Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.25 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.c.449.26 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.60951 | − | 2.53169i | 0.536504 | − | 0.843898i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.27619 | − | 3.58035i | 0.379366 | − | 0.596726i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.81894 | − | 8.14958i | −0.424326 | − | 0.905509i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.4366i | 1.22151i | 0.791820 | + | 0.610754i | \(0.209134\pi\) | ||||
−0.791820 | + | 0.610754i | \(0.790866\pi\) | |||||||
\(12\) | 3.21903 | − | 5.06339i | 0.268252 | − | 0.421949i | ||||
\(13\) | − | 19.9431i | − | 1.53409i | −0.641595 | − | 0.767044i | \(-0.721727\pi\) | ||
0.641595 | − | 0.767044i | \(-0.278273\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 16.8546 | 0.991444 | 0.495722 | − | 0.868481i | \(-0.334903\pi\) | ||||
0.495722 | + | 0.868481i | \(0.334903\pi\) | |||||||
\(18\) | −5.40079 | − | 11.5253i | −0.300044 | − | 0.640292i | ||||
\(19\) | 20.2080 | 1.06358 | 0.531790 | − | 0.846876i | \(-0.321519\pi\) | ||||
0.531790 | + | 0.846876i | \(0.321519\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.69823 | − | 4.25837i | −0.318963 | − | 0.202780i | ||||
\(22\) | 19.0022i | 0.863736i | ||||||||
\(23\) | −6.13260 | −0.266635 | −0.133317 | − | 0.991073i | \(-0.542563\pi\) | ||||
−0.133317 | + | 0.991073i | \(0.542563\pi\) | |||||||
\(24\) | 4.55239 | − | 7.16071i | 0.189683 | − | 0.298363i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 28.2039i | − | 1.08476i | ||||||
\(27\) | −26.7789 | − | 3.44849i | −0.991810 | − | 0.127722i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | − | 46.5221i | − | 1.60421i | −0.597183 | − | 0.802105i | \(-0.703713\pi\) | ||
0.597183 | − | 0.802105i | \(-0.296287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.2147 | −0.555314 | −0.277657 | − | 0.960680i | \(-0.589558\pi\) | ||||
−0.277657 | + | 0.960680i | \(0.589558\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 34.0173 | + | 21.6264i | 1.03083 | + | 0.655344i | ||||
\(34\) | 23.8359 | 0.701057 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.63787 | − | 16.2992i | −0.212163 | − | 0.452755i | ||||
\(37\) | − | 64.7559i | − | 1.75016i | −0.483978 | − | 0.875080i | \(-0.660809\pi\) | ||
0.483978 | − | 0.875080i | \(-0.339191\pi\) | |||||||
\(38\) | 28.5785 | 0.752065 | ||||||||
\(39\) | −50.4899 | − | 32.0987i | −1.29461 | − | 0.823045i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.5496i | 1.52560i | 0.646634 | + | 0.762800i | \(0.276176\pi\) | ||||
−0.646634 | + | 0.762800i | \(0.723824\pi\) | |||||||
\(42\) | −9.47273 | − | 6.02225i | −0.225541 | − | 0.143387i | ||||
\(43\) | − | 71.0317i | − | 1.65190i | −0.563744 | − | 0.825949i | \(-0.690640\pi\) | ||
0.563744 | − | 0.825949i | \(-0.309360\pi\) | |||||||
\(44\) | 26.8732i | 0.610754i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.67280 | −0.188539 | ||||||||
\(47\) | −47.6863 | −1.01460 | −0.507301 | − | 0.861769i | \(-0.669357\pi\) | ||||
−0.507301 | + | 0.861769i | \(0.669357\pi\) | |||||||
\(48\) | 6.43805 | − | 10.1268i | 0.134126 | − | 0.210974i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 27.1276 | − | 42.6705i | 0.531914 | − | 0.836677i | ||||
\(52\) | − | 39.8863i | − | 0.767044i | ||||||
\(53\) | 36.2448 | 0.683864 | 0.341932 | − | 0.939725i | \(-0.388919\pi\) | ||||
0.341932 | + | 0.939725i | \(0.388919\pi\) | |||||||
\(54\) | −37.8710 | − | 4.87690i | −0.701316 | − | 0.0903129i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | 32.5251 | − | 51.1605i | 0.570616 | − | 0.897553i | ||||
\(58\) | − | 65.7922i | − | 1.13435i | ||||||
\(59\) | − | 2.49151i | − | 0.0422290i | −0.999777 | − | 0.0211145i | \(-0.993279\pi\) | ||
0.999777 | − | 0.0211145i | \(-0.00672145\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5448 | 0.205653 | 0.102826 | − | 0.994699i | \(-0.467211\pi\) | ||||
0.102826 | + | 0.994699i | \(0.467211\pi\) | |||||||
\(62\) | −24.3453 | −0.392666 | ||||||||
\(63\) | −21.5618 | + | 10.1040i | −0.342250 | + | 0.160380i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 48.1077 | + | 30.5843i | 0.728905 | + | 0.463398i | ||||
\(67\) | 118.236i | 1.76471i | 0.470581 | + | 0.882357i | \(0.344044\pi\) | ||||
−0.470581 | + | 0.882357i | \(0.655956\pi\) | |||||||
\(68\) | 33.7091 | 0.495722 | ||||||||
\(69\) | −9.87050 | + | 15.5259i | −0.143051 | + | 0.225012i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.94718i | − | 0.111932i | −0.998433 | − | 0.0559660i | \(-0.982176\pi\) | ||
0.998433 | − | 0.0559660i | \(-0.0178239\pi\) | |||||||
\(72\) | −10.8016 | − | 23.0505i | −0.150022 | − | 0.320146i | ||||
\(73\) | 73.2141i | 1.00293i | 0.865177 | + | 0.501466i | \(0.167206\pi\) | ||||
−0.865177 | + | 0.501466i | \(0.832794\pi\) | |||||||
\(74\) | − | 91.5787i | − | 1.23755i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.4161 | 0.531790 | ||||||||
\(77\) | 35.5499 | 0.461687 | ||||||||
\(78\) | −71.4035 | − | 45.3945i | −0.915429 | − | 0.581980i | ||||
\(79\) | −108.171 | −1.36925 | −0.684627 | − | 0.728893i | \(-0.740035\pi\) | ||||
−0.684627 | + | 0.728893i | \(0.740035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.8315 | + | 62.2455i | −0.639894 | + | 0.768463i | ||||
\(82\) | 88.4585i | 1.07876i | ||||||||
\(83\) | 92.8713 | 1.11893 | 0.559466 | − | 0.828854i | \(-0.311006\pi\) | ||||
0.559466 | + | 0.828854i | \(0.311006\pi\) | |||||||
\(84\) | −13.3965 | − | 8.51674i | −0.159482 | − | 0.101390i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 100.454i | − | 1.16807i | ||||||
\(87\) | −117.780 | − | 74.8779i | −1.35379 | − | 0.860666i | ||||
\(88\) | 38.0044i | 0.431868i | ||||||||
\(89\) | − | 5.36877i | − | 0.0603233i | −0.999545 | − | 0.0301616i | \(-0.990398\pi\) | ||
0.999545 | − | 0.0301616i | \(-0.00960221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −52.7646 | −0.579831 | ||||||||
\(92\) | −12.2652 | −0.133317 | ||||||||
\(93\) | −27.7073 | + | 43.5824i | −0.297928 | + | 0.468628i | ||||
\(94\) | −67.4386 | −0.717432 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.10478 | − | 14.3214i | 0.0948415 | − | 0.149181i | ||||
\(97\) | 8.58686i | 0.0885243i | 0.999020 | + | 0.0442621i | \(0.0140937\pi\) | ||||
−0.999020 | + | 0.0442621i | \(0.985906\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 109.503 | − | 51.3135i | 1.10609 | − | 0.518318i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 38.8036i | − | 0.384194i | −0.981376 | − | 0.192097i | \(-0.938471\pi\) | ||
0.981376 | − | 0.192097i | \(-0.0615288\pi\) | |||||||
\(102\) | 38.3642 | − | 60.3453i | 0.376120 | − | 0.591620i | ||||
\(103\) | − | 8.45500i | − | 0.0820873i | −0.999157 | − | 0.0410437i | \(-0.986932\pi\) | ||
0.999157 | − | 0.0410437i | \(-0.0130683\pi\) | |||||||
\(104\) | − | 56.4077i | − | 0.542382i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.2579 | 0.483565 | ||||||||
\(107\) | 54.3515 | 0.507958 | 0.253979 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253979 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(108\) | −53.5577 | − | 6.89698i | −0.495905 | − | 0.0638609i | ||||
\(109\) | 102.194 | 0.937560 | 0.468780 | − | 0.883315i | \(-0.344694\pi\) | ||||
0.468780 | + | 0.883315i | \(0.344694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −163.942 | − | 104.225i | −1.47696 | − | 0.938968i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | 135.780 | 1.20159 | 0.600797 | − | 0.799402i | \(-0.294850\pi\) | ||||
0.600797 | + | 0.799402i | \(0.294850\pi\) | |||||||
\(114\) | 45.9974 | − | 72.3519i | 0.403486 | − | 0.634666i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 93.0442i | − | 0.802105i | ||||||
\(117\) | −162.528 | + | 76.1616i | −1.38913 | + | 0.650954i | ||||
\(118\) | − | 3.52352i | − | 0.0298604i | ||||||
\(119\) | − | 44.5930i | − | 0.374731i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.5418 | −0.492081 | ||||||||
\(122\) | 17.7411 | 0.145418 | ||||||||
