Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.14 | ||
Root | \(8.69480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.6.b.a.36.3 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.69480i | 1.53704i | 0.639827 | + | 0.768519i | \(0.279006\pi\) | ||||
−0.639827 | + | 0.768519i | \(0.720994\pi\) | |||||||
\(3\) | 28.4744 | 1.82663 | 0.913315 | − | 0.407253i | \(-0.133513\pi\) | ||||
0.913315 | + | 0.407253i | \(0.133513\pi\) | |||||||
\(4\) | −43.5996 | −1.36249 | ||||||||
\(5\) | 14.1700i | 0.253481i | 0.991936 | + | 0.126740i | \(0.0404515\pi\) | ||||
−0.991936 | + | 0.126740i | \(0.959548\pi\) | |||||||
\(6\) | 247.579i | 2.80760i | ||||||||
\(7\) | 47.5239 | 0.366579 | 0.183289 | − | 0.983059i | \(-0.441325\pi\) | ||||
0.183289 | + | 0.983059i | \(0.441325\pi\) | |||||||
\(8\) | − | 100.856i | − | 0.557156i | ||||||
\(9\) | 567.789 | 2.33658 | ||||||||
\(10\) | −123.205 | −0.389610 | ||||||||
\(11\) | −461.870 | −1.15090 | −0.575451 | − | 0.817836i | \(-0.695173\pi\) | ||||
−0.575451 | + | 0.817836i | \(0.695173\pi\) | |||||||
\(12\) | −1241.47 | −2.48876 | ||||||||
\(13\) | − | 290.335i | − | 0.476476i | −0.971207 | − | 0.238238i | \(-0.923430\pi\) | ||
0.971207 | − | 0.238238i | \(-0.0765698\pi\) | |||||||
\(14\) | 413.211i | 0.563445i | ||||||||
\(15\) | 403.482i | 0.463016i | ||||||||
\(16\) | −518.263 | −0.506116 | ||||||||
\(17\) | − | 1764.19i | − | 1.48055i | −0.672304 | − | 0.740275i | \(-0.734695\pi\) | ||
0.672304 | − | 0.740275i | \(-0.265305\pi\) | |||||||
\(18\) | 4936.81i | 3.59141i | ||||||||
\(19\) | 1717.31i | 1.09135i | 0.837995 | + | 0.545677i | \(0.183728\pi\) | ||||
−0.837995 | + | 0.545677i | \(0.816272\pi\) | |||||||
\(20\) | − | 617.807i | − | 0.345364i | ||||||
\(21\) | 1353.21 | 0.669604 | ||||||||
\(22\) | − | 4015.87i | − | 1.76898i | ||||||
\(23\) | − | 4414.83i | − | 1.74018i | −0.492890 | − | 0.870091i | \(-0.664060\pi\) | ||
0.492890 | − | 0.870091i | \(-0.335940\pi\) | |||||||
\(24\) | − | 2871.81i | − | 1.01772i | ||||||
\(25\) | 2924.21 | 0.935747 | ||||||||
\(26\) | 2524.40 | 0.732362 | ||||||||
\(27\) | 9248.15 | 2.44144 | ||||||||
\(28\) | −2072.02 | −0.499459 | ||||||||
\(29\) | 1387.78i | 0.306427i | 0.988193 | + | 0.153213i | \(0.0489622\pi\) | ||||
−0.988193 | + | 0.153213i | \(0.951038\pi\) | |||||||
\(30\) | −3508.20 | −0.711673 | ||||||||
\(31\) | 6726.60i | 1.25716i | 0.777744 | + | 0.628581i | \(0.216364\pi\) | ||||
−0.777744 | + | 0.628581i | \(0.783636\pi\) | |||||||
\(32\) | − | 7733.59i | − | 1.33508i | ||||||
\(33\) | −13151.5 | −2.10227 | ||||||||
\(34\) | 15339.3 | 2.27566 | ||||||||
\(35\) | 673.415i | 0.0929207i | ||||||||
\(36\) | −24755.3 | −3.18356 | ||||||||
\(37\) | 3814.02 | + | 7402.52i | 0.458013 | + | 0.888945i | ||||
\(38\) | −14931.7 | −1.67745 | ||||||||
\(39\) | − | 8267.10i | − | 0.870345i | ||||||
\(40\) | 1429.13 | 0.141228 | ||||||||
