Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,5,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (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: | \(36.5929669317\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.12 | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.5.d.a.235.11 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 0.345303 | 0.0138121 | 0.00690607 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690607 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(6\) | − | 14.6969i | − | 0.408248i | ||||||
\(7\) | 29.1133 | 0.594149 | 0.297075 | − | 0.954854i | \(-0.403989\pi\) | ||||
0.297075 | + | 0.954854i | \(0.403989\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 0.976665i | 0.00976665i | ||||||||
\(11\) | − | 119.336i | − | 0.986252i | −0.869958 | − | 0.493126i | \(-0.835854\pi\) | ||
0.869958 | − | 0.493126i | \(-0.164146\pi\) | |||||||
\(12\) | 41.5692 | 0.288675 | ||||||||
\(13\) | 304.514i | 1.80186i | 0.433968 | + | 0.900928i | \(0.357113\pi\) | ||||
−0.433968 | + | 0.900928i | \(0.642887\pi\) | |||||||
\(14\) | 82.3449i | 0.420127i | ||||||||
\(15\) | −1.79425 | −0.00797444 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | −229.594 | −0.794443 | −0.397222 | − | 0.917723i | \(-0.630026\pi\) | ||||
−0.397222 | + | 0.917723i | \(0.630026\pi\) | |||||||
\(18\) | 76.3675i | 0.235702i | ||||||||
\(19\) | −43.2841 | −0.119901 | −0.0599503 | − | 0.998201i | \(-0.519094\pi\) | ||||
−0.0599503 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(20\) | −2.76243 | −0.00690607 | ||||||||
\(21\) | −151.277 | −0.343032 | ||||||||
\(22\) | 337.535 | 0.697385 | ||||||||
\(23\) | − | 559.546i | − | 1.05774i | −0.848702 | − | 0.528871i | \(-0.822615\pi\) | ||
0.848702 | − | 0.528871i | \(-0.177385\pi\) | |||||||
\(24\) | 117.576i | 0.204124i | ||||||||
\(25\) | −624.881 | −0.999809 | ||||||||
\(26\) | −861.295 | −1.27410 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −232.906 | −0.297075 | ||||||||
\(29\) | −303.900 | −0.361355 | −0.180678 | − | 0.983542i | \(-0.557829\pi\) | ||||
−0.180678 | + | 0.983542i | \(0.557829\pi\) | |||||||
\(30\) | − | 5.07490i | − | 0.00563878i | ||||||
\(31\) | − | 487.779i | − | 0.507574i | −0.967260 | − | 0.253787i | \(-0.918324\pi\) | ||
0.967260 | − | 0.253787i | \(-0.0816762\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 620.091i | 0.569413i | ||||||||
\(34\) | − | 649.390i | − | 0.561756i | ||||||
\(35\) | 10.0529 | 0.00820647 | ||||||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | 59.5851i | 0.0435245i | 0.999763 | + | 0.0217623i | \(0.00692769\pi\) | ||||
−0.999763 | + | 0.0217623i | \(0.993072\pi\) | |||||||
\(38\) | − | 122.426i | − | 0.0847825i | ||||||
\(39\) | − | 1582.30i | − | 1.04030i | ||||||
\(40\) | − | 7.81332i | − | 0.00488333i | ||||||
\(41\) | 2970.49 | 1.76710 | 0.883548 | − | 0.468341i | \(-0.155148\pi\) | ||||
0.883548 | + | 0.468341i | \(0.155148\pi\) | |||||||
\(42\) | − | 427.876i | − | 0.242560i | ||||||
\(43\) | − | 556.297i | − | 0.300864i | −0.988620 | − | 0.150432i | \(-0.951934\pi\) | ||
0.988620 | − | 0.150432i | \(-0.0480664\pi\) | |||||||
\(44\) | 954.692i | 0.493126i | ||||||||
\(45\) | 9.32319 | 0.00460404 | ||||||||
\(46\) | 1582.63 | 0.747937 | ||||||||
\(47\) | − | 880.855i | − | 0.398757i | −0.979923 | − | 0.199379i | \(-0.936108\pi\) | ||
0.979923 | − | 0.199379i | \(-0.0638924\pi\) | |||||||
\(48\) | −332.554 | −0.144338 | ||||||||
\(49\) | −1553.42 | −0.646987 | ||||||||
\(50\) | − | 1767.43i | − | 0.706972i | ||||||
\(51\) | 1193.01 | 0.458672 | ||||||||
\(52\) | − | 2436.11i | − | 0.900928i | ||||||
\(53\) | −913.151 | −0.325081 | −0.162540 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162540 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(54\) | − | 396.817i | − | 0.136083i | ||||||
\(55\) | − | 41.2073i | − | 0.0136222i | ||||||
\(56\) | − | 658.759i | − | 0.210063i | ||||||
\(57\) | 224.911 | 0.0692246 | ||||||||
\(58\) | − | 859.558i | − | 0.255517i | ||||||
\(59\) | 2730.34 | − | 2159.31i | 0.784355 | − | 0.620312i | ||||
\(60\) | 14.3540 | 0.00398722 | ||||||||
\(61\) | − | 2119.11i | − | 0.569500i | −0.958602 | − | 0.284750i | \(-0.908089\pi\) | ||
0.958602 | − | 0.284750i | \(-0.0919105\pi\) | |||||||
\(62\) | 1379.65 | 0.358909 | ||||||||
\(63\) | 786.059 | 0.198050 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 105.150i | 0.0248875i | ||||||||
\(66\) | −1753.88 | −0.402636 | ||||||||
\(67\) | − | 5970.68i | − | 1.33007i | −0.746813 | − | 0.665034i | \(-0.768417\pi\) | ||
0.746813 | − | 0.665034i | \(-0.231583\pi\) | |||||||
\(68\) | 1836.75 | 0.397222 | ||||||||
\(69\) | 2907.49i | 0.610688i | ||||||||
\(70\) | 28.4340i | 0.00580285i | ||||||||
\(71\) | 3795.02 | 0.752832 | 0.376416 | − | 0.926451i | \(-0.377156\pi\) | ||||
0.376416 | + | 0.926451i | \(0.377156\pi\) | |||||||
\(72\) | − | 610.940i | − | 0.117851i | ||||||
\(73\) | − | 8963.57i | − | 1.68204i | −0.541007 | − | 0.841018i | \(-0.681957\pi\) | ||
0.541007 | − | 0.841018i | \(-0.318043\pi\) | |||||||
\(74\) | −168.532 | −0.0307765 | ||||||||
\(75\) | 3246.98 | 0.577240 | ||||||||
\(76\) | 346.273 | 0.0599503 | ||||||||
\(77\) | − | 3474.28i | − | 0.585981i | ||||||
\(78\) | 4475.42 | 0.735605 | ||||||||
\(79\) | 2347.21 | 0.376095 | 0.188047 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188047 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(80\) | 22.0994 | 0.00345303 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 8401.81i | 1.24952i | ||||||||
\(83\) | − | 193.448i | − | 0.0280807i | −0.999901 | − | 0.0140403i | \(-0.995531\pi\) | ||
0.999901 | − | 0.0140403i | \(-0.00446933\pi\) | |||||||
\(84\) | 1210.22 | 0.171516 | ||||||||
\(85\) | −79.2796 | −0.0109730 | ||||||||
\(86\) | 1573.44 | 0.212743 | ||||||||
\(87\) | 1579.11 | 0.208629 | ||||||||
\(88\) | −2700.28 | −0.348693 | ||||||||
\(89\) | 769.166i | 0.0971047i | 0.998821 | + | 0.0485523i | \(0.0154608\pi\) | ||||
−0.998821 | + | 0.0485523i | \(0.984539\pi\) | |||||||
\(90\) | 26.3700i | 0.00325555i | ||||||||
\(91\) | 8865.40i | 1.07057i | ||||||||
\(92\) | 4476.37i | 0.528871i | ||||||||
\(93\) | 2534.57i | 0.293048i | ||||||||
\(94\) | 2491.43 | 0.281964 | ||||||||
\(95\) | −14.9461 | −0.00165608 | ||||||||
\(96\) | − | 940.604i | − | 0.102062i | ||||||
\(97\) | − | 3332.34i | − | 0.354166i | −0.984196 | − | 0.177083i | \(-0.943334\pi\) | ||
0.984196 | − | 0.177083i | \(-0.0566660\pi\) | |||||||
\(98\) | − | 4393.72i | − | 0.457489i | ||||||
\(99\) | − | 3222.09i | − | 0.328751i | ||||||
\(100\) | 4999.05 | 0.499905 | ||||||||
\(101\) | 567.019i | 0.0555847i | 0.999614 | + | 0.0277923i | \(0.00884772\pi\) | ||||
−0.999614 | + | 0.0277923i | \(0.991152\pi\) | |||||||
\(102\) | 3374.33i | 0.324330i | ||||||||
\(103\) | − | 10647.0i | − | 1.00358i | −0.864989 | − | 0.501790i | \(-0.832675\pi\) | ||
0.864989 | − | 0.501790i | \(-0.167325\pi\) | |||||||
\(104\) | 6890.36 | 0.637052 | ||||||||
\(105\) | −52.2365 | −0.00473801 | ||||||||
\(106\) | − | 2582.78i | − | 0.229867i | ||||||
\(107\) | −2700.26 | −0.235851 | −0.117925 | − | 0.993022i | \(-0.537624\pi\) | ||||
−0.117925 | + | 0.993022i | \(0.537624\pi\) | |||||||
\(108\) | 1122.37 | 0.0962250 | ||||||||
\(109\) | − | 3409.15i | − | 0.286941i | −0.989655 | − | 0.143471i | \(-0.954174\pi\) | ||
0.989655 | − | 0.143471i | \(-0.0458263\pi\) | |||||||
\(110\) | 116.552 | 0.00963238 | ||||||||
\(111\) | − | 309.613i | − | 0.0251289i | ||||||
\(112\) | 1863.25 | 0.148537 | ||||||||
\(113\) | − | 19110.5i | − | 1.49663i | −0.663344 | − | 0.748314i | \(-0.730863\pi\) | ||