\(123\) | 158.356 | + | 100.674i | 1.28745 | + | 0.818491i | ||||
\(124\) | −34.4295 | −0.277657 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −30.4930 | + | 14.2892i | −0.242008 | + | 0.113406i | ||||
\(127\) | 181.101i | 1.42599i | 0.701167 | + | 0.712997i | \(0.252663\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −179.830 | − | 114.326i | −1.39403 | − | 0.886251i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.01429i | − | 0.0306434i | −0.999883 | − | 0.0153217i | \(-0.995123\pi\) | ||
0.999883 | − | 0.0153217i | \(-0.00487725\pi\) | |||||||
\(132\) | 68.0346 | + | 43.2527i | 0.515414 | + | 0.327672i | ||||
\(133\) | − | 53.4654i | − | 0.401996i | ||||||
\(134\) | 167.211i | 1.24784i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 47.6719 | 0.350528 | ||||||||
\(137\) | 78.4136 | 0.572362 | 0.286181 | − | 0.958176i | \(-0.407614\pi\) | ||||
0.286181 | + | 0.958176i | \(0.407614\pi\) | |||||||
\(138\) | −13.9590 | + | 21.9569i | −0.101152 | + | 0.159108i | ||||
\(139\) | 41.0289 | 0.295172 | 0.147586 | − | 0.989049i | \(-0.452850\pi\) | ||||
0.147586 | + | 0.989049i | \(0.452850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −76.7517 | + | 120.727i | −0.544338 | + | 0.856220i | ||||
\(142\) | − | 11.2390i | − | 0.0791479i | ||||||
\(143\) | 267.968 | 1.87390 | ||||||||
\(144\) | −15.2757 | − | 32.5983i | −0.106082 | − | 0.226377i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 103.540i | 0.709180i | ||||||||
\(147\) | −11.2666 | + | 17.7218i | −0.0766435 | + | 0.120557i | ||||
\(148\) | − | 129.512i | − | 0.875080i | ||||||
\(149\) | − | 22.0376i | − | 0.147903i | −0.997262 | − | 0.0739515i | \(-0.976439\pi\) | ||
0.997262 | − | 0.0739515i | \(-0.0235610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −96.2729 | −0.637569 | −0.318784 | − | 0.947827i | \(-0.603275\pi\) | ||||
−0.318784 | + | 0.947827i | \(0.603275\pi\) | |||||||
\(152\) | 57.1569 | 0.376033 | ||||||||
\(153\) | −64.3665 | − | 137.358i | −0.420696 | − | 0.897762i | ||||
\(154\) | 50.2751 | 0.326462 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −100.980 | − | 64.1975i | −0.647306 | − | 0.411522i | ||||
\(157\) | 21.6287i | 0.137763i | 0.997625 | + | 0.0688813i | \(0.0219430\pi\) | ||||
−0.997625 | + | 0.0688813i | \(0.978057\pi\) | |||||||
\(158\) | −152.977 | −0.968209 | ||||||||
\(159\) | 58.3365 | − | 91.7607i | 0.366896 | − | 0.577111i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.2253i | 0.100778i | ||||||||
\(162\) | −73.3007 | + | 88.0284i | −0.452474 | + | 0.543385i | ||||
\(163\) | 223.849i | 1.37331i | 0.726985 | + | 0.686654i | \(0.240921\pi\) | ||||
−0.726985 | + | 0.686654i | \(0.759079\pi\) | |||||||
\(164\) | 125.099i | 0.762800i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 131.340 | 0.791204 | ||||||||
\(167\) | 287.979 | 1.72442 | 0.862212 | − | 0.506548i | \(-0.169079\pi\) | ||||
0.862212 | + | 0.506548i | \(0.169079\pi\) | |||||||
\(168\) | −18.9455 | − | 12.0445i | −0.112771 | − | 0.0716934i | ||||
\(169\) | −228.729 | −1.35342 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −77.1732 | − | 164.687i | −0.451305 | − | 0.963082i | ||||
\(172\) | − | 142.063i | − | 0.825949i | ||||||
\(173\) | −289.069 | −1.67092 | −0.835458 | − | 0.549554i | \(-0.814798\pi\) | ||||
−0.835458 | + | 0.549554i | \(0.814798\pi\) | |||||||
\(174\) | −166.566 | − | 105.893i | −0.957273 | − | 0.608582i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 53.7463i | 0.305377i | ||||||||
\(177\) | −6.30773 | − | 4.01011i | −0.0356369 | − | 0.0226560i | ||||
\(178\) | − | 7.59259i | − | 0.0426550i | ||||||
\(179\) | − | 46.6099i | − | 0.260391i | −0.991488 | − | 0.130195i | \(-0.958440\pi\) | ||
0.991488 | − | 0.130195i | \(-0.0415605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −138.088 | −0.762920 | −0.381460 | − | 0.924385i | \(-0.624579\pi\) | ||||
−0.381460 | + | 0.924385i | \(0.624579\pi\) | |||||||
\(182\) | −74.6204 | −0.410002 | ||||||||
\(183\) | 20.1911 | − | 31.7596i | 0.110334 | − | 0.173550i | ||||
\(184\) | −17.3456 | −0.0942696 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −39.1841 | + | 61.6349i | −0.210667 | + | 0.331370i | ||||
\(187\) | 226.468i | 1.21106i | ||||||||
\(188\) | −95.3726 | −0.507301 | ||||||||
\(189\) | −9.12384 | + | 70.8502i | −0.0482743 | + | 0.374869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7131i | 0.103210i | 0.998668 | + | 0.0516051i | \(0.0164337\pi\) | ||||
−0.998668 | + | 0.0516051i | \(0.983566\pi\) | |||||||
\(192\) | 12.8761 | − | 20.2535i | 0.0670630 | − | 0.105487i | ||||
\(193\) | − | 55.0627i | − | 0.285299i | −0.989773 | − | 0.142650i | \(-0.954438\pi\) | ||
0.989773 | − | 0.142650i | \(-0.0455622\pi\) | |||||||
\(194\) | 12.1436i | 0.0625961i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 225.696 | 1.14567 | 0.572833 | − | 0.819672i | \(-0.305844\pi\) | ||||
0.572833 | + | 0.819672i | \(0.305844\pi\) | |||||||
\(198\) | 154.860 | − | 72.5682i | 0.782121 | − | 0.366506i | ||||
\(199\) | −187.480 | −0.942109 | −0.471054 | − | 0.882104i | \(-0.656126\pi\) | ||||
−0.471054 | + | 0.882104i | \(0.656126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 299.337 | + | 190.302i | 1.48924 | + | 0.946776i | ||||
\(202\) | − | 54.8766i | − | 0.271666i | ||||||
\(203\) | −123.086 | −0.606334 | ||||||||
\(204\) | 54.2552 | − | 85.3411i | 0.265957 | − | 0.418339i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 11.9572i | − | 0.0580445i | ||||||
\(207\) | 23.4200 | + | 49.9781i | 0.113140 | + | 0.241440i | ||||
\(208\) | − | 79.7725i | − | 0.383522i | ||||||
\(209\) | 271.527i | 1.29917i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 346.309 | 1.64127 | 0.820637 | − | 0.571450i | \(-0.193619\pi\) | ||||
0.820637 | + | 0.571450i | \(0.193619\pi\) | |||||||
\(212\) | 72.4896 | 0.341932 | ||||||||
\(213\) | −20.1198 | − | 12.7911i | −0.0944592 | − | 0.0600520i | ||||
\(214\) | 76.8646 | 0.359180 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −75.7421 | − | 9.75380i | −0.350658 | − | 0.0451565i | ||||
\(217\) | 45.5459i | 0.209889i | ||||||||
\(218\) | 144.524 | 0.662955 | ||||||||
\(219\) | 185.356 | + | 117.839i | 0.846372 | + | 0.538078i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 336.133i | − | 1.52096i | ||||||
\(222\) | −231.849 | − | 147.397i | −1.04437 | − | 0.663951i | ||||
\(223\) | 316.434i | 1.41899i | 0.704712 | + | 0.709494i | \(0.251076\pi\) | ||||
−0.704712 | + | 0.709494i | \(0.748924\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 192.022 | 0.849655 | ||||||||
\(227\) | −7.78561 | −0.0342979 | −0.0171489 | − | 0.999853i | \(-0.505459\pi\) | ||||
−0.0171489 | + | 0.999853i | \(0.505459\pi\) | |||||||
\(228\) | 65.0502 | − | 102.321i | 0.285308 | − | 0.448777i | ||||
\(229\) | 121.893 | 0.532284 | 0.266142 | − | 0.963934i | \(-0.414251\pi\) | ||||
0.266142 | + | 0.963934i | \(0.414251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 57.2180 | − | 90.0013i | 0.247697 | − | 0.389616i | ||||
\(232\) | − | 131.584i | − | 0.567174i | ||||||
\(233\) | 80.1577 | 0.344024 | 0.172012 | − | 0.985095i | \(-0.444973\pi\) | ||||
0.172012 | + | 0.985095i | \(0.444973\pi\) | |||||||
\(234\) | −229.850 | + | 107.709i | −0.982264 | + | 0.460294i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 4.98302i | − | 0.0211145i | ||||||
\(237\) | −174.103 | + | 273.856i | −0.734611 | + | 1.15551i | ||||
\(238\) | − | 63.0640i | − | 0.264975i | ||||||
\(239\) | 116.255i | 0.486424i | 0.969973 | + | 0.243212i | \(0.0782011\pi\) | ||||
−0.969973 | + | 0.243212i | \(0.921799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 94.7516 | 0.393160 | 0.196580 | − | 0.980488i | \(-0.437016\pi\) | ||||
0.196580 | + | 0.980488i | \(0.437016\pi\) | |||||||
\(242\) | −84.2049 | −0.347954 | ||||||||
\(243\) | 74.1631 | + | 231.406i | 0.305198 | + | 0.952289i | ||||
\(244\) | 25.0896 | 0.102826 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 223.950 | + | 142.375i | 0.910365 | + | 0.578761i | ||||
