Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,3,Mod(91,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.b (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: | \(3.76022764817\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1358954496.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 8x^{6} + 20x^{4} + 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Root | \(-1.21752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 138.91 |
Dual form | 138.3.b.a.91.6 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 6.00464i | − | 1.20093i | −0.799652 | − | 0.600464i | \(-0.794982\pi\) | ||
0.799652 | − | 0.600464i | \(-0.205018\pi\) | |||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | − | 4.69017i | − | 0.670024i | −0.942214 | − | 0.335012i | \(-0.891260\pi\) | ||
0.942214 | − | 0.335012i | \(-0.108740\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 8.49185i | − | 0.849185i | ||||||
\(11\) | − | 6.16614i | − | 0.560559i | −0.959918 | − | 0.280279i | \(-0.909573\pi\) | ||
0.959918 | − | 0.280279i | \(-0.0904271\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | 8.71279 | 0.670215 | 0.335107 | − | 0.942180i | \(-0.391227\pi\) | ||||
0.335107 | + | 0.942180i | \(0.391227\pi\) | |||||||
\(14\) | − | 6.63290i | − | 0.473779i | ||||||
\(15\) | 10.4003i | 0.693356i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 14.0774i | − | 0.828085i | −0.910258 | − | 0.414043i | \(-0.864116\pi\) | ||
0.910258 | − | 0.414043i | \(-0.135884\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 14.6472i | 0.770904i | 0.922728 | + | 0.385452i | \(0.125954\pi\) | ||||
−0.922728 | + | 0.385452i | \(0.874046\pi\) | |||||||
\(20\) | − | 12.0093i | − | 0.600464i | ||||||
\(21\) | 8.12361i | 0.386839i | ||||||||
\(22\) | − | 8.72025i | − | 0.396375i | ||||||
\(23\) | 9.92304 | + | 20.7493i | 0.431437 | + | 0.902143i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −11.0557 | −0.442229 | ||||||||
\(26\) | 12.3218 | 0.473914 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 9.38034i | − | 0.335012i | ||||||
\(29\) | 1.08244 | 0.0373256 | 0.0186628 | − | 0.999826i | \(-0.494059\pi\) | ||||
0.0186628 | + | 0.999826i | \(0.494059\pi\) | |||||||
\(30\) | 14.7083i | 0.490277i | ||||||||
\(31\) | −48.1396 | −1.55289 | −0.776446 | − | 0.630184i | \(-0.782979\pi\) | ||||
−0.776446 | + | 0.630184i | \(0.782979\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 10.6801i | 0.323639i | ||||||||
\(34\) | − | 19.9085i | − | 0.585545i | ||||||
\(35\) | −28.1628 | −0.804651 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 56.9392i | 1.53890i | 0.638708 | + | 0.769449i | \(0.279469\pi\) | ||||
−0.638708 | + | 0.769449i | \(0.720531\pi\) | |||||||
\(38\) | 20.7142i | 0.545111i | ||||||||
\(39\) | −15.0910 | −0.386949 | ||||||||
\(40\) | − | 16.9837i | − | 0.424592i | ||||||
\(41\) | 22.8431 | 0.557148 | 0.278574 | − | 0.960415i | \(-0.410138\pi\) | ||||
0.278574 | + | 0.960415i | \(0.410138\pi\) | |||||||
\(42\) | 11.4885i | 0.273536i | ||||||||
\(43\) | 47.9731i | 1.11565i | 0.829957 | + | 0.557827i | \(0.188365\pi\) | ||||
−0.829957 | + | 0.557827i | \(0.811635\pi\) | |||||||
\(44\) | − | 12.3323i | − | 0.280279i | ||||||
\(45\) | − | 18.0139i | − | 0.400309i | ||||||
\(46\) | 14.0333 | + | 29.3439i | 0.305072 | + | 0.637912i | ||||
\(47\) | 7.39962 | 0.157439 | 0.0787194 | − | 0.996897i | \(-0.474917\pi\) | ||||
0.0787194 | + | 0.996897i | \(0.474917\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 27.0023 | 0.551067 | ||||||||
\(50\) | −15.6352 | −0.312703 | ||||||||
\(51\) | 24.3829i | 0.478095i | ||||||||
\(52\) | 17.4256 | 0.335107 | ||||||||
\(53\) | − | 86.2935i | − | 1.62818i | −0.580739 | − | 0.814090i | \(-0.697236\pi\) | ||
0.580739 | − | 0.814090i | \(-0.302764\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | −37.0255 | −0.673191 | ||||||||
\(56\) | − | 13.2658i | − | 0.236889i | ||||||
\(57\) | − | 25.3697i | − | 0.445082i | ||||||
\(58\) | 1.53081 | 0.0263932 | ||||||||
\(59\) | 87.6447 | 1.48550 | 0.742751 | − | 0.669567i | \(-0.233520\pi\) | ||||
0.742751 | + | 0.669567i | \(0.233520\pi\) | |||||||
\(60\) | 20.8007i | 0.346678i | ||||||||
\(61\) | 0.0196058i | 0.000321407i | 1.00000 | 0.000160703i | \(5.11535e-5\pi\) | |||||
−1.00000 | 0.000160703i | \(0.999949\pi\) | ||||||||
\(62\) | −68.0797 | −1.09806 | ||||||||
\(63\) | − | 14.0705i | − | 0.223341i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 52.3172i | − | 0.804880i | ||||||
\(66\) | 15.1039i | 0.228847i | ||||||||
\(67\) | 104.894i | 1.56558i | 0.622287 | + | 0.782789i | \(0.286203\pi\) | ||||
−0.622287 | + | 0.782789i | \(0.713797\pi\) | |||||||
\(68\) | − | 28.1549i | − | 0.414043i | ||||||
\(69\) | −17.1872 | − | 35.9388i | −0.249090 | − | 0.520853i | ||||
\(70\) | −39.8282 | −0.568974 | ||||||||
\(71\) | −7.78407 | −0.109635 | −0.0548174 | − | 0.998496i | \(-0.517458\pi\) | ||||
−0.0548174 | + | 0.998496i | \(0.517458\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | 19.7199 | 0.270135 | 0.135067 | − | 0.990836i | \(-0.456875\pi\) | ||||
0.135067 | + | 0.990836i | \(0.456875\pi\) | |||||||
\(74\) | 80.5242i | 1.08817i | ||||||||
\(75\) | 19.1491 | 0.255321 | ||||||||
\(76\) | 29.2943i | 0.385452i | ||||||||
\(77\) | −28.9203 | −0.375588 | ||||||||
\(78\) | −21.3419 | −0.273614 | ||||||||
\(79\) | − | 46.2745i | − | 0.585753i | −0.956150 | − | 0.292876i | \(-0.905388\pi\) | ||
0.956150 | − | 0.292876i | \(-0.0946125\pi\) | |||||||
\(80\) | − | 24.0186i | − | 0.300232i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 32.3050 | 0.393963 | ||||||||
\(83\) | 16.9890i | 0.204687i | 0.994749 | + | 0.102344i | \(0.0326341\pi\) | ||||
−0.994749 | + | 0.102344i | \(0.967366\pi\) | |||||||
\(84\) | 16.2472i | 0.193419i | ||||||||
\(85\) | −84.5300 | −0.994471 | ||||||||
\(86\) | 67.8442i | 0.788886i | ||||||||
\(87\) | −1.87485 | −0.0215500 | ||||||||
\(88\) | − | 17.4405i | − | 0.198187i | ||||||
\(89\) | − | 88.0122i | − | 0.988901i | −0.869206 | − | 0.494451i | \(-0.835369\pi\) | ||
0.869206 | − | 0.494451i | \(-0.164631\pi\) | |||||||
\(90\) | − | 25.4755i | − | 0.283062i | ||||||
\(91\) | − | 40.8645i | − | 0.449060i | ||||||
\(92\) | 19.8461 | + | 41.4986i | 0.215718 | + | 0.451072i | ||||
\(93\) | 83.3803 | 0.896563 | ||||||||
\(94\) | 10.4646 | 0.111326 | ||||||||
\(95\) | 87.9510 | 0.925800 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | − | 38.8992i | − | 0.401023i | −0.979691 | − | 0.200511i | \(-0.935740\pi\) | ||
0.979691 | − | 0.200511i | \(-0.0642604\pi\) | |||||||
\(98\) | 38.1870 | 0.389663 | ||||||||
\(99\) | − | 18.4984i | − | 0.186853i | ||||||
\(100\) | −22.1115 | −0.221115 | ||||||||
\(101\) | −5.54609 | −0.0549118 | −0.0274559 | − | 0.999623i | \(-0.508741\pi\) | ||||
−0.0274559 | + | 0.999623i | \(0.508741\pi\) | |||||||
\(102\) | 34.4826i | 0.338064i | ||||||||
\(103\) | − | 40.6192i | − | 0.394361i | −0.980367 | − | 0.197181i | \(-0.936821\pi\) | ||
0.980367 | − | 0.197181i | \(-0.0631785\pi\) | |||||||
\(104\) | 24.6435 | 0.236957 | ||||||||
\(105\) | 48.7794 | 0.464566 | ||||||||
\(106\) | − | 122.037i | − | 1.15130i | ||||||
\(107\) | 124.844i | 1.16677i | 0.812197 | + | 0.583383i | \(0.198271\pi\) | ||||
−0.812197 | + | 0.583383i | \(0.801729\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | − | 77.9912i | − | 0.715515i | −0.933814 | − | 0.357758i | \(-0.883541\pi\) | ||
0.933814 | − | 0.357758i | \(-0.116459\pi\) | |||||||
\(110\) | −52.3620 | −0.476018 | ||||||||
\(111\) | − | 98.6216i | − | 0.888483i | ||||||
\(112\) | − | 18.7607i | − | 0.167506i | ||||||