0.663344 | − | 0.748314i | \(-0.269137\pi\) | |||||||
\(114\) | 636.144i | 0.0489492i | ||||||||
\(115\) | − | 193.213i | − | 0.0146097i | ||||||
\(116\) | 2431.20 | 0.180678 | ||||||||
\(117\) | 8221.87i | 0.600619i | ||||||||
\(118\) | 6107.44 | + | 7722.57i | 0.438627 | + | 0.554623i | ||||
\(119\) | −6684.24 | −0.472018 | ||||||||
\(120\) | 40.5992i | 0.00281939i | ||||||||
\(121\) | 399.803 | 0.0273071 | ||||||||
\(122\) | 5993.74 | 0.402697 | ||||||||
\(123\) | −15435.1 | −1.02023 | ||||||||
\(124\) | 3902.23i | 0.253787i | ||||||||
\(125\) | −431.588 | −0.0276216 | ||||||||
\(126\) | 2223.31i | 0.140042i | ||||||||
\(127\) | −8527.84 | −0.528727 | −0.264364 | − | 0.964423i | \(-0.585162\pi\) | ||||
−0.264364 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | 2890.60i | 0.173704i | ||||||||
\(130\) | −297.408 | −0.0175981 | ||||||||
\(131\) | 15700.1i | 0.914872i | 0.889242 | + | 0.457436i | \(0.151232\pi\) | ||||
−0.889242 | + | 0.457436i | \(0.848768\pi\) | |||||||
\(132\) | − | 4960.72i | − | 0.284706i | ||||||
\(133\) | −1260.14 | −0.0712388 | ||||||||
\(134\) | 16887.6 | 0.940500 | ||||||||
\(135\) | −48.4447 | −0.00265815 | ||||||||
\(136\) | 5195.12i | 0.280878i | ||||||||
\(137\) | 14785.4 | 0.787758 | 0.393879 | − | 0.919162i | \(-0.371133\pi\) | ||||
0.393879 | + | 0.919162i | \(0.371133\pi\) | |||||||
\(138\) | −8223.61 | −0.431822 | ||||||||
\(139\) | −32415.5 | −1.67773 | −0.838867 | − | 0.544336i | \(-0.816782\pi\) | ||||
−0.838867 | + | 0.544336i | \(0.816782\pi\) | |||||||
\(140\) | −80.4234 | −0.00410323 | ||||||||
\(141\) | 4577.06i | 0.230223i | ||||||||
\(142\) | 10733.9i | 0.532332i | ||||||||
\(143\) | 36339.6 | 1.77708 | ||||||||
\(144\) | 1728.00 | 0.0833333 | ||||||||
\(145\) | −104.938 | −0.00499109 | ||||||||
\(146\) | 25352.8 | 1.18938 | ||||||||
\(147\) | 8071.78 | 0.373538 | ||||||||
\(148\) | − | 476.681i | − | 0.0217623i | ||||||
\(149\) | − | 14683.3i | − | 0.661379i | −0.943740 | − | 0.330690i | \(-0.892719\pi\) | ||
0.943740 | − | 0.330690i | \(-0.107281\pi\) | |||||||
\(150\) | 9183.83i | 0.408170i | ||||||||
\(151\) | 18534.9i | 0.812899i | 0.913673 | + | 0.406450i | \(0.133233\pi\) | ||||
−0.913673 | + | 0.406450i | \(0.866767\pi\) | |||||||
\(152\) | 979.407i | 0.0423912i | ||||||||
\(153\) | −6199.04 | −0.264814 | ||||||||
\(154\) | 9826.75 | 0.414351 | ||||||||
\(155\) | − | 168.432i | − | 0.00701068i | ||||||
\(156\) | 12658.4i | 0.520151i | ||||||||
\(157\) | − | 25038.4i | − | 1.01580i | −0.861417 | − | 0.507899i | \(-0.830422\pi\) | ||
0.861417 | − | 0.507899i | \(-0.169578\pi\) | |||||||
\(158\) | 6638.90i | 0.265939i | ||||||||
\(159\) | 4744.87 | 0.187685 | ||||||||
\(160\) | 62.5066i | 0.00244166i | ||||||||
\(161\) | − | 16290.2i | − | 0.628457i | ||||||
\(162\) | 2061.92i | 0.0785674i | ||||||||
\(163\) | −34771.0 | −1.30871 | −0.654353 | − | 0.756189i | \(-0.727059\pi\) | ||||
−0.654353 | + | 0.756189i | \(0.727059\pi\) | |||||||
\(164\) | −23763.9 | −0.883548 | ||||||||
\(165\) | 214.119i | 0.00786481i | ||||||||
\(166\) | 547.153 | 0.0198561 | ||||||||
\(167\) | −5171.96 | −0.185448 | −0.0927239 | − | 0.995692i | \(-0.529557\pi\) | ||||
−0.0927239 | + | 0.995692i | \(0.529557\pi\) | |||||||
\(168\) | 3423.01i | 0.121280i | ||||||||
\(169\) | −64167.6 | −2.24669 | ||||||||
\(170\) | − | 224.237i | − | 0.00775905i | ||||||
\(171\) | −1168.67 | −0.0399668 | ||||||||
\(172\) | 4450.37i | 0.150432i | ||||||||
\(173\) | − | 26548.2i | − | 0.887041i | −0.896264 | − | 0.443520i | \(-0.853729\pi\) | ||
0.896264 | − | 0.443520i | \(-0.146271\pi\) | |||||||
\(174\) | 4466.40i | 0.147523i | ||||||||
\(175\) | −18192.3 | −0.594036 | ||||||||
\(176\) | − | 7637.54i | − | 0.246563i | ||||||
\(177\) | −14187.3 | + | 11220.1i | −0.452848 | + | 0.358137i | ||||
\(178\) | −2175.53 | −0.0686634 | ||||||||
\(179\) | − | 16799.7i | − | 0.524319i | −0.965025 | − | 0.262160i | \(-0.915565\pi\) | ||
0.965025 | − | 0.262160i | \(-0.0844347\pi\) | |||||||
\(180\) | −74.5855 | −0.00230202 | ||||||||
\(181\) | 35844.6 | 1.09412 | 0.547062 | − | 0.837092i | \(-0.315746\pi\) | ||||
0.547062 | + | 0.837092i | \(0.315746\pi\) | |||||||
\(182\) | −25075.1 | −0.757008 | ||||||||
\(183\) | 11011.2i | 0.328801i | ||||||||
\(184\) | −12661.1 | −0.373968 | ||||||||
\(185\) | 20.5749i | 0.000601167i | ||||||||
\(186\) | −7168.85 | −0.207216 | ||||||||
\(187\) | 27398.9i | 0.783521i | ||||||||
\(188\) | 7046.84i | 0.199379i | ||||||||
\(189\) | −4084.48 | −0.114344 | ||||||||
\(190\) | − | 42.2741i | − | 0.00117103i | ||||||
\(191\) | − | 47215.5i | − | 1.29425i | −0.762385 | − | 0.647124i | \(-0.775972\pi\) | ||
0.762385 | − | 0.647124i | \(-0.224028\pi\) | |||||||
\(192\) | 2660.43 | 0.0721688 | ||||||||
\(193\) | −70854.2 | −1.90218 | −0.951089 | − | 0.308918i | \(-0.900033\pi\) | ||||
−0.951089 | + | 0.308918i | \(0.900033\pi\) | |||||||
\(194\) | 9425.29 | 0.250433 | ||||||||
\(195\) | − | 546.373i | − | 0.0143688i | ||||||
\(196\) | 12427.3 | 0.323493 | ||||||||
\(197\) | −25965.9 | −0.669070 | −0.334535 | − | 0.942383i | \(-0.608579\pi\) | ||||
−0.334535 | + | 0.942383i | \(0.608579\pi\) | |||||||
\(198\) | 9113.43 | 0.232462 | ||||||||
\(199\) | 62151.9 | 1.56945 | 0.784726 | − | 0.619843i | \(-0.212804\pi\) | ||||
0.784726 | + | 0.619843i | \(0.212804\pi\) | |||||||
\(200\) | 14139.4i | 0.353486i | ||||||||
\(201\) | 31024.5i | 0.767915i | ||||||||
\(202\) | −1603.77 | −0.0393043 | ||||||||
\(203\) | −8847.53 | −0.214699 | ||||||||
\(204\) | −9544.05 | −0.229336 | ||||||||
\(205\) | 1025.72 | 0.0244074 | ||||||||
\(206\) | 30114.2 | 0.709638 | ||||||||
\(207\) | − | 15107.7i | − | 0.352581i | ||||||
\(208\) | 19488.9i | 0.450464i | ||||||||
\(209\) | 5165.37i | 0.118252i | ||||||||
\(210\) | − | 147.747i | − | 0.00335028i | ||||||
\(211\) | 63638.5i | 1.42940i | 0.699429 | + | 0.714702i | \(0.253438\pi\) | ||||
−0.699429 | + | 0.714702i | \(0.746562\pi\) | |||||||
\(212\) | 7305.21 | 0.162540 | ||||||||
\(213\) | −19719.5 | −0.434648 | ||||||||
\(214\) | − | 7637.48i | − | 0.166772i | ||||||
\(215\) | − | 192.091i | − | 0.00415557i | ||||||
\(216\) | 3174.54i | 0.0680414i | ||||||||
\(217\) | − | 14200.8i | − | 0.301575i | ||||||
\(218\) | 9642.53 | 0.202898 | ||||||||
\(219\) | 46576.1i | 0.971124i | ||||||||
\(220\) | 329.658i | 0.00681112i | ||||||||
\(221\) | − | 69914.5i | − | 1.43147i | ||||||
\(222\) | 875.719 | 0.0177688 | ||||||||
\(223\) | −52958.8 | −1.06495 | −0.532474 | − | 0.846446i | \(-0.678738\pi\) | ||||
−0.532474 | + | 0.846446i | \(0.678738\pi\) | |||||||
\(224\) | 5270.07i | 0.105032i | ||||||||
\(225\) | −16871.8 | −0.333270 | ||||||||
\(226\) | 54052.5 | 1.05828 | ||||||||
\(227\) | − | 28531.2i | − | 0.553693i | −0.960914 | − | 0.276846i | \(-0.910711\pi\) | ||
0.960914 | − | 0.276846i | \(-0.0892893\pi\) | |||||||
\(228\) | −1799.29 | −0.0346123 | ||||||||
\(229\) | 52400.1i | 0.999220i | 0.866251 | + | 0.499610i | \(0.166523\pi\) | ||||
−0.866251 | + | 0.499610i | \(0.833477\pi\) | |||||||
\(230\) | 546.489 | 0.0103306 | ||||||||
\(231\) | 18052.9i | 0.338316i | ||||||||
\(232\) | 6876.47i | 0.127758i | ||||||||
\(233\) | 82040.4i | 1.51118i | 0.655046 | + | 0.755589i | \(0.272649\pi\) | ||||
−0.655046 | + | 0.755589i | \(0.727351\pi\) | |||||||
\(234\) | −23255.0 | −0.424702 | ||||||||
\(235\) | − | 304.162i | − | 0.00550769i | ||||||
\(236\) | −21842.7 | + | 17274.4i | −0.392178 | + | 0.310156i | ||||
\(237\) | −12196.4 | −0.217138 | ||||||||
\(238\) | − | 18905.9i | − | 0.333767i | ||||||
