | − | 0.131147i | ||||
\(892\) | −448.447 | −0.502743 | ||||||||
\(893\) | − | 356.762i | − | 0.399510i | ||||||
\(894\) | 171.184 | + | 55.3351i | 0.191481 | + | 0.0618961i | ||||
\(895\) | 225.921 | 0.252426 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | −2.64388 | + | 8.17909i | −0.00294747 | + | 0.00911827i | ||||
\(898\) | −616.005 | −0.685974 | ||||||||
\(899\) | − | 52.4132i | − | 0.0583017i | ||||||
\(900\) | 72.9712 | + | 52.6802i | 0.0810791 | + | 0.0585335i | ||||
\(901\) | −204.063 | −0.226485 | ||||||||
\(902\) | 446.074i | 0.494539i | ||||||||
\(903\) | −153.385 | − | 49.5815i | −0.169862 | − | 0.0549076i | ||||
\(904\) | 245.845 | 0.271952 | ||||||||
\(905\) | 548.404i | 0.605971i | ||||||||
\(906\) | 138.594 | − | 428.754i | 0.152974 | − | 0.473238i | ||||
\(907\) | 660.255 | 0.727955 | 0.363977 | − | 0.931408i | \(-0.381419\pi\) | ||||
0.363977 | + | 0.931408i | \(0.381419\pi\) | |||||||
\(908\) | 772.623i | 0.850907i | ||||||||
\(909\) | −505.249 | + | 699.858i | −0.555829 | + | 0.769920i | ||||
\(910\) | 171.178 | 0.188108 | ||||||||
\(911\) | 1120.41i | 1.22987i | 0.788577 | + | 0.614936i | \(0.210818\pi\) | ||||
−0.788577 | + | 0.614936i | \(0.789182\pi\) | |||||||
\(912\) | 71.0830 | + | 22.9775i | 0.0779419 | + | 0.0251946i | ||||
\(913\) | −717.115 | −0.785449 | ||||||||
\(914\) | − | 569.996i | − | 0.623628i | ||||||
\(915\) | 39.4289 | − | 121.977i | 0.0430916 | − | 0.133308i | ||||
\(916\) | −319.821 | −0.349150 | ||||||||
\(917\) | − | 684.106i | − | 0.746026i | ||||||
\(918\) | 112.309 | + | 153.115i | 0.122341 | + | 0.166792i | ||||
\(919\) | −470.684 | −0.512170 | −0.256085 | − | 0.966654i | \(-0.582433\pi\) | ||||
−0.256085 | + | 0.966654i | \(0.582433\pi\) | |||||||
\(920\) | − | 0.885719i | − | 0.000962738i | ||||||
\(921\) | −463.932 | − | 149.965i | −0.503726 | − | 0.162829i | ||||
\(922\) | −1219.38 | −1.32254 | ||||||||
\(923\) | 632.118i | 0.684851i | ||||||||
\(924\) | −22.3779 | + | 69.2281i | −0.0242185 | + | 0.0749222i | ||||
\(925\) | 194.166 | 0.209910 | ||||||||
\(926\) | 120.280i | 0.129892i | ||||||||
\(927\) | −992.535 | − | 716.542i | −1.07070 | − | 0.772969i | ||||
\(928\) | 9.97107 | 0.0107447 | ||||||||
\(929\) | − | 121.743i | − | 0.131048i | −0.997851 | − | 0.0655238i | \(-0.979128\pi\) | ||
0.997851 | − | 0.0655238i | \(-0.0208718\pi\) | |||||||
\(930\) | −268.420 | − | 86.7662i | −0.288623 | − | 0.0932970i | ||||
\(931\) | 43.5776 | 0.0468073 | ||||||||
\(932\) | − | 570.527i | − | 0.612153i | ||||||
\(933\) | −120.843 | + | 373.840i | −0.129521 | + | 0.400686i | ||||
\(934\) | −720.705 | −0.771632 | ||||||||