\(113\) | − | 68.3531i | − | 0.604895i | −0.953166 | − | 0.302448i | \(-0.902196\pi\) | ||
0.953166 | − | 0.302448i | \(-0.0978037\pi\) | |||||||
\(114\) | − | 35.8781i | − | 0.314720i | ||||||
\(115\) | 124.592 | − | 59.5843i | 1.08341 | − | 0.518125i | ||||
\(116\) | 2.16489 | 0.0186628 | ||||||||
\(117\) | 26.1384 | 0.223405 | ||||||||
\(118\) | 123.948 | 1.05041 | ||||||||
\(119\) | −66.0256 | −0.554837 | ||||||||
\(120\) | 29.4166i | 0.245138i | ||||||||
\(121\) | 82.9787 | 0.685774 | ||||||||
\(122\) | 0.0277268i | 0.000227269i | ||||||||
\(123\) | −39.5653 | −0.321669 | ||||||||
\(124\) | −96.2793 | −0.776446 | ||||||||
\(125\) | − | 83.7304i | − | 0.669843i | ||||||
\(126\) | − | 19.8987i | − | 0.157926i | ||||||
\(127\) | −178.475 | −1.40531 | −0.702656 | − | 0.711530i | \(-0.748003\pi\) | ||||
−0.702656 | + | 0.711530i | \(0.748003\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 83.0919i | − | 0.644123i | ||||||
\(130\) | − | 73.9877i | − | 0.569136i | ||||||
\(131\) | −224.058 | −1.71037 | −0.855184 | − | 0.518325i | \(-0.826556\pi\) | ||||
−0.855184 | + | 0.518325i | \(0.826556\pi\) | |||||||
\(132\) | 21.3602i | 0.161819i | ||||||||
\(133\) | 68.6978 | 0.516525 | ||||||||
\(134\) | 148.342i | 1.10703i | ||||||||
\(135\) | 31.2010i | 0.231119i | ||||||||
\(136\) | − | 39.8170i | − | 0.292772i | ||||||
\(137\) | 235.813i | 1.72126i | 0.509227 | + | 0.860632i | \(0.329931\pi\) | ||||
−0.509227 | + | 0.860632i | \(0.670069\pi\) | |||||||
\(138\) | −24.3064 | − | 50.8252i | −0.176133 | − | 0.368298i | ||||
\(139\) | 147.556 | 1.06156 | 0.530778 | − | 0.847511i | \(-0.321900\pi\) | ||||
0.530778 | + | 0.847511i | \(0.321900\pi\) | |||||||
\(140\) | −56.3256 | −0.402326 | ||||||||
\(141\) | −12.8165 | −0.0908973 | ||||||||
\(142\) | −11.0083 | −0.0775235 | ||||||||
\(143\) | − | 53.7244i | − | 0.375695i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | − | 6.49969i | − | 0.0448254i | ||||||
\(146\) | 27.8881 | 0.191014 | ||||||||
\(147\) | −46.7693 | −0.318159 | ||||||||
\(148\) | 113.878i | 0.769449i | ||||||||
\(149\) | 238.929i | 1.60355i | 0.597625 | + | 0.801775i | \(0.296111\pi\) | ||||
−0.597625 | + | 0.801775i | \(0.703889\pi\) | |||||||
\(150\) | 27.0809 | 0.180539 | ||||||||
\(151\) | 196.451 | 1.30100 | 0.650500 | − | 0.759506i | \(-0.274559\pi\) | ||||
0.650500 | + | 0.759506i | \(0.274559\pi\) | |||||||
\(152\) | 41.4285i | 0.272556i | ||||||||
\(153\) | − | 42.2323i | − | 0.276028i | ||||||
\(154\) | −40.8994 | −0.265581 | ||||||||
\(155\) | 289.061i | 1.86491i | ||||||||
\(156\) | −30.1820 | −0.193474 | ||||||||
\(157\) | 189.728i | 1.20846i | 0.796811 | + | 0.604229i | \(0.206519\pi\) | ||||
−0.796811 | + | 0.604229i | \(0.793481\pi\) | |||||||
\(158\) | − | 65.4420i | − | 0.414190i | ||||||
\(159\) | 149.465i | 0.940030i | ||||||||
\(160\) | − | 33.9674i | − | 0.212296i | ||||||
\(161\) | 97.3177 | − | 46.5408i | 0.604458 | − | 0.289073i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −76.3170 | −0.468202 | −0.234101 | − | 0.972212i | \(-0.575215\pi\) | ||||
−0.234101 | + | 0.972212i | \(0.575215\pi\) | |||||||
\(164\) | 45.6861 | 0.278574 | ||||||||
\(165\) | 64.1300 | 0.388667 | ||||||||
\(166\) | 24.0261i | 0.144736i | ||||||||
\(167\) | −145.600 | −0.871856 | −0.435928 | − | 0.899982i | \(-0.643580\pi\) | ||||
−0.435928 | + | 0.899982i | \(0.643580\pi\) | |||||||
\(168\) | 22.9771i | 0.136768i | ||||||||
\(169\) | −93.0872 | −0.550812 | ||||||||
\(170\) | −119.544 | −0.703197 | ||||||||
\(171\) | 43.9415i | 0.256968i | ||||||||
\(172\) | 95.9462i | 0.557827i | ||||||||
\(173\) | −297.300 | −1.71849 | −0.859247 | − | 0.511560i | \(-0.829068\pi\) | ||||
−0.859247 | + | 0.511560i | \(0.829068\pi\) | |||||||
\(174\) | −2.65143 | −0.0152381 | ||||||||
\(175\) | 51.8533i | 0.296304i | ||||||||
\(176\) | − | 24.6646i | − | 0.140140i | ||||||
\(177\) | −151.805 | −0.857656 | ||||||||
\(178\) | − | 124.468i | − | 0.699259i | ||||||
\(179\) | −215.202 | −1.20225 | −0.601123 | − | 0.799157i | \(-0.705280\pi\) | ||||
−0.601123 | + | 0.799157i | \(0.705280\pi\) | |||||||
\(180\) | − | 36.0279i | − | 0.200155i | ||||||
\(181\) | 81.8052i | 0.451962i | 0.974132 | + | 0.225981i | \(0.0725588\pi\) | ||||
−0.974132 | + | 0.225981i | \(0.927441\pi\) | |||||||
\(182\) | − | 57.7911i | − | 0.317534i | ||||||
\(183\) | − | 0.0339583i | − | 0.000185564i | ||||||
\(184\) | 28.0666 | + | 58.6879i | 0.152536 | + | 0.318956i | ||||
\(185\) | 341.900 | 1.84811 | ||||||||
\(186\) | 117.918 | 0.633965 | ||||||||
\(187\) | −86.8036 | −0.464190 | ||||||||
\(188\) | 14.7992 | 0.0787194 | ||||||||
\(189\) | 24.3708i | 0.128946i | ||||||||
\(190\) | 124.382 | 0.654640 | ||||||||
\(191\) | 124.361i | 0.651106i | 0.945524 | + | 0.325553i | \(0.105550\pi\) | ||||
−0.945524 | + | 0.325553i | \(0.894450\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | −346.137 | −1.79346 | −0.896729 | − | 0.442581i | \(-0.854063\pi\) | ||||
−0.896729 | + | 0.442581i | \(0.854063\pi\) | |||||||
\(194\) | − | 55.0118i | − | 0.283566i | ||||||
\(195\) | 90.6161i | 0.464698i | ||||||||
\(196\) | 54.0046 | 0.275534 | ||||||||
\(197\) | 213.943 | 1.08601 | 0.543003 | − | 0.839731i | \(-0.317287\pi\) | ||||
0.543003 | + | 0.839731i | \(0.317287\pi\) | |||||||
\(198\) | − | 26.1607i | − | 0.132125i | ||||||
\(199\) | − | 374.684i | − | 1.88284i | −0.337243 | − | 0.941418i | \(-0.609494\pi\) | ||
0.337243 | − | 0.941418i | \(-0.390506\pi\) | |||||||
\(200\) | −31.2703 | −0.156352 | ||||||||
\(201\) | − | 181.681i | − | 0.903887i | ||||||
\(202\) | −7.84336 | −0.0388285 | ||||||||
\(203\) | − | 5.07685i | − | 0.0250091i | ||||||
\(204\) | 48.7657i | 0.239048i | ||||||||
\(205\) | − | 137.164i | − | 0.669095i | ||||||
\(206\) | − | 57.4442i | − | 0.278855i | ||||||
\(207\) | 29.7691 | + | 62.2479i | 0.143812 | + | 0.300714i | ||||
\(208\) | 34.8512 | 0.167554 | ||||||||
\(209\) | 90.3166 | 0.432137 | ||||||||
\(210\) | 68.9845 | 0.328498 | ||||||||
\(211\) | −185.158 | −0.877524 | −0.438762 | − | 0.898603i | \(-0.644583\pi\) | ||||
−0.438762 | + | 0.898603i | \(0.644583\pi\) | |||||||
\(212\) | − | 172.587i | − | 0.814090i | ||||||
\(213\) | 13.4824 | 0.0632977 | ||||||||
\(214\) | 176.556i | 0.825028i | ||||||||
\(215\) | 288.061 | 1.33982 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 225.783i | 1.04048i | ||||||||
\(218\) | − | 110.296i | − | 0.505946i | ||||||
\(219\) | −34.1558 | −0.155962 | ||||||||
\(220\) | −74.0510 | −0.336595 | ||||||||
\(221\) | − | 122.654i | − | 0.554995i | ||||||
\(222\) | − | 139.472i | − | 0.628253i | ||||||
\(223\) | 290.940 | 1.30467 | 0.652333 | − | 0.757933i | \(-0.273790\pi\) | ||||
0.652333 | + | 0.757933i | \(0.273790\pi\) | |||||||
\(224\) | − | 26.5316i | − | 0.118445i | ||||||
\(225\) | −33.1672 | −0.147410 | ||||||||
\(226\) | − | 96.6659i | − | 0.427725i | ||||||
\(227\) | − | 0.735161i | − | 0.00323860i | −0.999999 | − | 0.00161930i | \(-0.999485\pi\) | ||
0.999999 | − | 0.00161930i | \(-0.000515439\pi\) | |||||||
\(228\) | − | 50.7393i | − | 0.222541i | ||||||
\(229\) | 145.885i | 0.637054i | 0.947914 | + | 0.318527i | \(0.103188\pi\) | ||||
−0.947914 | + | 0.318527i | \(0.896812\pi\) | |||||||
\(230\) | 176.200 | − | 84.2650i | 0.766086 | − | 0.366369i | ||||
\(231\) | 50.0914 | 0.216846 | ||||||||
\(232\) | 3.06161 | 0.0131966 | ||||||||
\(233\) | 225.010 | 0.965708 | 0.482854 | − | 0.875701i | \(-0.339600\pi\) | ||||
0.482854 | + | 0.875701i | \(0.339600\pi\) | |||||||
\(234\) | 36.9653 | 0.157971 | ||||||||
\(235\) | − | 44.4321i | − | 0.189073i | ||||||
\(236\) | 175.289 | 0.742751 | ||||||||
\(237\) | 80.1498i | 0.338185i | ||||||||