\(239\) | −37747.8 | −0.660839 | −0.330420 | − | 0.943834i | \(-0.607190\pi\) | ||||
−0.330420 | + | 0.943834i | \(0.607190\pi\) | |||||||
\(240\) | −114.832 | −0.00199361 | ||||||||
\(241\) | −29181.0 | −0.502418 | −0.251209 | − | 0.967933i | \(-0.580828\pi\) | ||||
−0.251209 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(242\) | 1130.81i | 0.0193090i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 16952.9i | 0.284750i | ||||||||
\(245\) | −536.400 | −0.00893627 | ||||||||
\(246\) | − | 43657.1i | − | 0.721414i | ||||||
\(247\) | − | 13180.6i | − | 0.216044i | ||||||
\(248\) | −11037.2 | −0.179454 | ||||||||
\(249\) | 1005.18i | 0.0162124i | ||||||||
\(250\) | − | 1220.72i | − | 0.0195314i | ||||||
\(251\) | 22064.7 | 0.350228 | 0.175114 | − | 0.984548i | \(-0.443971\pi\) | ||||
0.175114 | + | 0.984548i | \(0.443971\pi\) | |||||||
\(252\) | −6288.47 | −0.0990248 | ||||||||
\(253\) | −66774.2 | −1.04320 | ||||||||
\(254\) | − | 24120.4i | − | 0.373867i | ||||||
\(255\) | 411.949 | 0.00633524 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 3793.21 | 0.0574302 | 0.0287151 | − | 0.999588i | \(-0.490858\pi\) | ||||
0.0287151 | + | 0.999588i | \(0.490858\pi\) | |||||||
\(258\) | −8175.86 | −0.122827 | ||||||||
\(259\) | 1734.72i | 0.0258601i | ||||||||
\(260\) | − | 841.197i | − | 0.0124437i | ||||||
\(261\) | −8205.29 | −0.120452 | ||||||||
\(262\) | −44406.7 | −0.646913 | ||||||||
\(263\) | 56116.8 | 0.811301 | 0.405650 | − | 0.914028i | \(-0.367045\pi\) | ||||
0.405650 | + | 0.914028i | \(0.367045\pi\) | |||||||
\(264\) | 14031.0 | 0.201318 | ||||||||
\(265\) | −315.314 | −0.00449006 | ||||||||
\(266\) | − | 3564.22i | − | 0.0503734i | ||||||
\(267\) | − | 3996.70i | − | 0.0560634i | ||||||
\(268\) | 47765.4i | 0.665034i | ||||||||
\(269\) | 48707.5i | 0.673117i | 0.941662 | + | 0.336559i | \(0.109263\pi\) | ||||
−0.941662 | + | 0.336559i | \(0.890737\pi\) | |||||||
\(270\) | − | 137.022i | − | 0.00187959i | ||||||
\(271\) | 114277. | 1.55603 | 0.778017 | − | 0.628244i | \(-0.216226\pi\) | ||||
0.778017 | + | 0.628244i | \(0.216226\pi\) | |||||||
\(272\) | −14694.0 | −0.198611 | ||||||||
\(273\) | − | 46066.0i | − | 0.618095i | ||||||
\(274\) | 41819.5i | 0.557029i | ||||||||
\(275\) | 74571.1i | 0.986064i | ||||||||
\(276\) | − | 23259.9i | − | 0.305344i | ||||||
\(277\) | −4230.31 | −0.0551332 | −0.0275666 | − | 0.999620i | \(-0.508776\pi\) | ||||
−0.0275666 | + | 0.999620i | \(0.508776\pi\) | |||||||
\(278\) | − | 91684.9i | − | 1.18634i | ||||||
\(279\) | − | 13170.0i | − | 0.169191i | ||||||
\(280\) | − | 227.472i | − | 0.00290142i | ||||||
\(281\) | −74894.7 | −0.948502 | −0.474251 | − | 0.880390i | \(-0.657281\pi\) | ||||
−0.474251 | + | 0.880390i | \(0.657281\pi\) | |||||||
\(282\) | −12945.9 | −0.162792 | ||||||||
\(283\) | 10199.3i | 0.127349i | 0.997971 | + | 0.0636747i | \(0.0202820\pi\) | ||||
−0.997971 | + | 0.0636747i | \(0.979718\pi\) | |||||||
\(284\) | −30360.2 | −0.376416 | ||||||||
\(285\) | 77.6624 | 0.000956139 | ||||||||
\(286\) | 102784.i | 1.25659i | ||||||||
\(287\) | 86480.7 | 1.04992 | ||||||||
\(288\) | 4887.52i | 0.0589256i | ||||||||
\(289\) | −30807.6 | −0.368860 | ||||||||
\(290\) | − | 296.808i | − | 0.00352923i | ||||||
\(291\) | 17315.4i | 0.204478i | ||||||||
\(292\) | 71708.5i | 0.841018i | ||||||||
\(293\) | 75241.2 | 0.876437 | 0.438218 | − | 0.898869i | \(-0.355610\pi\) | ||||
0.438218 | + | 0.898869i | \(0.355610\pi\) | |||||||
\(294\) | 22830.5i | 0.264131i | ||||||||
\(295\) | 942.796 | − | 745.616i | 0.0108336 | − | 0.00856783i | ||||
\(296\) | 1348.26 | 0.0153883 | ||||||||
\(297\) | 16742.4i | 0.189804i | ||||||||
\(298\) | 41530.6 | 0.467666 | ||||||||
\(299\) | 170389. | 1.90590 | ||||||||
\(300\) | −25975.8 | −0.288620 | ||||||||
\(301\) | − | 16195.6i | − | 0.178758i | ||||||
\(302\) | −52424.6 | −0.574806 | ||||||||
\(303\) | − | 2946.32i | − | 0.0320918i | ||||||
\(304\) | −2770.18 | −0.0299751 | ||||||||
\(305\) | − | 731.735i | − | 0.00786600i | ||||||
\(306\) | − | 17533.5i | − | 0.187252i | ||||||
\(307\) | 135267. | 1.43521 | 0.717606 | − | 0.696449i | \(-0.245238\pi\) | ||||
0.717606 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(308\) | 27794.2i | 0.292990i | ||||||||
\(309\) | 55323.4i | 0.579417i | ||||||||
\(310\) | 476.396 | 0.00495730 | ||||||||
\(311\) | −63636.5 | −0.657938 | −0.328969 | − | 0.944341i | \(-0.606701\pi\) | ||||
−0.328969 | + | 0.944341i | \(0.606701\pi\) | |||||||
\(312\) | −35803.4 | −0.367802 | ||||||||
\(313\) | − | 10716.1i | − | 0.109383i | −0.998503 | − | 0.0546913i | \(-0.982583\pi\) | ||
0.998503 | − | 0.0546913i | \(-0.0174175\pi\) | |||||||
\(314\) | 70819.3 | 0.718277 | ||||||||
\(315\) | 271.429 | 0.00273549 | ||||||||
\(316\) | −18777.6 | −0.188047 | ||||||||
\(317\) | 46383.2 | 0.461575 | 0.230787 | − | 0.973004i | \(-0.425870\pi\) | ||||
0.230787 | + | 0.973004i | \(0.425870\pi\) | |||||||
\(318\) | 13420.5i | 0.132714i | ||||||||
\(319\) | 36266.3i | 0.356387i | ||||||||
\(320\) | −176.795 | −0.00172652 | ||||||||
\(321\) | 14030.9 | 0.136169 | ||||||||
\(322\) | 46075.7 | 0.444386 | ||||||||
\(323\) | 9937.77 | 0.0952541 | ||||||||
\(324\) | −5832.00 | −0.0555556 | ||||||||
\(325\) | − | 190285.i | − | 1.80151i | ||||||
\(326\) | − | 98347.3i | − | 0.925395i | ||||||
\(327\) | 17714.5i | 0.165666i | ||||||||
\(328\) | − | 67214.4i | − | 0.624762i | ||||||
\(329\) | − | 25644.6i | − | 0.236921i | ||||||
\(330\) | −605.621 | −0.00556126 | ||||||||
\(331\) | 77389.4 | 0.706359 | 0.353179 | − | 0.935556i | \(-0.385101\pi\) | ||||
0.353179 | + | 0.935556i | \(0.385101\pi\) | |||||||
\(332\) | 1547.58i | 0.0140403i | ||||||||
\(333\) | 1608.80i | 0.0145082i | ||||||||
\(334\) | − | 14628.5i | − | 0.131131i | ||||||
\(335\) | − | 2061.69i | − | 0.0183711i | ||||||
\(336\) | −9681.74 | −0.0857580 | ||||||||
\(337\) | 27283.2i | 0.240234i | 0.992760 | + | 0.120117i | \(0.0383270\pi\) | ||||
−0.992760 | + | 0.120117i | \(0.961673\pi\) | |||||||
\(338\) | − | 181493.i | − | 1.58865i | ||||||
\(339\) | 99300.8i | 0.864079i | ||||||||
\(340\) | 634.237 | 0.00548648 | ||||||||
\(341\) | −58209.8 | −0.500596 | ||||||||
\(342\) | − | 3305.50i | − | 0.0282608i | ||||||
\(343\) | −115126. | −0.978556 | ||||||||
\(344\) | −12587.6 | −0.106371 | ||||||||
\(345\) | 1003.96i | 0.00843490i | ||||||||
\(346\) | 75089.8 | 0.627233 | ||||||||
\(347\) | 23270.3i | 0.193260i | 0.995320 | + | 0.0966302i | \(0.0308064\pi\) | ||||
−0.995320 | + | 0.0966302i | \(0.969194\pi\) | |||||||
\(348\) | −12632.9 | −0.104314 | ||||||||
\(349\) | 127246.i | 1.04471i | 0.852729 | + | 0.522354i | \(0.174946\pi\) | ||||
−0.852729 | + | 0.522354i | \(0.825054\pi\) | |||||||
\(350\) | − | 51455.7i | − | 0.420047i | ||||||
\(351\) | − | 42722.1i | − | 0.346767i | ||||||
\(352\) | 21602.2 | 0.174346 | ||||||||
\(353\) | − | 233504.i | − | 1.87390i | −0.349469 | − | 0.936948i | \(-0.613638\pi\) | ||
0.349469 | − | 0.936948i | \(-0.386362\pi\) | |||||||
\(354\) | −31735.2 | − | 40127.6i | −0.253241 | − | 0.320212i | ||||
\(355\) | 1310.43 | 0.0103982 | ||||||||
\(356\) | − | 6153.33i | − | 0.0485523i | ||||||
\(357\) | 34732.3 | 0.272519 | ||||||||
\(358\) | 47516.7 | 0.370750 | ||||||||
\(359\) | −155352. | −1.20539 | −0.602697 | − | 0.797970i | \(-0.705907\pi\) | ||||
−0.602697 | + | 0.797970i | \(0.705907\pi\) | |||||||
\(360\) | − | 210.960i | − | 0.00162778i | ||||||
\(361\) | −128447. | −0.985624 | ||||||||
\(362\) | 101384.i | 0.773662i | ||||||||
\(363\) | −2077.44 | −0.0157658 | ||||||||