\(247\) | − | 403.012i | − | 1.63163i | ||||||
\(248\) | −48.6906 | −0.196333 | ||||||||
\(249\) | 149.478 | − | 235.122i | 0.600311 | − | 0.944263i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 46.8378i | − | 0.186605i | −0.995638 | − | 0.0933023i | \(-0.970258\pi\) | ||
0.995638 | − | 0.0933023i | \(-0.0297423\pi\) | |||||||
\(252\) | −43.1235 | + | 20.2079i | −0.171125 | + | 0.0801901i | ||||
\(253\) | − | 82.4012i | − | 0.325696i | ||||||
\(254\) | 256.116i | 1.00833i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 58.1337 | 0.226201 | 0.113101 | − | 0.993584i | \(-0.463922\pi\) | ||||
0.113101 | + | 0.993584i | \(0.463922\pi\) | |||||||
\(258\) | −254.318 | − | 161.682i | −0.985731 | − | 0.626674i | ||||
\(259\) | −171.328 | −0.661498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −379.136 | + | 177.665i | −1.45263 | + | 0.680708i | ||||
\(262\) | − | 5.67707i | − | 0.0216682i | ||||||
\(263\) | 372.471 | 1.41624 | 0.708121 | − | 0.706092i | \(-0.249543\pi\) | ||||
0.708121 | + | 0.706092i | \(0.249543\pi\) | |||||||
\(264\) | 96.2155 | + | 61.1686i | 0.364453 | + | 0.231699i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 75.6115i | − | 0.284254i | ||||||
\(267\) | −13.5921 | − | 8.64111i | −0.0509067 | − | 0.0323637i | ||||
\(268\) | 236.472i | 0.882357i | ||||||||
\(269\) | 198.582i | 0.738221i | 0.929385 | + | 0.369111i | \(0.120338\pi\) | ||||
−0.929385 | + | 0.369111i | \(0.879662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 334.221 | 1.23329 | 0.616644 | − | 0.787242i | \(-0.288492\pi\) | ||||
0.616644 | + | 0.787242i | \(0.288492\pi\) | |||||||
\(272\) | 67.4182 | 0.247861 | ||||||||
\(273\) | −84.9253 | + | 133.584i | −0.311082 | + | 0.489318i | ||||
\(274\) | 110.894 | 0.404721 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −19.7410 | + | 31.0517i | −0.0715253 | + | 0.112506i | ||||
\(277\) | − | 466.582i | − | 1.68441i | −0.539156 | − | 0.842206i | \(-0.681257\pi\) | ||
0.539156 | − | 0.842206i | \(-0.318743\pi\) | |||||||
\(278\) | 58.0237 | 0.208718 | ||||||||
\(279\) | 65.7420 | + | 140.293i | 0.235634 | + | 0.502842i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 516.652i | 1.83862i | 0.393536 | + | 0.919309i | \(0.371252\pi\) | ||||
−0.393536 | + | 0.919309i | \(0.628748\pi\) | |||||||
\(282\) | −108.543 | + | 170.734i | −0.384905 | + | 0.605439i | ||||
\(283\) | − | 476.620i | − | 1.68417i | −0.539346 | − | 0.842084i | \(-0.681328\pi\) | ||
0.539346 | − | 0.842084i | \(-0.318672\pi\) | |||||||
\(284\) | − | 15.8944i | − | 0.0559660i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 378.964 | 1.32505 | ||||||||
\(287\) | 165.491 | 0.576623 | ||||||||
\(288\) | −21.6032 | − | 46.1010i | −0.0750110 | − | 0.160073i | ||||
\(289\) | −4.92410 | −0.0170384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.7393 | + | 13.8207i | 0.0747054 | + | 0.0474937i | ||||
\(292\) | 146.428i | 0.501466i | ||||||||
\(293\) | −169.952 | −0.580041 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(294\) | −15.9334 | + | 25.0625i | −0.0541951 | + | 0.0852465i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 183.157i | − | 0.618775i | ||||||
\(297\) | 46.3359 | − | 359.817i | 0.156013 | − | 1.21150i | ||||
\(298\) | − | 31.1658i | − | 0.104583i | ||||||
\(299\) | 122.303i | 0.409041i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −187.932 | −0.624359 | ||||||||
\(302\) | −136.150 | −0.450829 | ||||||||
\(303\) | −98.2388 | − | 62.4549i | −0.324220 | − | 0.206122i | ||||
\(304\) | 80.8321 | 0.265895 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −91.0279 | − | 194.253i | −0.297477 | − | 0.634814i | ||||
\(307\) | 312.115i | 1.01666i | 0.861162 | + | 0.508331i | \(0.169737\pi\) | ||||
−0.861162 | + | 0.508331i | \(0.830263\pi\) | |||||||
\(308\) | 71.0997 | 0.230843 | ||||||||
\(309\) | −21.4055 | − | 13.6084i | −0.0692733 | − | 0.0440402i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 425.633i | 1.36859i | 0.729204 | + | 0.684297i | \(0.239891\pi\) | ||||
−0.729204 | + | 0.684297i | \(0.760109\pi\) | |||||||
\(312\) | −142.807 | − | 90.7889i | −0.457715 | − | 0.290990i | ||||
\(313\) | 399.201i | 1.27540i | 0.770283 | + | 0.637702i | \(0.220115\pi\) | ||||
−0.770283 | + | 0.637702i | \(0.779885\pi\) | |||||||
\(314\) | 30.5876i | 0.0974128i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −216.342 | −0.684627 | ||||||||
\(317\) | 237.853 | 0.750326 | 0.375163 | − | 0.926959i | \(-0.377587\pi\) | ||||
0.375163 | + | 0.926959i | \(0.377587\pi\) | |||||||
\(318\) | 82.5003 | − | 129.769i | 0.259435 | − | 0.408079i | ||||
\(319\) | 625.098 | 1.95956 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 87.4794 | − | 137.601i | 0.272521 | − | 0.428664i | ||||
\(322\) | 22.9461i | 0.0712611i | ||||||||
\(323\) | 340.597 | 1.05448 | ||||||||
\(324\) | −103.663 | + | 124.491i | −0.319947 | + | 0.384231i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 316.570i | 0.971075i | ||||||||
\(327\) | 164.483 | − | 258.724i | 0.503005 | − | 0.791205i | ||||
\(328\) | 176.917i | 0.539381i | ||||||||
\(329\) | 126.166i | 0.383483i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −300.437 | −0.907665 | −0.453832 | − | 0.891087i | \(-0.649944\pi\) | ||||
−0.453832 | + | 0.891087i | \(0.649944\pi\) | |||||||
\(332\) | 185.743 | 0.559466 | ||||||||
\(333\) | −527.734 | + | 247.299i | −1.58479 | + | 0.742639i | ||||
\(334\) | 407.263 | 1.21935 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −26.7929 | − | 17.0335i | −0.0797408 | − | 0.0506949i | ||||
\(337\) | − | 19.8344i | − | 0.0588558i | −0.999567 | − | 0.0294279i | \(-0.990631\pi\) | ||
0.999567 | − | 0.0294279i | \(-0.00936855\pi\) | |||||||
\(338\) | −323.471 | −0.957016 | ||||||||
\(339\) | 218.540 | − | 343.753i | 0.644660 | − | 1.01402i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 231.307i | − | 0.678321i | ||||||
\(342\) | −109.139 | − | 232.903i | −0.319121 | − | 0.681002i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 200.908i | − | 0.584034i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −408.805 | −1.18152 | ||||||||
\(347\) | 27.7575 | 0.0799929 | 0.0399965 | − | 0.999200i | \(-0.487265\pi\) | ||||
0.0399965 | + | 0.999200i | \(0.487265\pi\) | |||||||
\(348\) | −235.559 | − | 149.756i | −0.676894 | − | 0.430333i | ||||
\(349\) | −299.360 | −0.857766 | −0.428883 | − | 0.903360i | \(-0.641093\pi\) | ||||
−0.428883 | + | 0.903360i | \(0.641093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −68.7737 | + | 534.055i | −0.195936 | + | 1.52152i | ||||
\(352\) | 76.0088i | 0.215934i | ||||||||
\(353\) | −679.926 | −1.92614 | −0.963068 | − | 0.269259i | \(-0.913221\pi\) | ||||
−0.963068 | + | 0.269259i | \(0.913221\pi\) | |||||||
\(354\) | −8.92048 | − | 5.67116i | −0.0251991 | − | 0.0160202i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.7375i | − | 0.0301616i | ||||||
\(357\) | −112.896 | − | 71.7729i | −0.316234 | − | 0.201045i | ||||
\(358\) | − | 65.9164i | − | 0.184124i | ||||||
\(359\) | − | 33.8301i | − | 0.0942344i | −0.998889 | − | 0.0471172i | \(-0.984997\pi\) | ||
0.998889 | − | 0.0471172i | \(-0.0150034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.3645 | 0.131204 | ||||||||
\(362\) | −195.287 | −0.539466 | ||||||||
\(363\) | −95.8334 | + | 150.742i | −0.264004 | + | 0.415266i | ||||
\(364\) | −105.529 | −0.289915 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 28.5545 | − | 44.9149i | 0.0780176 | − | 0.122718i | ||||
\(367\) | 300.646i | 0.819199i | 0.912265 | + | 0.409599i | \(0.134332\pi\) | ||||
−0.912265 | + | 0.409599i | \(0.865668\pi\) | |||||||
\(368\) | −24.5304 | −0.0666587 | ||||||||
\(369\) | 509.753 | − | 238.873i | 1.38145 | − | 0.647352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 95.8948i | − | 0.258476i | ||||||
\(372\) | −55.4147 | + | 87.1649i | −0.148964 | + | 0.234314i | ||||
\(373\) | 119.661i | 0.320807i | 0.987052 | + | 0.160403i | \(0.0512795\pi\) | ||||
−0.987052 | + | 0.160403i | \(0.948720\pi\) | |||||||