\(935\) | 50.9645i | 0.0545074i | ||||||||
\(936\) | −304.853 | + | 422.275i | −0.325698 | + | 0.451148i | ||||
\(937\) | −1283.85 | −1.37017 | −0.685087 | − | 0.728462i | \(-0.740236\pi\) | ||||
−0.685087 | + | 0.728462i | \(0.740236\pi\) | |||||||
\(938\) | 252.612i | 0.269309i | ||||||||
\(939\) | 588.798 | + | 190.328i | 0.627048 | + | 0.202692i | ||||
\(940\) | −256.288 | −0.272647 | ||||||||
\(941\) | 385.136i | 0.409283i | 0.978837 | + | 0.204642i | \(0.0656029\pi\) | ||||
−0.978837 | + | 0.204642i | \(0.934397\pi\) | |||||||
\(942\) | −139.006 | + | 430.028i | −0.147565 | + | 0.456505i | ||||
\(943\) | 9.63818 | 0.0102208 | ||||||||
\(944\) | 317.803i | 0.336656i | ||||||||
\(945\) | −128.800 | + | 94.4748i | −0.136297 | + | 0.0999733i | ||||
\(946\) | 131.635 | 0.139149 | ||||||||
\(947\) | − | 880.115i | − | 0.929372i | −0.885476 | − | 0.464686i | \(-0.846167\pi\) | ||
0.885476 | − | 0.464686i | \(-0.153833\pi\) | |||||||
\(948\) | 119.412 | + | 38.5997i | 0.125962 | + | 0.0407170i | ||||
\(949\) | −2277.70 | −2.40011 | ||||||||
\(950\) | 44.0200i | 0.0463369i | ||||||||
\(951\) | 203.229 | − | 628.708i | 0.213700 | − | 0.661102i | ||||
\(952\) | −37.2146 | −0.0390910 | ||||||||
\(953\) | − | 974.386i | − | 1.02244i | −0.859450 | − | 0.511220i | \(-0.829194\pi\) | ||
0.859450 | − | 0.511220i | \(-0.170806\pi\) | |||||||
\(954\) | 423.460 | + | 305.709i | 0.443878 | + | 0.320449i | ||||
\(955\) | 75.7768 | 0.0793475 | ||||||||
\(956\) | − | 554.495i | − | 0.580015i | ||||||
\(957\) | 23.0606 | + | 7.45430i | 0.0240968 | + | 0.00778924i | ||||
\(958\) | 293.277 | 0.306135 | ||||||||
\(959\) | − | 574.238i | − | 0.598789i | ||||||
\(960\) | 16.5064 | − | 51.0641i | 0.0171941 | − | 0.0531917i | ||||
\(961\) | −76.8058 | −0.0799228 | ||||||||
\(962\) | 1123.62i | 1.16800i | ||||||||
\(963\) | 405.952 | − | 562.314i | 0.421549 | − | 0.583919i | ||||
\(964\) | 133.719 | 0.138713 | ||||||||
\(965\) | − | 679.867i | − | 0.704526i | ||||||
\(966\) | 1.49579 | + | 0.483512i | 0.00154844 | + | 0.000500530i | ||||
\(967\) | −848.123 | −0.877066 | −0.438533 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438533 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(968\) | 282.828i | 0.292178i | ||||||||
\(969\) | −28.5668 | + | 88.3741i | −0.0294807 | + | 0.0912013i | ||||
\(970\) | 63.7545 | 0.0657262 | ||||||||
\(971\) | − | 591.259i | − | 0.608917i | −0.952526 | − | 0.304459i | \(-0.901524\pi\) | ||
0.952526 | − | 0.304459i | \(-0.0984755\pi\) | |||||||
\(972\) | −3.67523 | − | 485.986i | −0.00378110 | − | 0.499986i | ||||
\(973\) | −292.603 | −0.300722 | ||||||||
\(974\) | 40.2497i | 0.0413241i | ||||||||