\(364\) | − | 70923.2i | − | 0.535286i | ||||||
\(365\) | − | 3095.15i | − | 0.0232325i | ||||||
\(366\) | −31144.4 | −0.232497 | ||||||||
\(367\) | − | 69140.9i | − | 0.513337i | −0.966499 | − | 0.256669i | \(-0.917375\pi\) | ||
0.966499 | − | 0.256669i | \(-0.0826249\pi\) | |||||||
\(368\) | − | 35810.9i | − | 0.264436i | ||||||
\(369\) | 80203.1 | 0.589032 | ||||||||
\(370\) | −58.1947 | −0.000425089 | ||||||||
\(371\) | −26584.9 | −0.193146 | ||||||||
\(372\) | − | 20276.6i | − | 0.146524i | ||||||
\(373\) | 143374. | 1.03051 | 0.515254 | − | 0.857038i | \(-0.327698\pi\) | ||||
0.515254 | + | 0.857038i | \(0.327698\pi\) | |||||||
\(374\) | −77495.9 | −0.554033 | ||||||||
\(375\) | 2242.60 | 0.0159474 | ||||||||
\(376\) | −19931.5 | −0.140982 | ||||||||
\(377\) | − | 92541.7i | − | 0.651110i | ||||||
\(378\) | − | 11552.7i | − | 0.0808534i | ||||||
\(379\) | −354.370 | −0.00246705 | −0.00123353 | − | 0.999999i | \(-0.500393\pi\) | ||||
−0.00123353 | + | 0.999999i | \(0.500393\pi\) | |||||||
\(380\) | 119.569 | 0.000828041 | ||||||||
\(381\) | 44312.0 | 0.305261 | ||||||||
\(382\) | 133545. | 0.915171 | ||||||||
\(383\) | 265162. | 1.80764 | 0.903822 | − | 0.427908i | \(-0.140749\pi\) | ||||
0.903822 | + | 0.427908i | \(0.140749\pi\) | |||||||
\(384\) | 7524.83i | 0.0510310i | ||||||||
\(385\) | − | 1199.68i | − | 0.00809364i | ||||||
\(386\) | − | 200406.i | − | 1.34504i | ||||||
\(387\) | − | 15020.0i | − | 0.100288i | ||||||
\(388\) | 26658.8i | 0.177083i | ||||||||
\(389\) | 239961. | 1.58577 | 0.792887 | − | 0.609369i | \(-0.208577\pi\) | ||||
0.792887 | + | 0.609369i | \(0.208577\pi\) | |||||||
\(390\) | 1545.38 | 0.0101603 | ||||||||
\(391\) | 128468.i | 0.840316i | ||||||||
\(392\) | 35149.8i | 0.228744i | ||||||||
\(393\) | − | 81580.3i | − | 0.528202i | ||||||
\(394\) | − | 73442.7i | − | 0.473104i | ||||||
\(395\) | 810.498 | 0.00519467 | ||||||||
\(396\) | 25776.7i | 0.164375i | ||||||||
\(397\) | 5595.42i | 0.0355019i | 0.999842 | + | 0.0177510i | \(0.00565060\pi\) | ||||
−0.999842 | + | 0.0177510i | \(0.994349\pi\) | |||||||
\(398\) | 175792.i | 1.10977i | ||||||||
\(399\) | 6547.89 | 0.0411297 | ||||||||
\(400\) | −39992.4 | −0.249952 | ||||||||
\(401\) | − | 140372.i | − | 0.872953i | −0.899716 | − | 0.436477i | \(-0.856226\pi\) | ||
0.899716 | − | 0.436477i | \(-0.143774\pi\) | |||||||
\(402\) | −87750.7 | −0.542998 | ||||||||
\(403\) | 148535. | 0.914575 | ||||||||
\(404\) | − | 4536.16i | − | 0.0277923i | ||||||
\(405\) | 251.726 | 0.00153468 | ||||||||
\(406\) | − | 25024.6i | − | 0.151815i | ||||||
\(407\) | 7110.68 | 0.0429262 | ||||||||
\(408\) | − | 26994.6i | − | 0.162165i | ||||||
\(409\) | 132134.i | 0.789895i | 0.918704 | + | 0.394948i | \(0.129237\pi\) | ||||
−0.918704 | + | 0.394948i | \(0.870763\pi\) | |||||||
\(410\) | 2901.17i | 0.0172586i | ||||||||
\(411\) | −76827.4 | −0.454813 | ||||||||
\(412\) | 85175.9i | 0.501790i | ||||||||
\(413\) | 79489.2 | − | 62864.5i | 0.466024 | − | 0.368558i | ||||
\(414\) | 42731.1 | 0.249312 | ||||||||
\(415\) | − | 66.7982i | − | 0.000387854i | ||||||
\(416\) | −55122.9 | −0.318526 | ||||||||
\(417\) | 168436. | 0.968640 | ||||||||
\(418\) | −14609.9 | −0.0836169 | ||||||||
\(419\) | 124560.i | 0.709496i | 0.934962 | + | 0.354748i | \(0.115433\pi\) | ||||
−0.934962 | + | 0.354748i | \(0.884567\pi\) | |||||||
\(420\) | 417.892 | 0.00236900 | ||||||||
\(421\) | − | 223604.i | − | 1.26158i | −0.775953 | − | 0.630791i | \(-0.782731\pi\) | ||
0.775953 | − | 0.630791i | \(-0.217269\pi\) | |||||||
\(422\) | −179997. | −1.01074 | ||||||||
\(423\) | − | 23783.1i | − | 0.132919i | ||||||
\(424\) | 20662.3i | 0.114933i | ||||||||
\(425\) | 143469. | 0.794292 | ||||||||
\(426\) | − | 55775.2i | − | 0.307342i | ||||||
\(427\) | − | 61694.2i | − | 0.338368i | ||||||
\(428\) | 21602.0 | 0.117925 | ||||||||
\(429\) | −188826. | −1.02600 | ||||||||
\(430\) | 543.316 | 0.00293843 | ||||||||
\(431\) | − | 75329.6i | − | 0.405519i | −0.979229 | − | 0.202759i | \(-0.935009\pi\) | ||
0.979229 | − | 0.202759i | \(-0.0649909\pi\) | |||||||
\(432\) | −8978.95 | −0.0481125 | ||||||||
\(433\) | −296476. | −1.58130 | −0.790650 | − | 0.612269i | \(-0.790257\pi\) | ||||
−0.790650 | + | 0.612269i | \(0.790257\pi\) | |||||||
\(434\) | 40166.1 | 0.213245 | ||||||||
\(435\) | 545.272 | 0.00288161 | ||||||||
\(436\) | 27273.2i | 0.143471i | ||||||||
\(437\) | 24219.4i | 0.126824i | ||||||||
\(438\) | −131737. | −0.686688 | ||||||||
\(439\) | −68945.6 | −0.357748 | −0.178874 | − | 0.983872i | \(-0.557245\pi\) | ||||
−0.178874 | + | 0.983872i | \(0.557245\pi\) | |||||||
\(440\) | −932.414 | −0.00481619 | ||||||||
\(441\) | −41942.2 | −0.215662 | ||||||||
\(442\) | 197748. | 1.01220 | ||||||||
\(443\) | 132200.i | 0.673633i | 0.941570 | + | 0.336817i | \(0.109350\pi\) | ||||
−0.941570 | + | 0.336817i | \(0.890650\pi\) | |||||||
\(444\) | 2476.91i | 0.0125645i | ||||||||
\(445\) | 265.596i | 0.00134122i | ||||||||
\(446\) | − | 149790.i | − | 0.753032i | ||||||
\(447\) | 76296.5i | 0.381847i | ||||||||
\(448\) | −14906.0 | −0.0742686 | ||||||||
\(449\) | 7000.95 | 0.0347267 | 0.0173634 | − | 0.999849i | \(-0.494473\pi\) | ||||
0.0173634 | + | 0.999849i | \(0.494473\pi\) | |||||||
\(450\) | − | 47720.6i | − | 0.235657i | ||||||
\(451\) | − | 354487.i | − | 1.74280i | ||||||
\(452\) | 152884.i | 0.748314i | ||||||||
\(453\) | − | 96310.2i | − | 0.469327i | ||||||
\(454\) | 80698.5 | 0.391520 | ||||||||
\(455\) | 3061.25i | 0.0147869i | ||||||||
\(456\) | − | 5089.15i | − | 0.0244746i | ||||||
\(457\) | − | 111384.i | − | 0.533325i | −0.963790 | − | 0.266662i | \(-0.914079\pi\) | ||
0.963790 | − | 0.266662i | \(-0.0859209\pi\) | |||||||
\(458\) | −148210. | −0.706555 | ||||||||
\(459\) | 32211.2 | 0.152891 | ||||||||
\(460\) | 1545.70i | 0.00730484i | ||||||||
\(461\) | −64288.5 | −0.302504 | −0.151252 | − | 0.988495i | \(-0.548331\pi\) | ||||
−0.151252 | + | 0.988495i | \(0.548331\pi\) | |||||||
\(462\) | −51061.3 | −0.239226 | ||||||||
\(463\) | 181610.i | 0.847184i | 0.905853 | + | 0.423592i | \(0.139231\pi\) | ||||
−0.905853 | + | 0.423592i | \(0.860769\pi\) | |||||||
\(464\) | −19449.6 | −0.0903388 | ||||||||
\(465\) | 875.196i | 0.00404762i | ||||||||
\(466\) | −232045. | −1.06856 | ||||||||
\(467\) | − | 328713.i | − | 1.50724i | −0.657310 | − | 0.753620i | \(-0.728306\pi\) | ||
0.657310 | − | 0.753620i | \(-0.271694\pi\) | |||||||
\(468\) | − | 65775.0i | − | 0.300309i | ||||||
\(469\) | − | 173826.i | − | 0.790259i | ||||||
\(470\) | 860.301 | 0.00389453 | ||||||||
\(471\) | 130103.i | 0.586471i | ||||||||
\(472\) | −48859.5 | − | 61780.6i | −0.219313 | − | 0.277311i | ||||
\(473\) | −66386.5 | −0.296727 | ||||||||
\(474\) | − | 34496.7i | − | 0.153540i | ||||||
\(475\) | 27047.4 | 0.119878 | ||||||||
\(476\) | 53473.9 | 0.236009 | ||||||||
\(477\) | −24655.1 | −0.108360 | ||||||||
\(478\) | − | 106767.i | − | 0.467284i | ||||||
\(479\) | −98111.5 | −0.427611 | −0.213806 | − | 0.976876i | \(-0.568586\pi\) | ||||
−0.213806 | + | 0.976876i | \(0.568586\pi\) | |||||||
\(480\) | − | 324.794i | − | 0.00140969i | ||||||
\(481\) | −18144.5 | −0.0784250 | ||||||||
\(482\) | − | 82536.2i | − | 0.355263i | ||||||
\(483\) | 84646.5i | 0.362840i | ||||||||
\(484\) | −3198.43 | −0.0136535 | ||||||||
\(485\) | − | 1150.67i | − | 0.00489178i | ||||||
\(486\) | − | 10714.1i | − | 0.0453609i | ||||||
\(487\) | 91025.1 | 0.383798 | 0.191899 | − | 0.981415i | \(-0.438535\pi\) | ||||
0.191899 | + | 0.981415i | \(0.438535\pi\) | |||||||
\(488\) | −47949.9 | −0.201348 | ||||||||