\(374\) | 320.274i | 0.856347i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −134.877 | −0.358716 | ||||||||
\(377\) | −927.796 | −2.46100 | ||||||||
\(378\) | −12.9031 | + | 100.197i | −0.0341351 | + | 0.265072i | ||||
\(379\) | −149.138 | −0.393504 | −0.196752 | − | 0.980453i | \(-0.563039\pi\) | ||||
−0.196752 | + | 0.980453i | \(0.563039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 458.492 | + | 291.485i | 1.20339 | + | 0.765052i | ||||
\(382\) | 27.8786i | 0.0729806i | ||||||||
\(383\) | −296.924 | −0.775257 | −0.387629 | − | 0.921816i | \(-0.626706\pi\) | ||||
−0.387629 | + | 0.921816i | \(0.626706\pi\) | |||||||
\(384\) | 18.2096 | − | 28.6428i | 0.0474207 | − | 0.0745907i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 77.8705i | − | 0.201737i | ||||||
\(387\) | −578.878 | + | 271.265i | −1.49581 | + | 0.700944i | ||||
\(388\) | 17.1737i | 0.0442621i | ||||||||
\(389\) | 542.557i | 1.39475i | 0.716708 | + | 0.697374i | \(0.245648\pi\) | ||||
−0.716708 | + | 0.697374i | \(0.754352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −103.362 | −0.264353 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | −10.1630 | − | 6.46105i | −0.0258599 | − | 0.0164403i | ||||
\(394\) | 319.183 | 0.810109 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 219.005 | − | 102.627i | 0.553043 | − | 0.259159i | ||||
\(397\) | 598.546i | 1.50767i | 0.657062 | + | 0.753837i | \(0.271799\pi\) | ||||
−0.657062 | + | 0.753837i | \(0.728201\pi\) | |||||||
\(398\) | −265.136 | −0.666171 | ||||||||
\(399\) | −135.358 | − | 86.0533i | −0.339243 | − | 0.215672i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 430.276i | − | 1.07301i | −0.843898 | − | 0.536504i | \(-0.819745\pi\) | ||
0.843898 | − | 0.536504i | \(-0.180255\pi\) | |||||||
\(402\) | 423.326 | + | 269.128i | 1.05305 | + | 0.669472i | ||||
\(403\) | 343.316i | 0.851901i | ||||||||
\(404\) | − | 77.6072i | − | 0.192097i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −174.070 | −0.428743 | ||||||||
\(407\) | 870.098 | 2.13783 | ||||||||
\(408\) | 76.7285 | − | 120.691i | 0.188060 | − | 0.295810i | ||||
\(409\) | 680.639 | 1.66415 | 0.832077 | − | 0.554661i | \(-0.187152\pi\) | ||||
0.832077 | + | 0.554661i | \(0.187152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 126.208 | − | 198.519i | 0.307075 | − | 0.483015i | ||||
\(412\) | − | 16.9100i | − | 0.0410437i | ||||||
\(413\) | −6.59191 | −0.0159610 | ||||||||
\(414\) | 33.1209 | + | 70.6797i | 0.0800021 | + | 0.170724i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 112.815i | − | 0.271191i | ||||||
\(417\) | 66.0366 | − | 103.873i | 0.158361 | − | 0.249095i | ||||
\(418\) | 383.997i | 0.918653i | ||||||||
\(419\) | 630.755i | 1.50538i | 0.658374 | + | 0.752691i | \(0.271245\pi\) | ||||
−0.658374 | + | 0.752691i | \(0.728755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 174.563 | 0.414638 | 0.207319 | − | 0.978273i | \(-0.433526\pi\) | ||||
0.207319 | + | 0.978273i | \(0.433526\pi\) | |||||||
\(422\) | 489.755 | 1.16056 | ||||||||
\(423\) | 182.111 | + | 388.623i | 0.430522 | + | 0.918732i | ||||
\(424\) | 102.516 | 0.241783 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −28.4537 | − | 18.0893i | −0.0667928 | − | 0.0424632i | ||||
\(427\) | − | 33.1905i | − | 0.0777295i | ||||||
\(428\) | 108.703 | 0.253979 | ||||||||
\(429\) | 431.297 | − | 678.412i | 1.00536 | − | 1.58138i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 380.300i | 0.882367i | 0.897417 | + | 0.441183i | \(0.145441\pi\) | ||||
−0.897417 | + | 0.441183i | \(0.854559\pi\) | |||||||
\(432\) | −107.115 | − | 13.7940i | −0.247953 | − | 0.0319304i | ||||
\(433\) | − | 673.009i | − | 1.55429i | −0.629320 | − | 0.777146i | \(-0.716666\pi\) | ||
0.629320 | − | 0.777146i | \(-0.283334\pi\) | |||||||
\(434\) | 64.4117i | 0.148414i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 204.388 | 0.468780 | ||||||||
\(437\) | −123.928 | −0.283587 | ||||||||
\(438\) | 262.132 | + | 166.650i | 0.598476 | + | 0.380478i | ||||
\(439\) | −227.303 | −0.517775 | −0.258888 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258888 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.7326 | + | 57.0471i | 0.0606180 | + | 0.129358i | ||||
\(442\) | − | 475.363i | − | 1.07548i | ||||||
\(443\) | −583.446 | −1.31703 | −0.658517 | − | 0.752566i | \(-0.728816\pi\) | ||||
−0.658517 | + | 0.752566i | \(0.728816\pi\) | |||||||
\(444\) | −327.884 | − | 208.451i | −0.738478 | − | 0.469484i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 447.505i | 1.00338i | ||||||||
\(447\) | −55.7923 | − | 35.4697i | −0.124815 | − | 0.0793506i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | 513.491i | 1.14363i | 0.820382 | + | 0.571816i | \(0.193761\pi\) | ||||
−0.820382 | + | 0.571816i | \(0.806239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −840.453 | −1.86353 | ||||||||
\(452\) | 271.560 | 0.600797 | ||||||||
\(453\) | −154.952 | + | 243.733i | −0.342058 | + | 0.538043i | ||||
\(454\) | −11.0105 | −0.0242522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 91.9948 | − | 144.704i | 0.201743 | − | 0.317333i | ||||
\(457\) | − | 639.473i | − | 1.39928i | −0.714493 | − | 0.699642i | \(-0.753343\pi\) | ||
0.714493 | − | 0.699642i | \(-0.246657\pi\) | |||||||
\(458\) | 172.383 | 0.376382 | ||||||||
\(459\) | −451.346 | − | 58.1227i | −0.983324 | − | 0.126629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 482.830i | − | 1.04735i | −0.851917 | − | 0.523677i | \(-0.824560\pi\) | ||
0.851917 | − | 0.523677i | \(-0.175440\pi\) | |||||||
\(462\) | 80.9184 | − | 127.281i | 0.175148 | − | 0.275500i | ||||
\(463\) | − | 328.508i | − | 0.709521i | −0.934957 | − | 0.354760i | \(-0.884562\pi\) | ||
0.934957 | − | 0.354760i | \(-0.115438\pi\) | |||||||
\(464\) | − | 186.088i | − | 0.401053i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 113.360 | 0.243262 | ||||||||
\(467\) | −212.890 | −0.455868 | −0.227934 | − | 0.973677i | \(-0.573197\pi\) | ||||
−0.227934 | + | 0.973677i | \(0.573197\pi\) | |||||||
\(468\) | −325.057 | + | 152.323i | −0.694565 | + | 0.325477i | ||||
\(469\) | 312.823 | 0.666999 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 54.7573 | + | 34.8117i | 0.116257 | + | 0.0739102i | ||||
\(472\) | − | 7.04705i | − | 0.0149302i | ||||||
\(473\) | 954.423 | 2.01781 | ||||||||
\(474\) | −246.219 | + | 387.291i | −0.519449 | + | 0.817070i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 89.1859i | − | 0.187365i | ||||||
\(477\) | −138.417 | − | 295.380i | −0.290182 | − | 0.619246i | ||||
\(478\) | 164.410i | 0.343954i | ||||||||
\(479\) | 102.615i | 0.214228i | 0.994247 | + | 0.107114i | \(0.0341610\pi\) | ||||
−0.994247 | + | 0.107114i | \(0.965839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1291.44 | −2.68490 | ||||||||
\(482\) | 133.999 | 0.278006 | ||||||||
\(483\) | 41.0775 | + | 26.1149i | 0.0850467 | + | 0.0540681i | ||||
\(484\) | −119.084 | −0.246041 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 104.882 | + | 327.258i | 0.215807 | + | 0.673370i | ||||
\(487\) | − | 23.7100i | − | 0.0486858i | −0.999704 | − | 0.0243429i | \(-0.992251\pi\) | ||
0.999704 | − | 0.0243429i | \(-0.00774936\pi\) | |||||||
\(488\) | 35.4821 | 0.0727092 | ||||||||
\(489\) | 566.717 | + | 360.288i | 1.15893 | + | 0.736785i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 163.277i | − | 0.332540i | −0.986080 | − | 0.166270i | \(-0.946828\pi\) | ||
0.986080 | − | 0.166270i | \(-0.0531723\pi\) | |||||||
\(492\) | 316.713 | + | 201.349i | 0.643725 | + | 0.409246i | ||||
\(493\) | − | 784.109i | − | 1.59048i | ||||||
\(494\) | − | 569.944i | − | 1.15373i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.8590 | −0.138829 | ||||||||
\(497\) | −21.0263 | −0.0423064 | ||||||||
\(498\) | 211.393 | − | 332.512i | 0.424484 | − | 0.667695i | ||||
\(499\) | −311.153 | −0.623553 | −0.311776 | − | 0.950156i | \(-0.600924\pi\) | ||||