\(238\) | −93.3743 | −0.392329 | ||||||||
\(239\) | −211.317 | −0.884171 | −0.442086 | − | 0.896973i | \(-0.645761\pi\) | ||||
−0.442086 | + | 0.896973i | \(0.645761\pi\) | |||||||
\(240\) | 41.6014i | 0.173339i | ||||||||
\(241\) | − | 158.875i | − | 0.659231i | −0.944115 | − | 0.329616i | \(-0.893081\pi\) | ||
0.944115 | − | 0.329616i | \(-0.106919\pi\) | |||||||
\(242\) | 117.350 | 0.484915 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0.0392116i | 0.000160703i | ||||||||
\(245\) | − | 162.139i | − | 0.661792i | ||||||
\(246\) | −55.9538 | −0.227455 | ||||||||
\(247\) | 127.618i | 0.516671i | ||||||||
\(248\) | −136.159 | −0.549030 | ||||||||
\(249\) | − | 29.4259i | − | 0.118176i | ||||||
\(250\) | − | 118.413i | − | 0.473650i | ||||||
\(251\) | − | 322.852i | − | 1.28626i | −0.765756 | − | 0.643131i | \(-0.777635\pi\) | ||
0.765756 | − | 0.643131i | \(-0.222365\pi\) | |||||||
\(252\) | − | 28.1410i | − | 0.111671i | ||||||
\(253\) | 127.943 | − | 61.1869i | 0.505704 | − | 0.241846i | ||||
\(254\) | −252.401 | −0.993706 | ||||||||
\(255\) | 146.410 | 0.574158 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −349.762 | −1.36094 | −0.680471 | − | 0.732775i | \(-0.738225\pi\) | ||||
−0.680471 | + | 0.732775i | \(0.738225\pi\) | |||||||
\(258\) | − | 117.510i | − | 0.455464i | ||||||
\(259\) | 267.055 | 1.03110 | ||||||||
\(260\) | − | 104.634i | − | 0.402440i | ||||||
\(261\) | 3.24733 | 0.0124419 | ||||||||
\(262\) | −316.866 | −1.20941 | ||||||||
\(263\) | − | 262.536i | − | 0.998237i | −0.866534 | − | 0.499118i | \(-0.833657\pi\) | ||
0.866534 | − | 0.499118i | \(-0.166343\pi\) | |||||||
\(264\) | 30.2078i | 0.114424i | ||||||||
\(265\) | −518.162 | −1.95533 | ||||||||
\(266\) | 97.1533 | 0.365238 | ||||||||
\(267\) | 152.442i | 0.570942i | ||||||||
\(268\) | 209.787i | 0.782789i | ||||||||
\(269\) | 76.8118 | 0.285546 | 0.142773 | − | 0.989755i | \(-0.454398\pi\) | ||||
0.142773 | + | 0.989755i | \(0.454398\pi\) | |||||||
\(270\) | 44.1249i | 0.163426i | ||||||||
\(271\) | 371.450 | 1.37067 | 0.685333 | − | 0.728230i | \(-0.259657\pi\) | ||||
0.685333 | + | 0.728230i | \(0.259657\pi\) | |||||||
\(272\) | − | 56.3098i | − | 0.207021i | ||||||
\(273\) | 70.7794i | 0.259265i | ||||||||
\(274\) | 333.490i | 1.21712i | ||||||||
\(275\) | 68.1712i | 0.247895i | ||||||||
\(276\) | −34.3744 | − | 71.8777i | −0.124545 | − | 0.260426i | ||||
\(277\) | 259.023 | 0.935102 | 0.467551 | − | 0.883966i | \(-0.345136\pi\) | ||||
0.467551 | + | 0.883966i | \(0.345136\pi\) | |||||||
\(278\) | 208.676 | 0.750633 | ||||||||
\(279\) | −144.419 | −0.517631 | ||||||||
\(280\) | −79.6564 | −0.284487 | ||||||||
\(281\) | − | 250.908i | − | 0.892912i | −0.894806 | − | 0.446456i | \(-0.852686\pi\) | ||
0.894806 | − | 0.446456i | \(-0.147314\pi\) | |||||||
\(282\) | −18.1253 | −0.0642741 | ||||||||
\(283\) | 116.602i | 0.412021i | 0.978550 | + | 0.206011i | \(0.0660481\pi\) | ||||
−0.978550 | + | 0.206011i | \(0.933952\pi\) | |||||||
\(284\) | −15.5681 | −0.0548174 | ||||||||
\(285\) | −152.336 | −0.534511 | ||||||||
\(286\) | − | 75.9777i | − | 0.265656i | ||||||
\(287\) | − | 107.138i | − | 0.373303i | ||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 90.8255 | 0.314275 | ||||||||
\(290\) | − | 9.19195i | − | 0.0316964i | ||||||
\(291\) | 67.3754i | 0.231531i | ||||||||
\(292\) | 39.4397 | 0.135067 | ||||||||
\(293\) | − | 158.185i | − | 0.539881i | −0.962877 | − | 0.269940i | \(-0.912996\pi\) | ||
0.962877 | − | 0.269940i | \(-0.0870040\pi\) | |||||||
\(294\) | −66.1418 | −0.224972 | ||||||||
\(295\) | − | 526.275i | − | 1.78398i | ||||||
\(296\) | 161.048i | 0.544083i | ||||||||
\(297\) | 32.0402i | 0.107880i | ||||||||
\(298\) | 337.897i | 1.13388i | ||||||||
\(299\) | 86.4574 | + | 180.784i | 0.289155 | + | 0.604630i | ||||
\(300\) | 38.2982 | 0.127661 | ||||||||
\(301\) | 225.002 | 0.747515 | ||||||||
\(302\) | 277.824 | 0.919946 | ||||||||
\(303\) | 9.60611 | 0.0317033 | ||||||||
\(304\) | 58.5887i | 0.192726i | ||||||||
\(305\) | 0.117726 | 0.000385987 | ||||||||
\(306\) | − | 59.7255i | − | 0.195182i | ||||||
\(307\) | −76.3951 | −0.248844 | −0.124422 | − | 0.992229i | \(-0.539708\pi\) | ||||
−0.124422 | + | 0.992229i | \(0.539708\pi\) | |||||||
\(308\) | −57.8405 | −0.187794 | ||||||||
\(309\) | 70.3545i | 0.227685i | ||||||||
\(310\) | 408.794i | 1.31869i | ||||||||
\(311\) | −41.9614 | −0.134924 | −0.0674620 | − | 0.997722i | \(-0.521490\pi\) | ||||
−0.0674620 | + | 0.997722i | \(0.521490\pi\) | |||||||
\(312\) | −42.6838 | −0.136807 | ||||||||
\(313\) | 148.033i | 0.472947i | 0.971638 | + | 0.236474i | \(0.0759917\pi\) | ||||
−0.971638 | + | 0.236474i | \(0.924008\pi\) | |||||||
\(314\) | 268.316i | 0.854509i | ||||||||
\(315\) | −84.4884 | −0.268217 | ||||||||
\(316\) | − | 92.5490i | − | 0.292876i | ||||||
\(317\) | −569.463 | −1.79641 | −0.898206 | − | 0.439574i | \(-0.855129\pi\) | ||||
−0.898206 | + | 0.439574i | \(0.855129\pi\) | |||||||
\(318\) | 211.375i | 0.664701i | ||||||||
\(319\) | − | 6.67450i | − | 0.0209232i | ||||||
\(320\) | − | 48.0371i | − | 0.150116i | ||||||
\(321\) | − | 216.236i | − | 0.673633i | ||||||
\(322\) | 137.628 | − | 65.8186i | 0.427416 | − | 0.204406i | ||||
\(323\) | 206.195 | 0.638374 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −96.3263 | −0.296389 | ||||||||
\(326\) | −107.929 | −0.331069 | ||||||||
\(327\) | 135.085i | 0.413103i | ||||||||
\(328\) | 64.6099 | 0.196981 | ||||||||
\(329\) | − | 34.7055i | − | 0.105488i | ||||||
\(330\) | 90.6936 | 0.274829 | ||||||||
\(331\) | −222.086 | −0.670955 | −0.335478 | − | 0.942048i | \(-0.608898\pi\) | ||||
−0.335478 | + | 0.942048i | \(0.608898\pi\) | |||||||
\(332\) | 33.9781i | 0.102344i | ||||||||
\(333\) | 170.818i | 0.512966i | ||||||||
\(334\) | −205.909 | −0.616495 | ||||||||
\(335\) | 629.849 | 1.88015 | ||||||||
\(336\) | 32.4945i | 0.0967097i | ||||||||
\(337\) | 601.218i | 1.78403i | 0.452006 | + | 0.892015i | \(0.350708\pi\) | ||||
−0.452006 | + | 0.892015i | \(0.649292\pi\) | |||||||
\(338\) | −131.645 | −0.389483 | ||||||||
\(339\) | 118.391i | 0.349236i | ||||||||
\(340\) | −169.060 | −0.497235 | ||||||||
\(341\) | 296.836i | 0.870487i | ||||||||
\(342\) | 62.1427i | 0.181704i | ||||||||
\(343\) | − | 356.464i | − | 1.03925i | ||||||
\(344\) | 135.688i | 0.394443i | ||||||||
\(345\) | −215.800 | + | 103.203i | −0.625507 | + | 0.299139i | ||||
\(346\) | −420.445 | −1.21516 | ||||||||
\(347\) | −65.1900 | −0.187867 | −0.0939337 | − | 0.995578i | \(-0.529944\pi\) | ||||
−0.0939337 | + | 0.995578i | \(0.529944\pi\) | |||||||
\(348\) | −3.74970 | −0.0107750 | ||||||||
\(349\) | −529.604 | −1.51749 | −0.758746 | − | 0.651387i | \(-0.774187\pi\) | ||||
−0.758746 | + | 0.651387i | \(0.774187\pi\) | |||||||
\(350\) | 73.3316i | 0.209519i | ||||||||
\(351\) | −45.2730 | −0.128983 | ||||||||
\(352\) | − | 34.8810i | − | 0.0990937i | ||||||
\(353\) | 403.821 | 1.14397 | 0.571984 | − | 0.820265i | \(-0.306174\pi\) | ||||
0.571984 | + | 0.820265i | \(0.306174\pi\) | |||||||
\(354\) | −214.685 | −0.606454 | ||||||||
\(355\) | 46.7405i | 0.131664i | ||||||||
\(356\) | − | 176.024i | − | 0.494451i | ||||||
\(357\) | 114.360 | 0.320335 | ||||||||
\(358\) | −304.341 | −0.850116 | ||||||||
\(359\) | − | 244.100i | − | 0.679945i | −0.940435 | − | 0.339972i | \(-0.889582\pi\) | ||
0.940435 | − | 0.339972i | \(-0.110418\pi\) | |||||||
\(360\) | − | 50.9511i | − | 0.141531i | ||||||
\(361\) | 146.460 | 0.405707 | ||||||||
\(362\) | 115.690i | 0.319586i | ||||||||
\(363\) | −143.723 | −0.395932 | ||||||||
\(364\) | − | 81.7290i | − | 0.224530i | ||||||