\(489\) | 180675. | 0.755582 | ||||||||
\(490\) | − | 1517.17i | − | 0.00631890i | ||||||
\(491\) | 268985. | 1.11575 | 0.557873 | − | 0.829926i | \(-0.311617\pi\) | ||||
0.557873 | + | 0.829926i | \(0.311617\pi\) | |||||||
\(492\) | 123481. | 0.510116 | ||||||||
\(493\) | 69773.6 | 0.287076 | ||||||||
\(494\) | 37280.4 | 0.152766 | ||||||||
\(495\) | − | 1112.60i | − | 0.00454075i | ||||||
\(496\) | − | 31217.8i | − | 0.126893i | ||||||
\(497\) | 110486. | 0.447294 | ||||||||
\(498\) | −2843.09 | −0.0114639 | ||||||||
\(499\) | −290634. | −1.16720 | −0.583601 | − | 0.812041i | \(-0.698357\pi\) | ||||
−0.583601 | + | 0.812041i | \(0.698357\pi\) | |||||||
\(500\) | 3452.70 | 0.0138108 | ||||||||
\(501\) | 26874.3 | 0.107068 | ||||||||
\(502\) | 62408.5i | 0.247649i | ||||||||
\(503\) | 346973.i | 1.37139i | 0.727890 | + | 0.685693i | \(0.240501\pi\) | ||||
−0.727890 | + | 0.685693i | \(0.759499\pi\) | |||||||
\(504\) | − | 17786.5i | − | 0.0700211i | ||||||
\(505\) | 195.794i | 0.000767743i | ||||||||
\(506\) | − | 188866.i | − | 0.737654i | ||||||
\(507\) | 333425. | 1.29713 | ||||||||
\(508\) | 68222.7 | 0.264364 | ||||||||
\(509\) | 486734.i | 1.87869i | 0.342970 | + | 0.939346i | \(0.388567\pi\) | ||||
−0.342970 | + | 0.939346i | \(0.611433\pi\) | |||||||
\(510\) | 1165.17i | 0.00447969i | ||||||||
\(511\) | − | 260959.i | − | 0.999380i | ||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 6072.59 | 0.0230749 | ||||||||
\(514\) | 10728.8i | 0.0406093i | ||||||||
\(515\) | − | 3676.44i | − | 0.0138616i | ||||||
\(516\) | − | 23124.8i | − | 0.0868518i | ||||||
\(517\) | −105118. | −0.393275 | ||||||||
\(518\) | −4906.53 | −0.0182858 | ||||||||
\(519\) | 137949.i | 0.512133i | ||||||||
\(520\) | 2379.26 | 0.00879905 | ||||||||
\(521\) | −494832. | −1.82298 | −0.911490 | − | 0.411322i | \(-0.865067\pi\) | ||||
−0.911490 | + | 0.411322i | \(0.865067\pi\) | |||||||
\(522\) | − | 23208.1i | − | 0.0851723i | ||||||
\(523\) | −216797. | −0.792591 | −0.396296 | − | 0.918123i | \(-0.629704\pi\) | ||||
−0.396296 | + | 0.918123i | \(0.629704\pi\) | |||||||
\(524\) | − | 125601.i | − | 0.457436i | ||||||
\(525\) | 94530.2 | 0.342967 | ||||||||
\(526\) | 158722.i | 0.573676i | ||||||||
\(527\) | 111991.i | 0.403239i | ||||||||
\(528\) | 39685.8i | 0.142353i | ||||||||
\(529\) | −33250.5 | −0.118819 | ||||||||
\(530\) | − | 891.843i | − | 0.00317495i | ||||||
\(531\) | 73719.2 | − | 58301.3i | 0.261452 | − | 0.206771i | ||||
\(532\) | 10081.1 | 0.0356194 | ||||||||
\(533\) | 904554.i | 3.18405i | ||||||||
\(534\) | 11304.4 | 0.0396428 | ||||||||
\(535\) | −932.407 | −0.00325760 | ||||||||
\(536\) | −135101. | −0.470250 | ||||||||
\(537\) | 87293.8i | 0.302716i | ||||||||
\(538\) | −137765. | −0.475966 | ||||||||
\(539\) | 185379.i | 0.638092i | ||||||||
\(540\) | 387.558 | 0.00132907 | ||||||||
\(541\) | 311287.i | 1.06357i | 0.846879 | + | 0.531785i | \(0.178479\pi\) | ||||
−0.846879 | + | 0.531785i | \(0.821521\pi\) | |||||||
\(542\) | 323223.i | 1.10028i | ||||||||
\(543\) | −186254. | −0.631692 | ||||||||
\(544\) | − | 41561.0i | − | 0.140439i | ||||||
\(545\) | − | 1177.19i | − | 0.00396327i | ||||||
\(546\) | 130294. | 0.437059 | ||||||||
\(547\) | 318117. | 1.06319 | 0.531597 | − | 0.846998i | \(-0.321592\pi\) | ||||
0.531597 | + | 0.846998i | \(0.321592\pi\) | |||||||
\(548\) | −118283. | −0.393879 | ||||||||
\(549\) | − | 57215.9i | − | 0.189833i | ||||||
\(550\) | −210919. | −0.697252 | ||||||||
\(551\) | 13154.0 | 0.0433267 | ||||||||
\(552\) | 65788.9 | 0.215911 | ||||||||
\(553\) | 68334.9 | 0.223456 | ||||||||
\(554\) | − | 11965.1i | − | 0.0389850i | ||||||
\(555\) | − | 106.910i | − | 0.000347084i | ||||||
\(556\) | 259324. | 0.838867 | ||||||||
\(557\) | −458615. | −1.47822 | −0.739108 | − | 0.673587i | \(-0.764753\pi\) | ||||
−0.739108 | + | 0.673587i | \(0.764753\pi\) | |||||||
\(558\) | 37250.4 | 0.119636 | ||||||||
\(559\) | 169400. | 0.542113 | ||||||||
\(560\) | 643.387 | 0.00205162 | ||||||||
\(561\) | − | 142369.i | − | 0.452366i | ||||||
\(562\) | − | 211834.i | − | 0.670692i | ||||||
\(563\) | 218018.i | 0.687821i | 0.939003 | + | 0.343910i | \(0.111752\pi\) | ||||
−0.939003 | + | 0.343910i | \(0.888248\pi\) | |||||||
\(564\) | − | 36616.5i | − | 0.115111i | ||||||
\(565\) | − | 6598.90i | − | 0.0206716i | ||||||
\(566\) | −28848.0 | −0.0900497 | ||||||||
\(567\) | 21223.6 | 0.0660166 | ||||||||
\(568\) | − | 85871.6i | − | 0.266166i | ||||||
\(569\) | − | 180447.i | − | 0.557347i | −0.960386 | − | 0.278674i | \(-0.910105\pi\) | ||
0.960386 | − | 0.278674i | \(-0.0898948\pi\) | |||||||
\(570\) | 219.663i | 0.000676093i | ||||||||
\(571\) | − | 73565.0i | − | 0.225631i | −0.993616 | − | 0.112816i | \(-0.964013\pi\) | ||
0.993616 | − | 0.112816i | \(-0.0359869\pi\) | |||||||
\(572\) | −290717. | −0.888542 | ||||||||
\(573\) | 245339.i | 0.747234i | ||||||||
\(574\) | 244604.i | 0.742404i | ||||||||
\(575\) | 349649.i | 1.05754i | ||||||||
\(576\) | −13824.0 | −0.0416667 | ||||||||
\(577\) | 74461.1 | 0.223654 | 0.111827 | − | 0.993728i | \(-0.464330\pi\) | ||||
0.111827 | + | 0.993728i | \(0.464330\pi\) | |||||||
\(578\) | − | 87137.0i | − | 0.260824i | ||||||
\(579\) | 368169. | 1.09822 | ||||||||
\(580\) | 839.501 | 0.00249554 | ||||||||
\(581\) | − | 5631.91i | − | 0.0166841i | ||||||
\(582\) | −48975.3 | −0.144588 | ||||||||
\(583\) | 108972.i | 0.320611i | ||||||||
\(584\) | −202822. | −0.594689 | ||||||||
\(585\) | 2839.04i | 0.00829583i | ||||||||
\(586\) | 212814.i | 0.619734i | ||||||||
\(587\) | − | 68909.0i | − | 0.199986i | −0.994988 | − | 0.0999930i | \(-0.968118\pi\) | ||
0.994988 | − | 0.0999930i | \(-0.0318820\pi\) | |||||||
\(588\) | −64574.3 | −0.186769 | ||||||||
\(589\) | 21113.1i | 0.0608584i | ||||||||
\(590\) | 2108.92 | + | 2666.63i | 0.00605837 | + | 0.00766053i | ||||
\(591\) | 134923. | 0.386288 | ||||||||
\(592\) | 3813.45i | 0.0108811i | ||||||||
\(593\) | −103260. | −0.293645 | −0.146823 | − | 0.989163i | \(-0.546905\pi\) | ||||
−0.146823 | + | 0.989163i | \(0.546905\pi\) | |||||||
\(594\) | −47354.8 | −0.134212 | ||||||||
\(595\) | −2308.09 | −0.00651957 | ||||||||
\(596\) | 117466.i | 0.330690i | ||||||||
\(597\) | −322951. | −0.906124 | ||||||||
\(598\) | 481934.i | 1.34767i | ||||||||
\(599\) | 425655. | 1.18633 | 0.593163 | − | 0.805083i | \(-0.297879\pi\) | ||||
0.593163 | + | 0.805083i | \(0.297879\pi\) | |||||||
\(600\) | − | 73470.7i | − | 0.204085i | ||||||
\(601\) | 534156.i | 1.47883i | 0.673249 | + | 0.739416i | \(0.264898\pi\) | ||||
−0.673249 | + | 0.739416i | \(0.735102\pi\) | |||||||
\(602\) | 45808.2 | 0.126401 | ||||||||
\(603\) | − | 161208.i | − | 0.443356i | ||||||
\(604\) | − | 148279.i | − | 0.406450i | ||||||
\(605\) | 138.053 | 0.000377169 | ||||||||
\(606\) | 8333.45 | 0.0226924 | ||||||||
\(607\) | −632185. | −1.71580 | −0.857901 | − | 0.513816i | \(-0.828231\pi\) | ||||
−0.857901 | + | 0.513816i | \(0.828231\pi\) | |||||||
\(608\) | − | 7835.26i | − | 0.0211956i | ||||||
\(609\) | 45973.1 | 0.123956 | ||||||||
\(610\) | 2069.66 | 0.00556210 | ||||||||
\(611\) | 268233. | 0.718504 | ||||||||
\(612\) | 49592.3 | 0.132407 | ||||||||
\(613\) | − | 427346.i | − | 1.13726i | −0.822595 | − | 0.568628i | \(-0.807474\pi\) | ||
0.822595 | − | 0.568628i | \(-0.192526\pi\) | |||||||
\(614\) | 382594.i | 1.01485i | ||||||||
\(615\) | −5329.79 | −0.0140916 | ||||||||
\(616\) | −78614.0 | −0.207175 | ||||||||
\(617\) | −524329. | −1.37732 | −0.688658 | − | 0.725087i | \(-0.741800\pi\) | ||||
−0.688658 | + | 0.725087i | \(0.741800\pi\) | |||||||