−0.311776 | + | 0.950156i | \(0.600924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 463.505 | − | 729.074i | 0.925161 | − | 1.45524i | ||||
\(502\) | − | 66.2386i | − | 0.131949i | ||||||
\(503\) | −875.585 | −1.74073 | −0.870363 | − | 0.492411i | \(-0.836116\pi\) | ||||
−0.870363 | + | 0.492411i | \(0.836116\pi\) | |||||||
\(504\) | −60.9859 | + | 28.5783i | −0.121004 | + | 0.0567030i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 116.533i | − | 0.230302i | ||||||
\(507\) | −368.142 | + | 579.071i | −0.726118 | + | 1.14215i | ||||
\(508\) | 362.202i | 0.712997i | ||||||||
\(509\) | 151.027i | 0.296713i | 0.988934 | + | 0.148356i | \(0.0473983\pi\) | ||||
−0.988934 | + | 0.148356i | \(0.952602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 193.706 | 0.379073 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −541.148 | − | 69.6871i | −1.05487 | − | 0.135842i | ||||
\(514\) | 82.2135 | 0.159948 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −359.661 | − | 228.653i | −0.697017 | − | 0.443125i | ||||
\(517\) | − | 640.741i | − | 1.23934i | ||||||
\(518\) | −242.294 | −0.467750 | ||||||||
\(519\) | −465.260 | + | 731.833i | −0.896454 | + | 1.41008i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 974.956i | 1.87132i | 0.352906 | + | 0.935659i | \(0.385193\pi\) | ||||
−0.352906 | + | 0.935659i | \(0.614807\pi\) | |||||||
\(522\) | −536.179 | + | 251.256i | −1.02716 | + | 0.481334i | ||||
\(523\) | − | 103.233i | − | 0.197386i | −0.995118 | − | 0.0986932i | \(-0.968534\pi\) | ||
0.995118 | − | 0.0986932i | \(-0.0314662\pi\) | |||||||
\(524\) | − | 8.02858i | − | 0.0153217i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 526.754 | 1.00143 | ||||||||
\(527\) | −290.147 | −0.550563 | ||||||||
\(528\) | 136.069 | + | 86.5054i | 0.257707 | + | 0.163836i | ||||
\(529\) | −491.391 | −0.928906 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.3048 | + | 9.51491i | −0.0382387 | + | 0.0179189i | ||||
\(532\) | − | 106.931i | − | 0.200998i | ||||||
\(533\) | 1247.44 | 2.34040 | ||||||||
\(534\) | −19.2221 | − | 12.2204i | −0.0359965 | − | 0.0228846i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 334.421i | 0.623920i | ||||||||
\(537\) | −118.002 | − | 75.0193i | −0.219743 | − | 0.139701i | ||||
\(538\) | 280.837i | 0.522001i | ||||||||
\(539\) | − | 94.0561i | − | 0.174501i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −195.027 | −0.360493 | −0.180247 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180247 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(542\) | 472.660 | 0.872067 | ||||||||
\(543\) | −222.255 | + | 349.598i | −0.409310 | + | 0.643826i | ||||
\(544\) | 95.3437 | 0.175264 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −120.102 | + | 188.916i | −0.219968 | + | 0.346000i | ||||
\(547\) | − | 340.245i | − | 0.622019i | −0.950407 | − | 0.311010i | \(-0.899333\pi\) | ||
0.950407 | − | 0.311010i | \(-0.100667\pi\) | |||||||
\(548\) | 156.827 | 0.286181 | ||||||||
\(549\) | −47.9079 | − | 102.235i | −0.0872639 | − | 0.186221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 940.120i | − | 1.70621i | ||||||
\(552\) | −27.9180 | + | 43.9137i | −0.0505760 | + | 0.0795539i | ||||
\(553\) | 286.194i | 0.517530i | ||||||||
\(554\) | − | 659.847i | − | 1.19106i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 82.0579 | 0.147586 | ||||||||
\(557\) | 211.476 | 0.379669 | 0.189834 | − | 0.981816i | \(-0.439205\pi\) | ||||
0.189834 | + | 0.981816i | \(0.439205\pi\) | |||||||
\(558\) | 92.9732 | + | 198.404i | 0.166619 | + | 0.355563i | ||||
\(559\) | −1416.59 | −2.53416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 573.346 | + | 364.503i | 1.02201 | + | 0.649737i | ||||
\(562\) | 730.656i | 1.30010i | ||||||||
\(563\) | 265.804 | 0.472120 | 0.236060 | − | 0.971738i | \(-0.424144\pi\) | ||||
0.236060 | + | 0.971738i | \(0.424144\pi\) | |||||||
\(564\) | −153.503 | + | 241.454i | −0.272169 | + | 0.428110i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 674.042i | − | 1.19089i | ||||||
\(567\) | 164.686 | + | 137.133i | 0.290452 | + | 0.241857i | ||||
\(568\) | − | 22.4780i | − | 0.0395740i | ||||||
\(569\) | − | 211.136i | − | 0.371066i | −0.982638 | − | 0.185533i | \(-0.940599\pi\) | ||
0.982638 | − | 0.185533i | \(-0.0594011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 701.534 | 1.22861 | 0.614303 | − | 0.789070i | \(-0.289437\pi\) | ||||
0.614303 | + | 0.789070i | \(0.289437\pi\) | |||||||
\(572\) | 535.935 | 0.936950 | ||||||||
\(573\) | 49.9076 | + | 31.7285i | 0.0870988 | + | 0.0553727i | ||||
\(574\) | 234.039 | 0.407734 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −30.5515 | − | 65.1967i | −0.0530408 | − | 0.113189i | ||||
\(577\) | − | 636.245i | − | 1.10268i | −0.834281 | − | 0.551339i | \(-0.814117\pi\) | ||
0.834281 | − | 0.551339i | \(-0.185883\pi\) | |||||||
\(578\) | −6.96374 | −0.0120480 | ||||||||
\(579\) | −139.402 | − | 88.6242i | −0.240763 | − | 0.153064i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 245.714i | − | 0.422916i | ||||||
\(582\) | 30.7440 | + | 19.5454i | 0.0528247 | + | 0.0335831i | ||||
\(583\) | 487.007i | 0.835346i | ||||||||
\(584\) | 207.081i | 0.354590i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −240.349 | −0.410151 | ||||||||
\(587\) | 183.730 | 0.312998 | 0.156499 | − | 0.987678i | \(-0.449979\pi\) | ||||
0.156499 | + | 0.987678i | \(0.449979\pi\) | |||||||
\(588\) | −22.5332 | + | 35.4437i | −0.0383217 | + | 0.0602784i | ||||
\(589\) | −347.876 | −0.590621 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 363.261 | − | 571.394i | 0.614655 | − | 0.966825i | ||||
\(592\) | − | 259.024i | − | 0.437540i | ||||||
\(593\) | 383.317 | 0.646403 | 0.323202 | − | 0.946330i | \(-0.395241\pi\) | ||||
0.323202 | + | 0.946330i | \(0.395241\pi\) | |||||||
\(594\) | 65.5289 | − | 508.858i | 0.110318 | − | 0.856663i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 44.0751i | − | 0.0739515i | ||||||
\(597\) | −301.751 | + | 474.641i | −0.505445 | + | 0.795043i | ||||
\(598\) | 172.963i | 0.289236i | ||||||||
\(599\) | − | 508.749i | − | 0.849331i | −0.905350 | − | 0.424666i | \(-0.860392\pi\) | ||
0.905350 | − | 0.424666i | \(-0.139608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −268.140 | −0.446157 | −0.223079 | − | 0.974800i | \(-0.571611\pi\) | ||||
−0.223079 | + | 0.974800i | \(0.571611\pi\) | |||||||
\(602\) | −265.776 | −0.441489 | ||||||||
\(603\) | 963.573 | − | 451.535i | 1.59796 | − | 0.748814i | ||||
\(604\) | −192.546 | −0.318784 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −138.931 | − | 88.3246i | −0.229258 | − | 0.145750i | ||||
\(607\) | 553.549i | 0.911942i | 0.889995 | + | 0.455971i | \(0.150708\pi\) | ||||
−0.889995 | + | 0.455971i | \(0.849292\pi\) | |||||||
\(608\) | 114.314 | 0.188016 | ||||||||
\(609\) | −198.108 | + | 311.616i | −0.325301 | + | 0.511684i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 951.014i | 1.55649i | ||||||||
\(612\) | −128.733 | − | 274.715i | −0.210348 | − | 0.448881i | ||||
\(613\) | − | 1059.92i | − | 1.72907i | −0.502574 | − | 0.864534i | \(-0.667614\pi\) | ||
0.502574 | − | 0.864534i | \(-0.332386\pi\) | |||||||
\(614\) | 441.398i | 0.718889i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 100.550 | 0.163231 | ||||||||
\(617\) | −767.572 | −1.24404 | −0.622020 | − | 0.783002i | \(-0.713688\pi\) | ||||
−0.622020 | + | 0.783002i | \(0.713688\pi\) | |||||||
\(618\) | −30.2719 | − | 19.2452i | −0.0489836 | − | 0.0311411i | ||||
\(619\) | 253.548 | 0.409608 | 0.204804 | − | 0.978803i | \(-0.434344\pi\) | ||||
0.204804 | + | 0.978803i | \(0.434344\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 164.224 | + | 21.1482i | 0.264451 | + | 0.0340551i | ||||
\(622\) | 601.935i | 0.967742i | ||||||||
\(623\) | −14.2044 | −0.0228001 | ||||||||
\(624\) | −201.960 | − | 128.395i | −0.323653 | − | 0.205761i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 564.556i | 0.901847i | ||||||||
\(627\) | 687.423 | + | 437.026i | 1.09637 | + | 0.697011i | ||||