\(365\) | − | 118.411i | − | 0.324413i | ||||||
\(366\) | − | 0.0480242i | − | 0.000131214i | ||||||
\(367\) | − | 653.421i | − | 1.78044i | −0.455532 | − | 0.890219i | \(-0.650551\pi\) | ||
0.455532 | − | 0.890219i | \(-0.349449\pi\) | |||||||
\(368\) | 39.6922 | + | 82.9972i | 0.107859 | + | 0.225536i | ||||
\(369\) | 68.5292 | 0.185716 | ||||||||
\(370\) | 483.519 | 1.30681 | ||||||||
\(371\) | −404.731 | −1.09092 | ||||||||
\(372\) | 166.761 | 0.448281 | ||||||||
\(373\) | 496.872i | 1.33210i | 0.745909 | + | 0.666048i | \(0.232016\pi\) | ||||
−0.745909 | + | 0.666048i | \(0.767984\pi\) | |||||||
\(374\) | −122.759 | −0.328232 | ||||||||
\(375\) | 145.025i | 0.386734i | ||||||||
\(376\) | 20.9293 | 0.0556630 | ||||||||
\(377\) | 9.43111 | 0.0250162 | ||||||||
\(378\) | 34.4656i | 0.0911788i | ||||||||
\(379\) | − | 469.320i | − | 1.23831i | −0.785269 | − | 0.619155i | \(-0.787475\pi\) | ||
0.785269 | − | 0.619155i | \(-0.212525\pi\) | |||||||
\(380\) | 175.902 | 0.462900 | ||||||||
\(381\) | 309.127 | 0.811357 | ||||||||
\(382\) | 175.873i | 0.460401i | ||||||||
\(383\) | 135.332i | 0.353347i | 0.984270 | + | 0.176673i | \(0.0565336\pi\) | ||||
−0.984270 | + | 0.176673i | \(0.943466\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | 173.656i | 0.451054i | ||||||||
\(386\) | −489.512 | −1.26817 | ||||||||
\(387\) | 143.919i | 0.371885i | ||||||||
\(388\) | − | 77.7984i | − | 0.200511i | ||||||
\(389\) | 455.240i | 1.17028i | 0.810931 | + | 0.585142i | \(0.198961\pi\) | ||||
−0.810931 | + | 0.585142i | \(0.801039\pi\) | |||||||
\(390\) | 128.150i | 0.328591i | ||||||||
\(391\) | 292.097 | − | 139.691i | 0.747051 | − | 0.357266i | ||||
\(392\) | 76.3740 | 0.194832 | ||||||||
\(393\) | 388.080 | 0.987481 | ||||||||
\(394\) | 302.561 | 0.767922 | ||||||||
\(395\) | −277.862 | −0.703447 | ||||||||
\(396\) | − | 36.9969i | − | 0.0934264i | ||||||
\(397\) | 368.101 | 0.927207 | 0.463603 | − | 0.886043i | \(-0.346556\pi\) | ||||
0.463603 | + | 0.886043i | \(0.346556\pi\) | |||||||
\(398\) | − | 529.884i | − | 1.33137i | ||||||
\(399\) | −118.988 | −0.298216 | ||||||||
\(400\) | −44.2229 | −0.110557 | ||||||||
\(401\) | 442.864i | 1.10440i | 0.833712 | + | 0.552200i | \(0.186212\pi\) | ||||
−0.833712 | + | 0.552200i | \(0.813788\pi\) | |||||||
\(402\) | − | 256.936i | − | 0.639144i | ||||||
\(403\) | −419.431 | −1.04077 | ||||||||
\(404\) | −11.0922 | −0.0274559 | ||||||||
\(405\) | − | 54.0418i | − | 0.133436i | ||||||
\(406\) | − | 7.17975i | − | 0.0176841i | ||||||
\(407\) | 351.096 | 0.862643 | ||||||||
\(408\) | 68.9651i | 0.169032i | ||||||||
\(409\) | 120.960 | 0.295747 | 0.147873 | − | 0.989006i | \(-0.452757\pi\) | ||||
0.147873 | + | 0.989006i | \(0.452757\pi\) | |||||||
\(410\) | − | 193.980i | − | 0.473121i | ||||||
\(411\) | − | 408.441i | − | 0.993773i | ||||||
\(412\) | − | 81.2384i | − | 0.197181i | ||||||
\(413\) | − | 411.069i | − | 0.995323i | ||||||
\(414\) | 42.0999 | + | 88.0318i | 0.101691 | + | 0.212637i | ||||
\(415\) | 102.013 | 0.245815 | ||||||||
\(416\) | 49.2870 | 0.118478 | ||||||||
\(417\) | −255.575 | −0.612889 | ||||||||
\(418\) | 127.727 | 0.305567 | ||||||||
\(419\) | 546.060i | 1.30325i | 0.758543 | + | 0.651623i | \(0.225911\pi\) | ||||
−0.758543 | + | 0.651623i | \(0.774089\pi\) | |||||||
\(420\) | 97.5588 | 0.232283 | ||||||||
\(421\) | − | 794.995i | − | 1.88835i | −0.329447 | − | 0.944174i | \(-0.606862\pi\) | ||
0.329447 | − | 0.944174i | \(-0.393138\pi\) | |||||||
\(422\) | −261.852 | −0.620503 | ||||||||
\(423\) | 22.1989 | 0.0524796 | ||||||||
\(424\) | − | 244.075i | − | 0.575648i | ||||||
\(425\) | 155.636i | 0.366203i | ||||||||
\(426\) | 19.0670 | 0.0447582 | ||||||||
\(427\) | 0.0919546 | 0.000215350 | ||||||||
\(428\) | 249.688i | 0.583383i | ||||||||
\(429\) | 93.0533i | 0.216907i | ||||||||
\(430\) | 407.380 | 0.947396 | ||||||||
\(431\) | − | 461.422i | − | 1.07058i | −0.844667 | − | 0.535292i | \(-0.820201\pi\) | ||
0.844667 | − | 0.535292i | \(-0.179799\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 583.616i | 1.34784i | 0.738803 | + | 0.673921i | \(0.235391\pi\) | ||||
−0.738803 | + | 0.673921i | \(0.764609\pi\) | |||||||
\(434\) | 319.306i | 0.735727i | ||||||||
\(435\) | 11.2578i | 0.0258800i | ||||||||
\(436\) | − | 155.982i | − | 0.357758i | ||||||
\(437\) | −303.919 | + | 145.345i | −0.695466 | + | 0.332596i | ||||
\(438\) | −48.3036 | −0.110282 | ||||||||
\(439\) | 517.764 | 1.17942 | 0.589708 | − | 0.807617i | \(-0.299243\pi\) | ||||
0.589708 | + | 0.807617i | \(0.299243\pi\) | |||||||
\(440\) | −104.724 | −0.238009 | ||||||||
\(441\) | 81.0069 | 0.183689 | ||||||||
\(442\) | − | 173.459i | − | 0.392441i | ||||||
\(443\) | −50.3232 | −0.113596 | −0.0567981 | − | 0.998386i | \(-0.518089\pi\) | ||||
−0.0567981 | + | 0.998386i | \(0.518089\pi\) | |||||||
\(444\) | − | 197.243i | − | 0.444242i | ||||||
\(445\) | −528.482 | −1.18760 | ||||||||
\(446\) | 411.452 | 0.922538 | ||||||||
\(447\) | − | 413.837i | − | 0.925811i | ||||||
\(448\) | − | 37.5214i | − | 0.0837531i | ||||||
\(449\) | −495.693 | −1.10399 | −0.551997 | − | 0.833846i | \(-0.686134\pi\) | ||||
−0.551997 | + | 0.833846i | \(0.686134\pi\) | |||||||
\(450\) | −46.9055 | −0.104234 | ||||||||
\(451\) | − | 140.854i | − | 0.312314i | ||||||
\(452\) | − | 136.706i | − | 0.302448i | ||||||
\(453\) | −340.263 | −0.751133 | ||||||||
\(454\) | − | 1.03968i | − | 0.00229003i | ||||||
\(455\) | −245.377 | −0.539289 | ||||||||
\(456\) | − | 71.7562i | − | 0.157360i | ||||||
\(457\) | 184.249i | 0.403170i | 0.979471 | + | 0.201585i | \(0.0646092\pi\) | ||||
−0.979471 | + | 0.201585i | \(0.935391\pi\) | |||||||
\(458\) | 206.313i | 0.450465i | ||||||||
\(459\) | 73.1486i | 0.159365i | ||||||||
\(460\) | 249.184 | − | 119.169i | 0.541705 | − | 0.259062i | ||||
\(461\) | 160.194 | 0.347491 | 0.173746 | − | 0.984791i | \(-0.444413\pi\) | ||||
0.173746 | + | 0.984791i | \(0.444413\pi\) | |||||||
\(462\) | 70.8399 | 0.153333 | ||||||||
\(463\) | −458.195 | −0.989621 | −0.494811 | − | 0.869001i | \(-0.664763\pi\) | ||||
−0.494811 | + | 0.869001i | \(0.664763\pi\) | |||||||
\(464\) | 4.32977 | 0.00933141 | ||||||||
\(465\) | − | 500.669i | − | 1.07671i | ||||||
\(466\) | 318.212 | 0.682859 | ||||||||
\(467\) | 804.257i | 1.72218i | 0.508455 | + | 0.861089i | \(0.330217\pi\) | ||||
−0.508455 | + | 0.861089i | \(0.669783\pi\) | |||||||
\(468\) | 52.2768 | 0.111702 | ||||||||
\(469\) | 491.969 | 1.04898 | ||||||||
\(470\) | − | 62.8364i | − | 0.133695i | ||||||
\(471\) | − | 328.618i | − | 0.697703i | ||||||
\(472\) | 247.897 | 0.525205 | ||||||||
\(473\) | 295.809 | 0.625389 | ||||||||
\(474\) | 113.349i | 0.239133i | ||||||||
\(475\) | − | 161.935i | − | 0.340916i | ||||||
\(476\) | −132.051 | −0.277419 | ||||||||
\(477\) | − | 258.881i | − | 0.542726i | ||||||
\(478\) | −298.847 | −0.625204 | ||||||||
\(479\) | − | 396.331i | − | 0.827414i | −0.910410 | − | 0.413707i | \(-0.864234\pi\) | ||
0.910410 | − | 0.413707i | \(-0.135766\pi\) | |||||||
\(480\) | 58.8332i | 0.122569i | ||||||||
\(481\) | 496.100i | 1.03139i | ||||||||
\(482\) | − | 224.683i | − | 0.466147i | ||||||
\(483\) | −168.559 | + | 80.6110i | −0.348984 | + | 0.166896i | ||||
\(484\) | 165.957 | 0.342887 | ||||||||
\(485\) | −233.576 | −0.481600 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −636.665 | −1.30732 | −0.653660 | − | 0.756789i | \(-0.726767\pi\) | ||||
−0.653660 | + | 0.756789i | \(0.726767\pi\) | |||||||
\(488\) | 0.0554536i | 0.000113634i | ||||||||
\(489\) | 132.185 | 0.270317 | ||||||||
\(490\) | − | 229.299i | − | 0.467958i | ||||||