\(618\) | −156478. | −0.409710 | ||||||||
\(619\) | −215064. | −0.561289 | −0.280645 | − | 0.959812i | \(-0.590548\pi\) | ||||
−0.280645 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(620\) | 1347.45i | 0.00350534i | ||||||||
\(621\) | 78502.1i | 0.203563i | ||||||||
\(622\) | − | 179991.i | − | 0.465233i | ||||||
\(623\) | 22393.0i | 0.0576947i | ||||||||
\(624\) | − | 101267.i | − | 0.260076i | ||||||
\(625\) | 390401. | 0.999428 | ||||||||
\(626\) | 30309.7 | 0.0773452 | ||||||||
\(627\) | − | 26840.1i | − | 0.0682729i | ||||||
\(628\) | 200307.i | 0.507899i | ||||||||
\(629\) | − | 13680.4i | − | 0.0345778i | ||||||
\(630\) | 767.717i | 0.00193428i | ||||||||
\(631\) | 399375. | 1.00305 | 0.501525 | − | 0.865143i | \(-0.332773\pi\) | ||||
0.501525 | + | 0.865143i | \(0.332773\pi\) | |||||||
\(632\) | − | 53111.2i | − | 0.132970i | ||||||
\(633\) | − | 330675.i | − | 0.825267i | ||||||
\(634\) | 131191.i | 0.326383i | ||||||||
\(635\) | −2944.69 | −0.00730285 | ||||||||
\(636\) | −37959.0 | −0.0938427 | ||||||||
\(637\) | − | 473036.i | − | 1.16578i | ||||||
\(638\) | −102577. | −0.252004 | ||||||||
\(639\) | 102466. | 0.250944 | ||||||||
\(640\) | − | 500.053i | − | 0.00122083i | ||||||
\(641\) | 121848. | 0.296553 | 0.148277 | − | 0.988946i | \(-0.452627\pi\) | ||||
0.148277 | + | 0.988946i | \(0.452627\pi\) | |||||||
\(642\) | 39685.5i | 0.0962857i | ||||||||
\(643\) | −435859. | −1.05420 | −0.527102 | − | 0.849802i | \(-0.676721\pi\) | ||||
−0.527102 | + | 0.849802i | \(0.676721\pi\) | |||||||
\(644\) | 130322.i | 0.314228i | ||||||||
\(645\) | 998.135i | 0.00239922i | ||||||||
\(646\) | 28108.3i | 0.0673549i | ||||||||
\(647\) | 271725. | 0.649113 | 0.324557 | − | 0.945866i | \(-0.394785\pi\) | ||||
0.324557 | + | 0.945866i | \(0.394785\pi\) | |||||||
\(648\) | − | 16495.4i | − | 0.0392837i | ||||||
\(649\) | −257684. | − | 325829.i | −0.611784 | − | 0.773572i | ||||
\(650\) | 538207. | 1.27386 | ||||||||
\(651\) | 73789.8i | 0.174114i | ||||||||
\(652\) | 278168. | 0.654353 | ||||||||
\(653\) | −237640. | −0.557306 | −0.278653 | − | 0.960392i | \(-0.589888\pi\) | ||||
−0.278653 | + | 0.960392i | \(0.589888\pi\) | |||||||
\(654\) | −50104.1 | −0.117143 | ||||||||
\(655\) | 5421.31i | 0.0126363i | ||||||||
\(656\) | 190111. | 0.441774 | ||||||||
\(657\) | − | 242016.i | − | 0.560679i | ||||||
\(658\) | 72533.9 | 0.167529 | ||||||||
\(659\) | 796099.i | 1.83314i | 0.399870 | + | 0.916572i | \(0.369055\pi\) | ||||
−0.399870 | + | 0.916572i | \(0.630945\pi\) | |||||||
\(660\) | − | 1712.95i | − | 0.00393240i | ||||||
\(661\) | 92808.8 | 0.212416 | 0.106208 | − | 0.994344i | \(-0.466129\pi\) | ||||
0.106208 | + | 0.994344i | \(0.466129\pi\) | |||||||
\(662\) | 218890.i | 0.499471i | ||||||||
\(663\) | 363287.i | 0.826461i | ||||||||
\(664\) | −4377.23 | −0.00992803 | ||||||||
\(665\) | −435.132 | −0.000983960 | ||||||||
\(666\) | −4550.37 | −0.0102588 | ||||||||
\(667\) | 170046.i | 0.382221i | ||||||||
\(668\) | 41375.6 | 0.0927239 | ||||||||
\(669\) | 275182. | 0.614848 | ||||||||
\(670\) | 5831.35 | 0.0129903 | ||||||||
\(671\) | −252887. | −0.561670 | ||||||||
\(672\) | − | 27384.1i | − | 0.0606401i | ||||||
\(673\) | − | 434666.i | − | 0.959678i | −0.877356 | − | 0.479839i | \(-0.840695\pi\) | ||
0.877356 | − | 0.479839i | \(-0.159305\pi\) | |||||||
\(674\) | −77168.4 | −0.169871 | ||||||||
\(675\) | 87668.3 | 0.192413 | ||||||||
\(676\) | 513341. | 1.12334 | ||||||||
\(677\) | −468389. | −1.02195 | −0.510975 | − | 0.859596i | \(-0.670716\pi\) | ||||
−0.510975 | + | 0.859596i | \(0.670716\pi\) | |||||||
\(678\) | −280865. | −0.610996 | ||||||||
\(679\) | − | 97015.5i | − | 0.210427i | ||||||
\(680\) | 1793.89i | 0.00387952i | ||||||||
\(681\) | 148253.i | 0.319675i | ||||||||
\(682\) | − | 164642.i | − | 0.353975i | ||||||
\(683\) | 529417.i | 1.13490i | 0.823409 | + | 0.567449i | \(0.192069\pi\) | ||||
−0.823409 | + | 0.567449i | \(0.807931\pi\) | |||||||
\(684\) | 9349.36 | 0.0199834 | ||||||||
\(685\) | 5105.46 | 0.0108806 | ||||||||
\(686\) | − | 325626.i | − | 0.691943i | ||||||
\(687\) | − | 272279.i | − | 0.576900i | ||||||
\(688\) | − | 35603.0i | − | 0.0752159i | ||||||
\(689\) | − | 278067.i | − | 0.585749i | ||||||
\(690\) | −2839.64 | −0.00596438 | ||||||||
\(691\) | − | 398171.i | − | 0.833898i | −0.908930 | − | 0.416949i | \(-0.863099\pi\) | ||
0.908930 | − | 0.416949i | \(-0.136901\pi\) | |||||||
\(692\) | 212386.i | 0.443520i | ||||||||
\(693\) | − | 93805.5i | − | 0.195327i | ||||||
\(694\) | −65818.3 | −0.136656 | ||||||||
\(695\) | −11193.2 | −0.0231731 | ||||||||
\(696\) | − | 35731.2i | − | 0.0737613i | ||||||
\(697\) | −682006. | −1.40386 | ||||||||
\(698\) | −359907. | −0.738720 | ||||||||
\(699\) | − | 426294.i | − | 0.872479i | ||||||
\(700\) | 145539. | 0.297018 | ||||||||
\(701\) | 400569.i | 0.815156i | 0.913170 | + | 0.407578i | \(0.133627\pi\) | ||||
−0.913170 | + | 0.407578i | \(0.866373\pi\) | |||||||
\(702\) | 120836. | 0.245202 | ||||||||
\(703\) | − | 2579.09i | − | 0.00521862i | ||||||
\(704\) | 61100.3i | 0.123281i | ||||||||
\(705\) | 1580.47i | 0.00317987i | ||||||||
\(706\) | 660450. | 1.32504 | ||||||||
\(707\) | 16507.8i | 0.0330256i | ||||||||
\(708\) | 113498. | − | 89760.7i | 0.226424 | − | 0.179069i | ||||
\(709\) | −282000. | −0.560992 | −0.280496 | − | 0.959855i | \(-0.590499\pi\) | ||||
−0.280496 | + | 0.959855i | \(0.590499\pi\) | |||||||
\(710\) | 3706.47i | 0.00735264i | ||||||||
\(711\) | 63374.6 | 0.125365 | ||||||||
\(712\) | 17404.2 | 0.0343317 | ||||||||
\(713\) | −272934. | −0.536883 | ||||||||
\(714\) | 98237.9i | 0.192700i | ||||||||
\(715\) | 12548.2 | 0.0245453 | ||||||||
\(716\) | 134398.i | 0.262160i | ||||||||
\(717\) | 196143. | 0.381536 | ||||||||
\(718\) | − | 439403.i | − | 0.852342i | ||||||
\(719\) | − | 632803.i | − | 1.22408i | −0.790825 | − | 0.612042i | \(-0.790348\pi\) | ||
0.790825 | − | 0.612042i | \(-0.209652\pi\) | |||||||
\(720\) | 596.684 | 0.00115101 | ||||||||
\(721\) | − | 309969.i | − | 0.596276i | ||||||
\(722\) | − | 363304.i | − | 0.696941i | ||||||
\(723\) | 151629. | 0.290071 | ||||||||
\(724\) | −286757. | −0.547062 | ||||||||
\(725\) | 189901. | 0.361286 | ||||||||
\(726\) | − | 5875.88i | − | 0.0111481i | ||||||
\(727\) | −1.02381e6 | −1.93708 | −0.968542 | − | 0.248850i | \(-0.919947\pi\) | ||||
−0.968542 | + | 0.248850i | \(0.919947\pi\) | |||||||
\(728\) | 200601. | 0.378504 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 8754.41 | 0.0164279 | ||||||||
\(731\) | 127722.i | 0.239019i | ||||||||
\(732\) | − | 88089.7i | − | 0.164400i | ||||||
\(733\) | −187550. | −0.349067 | −0.174534 | − | 0.984651i | \(-0.555842\pi\) | ||||
−0.174534 | + | 0.984651i | \(0.555842\pi\) | |||||||
\(734\) | 195560. | 0.362984 | ||||||||
\(735\) | 2787.21 | 0.00515936 | ||||||||
\(736\) | 101289. | 0.186984 | ||||||||
\(737\) | −712520. | −1.31178 | ||||||||
\(738\) | 226849.i | 0.416508i | ||||||||
\(739\) | 709560.i | 1.29927i | 0.760245 | + | 0.649636i | \(0.225079\pi\) | ||||
−0.760245 | + | 0.649636i | \(0.774921\pi\) | |||||||
\(740\) | − | 164.599i | − | 0.000300583i | ||||||
\(741\) | 68488.4i | 0.124733i | ||||||||
\(742\) | − | 75193.3i | − | 0.136575i | ||||||
\(743\) | −889169. | −1.61067 | −0.805335 | − | 0.592820i | \(-0.798015\pi\) | ||||
−0.805335 | + | 0.592820i | \(0.798015\pi\) | |||||||
\(744\) | 57350.8 | 0.103608 | ||||||||
\(745\) | − | 5070.18i | − | 0.00913506i | ||||||
\(746\) | 405522.i | 0.728679i | ||||||||
\(747\) | − | 5223.09i | − | 0.00936023i | ||||||