\(628\) | 43.2574i | 0.0688813i | ||||||||
\(629\) | − | 1091.43i | − | 1.73519i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 906.659 | 1.43686 | 0.718430 | − | 0.695599i | \(-0.244861\pi\) | ||||
0.718430 | + | 0.695599i | \(0.244861\pi\) | |||||||
\(632\) | −305.954 | −0.484105 | ||||||||
\(633\) | 557.388 | − | 876.747i | 0.880550 | − | 1.38507i | ||||
\(634\) | 336.375 | 0.530560 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 116.673 | − | 183.521i | 0.183448 | − | 0.288556i | ||||
\(637\) | 139.602i | 0.219155i | ||||||||
\(638\) | 884.022 | 1.38561 | ||||||||
\(639\) | −64.7662 | + | 30.3498i | −0.101356 | + | 0.0474957i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 274.632i | − | 0.428444i | −0.976785 | − | 0.214222i | \(-0.931278\pi\) | ||
0.976785 | − | 0.214222i | \(-0.0687215\pi\) | |||||||
\(642\) | 123.715 | − | 194.598i | 0.192702 | − | 0.303111i | ||||
\(643\) | 330.746i | 0.514380i | 0.966361 | + | 0.257190i | \(0.0827965\pi\) | ||||
−0.966361 | + | 0.257190i | \(0.917203\pi\) | |||||||
\(644\) | 32.4507i | 0.0503892i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 481.677 | 0.745630 | ||||||||
\(647\) | 1040.01 | 1.60743 | 0.803717 | − | 0.595012i | \(-0.202853\pi\) | ||||
0.803717 | + | 0.595012i | \(0.202853\pi\) | |||||||
\(648\) | −146.601 | + | 176.057i | −0.226237 | + | 0.271693i | ||||
\(649\) | 33.4774 | 0.0515830 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 115.308 | + | 73.3068i | 0.177125 | + | 0.112606i | ||||
\(652\) | 447.698i | 0.686654i | ||||||||
\(653\) | 154.399 | 0.236445 | 0.118223 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118223 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(654\) | 232.614 | − | 365.891i | 0.355678 | − | 0.559466i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 250.198i | 0.381400i | ||||||||
\(657\) | 596.664 | − | 279.600i | 0.908165 | − | 0.425571i | ||||
\(658\) | 178.426i | 0.271164i | ||||||||
\(659\) | − | 1001.79i | − | 1.52016i | −0.649830 | − | 0.760080i | \(-0.725160\pi\) | ||
0.649830 | − | 0.760080i | \(-0.274840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1000.37 | 1.51342 | 0.756711 | − | 0.653749i | \(-0.226805\pi\) | ||||
0.756711 | + | 0.653749i | \(0.226805\pi\) | |||||||
\(662\) | −424.882 | −0.641816 | ||||||||
\(663\) | −850.985 | − | 541.010i | −1.28354 | − | 0.816003i | ||||
\(664\) | 262.680 | 0.395602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −746.328 | + | 349.733i | −1.12061 | + | 0.525125i | ||||
\(667\) | 285.301i | 0.427738i | ||||||||
\(668\) | 575.957 | 0.862212 | ||||||||
\(669\) | 801.114 | + | 509.305i | 1.19748 | + | 0.761293i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 168.560i | 0.251207i | ||||||||
\(672\) | −37.8909 | − | 24.0890i | −0.0563853 | − | 0.0358467i | ||||
\(673\) | − | 564.565i | − | 0.838878i | −0.907784 | − | 0.419439i | \(-0.862227\pi\) | ||
0.907784 | − | 0.419439i | \(-0.137773\pi\) | |||||||
\(674\) | − | 28.0501i | − | 0.0416174i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −457.457 | −0.676712 | ||||||||
\(677\) | 401.550 | 0.593131 | 0.296566 | − | 0.955013i | \(-0.404159\pi\) | ||||
0.296566 | + | 0.955013i | \(0.404159\pi\) | |||||||
\(678\) | 309.062 | − | 486.141i | 0.455844 | − | 0.717022i | ||||
\(679\) | 22.7187 | 0.0334590 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.5310 | + | 19.7108i | −0.0184009 | + | 0.0289439i | ||||
\(682\) | − | 327.118i | − | 0.479645i | ||||||
\(683\) | 860.803 | 1.26033 | 0.630163 | − | 0.776463i | \(-0.282988\pi\) | ||||
0.630163 | + | 0.776463i | \(0.282988\pi\) | |||||||
\(684\) | −154.346 | − | 329.374i | −0.225653 | − | 0.481541i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 196.189 | − | 308.596i | 0.285573 | − | 0.449193i | ||||
\(688\) | − | 284.127i | − | 0.412975i | ||||||
\(689\) | − | 722.835i | − | 1.04911i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.0935 | −0.0580224 | −0.0290112 | − | 0.999579i | \(-0.509236\pi\) | ||||
−0.0290112 | + | 0.999579i | \(0.509236\pi\) | |||||||
\(692\) | −578.137 | −0.835458 | ||||||||
\(693\) | −135.763 | − | 289.717i | −0.195906 | − | 0.418062i | ||||
\(694\) | 39.2551 | 0.0565635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −333.131 | − | 211.787i | −0.478637 | − | 0.304291i | ||||
\(697\) | 1054.25i | 1.51255i | ||||||||
\(698\) | −423.360 | −0.606532 | ||||||||
\(699\) | 129.015 | − | 202.935i | 0.184571 | − | 0.290321i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 888.946i | 1.26811i | 0.773287 | + | 0.634056i | \(0.218611\pi\) | ||||
−0.773287 | + | 0.634056i | \(0.781389\pi\) | |||||||
\(702\) | −97.2606 | + | 755.267i | −0.138548 | + | 1.07588i | ||||
\(703\) | − | 1308.59i | − | 1.86144i | ||||||
\(704\) | 107.493i | 0.152688i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −961.560 | −1.36198 | ||||||||
\(707\) | −102.665 | −0.145212 | ||||||||
\(708\) | −12.6155 | − | 8.02023i | −0.0178185 | − | 0.0113280i | ||||
\(709\) | −642.421 | −0.906094 | −0.453047 | − | 0.891487i | \(-0.649663\pi\) | ||||
−0.453047 | + | 0.891487i | \(0.649663\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 413.099 | + | 881.550i | 0.581011 | + | 1.23987i | ||||
\(712\) | − | 15.1852i | − | 0.0213275i | ||||||
\(713\) | 105.571 | 0.148066 | ||||||||
\(714\) | −159.659 | − | 101.502i | −0.223611 | − | 0.142160i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 93.2199i | − | 0.130195i | ||||||
\(717\) | 294.323 | + | 187.114i | 0.410492 | + | 0.260969i | ||||
\(718\) | − | 47.8430i | − | 0.0666338i | ||||||
\(719\) | − | 268.325i | − | 0.373192i | −0.982437 | − | 0.186596i | \(-0.940254\pi\) | ||
0.982437 | − | 0.186596i | \(-0.0597456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3698 | −0.0310261 | ||||||||
\(722\) | 66.9835 | 0.0927750 | ||||||||
\(723\) | 152.504 | − | 239.882i | 0.210932 | − | 0.331787i | ||||
\(724\) | −276.177 | −0.381460 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −135.529 | + | 213.181i | −0.186679 | + | 0.293638i | ||||
\(727\) | − | 23.6995i | − | 0.0325991i | −0.999867 | − | 0.0162995i | \(-0.994811\pi\) | ||
0.999867 | − | 0.0162995i | \(-0.00518853\pi\) | |||||||
\(728\) | −149.241 | −0.205001 | ||||||||
\(729\) | 705.216 | + | 184.693i | 0.967374 | + | 0.253351i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1197.21i | − | 1.63777i | ||||||
\(732\) | 40.3821 | − | 63.5193i | 0.0551668 | − | 0.0867749i | ||||
\(733\) | 308.228i | 0.420502i | 0.977647 | + | 0.210251i | \(0.0674282\pi\) | ||||
−0.977647 | + | 0.210251i | \(0.932572\pi\) | |||||||
\(734\) | 425.178i | 0.579261i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.6912 | −0.0471348 | ||||||||
\(737\) | −1588.69 | −2.15561 | ||||||||
\(738\) | 720.900 | − | 337.817i | 0.976830 | − | 0.457747i | ||||
\(739\) | −916.303 | −1.23992 | −0.619961 | − | 0.784632i | \(-0.712852\pi\) | ||||
−0.619961 | + | 0.784632i | \(0.712852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1020.30 | − | 648.652i | −1.37692 | − | 0.875374i | ||||
\(742\) | − | 135.616i | − | 0.182770i | ||||||
\(743\) | −1037.07 | −1.39579 | −0.697896 | − | 0.716199i | \(-0.745880\pi\) | ||||
−0.697896 | + | 0.716199i | \(0.745880\pi\) | |||||||
\(744\) | −78.3682 | + | 123.270i | −0.105334 | + | 0.165685i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 169.226i | 0.226845i | ||||||||
\(747\) | −354.670 | − | 756.862i | −0.474792 | − | 1.01320i | ||||
\(748\) | 452.935i | 0.605528i | ||||||||
\(749\) | − | 143.800i | − | 0.191990i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8752 | −0.0224703 | −0.0112352 | − | 0.999937i | \(-0.503576\pi\) | ||||
−0.0112352 | + | 0.999937i | \(0.503576\pi\) | |||||||
\(752\) | −190.745 | −0.253650 | ||||||||
\(753\) | −118.579 | − | 75.3860i | −0.157475 | − | 0.100114i | ||||
\(754\) | −1312.10 | −1.74019 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.2477 | + | 141.700i | −0.0241371 | + | 0.187434i | ||||