\(491\) | 928.442 | 1.89092 | 0.945461 | − | 0.325736i | \(-0.105612\pi\) | ||||
0.945461 | + | 0.325736i | \(0.105612\pi\) | |||||||
\(492\) | −79.1307 | −0.160835 | ||||||||
\(493\) | − | 15.2380i | − | 0.0309088i | ||||||
\(494\) | 180.479i | 0.365342i | ||||||||
\(495\) | −111.076 | −0.224397 | ||||||||
\(496\) | −192.559 | −0.388223 | ||||||||
\(497\) | 36.5086i | 0.0734580i | ||||||||
\(498\) | − | 41.6144i | − | 0.0835631i | ||||||
\(499\) | 457.999 | 0.917834 | 0.458917 | − | 0.888479i | \(-0.348238\pi\) | ||||
0.458917 | + | 0.888479i | \(0.348238\pi\) | |||||||
\(500\) | − | 167.461i | − | 0.334921i | ||||||
\(501\) | 252.186 | 0.503366 | ||||||||
\(502\) | − | 456.581i | − | 0.909524i | ||||||
\(503\) | − | 9.28932i | − | 0.0184678i | −0.999957 | − | 0.00923392i | \(-0.997061\pi\) | ||
0.999957 | − | 0.00923392i | \(-0.00293929\pi\) | |||||||
\(504\) | − | 39.7974i | − | 0.0789631i | ||||||
\(505\) | 33.3023i | 0.0659451i | ||||||||
\(506\) | 180.939 | − | 86.5314i | 0.357587 | − | 0.171011i | ||||
\(507\) | 161.232 | 0.318011 | ||||||||
\(508\) | −356.949 | −0.702656 | ||||||||
\(509\) | −294.128 | −0.577855 | −0.288928 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288928 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(510\) | 207.055 | 0.405991 | ||||||||
\(511\) | − | 92.4895i | − | 0.180997i | ||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 76.1090i | − | 0.148361i | ||||||
\(514\) | −494.638 | −0.962331 | ||||||||
\(515\) | −243.904 | −0.473600 | ||||||||
\(516\) | − | 166.184i | − | 0.322061i | ||||||
\(517\) | − | 45.6271i | − | 0.0882536i | ||||||
\(518\) | 377.672 | 0.729097 | ||||||||
\(519\) | 514.938 | 0.992174 | ||||||||
\(520\) | − | 147.975i | − | 0.284568i | ||||||
\(521\) | − | 235.388i | − | 0.451801i | −0.974150 | − | 0.225901i | \(-0.927468\pi\) | ||
0.974150 | − | 0.225901i | \(-0.0725325\pi\) | |||||||
\(522\) | 4.59242 | 0.00879774 | ||||||||
\(523\) | 512.874i | 0.980639i | 0.871543 | + | 0.490319i | \(0.163120\pi\) | ||||
−0.871543 | + | 0.490319i | \(0.836880\pi\) | |||||||
\(524\) | −448.116 | −0.855184 | ||||||||
\(525\) | − | 89.8125i | − | 0.171071i | ||||||
\(526\) | − | 371.282i | − | 0.705860i | ||||||
\(527\) | 677.683i | 1.28593i | ||||||||
\(528\) | 42.7203i | 0.0809097i | ||||||||
\(529\) | −332.066 | + | 411.792i | −0.627725 | + | 0.778435i | ||||
\(530\) | −732.791 | −1.38262 | ||||||||
\(531\) | 262.934 | 0.495168 | ||||||||
\(532\) | 137.396 | 0.258262 | ||||||||
\(533\) | 199.027 | 0.373409 | ||||||||
\(534\) | 215.585i | 0.403717i | ||||||||
\(535\) | 749.643 | 1.40120 | ||||||||
\(536\) | 296.684i | 0.553515i | ||||||||
\(537\) | 372.741 | 0.694117 | ||||||||
\(538\) | 108.628 | 0.201911 | ||||||||
\(539\) | − | 166.500i | − | 0.308905i | ||||||
\(540\) | 62.4021i | 0.115559i | ||||||||
\(541\) | −221.929 | −0.410220 | −0.205110 | − | 0.978739i | \(-0.565755\pi\) | ||||
−0.205110 | + | 0.978739i | \(0.565755\pi\) | |||||||
\(542\) | 525.310 | 0.969207 | ||||||||
\(543\) | − | 141.691i | − | 0.260941i | ||||||
\(544\) | − | 79.6341i | − | 0.146386i | ||||||
\(545\) | −468.309 | −0.859283 | ||||||||
\(546\) | 100.097i | 0.183328i | ||||||||
\(547\) | 378.530 | 0.692011 | 0.346006 | − | 0.938232i | \(-0.387538\pi\) | ||||
0.346006 | + | 0.938232i | \(0.387538\pi\) | |||||||
\(548\) | 471.627i | 0.860632i | ||||||||
\(549\) | 0.0588174i | 0.000107136i | ||||||||
\(550\) | 96.4086i | 0.175288i | ||||||||
\(551\) | 15.8547i | 0.0287745i | ||||||||
\(552\) | −48.6128 | − | 101.650i | −0.0880666 | − | 0.184149i | ||||
\(553\) | −217.035 | −0.392469 | ||||||||
\(554\) | 366.314 | 0.661217 | ||||||||
\(555\) | −592.188 | −1.06700 | ||||||||
\(556\) | 295.112 | 0.530778 | ||||||||
\(557\) | 256.556i | 0.460603i | 0.973119 | + | 0.230301i | \(0.0739712\pi\) | ||||
−0.973119 | + | 0.230301i | \(0.926029\pi\) | |||||||
\(558\) | −204.239 | −0.366020 | ||||||||
\(559\) | 417.980i | 0.747728i | ||||||||
\(560\) | −112.651 | −0.201163 | ||||||||
\(561\) | 150.348 | 0.268000 | ||||||||
\(562\) | − | 354.838i | − | 0.631384i | ||||||
\(563\) | − | 298.314i | − | 0.529864i | −0.964267 | − | 0.264932i | \(-0.914650\pi\) | ||
0.964267 | − | 0.264932i | \(-0.0853496\pi\) | |||||||
\(564\) | −25.6330 | −0.0454486 | ||||||||
\(565\) | −410.436 | −0.726436 | ||||||||
\(566\) | 164.900i | 0.291343i | ||||||||
\(567\) | − | 42.2115i | − | 0.0744472i | ||||||
\(568\) | −22.0167 | −0.0387617 | ||||||||
\(569\) | − | 361.429i | − | 0.635200i | −0.948225 | − | 0.317600i | \(-0.897123\pi\) | ||
0.948225 | − | 0.317600i | \(-0.102877\pi\) | |||||||
\(570\) | −215.435 | −0.377956 | ||||||||
\(571\) | 898.203i | 1.57303i | 0.617568 | + | 0.786517i | \(0.288118\pi\) | ||||
−0.617568 | + | 0.786517i | \(0.711882\pi\) | |||||||
\(572\) | − | 107.449i | − | 0.187847i | ||||||
\(573\) | − | 215.400i | − | 0.375916i | ||||||
\(574\) | − | 151.516i | − | 0.263965i | ||||||
\(575\) | −109.706 | − | 229.399i | −0.190794 | − | 0.398954i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | −573.615 | −0.994133 | −0.497067 | − | 0.867712i | \(-0.665590\pi\) | ||||
−0.497067 | + | 0.867712i | \(0.665590\pi\) | |||||||
\(578\) | 128.447 | 0.222226 | ||||||||
\(579\) | 599.527 | 1.03545 | ||||||||
\(580\) | − | 12.9994i | − | 0.0224127i | ||||||
\(581\) | 79.6814 | 0.137145 | ||||||||
\(582\) | 95.2832i | 0.163717i | ||||||||
\(583\) | −532.098 | −0.912690 | ||||||||
\(584\) | 55.7762 | 0.0955071 | ||||||||
\(585\) | − | 156.952i | − | 0.268293i | ||||||
\(586\) | − | 223.707i | − | 0.381753i | ||||||
\(587\) | −223.626 | −0.380965 | −0.190482 | − | 0.981691i | \(-0.561005\pi\) | ||||
−0.190482 | + | 0.981691i | \(0.561005\pi\) | |||||||
\(588\) | −93.5387 | −0.159079 | ||||||||
\(589\) | − | 705.110i | − | 1.19713i | ||||||
\(590\) | − | 744.265i | − | 1.26147i | ||||||
\(591\) | −370.560 | −0.627006 | ||||||||
\(592\) | 227.757i | 0.384725i | ||||||||
\(593\) | −278.419 | −0.469509 | −0.234754 | − | 0.972055i | \(-0.575429\pi\) | ||||
−0.234754 | + | 0.972055i | \(0.575429\pi\) | |||||||
\(594\) | 45.3117i | 0.0762824i | ||||||||
\(595\) | 396.460i | 0.666320i | ||||||||
\(596\) | 477.858i | 0.801775i | ||||||||
\(597\) | 648.972i | 1.08706i | ||||||||
\(598\) | 122.269 | + | 255.668i | 0.204464 | + | 0.427538i | ||||
\(599\) | −292.918 | −0.489012 | −0.244506 | − | 0.969648i | \(-0.578626\pi\) | ||||
−0.244506 | + | 0.969648i | \(0.578626\pi\) | |||||||
\(600\) | 54.1618 | 0.0902696 | ||||||||
\(601\) | 39.6741 | 0.0660135 | 0.0330067 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330067 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(602\) | 318.201 | 0.528573 | ||||||||
\(603\) | 314.681i | 0.521859i | ||||||||
\(604\) | 392.902 | 0.650500 | ||||||||
\(605\) | − | 498.257i | − | 0.823566i | ||||||
\(606\) | 13.5851 | 0.0224176 | ||||||||
\(607\) | 120.120 | 0.197892 | 0.0989458 | − | 0.995093i | \(-0.468453\pi\) | ||||
0.0989458 | + | 0.995093i | \(0.468453\pi\) | |||||||
\(608\) | 82.8569i | 0.136278i | ||||||||
\(609\) | 8.79336i | 0.0144390i | ||||||||
\(610\) | 0.166490 | 0.000272934 | ||||||||
\(611\) | 64.4714 | 0.105518 | ||||||||
\(612\) | − | 84.4647i | − | 0.138014i | ||||||
\(613\) | 414.040i | 0.675432i | 0.941248 | + | 0.337716i | \(0.109654\pi\) | ||||
−0.941248 | + | 0.337716i | \(0.890346\pi\) | |||||||
\(614\) | −108.039 | −0.175959 | ||||||||
\(615\) | 237.576i | 0.386302i | ||||||||
\(616\) | −81.7989 | −0.132790 | ||||||||
\(617\) | 154.341i | 0.250147i | 0.992147 | + | 0.125073i | \(0.0399167\pi\) | ||||
−0.992147 | + | 0.125073i | \(0.960083\pi\) | |||||||
\(618\) | 99.4963i | 0.160997i | ||||||||