\(748\) | − | 219192.i | − | 0.391761i | ||||||
\(749\) | −78613.4 | −0.140131 | ||||||||
\(750\) | 6343.02i | 0.0112765i | ||||||||
\(751\) | − | 362232.i | − | 0.642254i | −0.947036 | − | 0.321127i | \(-0.895938\pi\) | ||
0.947036 | − | 0.321127i | \(-0.104062\pi\) | |||||||
\(752\) | − | 56374.7i | − | 0.0996894i | ||||||
\(753\) | −114652. | −0.202204 | ||||||||
\(754\) | 261747. | 0.460405 | ||||||||
\(755\) | 6400.17i | 0.0112279i | ||||||||
\(756\) | 32675.9 | 0.0571720 | ||||||||
\(757\) | 617075. | 1.07683 | 0.538413 | − | 0.842681i | \(-0.319024\pi\) | ||||
0.538413 | + | 0.842681i | \(0.319024\pi\) | |||||||
\(758\) | − | 1002.31i | − | 0.00174447i | ||||||
\(759\) | 346969. | 0.602292 | ||||||||
\(760\) | 338.193i | 0.000585513i | ||||||||
\(761\) | 84132.5 | 0.145276 | 0.0726381 | − | 0.997358i | \(-0.476858\pi\) | ||||
0.0726381 | + | 0.997358i | \(0.476858\pi\) | |||||||
\(762\) | 125333.i | 0.215852i | ||||||||
\(763\) | − | 99251.6i | − | 0.170486i | ||||||
\(764\) | 377724.i | 0.647124i | ||||||||
\(765\) | −2140.55 | −0.00365765 | ||||||||
\(766\) | 749990.i | 1.27820i | ||||||||
\(767\) | 657538. | + | 831426.i | 1.11771 | + | 1.41330i | ||||
\(768\) | −21283.4 | −0.0360844 | ||||||||
\(769\) | − | 487601.i | − | 0.824540i | −0.911062 | − | 0.412270i | \(-0.864736\pi\) | ||
0.911062 | − | 0.412270i | \(-0.135264\pi\) | |||||||
\(770\) | 3393.21 | 0.00572307 | ||||||||
\(771\) | −19710.1 | −0.0331573 | ||||||||
\(772\) | 566834. | 0.951089 | ||||||||
\(773\) | − | 887763.i | − | 1.48572i | −0.669444 | − | 0.742862i | \(-0.733468\pi\) | ||
0.669444 | − | 0.742862i | \(-0.266532\pi\) | |||||||
\(774\) | 42483.0 | 0.0709142 | ||||||||
\(775\) | 304803.i | 0.507477i | ||||||||
\(776\) | −75402.3 | −0.125216 | ||||||||
\(777\) | − | 9013.87i | − | 0.0149303i | ||||||
\(778\) | 678712.i | 1.12131i | ||||||||
\(779\) | −128575. | −0.211876 | ||||||||
\(780\) | 4370.99i | 0.00718440i | ||||||||
\(781\) | − | 452885.i | − | 0.742482i | ||||||
\(782\) | −363363. | −0.594193 | ||||||||
\(783\) | 42636.0 | 0.0695429 | ||||||||
\(784\) | −99418.6 | −0.161747 | ||||||||
\(785\) | − | 8645.84i | − | 0.0140303i | ||||||
\(786\) | 230744. | 0.373495 | ||||||||
\(787\) | 99407.6 | 0.160498 | 0.0802491 | − | 0.996775i | \(-0.474428\pi\) | ||||
0.0802491 | + | 0.996775i | \(0.474428\pi\) | |||||||
\(788\) | 207727. | 0.334535 | ||||||||
\(789\) | −291592. | −0.468405 | ||||||||
\(790\) | 2292.43i | 0.00367318i | ||||||||
\(791\) | − | 556368.i | − | 0.889221i | ||||||
\(792\) | −72907.5 | −0.116231 | ||||||||
\(793\) | 645297. | 1.02616 | ||||||||
\(794\) | −15826.2 | −0.0251037 | ||||||||
\(795\) | 1638.42 | 0.00259233 | ||||||||
\(796\) | −497215. | −0.784726 | ||||||||
\(797\) | − | 578171.i | − | 0.910206i | −0.890439 | − | 0.455103i | \(-0.849602\pi\) | ||
0.890439 | − | 0.455103i | \(-0.150398\pi\) | |||||||
\(798\) | 18520.2i | 0.0290831i | ||||||||
\(799\) | 202239.i | 0.316790i | ||||||||
\(800\) | − | 113116.i | − | 0.176743i | ||||||
\(801\) | 20767.5i | 0.0323682i | ||||||||
\(802\) | 397031. | 0.617271 | ||||||||
\(803\) | −1.06968e6 | −1.65891 | ||||||||
\(804\) | − | 248196.i | − | 0.383958i | ||||||
\(805\) | − | 5625.07i | − | 0.00868033i | ||||||
\(806\) | 420121.i | 0.646702i | ||||||||
\(807\) | − | 253091.i | − | 0.388625i | ||||||
\(808\) | 12830.2 | 0.0196522 | ||||||||
\(809\) | − | 306114.i | − | 0.467720i | −0.972270 | − | 0.233860i | \(-0.924864\pi\) | ||
0.972270 | − | 0.233860i | \(-0.0751358\pi\) | |||||||
\(810\) | 711.989i | 0.00108518i | ||||||||
\(811\) | − | 1.15116e6i | − | 1.75023i | −0.483914 | − | 0.875116i | \(-0.660785\pi\) | ||
0.483914 | − | 0.875116i | \(-0.339215\pi\) | |||||||
\(812\) | 70780.2 | 0.107349 | ||||||||
\(813\) | −593799. | −0.898376 | ||||||||
\(814\) | 20112.0i | 0.0303534i | ||||||||
\(815\) | −12006.5 | −0.0180760 | ||||||||
\(816\) | 76352.4 | 0.114668 | ||||||||
\(817\) | 24078.8i | 0.0360737i | ||||||||
\(818\) | −373733. | −0.558540 | ||||||||
\(819\) | 239366.i | 0.356857i | ||||||||
\(820\) | −8205.75 | −0.0122037 | ||||||||
\(821\) | − | 387597.i | − | 0.575035i | −0.957775 | − | 0.287517i | \(-0.907170\pi\) | ||
0.957775 | − | 0.287517i | \(-0.0928299\pi\) | |||||||
\(822\) | − | 217301.i | − | 0.321601i | ||||||
\(823\) | 584601.i | 0.863097i | 0.902090 | + | 0.431549i | \(0.142033\pi\) | ||||
−0.902090 | + | 0.431549i | \(0.857967\pi\) | |||||||
\(824\) | −240914. | −0.354819 | ||||||||
\(825\) | − | 387483.i | − | 0.569304i | ||||||
\(826\) | 177808. | + | 224829.i | 0.260610 | + | 0.329529i | ||||
\(827\) | 993463. | 1.45258 | 0.726291 | − | 0.687388i | \(-0.241243\pi\) | ||||
0.726291 | + | 0.687388i | \(0.241243\pi\) | |||||||
\(828\) | 120862.i | 0.176290i | ||||||||
\(829\) | 277889. | 0.404355 | 0.202177 | − | 0.979349i | \(-0.435198\pi\) | ||||
0.202177 | + | 0.979349i | \(0.435198\pi\) | |||||||
\(830\) | 188.934 | 0.000274254 | ||||||||
\(831\) | 21981.4 | 0.0318312 | ||||||||
\(832\) | − | 155911.i | − | 0.225232i | ||||||
\(833\) | 356655. | 0.513994 | ||||||||
\(834\) | 476409.i | 0.684932i | ||||||||
\(835\) | −1785.89 | −0.00256143 | ||||||||
\(836\) | − | 41323.0i | − | 0.0591261i | ||||||
\(837\) | 68433.4i | 0.0976827i | ||||||||
\(838\) | −352309. | −0.501690 | ||||||||
\(839\) | − | 715635.i | − | 1.01664i | −0.861168 | − | 0.508320i | \(-0.830267\pi\) | ||
0.861168 | − | 0.508320i | \(-0.169733\pi\) | |||||||
\(840\) | 1181.98i | 0.00167514i | ||||||||
\(841\) | −614926. | −0.869422 | ||||||||
\(842\) | 632448. | 0.892073 | ||||||||
\(843\) | 389164. | 0.547618 | ||||||||
\(844\) | − | 509108.i | − | 0.714702i | ||||||
\(845\) | −22157.3 | −0.0310315 | ||||||||
\(846\) | 67268.7 | 0.0939880 | ||||||||
\(847\) | 11639.6 | 0.0162245 | ||||||||
\(848\) | −58441.7 | −0.0812701 | ||||||||
\(849\) | − | 52997.1i | − | 0.0735253i | ||||||
\(850\) | 405791.i | 0.561649i | ||||||||
\(851\) | 33340.6 | 0.0460378 | ||||||||
\(852\) | 157756. | 0.217324 | ||||||||
\(853\) | 214771. | 0.295173 | 0.147587 | − | 0.989049i | \(-0.452850\pi\) | ||||
0.147587 | + | 0.989049i | \(0.452850\pi\) | |||||||
\(854\) | 174498. | 0.239262 | ||||||||
\(855\) | −403.546 | −0.000552027 | ||||||||
\(856\) | 61099.8i | 0.0833858i | ||||||||
\(857\) | 178905.i | 0.243591i | 0.992555 | + | 0.121796i | \(0.0388653\pi\) | ||||
−0.992555 | + | 0.121796i | \(0.961135\pi\) | |||||||
\(858\) | − | 534081.i | − | 0.725492i | ||||||
\(859\) | − | 170699.i | − | 0.231337i | −0.993288 | − | 0.115668i | \(-0.963099\pi\) | ||
0.993288 | − | 0.115668i | \(-0.0369010\pi\) | |||||||
\(860\) | 1536.73i | 0.00207778i | ||||||||
\(861\) | −449367. | −0.606170 | ||||||||
\(862\) | 213064. | 0.286745 | ||||||||
\(863\) | − | 793327.i | − | 1.06520i | −0.846367 | − | 0.532600i | \(-0.821215\pi\) | ||
0.846367 | − | 0.532600i | \(-0.178785\pi\) | |||||||
\(864\) | − | 25396.3i | − | 0.0340207i | ||||||
\(865\) | − | 9167.20i | − | 0.0122519i | ||||||
\(866\) | − | 838561.i | − | 1.11815i | ||||||
\(867\) | 160081. | 0.212962 | ||||||||
\(868\) | 113607.i | 0.150787i | ||||||||
\(869\) | − | 280107.i | − | 0.370924i | ||||||
\(870\) | 1542.26i | 0.00203760i | ||||||||
\(871\) | 1.81815e6 | 2.39659 | ||||||||
\(872\) | −77140.3 | −0.101449 | ||||||||
\(873\) | − | 89973.3i | − | 0.118055i | ||||||
\(874\) | −68502.9 | −0.0896780 | ||||||||
\(875\) | −12565.0 | −0.0164114 | ||||||||
\(876\) | − | 372609.i | − | 0.485562i | ||||||
\(877\) | −1.39963e6 | −1.81976 | −0.909878 | − | 0.414876i | \(-0.863825\pi\) | ||||
−0.909878 | + | 0.414876i | \(0.863825\pi\) | |||||||