\(975\) | −292.018 | − | 94.3942i | −0.299505 | − | 0.0968146i | ||||
\(976\) | −76.4385 | −0.0783182 | ||||||||
\(977\) | 618.460i | 0.633020i | 0.948589 | + | 0.316510i | \(0.102511\pi\) | ||||
−0.948589 | + | 0.316510i | \(0.897489\pi\) | |||||||
\(978\) | −186.880 | + | 578.131i | −0.191084 | + | 0.591136i | ||||
\(979\) | 612.453 | 0.625590 | ||||||||
\(980\) | − | 31.3050i | − | 0.0319438i | ||||||
\(981\) | 1080.78 | + | 780.249i | 1.10171 | + | 0.795361i | ||||
\(982\) | 1071.37 | 1.09101 | ||||||||
\(983\) | − | 1865.84i | − | 1.89811i | −0.315118 | − | 0.949053i | \(-0.602044\pi\) | ||
0.315118 | − | 0.949053i | \(-0.397956\pi\) | |||||||
\(984\) | 555.667 | + | 179.618i | 0.564702 | + | 0.182539i | ||||
\(985\) | −562.842 | −0.571413 | ||||||||
\(986\) | 12.3966i | 0.0125726i | ||||||||
\(987\) | 139.907 | − | 432.816i | 0.141750 | − | 0.438517i | ||||
\(988\) | −254.738 | −0.257832 | ||||||||
\(989\) | − | 2.84420i | − | 0.00287583i | ||||||
\(990\) | 76.3503 | − | 105.758i | 0.0771215 | − | 0.106827i | ||||
\(991\) | 659.640 | 0.665631 | 0.332816 | − | 0.942992i | \(-0.392001\pi\) | ||||
0.332816 | + | 0.942992i | \(0.392001\pi\) | |||||||
\(992\) | 168.209i | 0.169565i | ||||||||
\(993\) | 1521.94 | + | 491.964i | 1.53267 | + | 0.495432i | ||||
\(994\) | 115.601 | 0.116299 | ||||||||
\(995\) | − | 830.235i | − | 0.834407i | ||||||
\(996\) | −288.757 | + | 893.298i | −0.289917 | + | 0.896885i | ||||
\(997\) | −1049.99 | −1.05315 | −0.526575 | − | 0.850129i | \(-0.676524\pi\) | ||||
−0.526575 | + | 0.850129i | \(0.676524\pi\) | |||||||
\(998\) | 234.744i | 0.235214i | ||||||||
\(999\) | −620.135 | − | 845.448i | −0.620755 | − | 0.846294i |
(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 | 210.3.e.a.71.8 | ✓ | 16 | |
3.2 | odd | 2 | inner | 210.3.e.a.71.16 | yes | 16 | |
4.3 | odd | 2 | 1680.3.l.c.1121.1 | 16 | |||
5.2 | odd | 4 | 1050.3.c.c.449.23 | 32 | |||
5.3 | odd | 4 | 1050.3.c.c.449.10 | 32 | |||
5.4 | even | 2 | 1050.3.e.d.701.9 | 16 | |||
12.11 | even | 2 | 1680.3.l.c.1121.2 | 16 | |||
15.2 | even | 4 | 1050.3.c.c.449.9 | 32 | |||
15.8 | even | 4 | 1050.3.c.c.449.24 | 32 | |||
15.14 | odd | 2 | 1050.3.e.d.701.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
210.3.e.a.71.16 | yes | 16 | 3.2 | odd | 2 | inner | |
1050.3.c.c.449.9 | 32 | 15.2 | even | 4 | |||
1050.3.c.c.449.10 | 32 | 5.3 | odd | 4 | |||
1050.3.c.c.449.23 | 32 | 5.2 | odd | 4 | |||
1050.3.c.c.449.24 | 32 | 15.8 | even | 4 | |||
1050.3.e.d.701.1 | 16 | 15.14 | odd | 2 | |||
1050.3.e.d.701.9 | 16 | 5.4 | even | 2 | |||
1680.3.l.c.1121.1 | 16 | 4.3 | odd | 2 | |||
1680.3.l.c.1121.2 | 16 | 12.11 | even | 2 |