\(619\) | − | 879.766i | − | 1.42127i | −0.703561 | − | 0.710635i | \(-0.748408\pi\) | ||
0.703561 | − | 0.710635i | \(-0.251592\pi\) | |||||||
\(620\) | 578.123i | 0.932456i | ||||||||
\(621\) | −51.5616 | − | 107.816i | −0.0830300 | − | 0.173618i | ||||
\(622\) | −59.3423 | −0.0954057 | ||||||||
\(623\) | −412.792 | −0.662588 | ||||||||
\(624\) | −60.3640 | −0.0967372 | ||||||||
\(625\) | −779.164 | −1.24666 | ||||||||
\(626\) | 209.350i | 0.334424i | ||||||||
\(627\) | −156.433 | −0.249494 | ||||||||
\(628\) | 379.456i | 0.604229i | ||||||||
\(629\) | 801.559 | 1.27434 | ||||||||
\(630\) | −119.485 | −0.189658 | ||||||||
\(631\) | − | 211.786i | − | 0.335636i | −0.985818 | − | 0.167818i | \(-0.946328\pi\) | ||
0.985818 | − | 0.167818i | \(-0.0536720\pi\) | |||||||
\(632\) | − | 130.884i | − | 0.207095i | ||||||
\(633\) | 320.702 | 0.506639 | ||||||||
\(634\) | −805.342 | −1.27026 | ||||||||
\(635\) | 1071.68i | 1.68768i | ||||||||
\(636\) | 298.929i | 0.470015i | ||||||||
\(637\) | 235.265 | 0.369334 | ||||||||
\(638\) | − | 9.43917i | − | 0.0147949i | ||||||
\(639\) | −23.3522 | −0.0365449 | ||||||||
\(640\) | − | 67.9348i | − | 0.106148i | ||||||
\(641\) | − | 106.224i | − | 0.165715i | −0.996561 | − | 0.0828576i | \(-0.973595\pi\) | ||
0.996561 | − | 0.0828576i | \(-0.0264047\pi\) | |||||||
\(642\) | − | 305.804i | − | 0.476330i | ||||||
\(643\) | 970.054i | 1.50864i | 0.656508 | + | 0.754319i | \(0.272033\pi\) | ||||
−0.656508 | + | 0.754319i | \(0.727967\pi\) | |||||||
\(644\) | 194.635 | − | 93.0815i | 0.302229 | − | 0.144537i | ||||
\(645\) | −498.937 | −0.773546 | ||||||||
\(646\) | 291.603 | 0.451399 | ||||||||
\(647\) | −297.519 | −0.459844 | −0.229922 | − | 0.973209i | \(-0.573847\pi\) | ||||
−0.229922 | + | 0.973209i | \(0.573847\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − | 540.430i | − | 0.832711i | ||||||
\(650\) | −136.226 | −0.209578 | ||||||||
\(651\) | − | 391.068i | − | 0.600719i | ||||||
\(652\) | −152.634 | −0.234101 | ||||||||
\(653\) | 1191.05 | 1.82396 | 0.911981 | − | 0.410232i | \(-0.134552\pi\) | ||||
0.911981 | + | 0.410232i | \(0.134552\pi\) | |||||||
\(654\) | 191.039i | 0.292108i | ||||||||
\(655\) | 1345.39i | 2.05403i | ||||||||
\(656\) | 91.3722 | 0.139287 | ||||||||
\(657\) | 59.1596 | 0.0900450 | ||||||||
\(658\) | − | 49.0810i | − | 0.0745911i | ||||||
\(659\) | − | 164.114i | − | 0.249034i | −0.992217 | − | 0.124517i | \(-0.960262\pi\) | ||
0.992217 | − | 0.124517i | \(-0.0397382\pi\) | |||||||
\(660\) | 128.260 | 0.194333 | ||||||||
\(661\) | − | 221.664i | − | 0.335346i | −0.985843 | − | 0.167673i | \(-0.946375\pi\) | ||
0.985843 | − | 0.167673i | \(-0.0536253\pi\) | |||||||
\(662\) | −314.077 | −0.474437 | ||||||||
\(663\) | 212.443i | 0.320427i | ||||||||
\(664\) | 48.0522i | 0.0723678i | ||||||||
\(665\) | − | 412.505i | − | 0.620309i | ||||||
\(666\) | 241.573i | 0.362722i | ||||||||
\(667\) | 10.7411 | + | 22.4599i | 0.0161037 | + | 0.0336731i | ||||
\(668\) | −291.200 | −0.435928 | ||||||||
\(669\) | −503.924 | −0.753249 | ||||||||
\(670\) | 890.741 | 1.32946 | ||||||||
\(671\) | 0.120892 | 0.000180167 | ||||||||
\(672\) | 45.9541i | 0.0683841i | ||||||||
\(673\) | 1194.29 | 1.77457 | 0.887286 | − | 0.461219i | \(-0.152588\pi\) | ||||
0.887286 | + | 0.461219i | \(0.152588\pi\) | |||||||
\(674\) | 850.251i | 1.26150i | ||||||||
\(675\) | 57.4472 | 0.0851070 | ||||||||
\(676\) | −186.174 | −0.275406 | ||||||||
\(677\) | 1102.28i | 1.62819i | 0.580732 | + | 0.814095i | \(0.302767\pi\) | ||||
−0.580732 | + | 0.814095i | \(0.697233\pi\) | |||||||
\(678\) | 167.430i | 0.246947i | ||||||||
\(679\) | −182.444 | −0.268695 | ||||||||
\(680\) | −239.087 | −0.351599 | ||||||||
\(681\) | 1.27334i | 0.00186980i | ||||||||
\(682\) | 419.790i | 0.615527i | ||||||||
\(683\) | 305.671 | 0.447542 | 0.223771 | − | 0.974642i | \(-0.428163\pi\) | ||||
0.223771 | + | 0.974642i | \(0.428163\pi\) | |||||||
\(684\) | 87.8830i | 0.128484i | ||||||||
\(685\) | 1415.97 | 2.06712 | ||||||||
\(686\) | − | 504.116i | − | 0.734863i | ||||||
\(687\) | − | 252.681i | − | 0.367803i | ||||||
\(688\) | 191.892i | 0.278913i | ||||||||
\(689\) | − | 751.858i | − | 1.09123i | ||||||
\(690\) | −305.187 | + | 145.951i | −0.442300 | + | 0.211523i | ||||
\(691\) | −471.859 | −0.682863 | −0.341432 | − | 0.939907i | \(-0.610912\pi\) | ||||
−0.341432 | + | 0.939907i | \(0.610912\pi\) | |||||||
\(692\) | −594.599 | −0.859247 | ||||||||
\(693\) | −86.7608 | −0.125196 | ||||||||
\(694\) | −92.1926 | −0.132842 | ||||||||
\(695\) | − | 886.022i | − | 1.27485i | ||||||
\(696\) | −5.30287 | −0.00761907 | ||||||||
\(697\) | − | 321.572i | − | 0.461366i | ||||||
\(698\) | −748.974 | −1.07303 | ||||||||
\(699\) | −389.729 | −0.557552 | ||||||||
\(700\) | 103.707i | 0.148152i | ||||||||
\(701\) | − | 77.3101i | − | 0.110285i | −0.998478 | − | 0.0551427i | \(-0.982439\pi\) | ||
0.998478 | − | 0.0551427i | \(-0.0175614\pi\) | |||||||
\(702\) | −64.0257 | −0.0912047 | ||||||||
\(703\) | −833.999 | −1.18634 | ||||||||
\(704\) | − | 49.3292i | − | 0.0700698i | ||||||
\(705\) | 76.9586i | 0.109161i | ||||||||
\(706\) | 571.088 | 0.808907 | ||||||||
\(707\) | 26.0121i | 0.0367923i | ||||||||
\(708\) | −303.610 | −0.428828 | ||||||||
\(709\) | − | 474.562i | − | 0.669341i | −0.942335 | − | 0.334670i | \(-0.891375\pi\) | ||
0.942335 | − | 0.334670i | \(-0.108625\pi\) | |||||||
\(710\) | 66.1011i | 0.0931002i | ||||||||
\(711\) | − | 138.823i | − | 0.195251i | ||||||
\(712\) | − | 248.936i | − | 0.349629i | ||||||
\(713\) | −477.692 | − | 998.864i | −0.669974 | − | 1.40093i | ||||
\(714\) | 161.729 | 0.226511 | ||||||||
\(715\) | −322.595 | −0.451183 | ||||||||
\(716\) | −430.404 | −0.601123 | ||||||||
\(717\) | 366.012 | 0.510477 | ||||||||
\(718\) | − | 345.210i | − | 0.480794i | ||||||
\(719\) | −286.574 | −0.398574 | −0.199287 | − | 0.979941i | \(-0.563863\pi\) | ||||
−0.199287 | + | 0.979941i | \(0.563863\pi\) | |||||||
\(720\) | − | 72.0557i | − | 0.100077i | ||||||
\(721\) | −190.511 | −0.264232 | ||||||||
\(722\) | 207.126 | 0.286878 | ||||||||
\(723\) | 275.179i | 0.380607i | ||||||||
\(724\) | 163.610i | 0.225981i | ||||||||
\(725\) | −11.9672 | −0.0165065 | ||||||||
\(726\) | −203.255 | −0.279966 | ||||||||
\(727\) | 189.093i | 0.260101i | 0.991507 | + | 0.130050i | \(0.0415139\pi\) | ||||
−0.991507 | + | 0.130050i | \(0.958486\pi\) | |||||||
\(728\) | − | 115.582i | − | 0.158767i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 167.458i | − | 0.229394i | ||||||
\(731\) | 675.339 | 0.923856 | ||||||||
\(732\) | − | 0.0679165i | − | 9.27821e-5i | ||||||
\(733\) | − | 777.152i | − | 1.06023i | −0.847924 | − | 0.530117i | \(-0.822148\pi\) | ||
0.847924 | − | 0.530117i | \(-0.177852\pi\) | |||||||
\(734\) | − | 924.077i | − | 1.25896i | ||||||
\(735\) | 280.833i | 0.382086i | ||||||||
\(736\) | 56.1332 | + | 117.376i | 0.0762680 | + | 0.159478i | ||||
\(737\) | 646.790 | 0.877598 | ||||||||
\(738\) | 96.9149 | 0.131321 | ||||||||
\(739\) | −343.771 | −0.465184 | −0.232592 | − | 0.972574i | \(-0.574721\pi\) | ||||
−0.232592 | + | 0.972574i | \(0.574721\pi\) | |||||||
\(740\) | 683.799 | 0.924053 | ||||||||
\(741\) | − | 221.041i | − | 0.298300i | ||||||
\(742\) | −572.376 | −0.771397 | ||||||||
\(743\) | − | 560.485i | − | 0.754354i | −0.926141 | − | 0.377177i | \(-0.876895\pi\) | ||
0.926141 | − | 0.377177i | \(-0.123105\pi\) | |||||||
\(744\) | 235.835 | 0.316983 | ||||||||
\(745\) | 1434.68 | 1.92575 | ||||||||
\(746\) | 702.683i | 0.941935i | ||||||||
\(747\) | 50.9671i | 0.0682290i | ||||||||
\(748\) | −173.607 | −0.232095 | ||||||||