\(757\) | − | 478.309i | − | 0.631848i | −0.948784 | − | 0.315924i | \(-0.897685\pi\) | ||
0.948784 | − | 0.315924i | \(-0.102315\pi\) | |||||||
\(758\) | −210.913 | −0.278249 | ||||||||
\(759\) | −208.614 | − | 132.626i | −0.274854 | − | 0.174738i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1498.03i | − | 1.96850i | −0.176790 | − | 0.984249i | \(-0.556571\pi\) | ||
0.176790 | − | 0.984249i | \(-0.443429\pi\) | |||||||
\(762\) | 648.406 | + | 412.222i | 0.850927 | + | 0.540973i | ||||
\(763\) | − | 270.380i | − | 0.354365i | ||||||
\(764\) | 39.4263i | 0.0516051i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −419.913 | −0.548190 | ||||||||
\(767\) | −49.6885 | −0.0647829 | ||||||||
\(768\) | 25.7522 | − | 40.5071i | 0.0335315 | − | 0.0527436i | ||||
\(769\) | 116.918 | 0.152038 | 0.0760192 | − | 0.997106i | \(-0.475779\pi\) | ||||
0.0760192 | + | 0.997106i | \(0.475779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 93.5670 | − | 147.177i | 0.121358 | − | 0.190891i | ||||
\(772\) | − | 110.125i | − | 0.142650i | ||||||
\(773\) | −1151.33 | −1.48943 | −0.744713 | − | 0.667385i | \(-0.767414\pi\) | ||||
−0.744713 | + | 0.667385i | \(0.767414\pi\) | |||||||
\(774\) | −818.658 | + | 383.627i | −1.05770 | + | 0.495642i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.2873i | 0.0312981i | ||||||||
\(777\) | −275.755 | + | 433.750i | −0.354897 | + | 0.558237i | ||||
\(778\) | 767.291i | 0.986235i | ||||||||
\(779\) | 1264.00i | 1.62260i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 106.783 | 0.136726 | ||||||||
\(782\) | −146.176 | −0.186926 | ||||||||
\(783\) | −160.431 | + | 1245.81i | −0.204893 | + | 1.59107i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.3726 | − | 9.13731i | −0.0182857 | − | 0.0116251i | ||||
\(787\) | 453.417i | 0.576133i | 0.957610 | + | 0.288066i | \(0.0930124\pi\) | ||||
−0.957610 | + | 0.288066i | \(0.906988\pi\) | |||||||
\(788\) | 451.393 | 0.572833 | ||||||||
\(789\) | 599.498 | − | 942.983i | 0.759819 | − | 1.19516i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 359.240i | − | 0.454160i | ||||||
\(792\) | 309.720 | − | 145.136i | 0.391061 | − | 0.183253i | ||||
\(793\) | − | 250.183i | − | 0.315489i | ||||||
\(794\) | 846.472i | 1.06609i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −374.959 | −0.471054 | ||||||||
\(797\) | −473.995 | −0.594724 | −0.297362 | − | 0.954765i | \(-0.596107\pi\) | ||||
−0.297362 | + | 0.954765i | \(0.596107\pi\) | |||||||
\(798\) | −191.425 | − | 121.698i | −0.239881 | − | 0.152503i | ||||
\(799\) | −803.731 | −1.00592 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43.7533 | + | 20.5030i | −0.0546233 | + | 0.0255968i | ||||
\(802\) | − | 608.502i | − | 0.758731i | ||||||
\(803\) | −983.747 | −1.22509 | ||||||||
\(804\) | 598.673 | + | 380.604i | 0.744619 | + | 0.473388i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 485.522i | 0.602385i | ||||||||
\(807\) | 502.747 | + | 319.620i | 0.622983 | + | 0.396059i | ||||
\(808\) | − | 109.753i | − | 0.135833i | ||||||
\(809\) | − | 875.429i | − | 1.08211i | −0.840986 | − | 0.541056i | \(-0.818025\pi\) | ||
0.840986 | − | 0.541056i | \(-0.181975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −764.492 | −0.942653 | −0.471326 | − | 0.881959i | \(-0.656225\pi\) | ||||
−0.471326 | + | 0.881959i | \(0.656225\pi\) | |||||||
\(812\) | −246.172 | −0.303167 | ||||||||
\(813\) | 537.933 | − | 846.145i | 0.661665 | − | 1.04077i | ||||
\(814\) | 1230.50 | 1.51168 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 108.510 | − | 170.682i | 0.132979 | − | 0.209169i | ||||
\(817\) | − | 1435.41i | − | 1.75693i | ||||||
\(818\) | 962.568 | 1.17673 | ||||||||
\(819\) | 201.505 | + | 430.009i | 0.246037 | + | 0.525042i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 531.214i | − | 0.647032i | −0.946223 | − | 0.323516i | \(-0.895135\pi\) | ||
0.946223 | − | 0.323516i | \(-0.104865\pi\) | |||||||
\(822\) | 178.485 | − | 280.748i | 0.217135 | − | 0.341543i | ||||
\(823\) | − | 655.979i | − | 0.797059i | −0.917156 | − | 0.398529i | \(-0.869521\pi\) | ||
0.917156 | − | 0.398529i | \(-0.130479\pi\) | |||||||
\(824\) | − | 23.9143i | − | 0.0290223i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.32237 | −0.0112862 | ||||||||
\(827\) | 1340.71 | 1.62118 | 0.810588 | − | 0.585617i | \(-0.199148\pi\) | ||||
0.810588 | + | 0.585617i | \(0.199148\pi\) | |||||||
\(828\) | 46.8400 | + | 99.9563i | 0.0565701 | + | 0.120720i | ||||
\(829\) | −753.042 | −0.908374 | −0.454187 | − | 0.890906i | \(-0.650070\pi\) | ||||
−0.454187 | + | 0.890906i | \(0.650070\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1181.24 | − | 750.970i | −1.42147 | − | 0.903694i | ||||
\(832\) | − | 159.545i | − | 0.191761i | ||||||
\(833\) | −117.982 | −0.141635 | ||||||||
\(834\) | 93.3899 | − | 146.898i | 0.111978 | − | 0.176137i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 543.054i | 0.649586i | ||||||||
\(837\) | 460.991 | + | 59.3648i | 0.550766 | + | 0.0709257i | ||||
\(838\) | 892.023i | 1.06447i | ||||||||
\(839\) | − | 1123.90i | − | 1.33957i | −0.742556 | − | 0.669784i | \(-0.766387\pi\) | ||
0.742556 | − | 0.669784i | \(-0.233613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1323.30 | −1.57349 | ||||||||
\(842\) | 246.869 | 0.293193 | ||||||||
\(843\) | 1308.00 | + | 831.558i | 1.55161 | + | 0.986427i | ||||
\(844\) | 692.617 | 0.820637 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 257.544 | + | 549.597i | 0.304425 | + | 0.649641i | ||||
\(847\) | 157.533i | 0.185989i | ||||||||
\(848\) | 144.979 | 0.170966 | ||||||||
\(849\) | −1206.65 | − | 767.126i | −1.42127 | − | 0.903564i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 397.122i | 0.466653i | ||||||||
\(852\) | −40.2396 | − | 25.5822i | −0.0472296 | − | 0.0300260i | ||||
\(853\) | 849.611i | 0.996027i | 0.867169 | + | 0.498014i | \(0.165937\pi\) | ||||
−0.867169 | + | 0.498014i | \(0.834063\pi\) | |||||||
\(854\) | − | 46.9384i | − | 0.0549630i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 153.729 | 0.179590 | ||||||||
\(857\) | −474.061 | −0.553164 | −0.276582 | − | 0.960990i | \(-0.589202\pi\) | ||||
−0.276582 | + | 0.960990i | \(0.589202\pi\) | |||||||
\(858\) | 609.947 | − | 959.419i | 0.710894 | − | 1.11820i | ||||
\(859\) | −357.378 | −0.416039 | −0.208020 | − | 0.978125i | \(-0.566702\pi\) | ||||
−0.208020 | + | 0.978125i | \(0.566702\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 266.359 | − | 418.972i | 0.309361 | − | 0.486611i | ||||
\(862\) | 537.826i | 0.623928i | ||||||||
\(863\) | −39.7566 | −0.0460680 | −0.0230340 | − | 0.999735i | \(-0.507333\pi\) | ||||
−0.0230340 | + | 0.999735i | \(0.507333\pi\) | |||||||
\(864\) | −151.484 | − | 19.5076i | −0.175329 | − | 0.0225782i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 951.778i | − | 1.09905i | ||||||
\(867\) | −7.92541 | + | 12.4663i | −0.00914119 | + | 0.0143787i | ||||
\(868\) | 91.0918i | 0.104945i | ||||||||
\(869\) | − | 1453.45i | − | 1.67256i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2357.99 | 2.70722 | ||||||||
\(872\) | 289.049 | 0.331478 | ||||||||
\(873\) | 69.9793 | − | 32.7927i | 0.0801596 | − | 0.0375632i | ||||
\(874\) | −175.260 | −0.200527 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 370.711 | + | 235.678i | 0.423186 | + | 0.269039i | ||||
\(877\) | − | 758.777i | − | 0.865196i | −0.901587 | − | 0.432598i | \(-0.857597\pi\) | ||
0.901587 | − | 0.432598i | \(-0.142403\pi\) | |||||||
\(878\) | −321.455 | −0.366122 | ||||||||
\(879\) | −273.540 | + | 430.266i | −0.311195 | + | 0.489495i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 568.736i | 0.645557i | 0.946474 | + | 0.322779i | \(0.104617\pi\) | ||||
−0.946474 | + | 0.322779i | \(0.895383\pi\) | |||||||
\(882\) | 37.8055 | + | 80.6768i | 0.0428634 | + | 0.0914703i | ||||
\(883\) | 38.0294i | 0.0430684i | 0.999768 | + | 0.0215342i | \(0.00685508\pi\) | ||||
−0.999768 | + | 0.0215342i | \(0.993145\pi\) | |||||||