\(878\) | − | 195008.i | − | 0.252966i | ||||||
\(879\) | −390965. | −0.506011 | ||||||||
\(880\) | − | 2637.27i | − | 0.00340556i | ||||||
\(881\) | − | 147593.i | − | 0.190158i | −0.995470 | − | 0.0950790i | \(-0.969690\pi\) | ||
0.995470 | − | 0.0950790i | \(-0.0303104\pi\) | |||||||
\(882\) | − | 118631.i | − | 0.152496i | ||||||
\(883\) | 561869. | 0.720633 | 0.360316 | − | 0.932830i | \(-0.382669\pi\) | ||||
0.360316 | + | 0.932830i | \(0.382669\pi\) | |||||||
\(884\) | 559316.i | 0.715736i | ||||||||
\(885\) | −4898.91 | + | 3874.33i | −0.00625479 | + | 0.00494664i | ||||
\(886\) | −373918. | −0.476331 | ||||||||
\(887\) | 446523.i | 0.567541i | 0.958892 | + | 0.283770i | \(0.0915853\pi\) | ||||
−0.958892 | + | 0.283770i | \(0.908415\pi\) | |||||||
\(888\) | −7005.75 | −0.00888441 | ||||||||
\(889\) | −248274. | −0.314143 | ||||||||
\(890\) | −751.218 | −0.000948388 | ||||||||
\(891\) | − | 86996.3i | − | 0.109584i | ||||||
\(892\) | 423670. | 0.532474 | ||||||||
\(893\) | 38127.0i | 0.0478112i | ||||||||
\(894\) | −215799. | −0.270007 | ||||||||
\(895\) | − | 5800.99i | − | 0.00724196i | ||||||
\(896\) | − | 42160.6i | − | 0.0525159i | ||||||
\(897\) | −885369. | −1.10037 | ||||||||
\(898\) | 19801.7i | 0.0245555i | ||||||||
\(899\) | 148236.i | 0.183415i | ||||||||
\(900\) | 134974. | 0.166635 | ||||||||
\(901\) | 209654. | 0.258258 | ||||||||
\(902\) | 1.00264e6 | 1.23235 | ||||||||
\(903\) | 84155.0i | 0.103206i | ||||||||
\(904\) | −432420. | −0.529138 | ||||||||
\(905\) | 12377.2 | 0.0151122 | ||||||||
\(906\) | 272406. | 0.331865 | ||||||||
\(907\) | 946148. | 1.15012 | 0.575062 | − | 0.818110i | \(-0.304978\pi\) | ||||
0.575062 | + | 0.818110i | \(0.304978\pi\) | |||||||
\(908\) | 228250.i | 0.276846i | ||||||||
\(909\) | 15309.5i | 0.0185282i | ||||||||
\(910\) | −8658.53 | −0.0104559 | ||||||||
\(911\) | 1.06764e6 | 1.28644 | 0.643219 | − | 0.765683i | \(-0.277599\pi\) | ||||
0.643219 | + | 0.765683i | \(0.277599\pi\) | |||||||
\(912\) | 14394.3 | 0.0173062 | ||||||||
\(913\) | −23085.4 | −0.0276946 | ||||||||
\(914\) | 315043. | 0.377118 | ||||||||
\(915\) | 3802.21i | 0.00454144i | ||||||||
\(916\) | − | 419201.i | − | 0.499610i | ||||||
\(917\) | 457083.i | 0.543571i | ||||||||
\(918\) | 91106.9i | 0.108110i | ||||||||
\(919\) | 954937.i | 1.13069i | 0.824854 | + | 0.565345i | \(0.191257\pi\) | ||||
−0.824854 | + | 0.565345i | \(0.808743\pi\) | |||||||
\(920\) | −4371.91 | −0.00516530 | ||||||||
\(921\) | −702869. | −0.828620 | ||||||||
\(922\) | − | 181835.i | − | 0.213903i | ||||||
\(923\) | 1.15564e6i | 1.35649i | ||||||||
\(924\) | − | 144423.i | − | 0.169158i | ||||||
\(925\) | − | 37233.6i | − | 0.0435162i | ||||||
\(926\) | −513671. | −0.599050 | ||||||||
\(927\) | − | 287469.i | − | 0.334527i | ||||||
\(928\) | − | 55011.7i | − | 0.0638792i | ||||||
\(929\) | − | 139772.i | − | 0.161952i | −0.996716 | − | 0.0809762i | \(-0.974196\pi\) | ||
0.996716 | − | 0.0809762i | \(-0.0258038\pi\) | |||||||
\(930\) | −2475.43 | −0.00286210 | ||||||||
\(931\) | 67238.2 | 0.0775741 | ||||||||
\(932\) | − | 656323.i | − | 0.755589i | ||||||
\(933\) | 330665. | 0.379861 | ||||||||
\(934\) | 929740. | 1.06578 | ||||||||
\(935\) | 9460.95i | 0.0108221i | ||||||||
\(936\) | 186040. | 0.212351 | ||||||||
\(937\) | 1.40914e6i | 1.60500i | 0.596654 | + | 0.802498i | \(0.296496\pi\) | ||||
−0.596654 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(938\) | 491654. | 0.558797 | ||||||||
\(939\) | 55682.5i | 0.0631521i | ||||||||
\(940\) | 2433.30i | 0.00275385i | ||||||||
\(941\) | − | 1.13063e6i | − | 1.27686i | −0.769682 | − | 0.638428i | \(-0.779585\pi\) | ||
0.769682 | − | 0.638428i | \(-0.220415\pi\) | |||||||
\(942\) | −367988. | −0.414698 | ||||||||
\(943\) | − | 1.66212e6i | − | 1.86913i | ||||||
\(944\) | 174742. | − | 138196.i | 0.196089 | − | 0.155078i | ||||
\(945\) | −1410.39 | −0.00157934 | ||||||||
\(946\) | − | 187769.i | − | 0.209818i | ||||||
\(947\) | −1.52196e6 | −1.69708 | −0.848542 | − | 0.529128i | \(-0.822519\pi\) | ||||
−0.848542 | + | 0.529128i | \(0.822519\pi\) | |||||||
\(948\) | 97571.5 | 0.108569 | ||||||||
\(949\) | 2.72953e6 | 3.03079 | ||||||||
\(950\) | 76501.6i | 0.0847663i | ||||||||
\(951\) | −241014. | −0.266490 | ||||||||
\(952\) | 151247.i | 0.166883i | ||||||||
\(953\) | 1.28184e6 | 1.41139 | 0.705696 | − | 0.708515i | \(-0.250634\pi\) | ||||
0.705696 | + | 0.708515i | \(0.250634\pi\) | |||||||
\(954\) | − | 69735.1i | − | 0.0766222i | ||||||
\(955\) | − | 16303.7i | − | 0.0178763i | ||||||
\(956\) | 301982. | 0.330420 | ||||||||
\(957\) | − | 188445.i | − | 0.205760i | ||||||
\(958\) | − | 277501.i | − | 0.302367i | ||||||
\(959\) | 430453. | 0.468046 | ||||||||
\(960\) | 918.655 | 0.000996805 | ||||||||
\(961\) | 685593. | 0.742369 | ||||||||
\(962\) | − | 51320.3i | − | 0.0554548i | ||||||
\(963\) | −72906.9 | −0.0786169 | ||||||||
\(964\) | 233448. | 0.251209 | ||||||||
\(965\) | −24466.2 | −0.0262731 | ||||||||
\(966\) | −239416. | −0.256566 | ||||||||
\(967\) | 553590.i | 0.592018i | 0.955185 | + | 0.296009i | \(0.0956559\pi\) | ||||
−0.955185 | + | 0.296009i | \(0.904344\pi\) | |||||||
\(968\) | − | 9046.51i | − | 0.00965452i | ||||||
\(969\) | −51638.2 | −0.0549950 | ||||||||
\(970\) | 3254.58 | 0.00345901 | ||||||||
\(971\) | 135852. | 0.144088 | 0.0720442 | − | 0.997401i | \(-0.477048\pi\) | ||||
0.0720442 | + | 0.997401i | \(0.477048\pi\) | |||||||
\(972\) | 30304.0 | 0.0320750 | ||||||||
\(973\) | −943722. | −0.996824 | ||||||||
\(974\) | 257458.i | 0.271386i | ||||||||
\(975\) | 988749.i | 1.04010i | ||||||||
\(976\) | − | 135623.i | − | 0.142375i | ||||||
\(977\) | − | 1.45788e6i | − | 1.52733i | −0.645610 | − | 0.763667i | \(-0.723397\pi\) | ||
0.645610 | − | 0.763667i | \(-0.276603\pi\) | |||||||
\(978\) | 511027.i | 0.534277i | ||||||||
\(979\) | 91789.6 | 0.0957697 | ||||||||
\(980\) | 4291.20 | 0.00446813 | ||||||||
\(981\) | − | 92047.1i | − | 0.0956471i | ||||||
\(982\) | 760805.i | 0.788952i | ||||||||
\(983\) | − | 1.31374e6i | − | 1.35958i | −0.733409 | − | 0.679788i | \(-0.762072\pi\) | ||
0.733409 | − | 0.679788i | \(-0.237928\pi\) | |||||||
\(984\) | 349257.i | 0.360707i | ||||||||
\(985\) | −8966.12 | −0.00924128 | ||||||||
\(986\) | 197350.i | 0.202994i | ||||||||
\(987\) | 133253.i | 0.136787i | ||||||||
\(988\) | 105445.i | 0.108022i | ||||||||
\(989\) | −311273. | −0.318236 | ||||||||
\(990\) | 3146.90 | 0.00321079 | ||||||||
\(991\) | − | 922836.i | − | 0.939674i | −0.882753 | − | 0.469837i | \(-0.844313\pi\) | ||
0.882753 | − | 0.469837i | \(-0.155687\pi\) | |||||||
\(992\) | 88297.4 | 0.0897272 | ||||||||
\(993\) | −402127. | −0.407816 | ||||||||
\(994\) | 312501.i | 0.316285i | ||||||||
\(995\) | 21461.2 | 0.0216775 | ||||||||
\(996\) | − | 8041.48i | − | 0.00810620i | ||||||
\(997\) | −11980.4 | −0.0120526 | −0.00602629 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602629 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(998\) | − | 822038.i | − | 0.825336i | ||||||
\(999\) | − | 8359.56i | − | 0.00837630i |
(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 | 354.5.d.a.235.12 | yes | 40 | |
3.2 | odd | 2 | 1062.5.d.b.235.21 | 40 | |||
59.58 | odd | 2 | inner | 354.5.d.a.235.11 | ✓ | 40 | |
177.176 | even | 2 | 1062.5.d.b.235.22 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.5.d.a.235.11 | ✓ | 40 | 59.58 | odd | 2 | inner | |
354.5.d.a.235.12 | yes | 40 | 1.1 | even | 1 | trivial | |
1062.5.d.b.235.21 | 40 | 3.2 | odd | 2 | |||
1062.5.d.b.235.22 | 40 | 177.176 | even | 2 |