\(749\) | 585.539 | 0.781762 | ||||||||
\(750\) | 205.097i | 0.273462i | ||||||||
\(751\) | − | 1220.79i | − | 1.62555i | −0.582576 | − | 0.812776i | \(-0.697955\pi\) | ||
0.582576 | − | 0.812776i | \(-0.302045\pi\) | |||||||
\(752\) | 29.5985 | 0.0393597 | ||||||||
\(753\) | 559.195i | 0.742623i | ||||||||
\(754\) | 13.3376 | 0.0176891 | ||||||||
\(755\) | − | 1179.62i | − | 1.56241i | ||||||
\(756\) | 48.7417i | 0.0644731i | ||||||||
\(757\) | − | 595.690i | − | 0.786908i | −0.919344 | − | 0.393454i | \(-0.871280\pi\) | ||
0.919344 | − | 0.393454i | \(-0.128720\pi\) | |||||||
\(758\) | − | 663.718i | − | 0.875618i | ||||||
\(759\) | −221.604 | + | 105.979i | −0.291968 | + | 0.139630i | ||||
\(760\) | 248.763 | 0.327320 | ||||||||
\(761\) | −387.684 | −0.509440 | −0.254720 | − | 0.967015i | \(-0.581983\pi\) | ||||
−0.254720 | + | 0.967015i | \(0.581983\pi\) | |||||||
\(762\) | 437.172 | 0.573716 | ||||||||
\(763\) | −365.792 | −0.479413 | ||||||||
\(764\) | 248.722i | 0.325553i | ||||||||
\(765\) | −253.590 | −0.331490 | ||||||||
\(766\) | 191.388i | 0.249854i | ||||||||
\(767\) | 763.630 | 0.995606 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | − | 487.155i | − | 0.633492i | −0.948510 | − | 0.316746i | \(-0.897410\pi\) | ||
0.948510 | − | 0.316746i | \(-0.102590\pi\) | |||||||
\(770\) | 245.587i | 0.318944i | ||||||||
\(771\) | 605.805 | 0.785740 | ||||||||
\(772\) | −692.274 | −0.896729 | ||||||||
\(773\) | − | 1216.60i | − | 1.57386i | −0.617041 | − | 0.786931i | \(-0.711669\pi\) | ||
0.617041 | − | 0.786931i | \(-0.288331\pi\) | |||||||
\(774\) | 203.533i | 0.262962i | ||||||||
\(775\) | 532.219 | 0.686734 | ||||||||
\(776\) | − | 110.024i | − | 0.141783i | ||||||
\(777\) | −462.552 | −0.595306 | ||||||||
\(778\) | 643.807i | 0.827515i | ||||||||
\(779\) | 334.586i | 0.429507i | ||||||||
\(780\) | 181.232i | 0.232349i | ||||||||
\(781\) | 47.9977i | 0.0614567i | ||||||||
\(782\) | 413.088 | − | 197.553i | 0.528245 | − | 0.252625i | ||||
\(783\) | −5.62454 | −0.00718332 | ||||||||
\(784\) | 108.009 | 0.137767 | ||||||||
\(785\) | 1139.25 | 1.45127 | ||||||||
\(786\) | 548.828 | 0.698255 | ||||||||
\(787\) | 169.922i | 0.215911i | 0.994156 | + | 0.107955i | \(0.0344303\pi\) | ||||
−0.994156 | + | 0.107955i | \(0.965570\pi\) | |||||||
\(788\) | 427.886 | 0.543003 | ||||||||
\(789\) | 454.726i | 0.576332i | ||||||||
\(790\) | −392.956 | −0.497412 | ||||||||
\(791\) | −320.588 | −0.405294 | ||||||||
\(792\) | − | 52.3215i | − | 0.0660625i | ||||||
\(793\) | 0.170821i | 0.000215412i | ||||||||
\(794\) | 520.574 | 0.655634 | ||||||||
\(795\) | 897.482 | 1.12891 | ||||||||
\(796\) | − | 749.369i | − | 0.941418i | ||||||
\(797\) | − | 199.739i | − | 0.250614i | −0.992118 | − | 0.125307i | \(-0.960008\pi\) | ||
0.992118 | − | 0.125307i | \(-0.0399916\pi\) | |||||||
\(798\) | −168.274 | −0.210870 | ||||||||
\(799\) | − | 104.168i | − | 0.130373i | ||||||
\(800\) | −62.5406 | −0.0781758 | ||||||||
\(801\) | − | 264.037i | − | 0.329634i | ||||||
\(802\) | 626.305i | 0.780929i | ||||||||
\(803\) | − | 121.595i | − | 0.151426i | ||||||
\(804\) | − | 363.362i | − | 0.451943i | ||||||
\(805\) | −279.461 | − | 584.358i | −0.347156 | − | 0.725911i | ||||
\(806\) | −593.165 | −0.735936 | ||||||||
\(807\) | −133.042 | −0.164860 | ||||||||
\(808\) | −15.6867 | −0.0194143 | ||||||||
\(809\) | 1223.51 | 1.51238 | 0.756188 | − | 0.654354i | \(-0.227059\pi\) | ||||
0.756188 | + | 0.654354i | \(0.227059\pi\) | |||||||
\(810\) | − | 76.4266i | − | 0.0943538i | ||||||
\(811\) | −825.239 | −1.01756 | −0.508779 | − | 0.860897i | \(-0.669903\pi\) | ||||
−0.508779 | + | 0.860897i | \(0.669903\pi\) | |||||||
\(812\) | − | 10.1537i | − | 0.0125045i | ||||||
\(813\) | −643.371 | −0.791354 | ||||||||
\(814\) | 496.524 | 0.609980 | ||||||||
\(815\) | 458.256i | 0.562278i | ||||||||
\(816\) | 97.5314i | 0.119524i | ||||||||
\(817\) | −702.671 | −0.860062 | ||||||||
\(818\) | 171.064 | 0.209125 | ||||||||
\(819\) | − | 122.593i | − | 0.149687i | ||||||
\(820\) | − | 274.329i | − | 0.334547i | ||||||
\(821\) | −552.657 | −0.673151 | −0.336576 | − | 0.941656i | \(-0.609269\pi\) | ||||
−0.336576 | + | 0.941656i | \(0.609269\pi\) | |||||||
\(822\) | − | 577.622i | − | 0.702703i | ||||||
\(823\) | 1203.74 | 1.46262 | 0.731310 | − | 0.682046i | \(-0.238909\pi\) | ||||
0.731310 | + | 0.682046i | \(0.238909\pi\) | |||||||
\(824\) | − | 114.888i | − | 0.139428i | ||||||
\(825\) | − | 118.076i | − | 0.143122i | ||||||
\(826\) | − | 581.339i | − | 0.703800i | ||||||
\(827\) | − | 332.187i | − | 0.401677i | −0.979624 | − | 0.200839i | \(-0.935633\pi\) | ||
0.979624 | − | 0.200839i | \(-0.0643667\pi\) | |||||||
\(828\) | 59.5383 | + | 124.496i | 0.0719061 | + | 0.150357i | ||||
\(829\) | 907.749 | 1.09499 | 0.547496 | − | 0.836808i | \(-0.315581\pi\) | ||||
0.547496 | + | 0.836808i | \(0.315581\pi\) | |||||||
\(830\) | 144.268 | 0.173817 | ||||||||
\(831\) | −448.642 | −0.539882 | ||||||||
\(832\) | 69.7024 | 0.0837769 | ||||||||
\(833\) | − | 380.123i | − | 0.456331i | ||||||
\(834\) | −361.437 | −0.433378 | ||||||||
\(835\) | 874.275i | 1.04704i | ||||||||
\(836\) | 180.633 | 0.216068 | ||||||||
\(837\) | 250.141 | 0.298854 | ||||||||
\(838\) | 772.245i | 0.921534i | ||||||||
\(839\) | − | 35.1836i | − | 0.0419352i | −0.999780 | − | 0.0209676i | \(-0.993325\pi\) | ||
0.999780 | − | 0.0209676i | \(-0.00667469\pi\) | |||||||
\(840\) | 137.969 | 0.164249 | ||||||||
\(841\) | −839.828 | −0.998607 | ||||||||
\(842\) | − | 1124.29i | − | 1.33526i | ||||||
\(843\) | 434.586i | 0.515523i | ||||||||
\(844\) | −370.315 | −0.438762 | ||||||||
\(845\) | 558.955i | 0.661486i | ||||||||
\(846\) | 31.3939 | 0.0371087 | ||||||||
\(847\) | − | 389.184i | − | 0.459485i | ||||||
\(848\) | − | 345.174i | − | 0.407045i | ||||||
\(849\) | − | 201.961i | − | 0.237881i | ||||||
\(850\) | 220.103i | 0.258945i | ||||||||
\(851\) | −1181.45 | + | 565.010i | −1.38831 | + | 0.663937i | ||||
\(852\) | 26.9648 | 0.0316488 | ||||||||
\(853\) | −1236.74 | −1.44987 | −0.724933 | − | 0.688819i | \(-0.758129\pi\) | ||||
−0.724933 | + | 0.688819i | \(0.758129\pi\) | |||||||
\(854\) | 0.130043 | 0.000152276 | ||||||||
\(855\) | 263.853 | 0.308600 | ||||||||
\(856\) | 353.112i | 0.412514i | ||||||||
\(857\) | −1604.20 | −1.87188 | −0.935938 | − | 0.352166i | \(-0.885445\pi\) | ||||
−0.935938 | + | 0.352166i | \(0.885445\pi\) | |||||||
\(858\) | 131.597i | 0.153377i | ||||||||
\(859\) | −465.805 | −0.542265 | −0.271132 | − | 0.962542i | \(-0.587398\pi\) | ||||
−0.271132 | + | 0.962542i | \(0.587398\pi\) | |||||||
\(860\) | 576.123 | 0.669910 | ||||||||
\(861\) | 185.568i | 0.215526i | ||||||||
\(862\) | − | 652.549i | − | 0.757018i | ||||||
\(863\) | 703.235 | 0.814873 | 0.407437 | − | 0.913234i | \(-0.366423\pi\) | ||||
0.407437 | + | 0.913234i | \(0.366423\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | 1785.18i | 2.06379i | ||||||||
\(866\) | 825.358i | 0.953069i | ||||||||
\(867\) | −157.314 | −0.181447 | ||||||||
\(868\) | 451.566i | 0.520238i | ||||||||
\(869\) | −285.335 | −0.328349 | ||||||||
\(870\) | 15.9209i | 0.0182999i | ||||||||
\(871\) | 913.917i | 1.04927i | ||||||||
\(872\) | − | 220.592i | − | 0.252973i | ||||||
\(873\) | − | 116.698i | − | 0.133674i | ||||||
\(874\) | −429.806 | + | 205.548i | −0.491769 | + | 0.235181i | ||||
\(875\) | −392.710 | −0.448811 | ||||||||
\(876\) | −68.3116 | −0.0779812 | ||||||||
\(877\) | 1178.27 | 1.34352 | 0.671762 | − | 0.740767i | \(-0.265538\pi\) | ||||
0.671762 | + | 0.740767i | \(0.265538\pi\) | |||||||
\(878\) | 732.228 | 0.833973 | ||||||||
\(879\) | 273.984i | 0.311700i | ||||||||