\(884\) | − | 672.265i | − | 0.760481i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −825.118 | −0.931284 | ||||||||
\(887\) | −906.851 | −1.02238 | −0.511190 | − | 0.859468i | \(-0.670795\pi\) | ||||
−0.511190 | + | 0.859468i | \(0.670795\pi\) | |||||||
\(888\) | −463.698 | − | 294.794i | −0.522183 | − | 0.331975i | ||||
\(889\) | 479.149 | 0.538975 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −836.367 | − | 696.438i | −0.938683 | − | 0.781636i | ||||
\(892\) | 632.868i | 0.709494i | ||||||||
\(893\) | −963.646 | −1.07911 | ||||||||
\(894\) | −78.9022 | − | 50.1618i | −0.0882575 | − | 0.0561094i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | 309.634 | + | 196.849i | 0.345189 | + | 0.219452i | ||||
\(898\) | 726.185i | 0.808670i | ||||||||
\(899\) | 800.866i | 0.890841i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 610.890 | 0.678013 | ||||||||
\(902\) | −1188.58 | −1.31772 | ||||||||
\(903\) | −302.479 | + | 475.786i | −0.334971 | + | 0.526895i | ||||
\(904\) | 384.044 | 0.424828 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −219.136 | + | 344.691i | −0.241872 | + | 0.380454i | ||||
\(907\) | 108.414i | 0.119530i | 0.998212 | + | 0.0597652i | \(0.0190352\pi\) | ||||
−0.998212 | + | 0.0597652i | \(0.980965\pi\) | |||||||
\(908\) | −15.5712 | −0.0171489 | ||||||||
\(909\) | −316.233 | + | 148.188i | −0.347891 | + | 0.163024i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 348.871i | 0.382954i | 0.981497 | + | 0.191477i | \(0.0613278\pi\) | ||||
−0.981497 | + | 0.191477i | \(0.938672\pi\) | |||||||
\(912\) | 130.100 | − | 204.642i | 0.142654 | − | 0.224388i | ||||
\(913\) | 1247.87i | 1.36678i | ||||||||
\(914\) | − | 904.352i | − | 0.989444i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 243.786 | 0.266142 | ||||||||
\(917\) | −10.6208 | −0.0115821 | ||||||||
\(918\) | −638.299 | − | 82.1979i | −0.695315 | − | 0.0895402i | ||||
\(919\) | 1186.93 | 1.29155 | 0.645773 | − | 0.763529i | \(-0.276535\pi\) | ||||
0.645773 | + | 0.763529i | \(0.276535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 790.180 | + | 502.354i | 0.857959 | + | 0.545444i | ||||
\(922\) | − | 682.825i | − | 0.740591i | ||||||
\(923\) | −158.492 | −0.171714 | ||||||||
\(924\) | 114.436 | − | 180.003i | 0.123848 | − | 0.194808i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 464.581i | − | 0.501707i | ||||||
\(927\) | −68.9047 | + | 32.2891i | −0.0743309 | + | 0.0348318i | ||||
\(928\) | − | 263.169i | − | 0.283587i | ||||||
\(929\) | − | 515.060i | − | 0.554424i | −0.960809 | − | 0.277212i | \(-0.910589\pi\) | ||
0.960809 | − | 0.277212i | \(-0.0894105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −141.456 | −0.151940 | ||||||||
\(932\) | 160.315 | 0.172012 | ||||||||
\(933\) | 1077.57 | + | 685.061i | 1.15495 | + | 0.734256i | ||||
\(934\) | −301.072 | −0.322347 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −459.699 | + | 215.417i | −0.491132 | + | 0.230147i | ||||
\(937\) | − | 489.541i | − | 0.522456i | −0.965277 | − | 0.261228i | \(-0.915873\pi\) | ||
0.965277 | − | 0.261228i | \(-0.0841274\pi\) | |||||||
\(938\) | 442.398 | 0.471640 | ||||||||
\(939\) | 1010.66 | + | 642.520i | 1.07631 | + | 0.684260i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 833.933i | 0.886220i | 0.896467 | + | 0.443110i | \(0.146125\pi\) | ||||
−0.896467 | + | 0.443110i | \(0.853875\pi\) | |||||||
\(942\) | 77.4385 | + | 49.2312i | 0.0822065 | + | 0.0522624i | ||||
\(943\) | − | 383.592i | − | 0.406778i | ||||||
\(944\) | − | 9.96603i | − | 0.0105572i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1349.76 | 1.42681 | ||||||||
\(947\) | −854.924 | −0.902771 | −0.451385 | − | 0.892329i | \(-0.649070\pi\) | ||||
−0.451385 | + | 0.892329i | \(0.649070\pi\) | |||||||
\(948\) | −348.206 | + | 547.712i | −0.367306 | + | 0.577755i | ||||
\(949\) | 1460.12 | 1.53859 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 382.828 | − | 602.171i | 0.402553 | − | 0.633198i | ||||
\(952\) | − | 126.128i | − | 0.132487i | ||||||
\(953\) | 1564.07 | 1.64121 | 0.820603 | − | 0.571498i | \(-0.193638\pi\) | ||||
0.820603 | + | 0.571498i | \(0.193638\pi\) | |||||||
\(954\) | −195.751 | − | 417.731i | −0.205189 | − | 0.437873i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 232.511i | 0.243212i | ||||||||
\(957\) | 1006.10 | − | 1582.56i | 1.05131 | − | 1.65366i | ||||
\(958\) | 145.120i | 0.151482i | ||||||||
\(959\) | − | 207.463i | − | 0.216332i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −664.653 | −0.691626 | ||||||||
\(962\) | −1826.37 | −1.89851 | ||||||||
\(963\) | −207.565 | − | 442.942i | −0.215540 | − | 0.459960i | ||||
\(964\) | 189.503 | 0.196580 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 58.0924 | + | 36.9320i | 0.0601371 | + | 0.0382319i | ||||
\(967\) | 64.0844i | 0.0662714i | 0.999451 | + | 0.0331357i | \(0.0105493\pi\) | ||||
−0.999451 | + | 0.0331357i | \(0.989451\pi\) | |||||||
\(968\) | −168.410 | −0.173977 | ||||||||
\(969\) | 548.196 | − | 862.288i | 0.565733 | − | 0.889874i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 400.825i | − | 0.412796i | −0.978468 | − | 0.206398i | \(-0.933826\pi\) | ||
0.978468 | − | 0.206398i | \(-0.0661742\pi\) | |||||||
\(972\) | 148.326 | + | 462.812i | 0.152599 | + | 0.476144i | ||||
\(973\) | − | 108.552i | − | 0.111565i | ||||||
\(974\) | − | 33.5310i | − | 0.0344261i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50.1793 | 0.0514132 | ||||||||
\(977\) | −1473.80 | −1.50850 | −0.754248 | − | 0.656590i | \(-0.771998\pi\) | ||||
−0.754248 | + | 0.656590i | \(0.771998\pi\) | |||||||
\(978\) | 801.459 | + | 509.524i | 0.819488 | + | 0.520986i | ||||
\(979\) | 72.1380 | 0.0736854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −390.273 | − | 832.839i | −0.397831 | − | 0.848970i | ||||
\(982\) | − | 230.909i | − | 0.235141i | ||||||
\(983\) | 1166.05 | 1.18622 | 0.593109 | − | 0.805122i | \(-0.297900\pi\) | ||||
0.593109 | + | 0.805122i | \(0.297900\pi\) | |||||||
\(984\) | 447.900 | + | 284.750i | 0.455183 | + | 0.289380i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1108.90i | − | 1.12464i | ||||||
\(987\) | 319.414 | + | 203.066i | 0.323621 | + | 0.205741i | ||||
\(988\) | − | 806.023i | − | 0.815813i | ||||||
\(989\) | 435.609i | 0.440454i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 575.510 | 0.580736 | 0.290368 | − | 0.956915i | \(-0.406222\pi\) | ||||
0.290368 | + | 0.956915i | \(0.406222\pi\) | |||||||
\(992\) | −97.3813 | −0.0981666 | ||||||||
\(993\) | −483.557 | + | 760.614i | −0.486966 | + | 0.765976i | ||||
\(994\) | −29.7356 | −0.0299151 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 298.955 | − | 470.243i | 0.300156 | − | 0.472132i | ||||
\(997\) | − | 304.683i | − | 0.305600i | −0.988257 | − | 0.152800i | \(-0.951171\pi\) | ||
0.988257 | − | 0.152800i | \(-0.0488290\pi\) | |||||||
\(998\) | −440.036 | −0.440918 | ||||||||
\(999\) | −223.310 | + | 1734.09i | −0.223534 | + | 1.73583i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.c.c.449.25 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.c.449.7 | 32 | ||
5.2 | odd | 4 | 210.3.e.a.71.10 | yes | 16 | ||
5.3 | odd | 4 | 1050.3.e.d.701.7 | 16 | |||
5.4 | even | 2 | inner | 1050.3.c.c.449.8 | 32 | ||
15.2 | even | 4 | 210.3.e.a.71.2 | ✓ | 16 | ||
15.8 | even | 4 | 1050.3.e.d.701.15 | 16 | |||
15.14 | odd | 2 | inner | 1050.3.c.c.449.26 | 32 | ||
20.7 | even | 4 | 1680.3.l.c.1121.14 | 16 | |||
60.47 | odd | 4 | 1680.3.l.c.1121.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.2 | ✓ | 16 | 15.2 | even | 4 | ||
210.3.e.a.71.10 | yes | 16 | 5.2 | odd | 4 | ||
1050.3.c.c.449.7 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.c.449.8 | 32 | 5.4 | even | 2 | inner | ||
1050.3.c.c.449.25 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.c.c.449.26 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.e.d.701.7 | 16 | 5.3 | odd | 4 | |||
1050.3.e.d.701.15 | 16 | 15.8 | even | 4 | |||
1680.3.l.c.1121.13 | 16 | 60.47 | odd | 4 | |||
1680.3.l.c.1121.14 | 16 | 20.7 | even | 4 |