\(880\) | −148.102 | −0.168298 | ||||||||
\(881\) | 1220.58i | 1.38545i | 0.721203 | + | 0.692724i | \(0.243590\pi\) | ||||
−0.721203 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(882\) | 114.561 | 0.129888 | ||||||||
\(883\) | 399.783 | 0.452756 | 0.226378 | − | 0.974040i | \(-0.427312\pi\) | ||||
0.226378 | + | 0.974040i | \(0.427312\pi\) | |||||||
\(884\) | − | 245.308i | − | 0.277497i | ||||||
\(885\) | 911.535i | 1.02998i | ||||||||
\(886\) | −71.1677 | −0.0803247 | ||||||||
\(887\) | −1467.55 | −1.65451 | −0.827256 | − | 0.561825i | \(-0.810099\pi\) | ||||
−0.827256 | + | 0.561825i | \(0.810099\pi\) | |||||||
\(888\) | − | 278.944i | − | 0.314126i | ||||||
\(889\) | 837.077i | 0.941593i | ||||||||
\(890\) | −747.386 | −0.839760 | ||||||||
\(891\) | − | 55.4953i | − | 0.0622843i | ||||||
\(892\) | 581.881 | 0.652333 | ||||||||
\(893\) | 108.384i | 0.121370i | ||||||||
\(894\) | − | 585.254i | − | 0.654647i | ||||||
\(895\) | 1292.21i | 1.44381i | ||||||||
\(896\) | − | 53.0632i | − | 0.0592224i | ||||||
\(897\) | −149.749 | − | 313.128i | −0.166944 | − | 0.349083i | ||||
\(898\) | −701.016 | −0.780641 | ||||||||
\(899\) | −52.1085 | −0.0579627 | ||||||||
\(900\) | −66.3344 | −0.0737048 | ||||||||
\(901\) | −1214.79 | −1.34827 | ||||||||
\(902\) | − | 199.197i | − | 0.220839i | ||||||
\(903\) | −389.715 | −0.431578 | ||||||||
\(904\) | − | 193.332i | − | 0.213863i | ||||||
\(905\) | 491.211 | 0.542775 | ||||||||
\(906\) | −481.205 | −0.531131 | ||||||||
\(907\) | 0.658645i | 0.000726179i | 1.00000 | 0.000363090i | \(0.000115575\pi\) | |||||
−1.00000 | 0.000363090i | \(0.999884\pi\) | ||||||||
\(908\) | − | 1.47032i | − | 0.00161930i | ||||||
\(909\) | −16.6383 | −0.0183039 | ||||||||
\(910\) | −347.015 | −0.381335 | ||||||||
\(911\) | 912.515i | 1.00166i | 0.865545 | + | 0.500832i | \(0.166972\pi\) | ||||
−0.865545 | + | 0.500832i | \(0.833028\pi\) | |||||||
\(912\) | − | 101.479i | − | 0.111270i | ||||||
\(913\) | 104.757 | 0.114739 | ||||||||
\(914\) | 260.567i | 0.285084i | ||||||||
\(915\) | −0.203907 | −0.000222849 | ||||||||
\(916\) | 291.771i | 0.318527i | ||||||||
\(917\) | 1050.87i | 1.14599i | ||||||||
\(918\) | 103.448i | 0.112688i | ||||||||
\(919\) | 536.529i | 0.583818i | 0.956446 | + | 0.291909i | \(0.0942904\pi\) | ||||
−0.956446 | + | 0.291909i | \(0.905710\pi\) | |||||||
\(920\) | 352.400 | − | 168.530i | 0.383043 | − | 0.183185i | ||||
\(921\) | 132.320 | 0.143670 | ||||||||
\(922\) | 226.548 | 0.245714 | ||||||||
\(923\) | −67.8210 | −0.0734789 | ||||||||
\(924\) | 100.183 | 0.108423 | ||||||||
\(925\) | − | 629.505i | − | 0.680546i | ||||||
\(926\) | −647.985 | −0.699768 | ||||||||
\(927\) | − | 121.858i | − | 0.131454i | ||||||
\(928\) | 6.12323 | 0.00659830 | ||||||||
\(929\) | −1075.21 | −1.15738 | −0.578691 | − | 0.815547i | \(-0.696436\pi\) | ||||
−0.578691 | + | 0.815547i | \(0.696436\pi\) | |||||||
\(930\) | − | 708.053i | − | 0.761347i | ||||||
\(931\) | 395.507i | 0.424820i | ||||||||
\(932\) | 450.020 | 0.482854 | ||||||||
\(933\) | 72.6792 | 0.0778984 | ||||||||
\(934\) | 1137.39i | 1.21776i | ||||||||
\(935\) | 521.224i | 0.557459i | ||||||||
\(936\) | 73.9305 | 0.0789856 | ||||||||
\(937\) | − | 429.773i | − | 0.458669i | −0.973348 | − | 0.229335i | \(-0.926345\pi\) | ||
0.973348 | − | 0.229335i | \(-0.0736550\pi\) | |||||||
\(938\) | 695.750 | 0.741738 | ||||||||
\(939\) | − | 256.400i | − | 0.273056i | ||||||
\(940\) | − | 88.8641i | − | 0.0945363i | ||||||
\(941\) | 746.559i | 0.793367i | 0.917955 | + | 0.396684i | \(0.129839\pi\) | ||||
−0.917955 | + | 0.396684i | \(0.870161\pi\) | |||||||
\(942\) | − | 464.737i | − | 0.493351i | ||||||
\(943\) | 226.673 | + | 473.977i | 0.240374 | + | 0.502627i | ||||
\(944\) | 350.579 | 0.371376 | ||||||||
\(945\) | 146.338 | 0.154855 | ||||||||
\(946\) | 418.337 | 0.442217 | ||||||||
\(947\) | 472.748 | 0.499206 | 0.249603 | − | 0.968348i | \(-0.419700\pi\) | ||||
0.249603 | + | 0.968348i | \(0.419700\pi\) | |||||||
\(948\) | 160.300i | 0.169092i | ||||||||
\(949\) | 171.815 | 0.181048 | ||||||||
\(950\) | − | 229.011i | − | 0.241064i | ||||||
\(951\) | 986.338 | 1.03716 | ||||||||
\(952\) | −186.749 | −0.196165 | ||||||||
\(953\) | − | 1583.70i | − | 1.66181i | −0.556417 | − | 0.830903i | \(-0.687824\pi\) | ||
0.556417 | − | 0.830903i | \(-0.312176\pi\) | |||||||
\(954\) | − | 366.112i | − | 0.383766i | ||||||
\(955\) | 746.744 | 0.781931 | ||||||||
\(956\) | −422.634 | −0.442086 | ||||||||
\(957\) | 11.5606i | 0.0120800i | ||||||||
\(958\) | − | 560.497i | − | 0.585070i | ||||||
\(959\) | 1106.00 | 1.15329 | ||||||||
\(960\) | 83.2028i | 0.0866695i | ||||||||
\(961\) | 1356.43 | 1.41147 | ||||||||
\(962\) | 701.591i | 0.729305i | ||||||||
\(963\) | 374.532i | 0.388922i | ||||||||
\(964\) | − | 317.750i | − | 0.329616i | ||||||
\(965\) | 2078.43i | 2.15381i | ||||||||
\(966\) | −238.379 | + | 114.001i | −0.246769 | + | 0.118014i | ||||
\(967\) | 656.660 | 0.679069 | 0.339535 | − | 0.940594i | \(-0.389730\pi\) | ||||
0.339535 | + | 0.940594i | \(0.389730\pi\) | |||||||
\(968\) | 234.699 | 0.242458 | ||||||||
\(969\) | −357.140 | −0.368565 | ||||||||
\(970\) | −330.326 | −0.340542 | ||||||||
\(971\) | 963.625i | 0.992405i | 0.868207 | + | 0.496202i | \(0.165273\pi\) | ||||
−0.868207 | + | 0.496202i | \(0.834727\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | − | 692.064i | − | 0.711268i | ||||||
\(974\) | −900.380 | −0.924414 | ||||||||
\(975\) | 166.842 | 0.171120 | ||||||||
\(976\) | 0.0784233i | 8.03517e-5i | ||||||||
\(977\) | 313.286i | 0.320661i | 0.987063 | + | 0.160330i | \(0.0512560\pi\) | ||||
−0.987063 | + | 0.160330i | \(0.948744\pi\) | |||||||
\(978\) | 186.938 | 0.191143 | ||||||||
\(979\) | −542.696 | −0.554337 | ||||||||
\(980\) | − | 324.278i | − | 0.330896i | ||||||
\(981\) | − | 233.974i | − | 0.238505i | ||||||
\(982\) | 1313.02 | 1.33708 | ||||||||
\(983\) | − | 671.993i | − | 0.683614i | −0.939770 | − | 0.341807i | \(-0.888961\pi\) | ||
0.939770 | − | 0.341807i | \(-0.111039\pi\) | |||||||
\(984\) | −111.908 | −0.113727 | ||||||||
\(985\) | − | 1284.65i | − | 1.30422i | ||||||
\(986\) | − | 21.5498i | − | 0.0218558i | ||||||
\(987\) | 60.1117i | 0.0609034i | ||||||||
\(988\) | 255.236i | 0.258336i | ||||||||
\(989\) | −995.408 | + | 476.039i | −1.00648 | + | 0.481334i | ||||
\(990\) | −157.086 | −0.158673 | ||||||||
\(991\) | −1319.81 | −1.33179 | −0.665896 | − | 0.746044i | \(-0.731951\pi\) | ||||
−0.665896 | + | 0.746044i | \(0.731951\pi\) | |||||||
\(992\) | −272.319 | −0.274515 | ||||||||
\(993\) | 384.665 | 0.387376 | ||||||||
\(994\) | 51.6310i | 0.0519426i | ||||||||
\(995\) | −2249.84 | −2.26115 | ||||||||
\(996\) | − | 58.8517i | − | 0.0590881i | ||||||
\(997\) | −828.619 | −0.831112 | −0.415556 | − | 0.909568i | \(-0.636413\pi\) | ||||
−0.415556 | + | 0.909568i | \(0.636413\pi\) | |||||||
\(998\) | 647.708 | 0.649006 | ||||||||
\(999\) | − | 295.865i | − | 0.296161i |
(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 | 138.3.b.a.91.5 | ✓ | 8 | |
3.2 | odd | 2 | 414.3.b.c.91.4 | 8 | |||
4.3 | odd | 2 | 1104.3.c.c.1057.5 | 8 | |||
23.22 | odd | 2 | inner | 138.3.b.a.91.6 | yes | 8 | |
69.68 | even | 2 | 414.3.b.c.91.1 | 8 | |||
92.91 | even | 2 | 1104.3.c.c.1057.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.3.b.a.91.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
138.3.b.a.91.6 | yes | 8 | 23.22 | odd | 2 | inner | |
414.3.b.c.91.1 | 8 | 69.68 | even | 2 | |||
414.3.b.c.91.4 | 8 | 3.2 | odd | 2 | |||
1104.3.c.c.1057.5 | 8 | 4.3 | odd | 2 | |||
1104.3.c.c.1057.8 | 8 | 92.91 | even | 2 |