\(41\) | 2517.60 | 0.233899 | 0.116949 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116949 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(42\) | 11765.9i | 1.02921i | ||||||||
\(43\) | − | 17522.4i | − | 1.44518i | −0.691277 | − | 0.722590i | \(-0.742952\pi\) | ||
0.691277 | − | 0.722590i | \(-0.257048\pi\) | |||||||
\(44\) | 20137.4 | 1.56809 | ||||||||
\(45\) | 8045.57i | 0.592278i | ||||||||
\(46\) | 38386.1 | 2.67473 | ||||||||
\(47\) | −3097.14 | −0.204511 | −0.102255 | − | 0.994758i | \(-0.532606\pi\) | ||||
−0.102255 | + | 0.994758i | \(0.532606\pi\) | |||||||
\(48\) | −14757.2 | −0.924488 | ||||||||
\(49\) | −14548.5 | −0.865620 | ||||||||
\(50\) | 25425.4i | 1.43828i | ||||||||
\(51\) | − | 50234.2i | − | 2.70442i | ||||||
\(52\) | 12658.5i | 0.649192i | ||||||||
\(53\) | −6600.17 | −0.322750 | −0.161375 | − | 0.986893i | \(-0.551593\pi\) | ||||
−0.161375 | + | 0.986893i | \(0.551593\pi\) | |||||||
\(54\) | 80410.8i | 3.75258i | ||||||||
\(55\) | − | 6544.71i | − | 0.291732i | ||||||
\(56\) | − | 4793.07i | − | 0.204242i | ||||||
\(57\) | 48899.4i | 1.99350i | ||||||||
\(58\) | −12066.5 | −0.470990 | ||||||||
\(59\) | − | 3587.53i | − | 0.134173i | −0.997747 | − | 0.0670866i | \(-0.978630\pi\) | ||
0.997747 | − | 0.0670866i | \(-0.0213704\pi\) | |||||||
\(60\) | − | 17591.6i | − | 0.630853i | ||||||
\(61\) | − | 2461.47i | − | 0.0846973i | −0.999103 | − | 0.0423487i | \(-0.986516\pi\) | ||
0.999103 | − | 0.0423487i | \(-0.0134840\pi\) | |||||||
\(62\) | −58486.4 | −1.93231 | ||||||||
\(63\) | 26983.5 | 0.856540 | ||||||||
\(64\) | 50657.6 | 1.54595 | ||||||||
\(65\) | 4114.05 | 0.120778 | ||||||||
\(66\) | − | 114349.i | − | 3.23127i | ||||||
\(67\) | 36376.0 | 0.989982 | 0.494991 | − | 0.868898i | \(-0.335171\pi\) | ||||
0.494991 | + | 0.868898i | \(0.335171\pi\) | |||||||
\(68\) | 76918.0i | 2.01723i | ||||||||
\(69\) | − | 125710.i | − | 3.17867i | ||||||
\(70\) | −5855.21 | −0.142823 | ||||||||
\(71\) | −70209.2 | −1.65291 | −0.826453 | − | 0.563005i | \(-0.809645\pi\) | ||||
−0.826453 | + | 0.563005i | \(0.809645\pi\) | |||||||
\(72\) | − | 57264.9i | − | 1.30184i | ||||||
\(73\) | −49658.6 | −1.09065 | −0.545327 | − | 0.838223i | \(-0.683595\pi\) | ||||
−0.545327 | + | 0.838223i | \(0.683595\pi\) | |||||||
\(74\) | −64363.4 | + | 33162.1i | −1.36634 | + | 0.703984i | ||||
\(75\) | 83265.0 | 1.70926 | ||||||||
\(76\) | − | 74874.2i | − | 1.48696i | ||||||
\(77\) | −21949.9 | −0.421896 | ||||||||
\(78\) | 71880.8 | 1.33775 | ||||||||
\(79\) | 62511.9i | 1.12692i | 0.826142 | + | 0.563462i | \(0.190531\pi\) | ||||
−0.826142 | + | 0.563462i | \(0.809469\pi\) | |||||||
\(80\) | − | 7343.80i | − | 0.128291i | ||||||
\(81\) | 125362. | 2.12302 | ||||||||
\(82\) | 21890.1i | 0.359511i | ||||||||
\(83\) | −59096.3 | −0.941598 | −0.470799 | − | 0.882241i | \(-0.656034\pi\) | ||||
−0.470799 | + | 0.882241i | \(0.656034\pi\) | |||||||
\(84\) | −58999.5 | −0.912326 | ||||||||
\(85\) | 24998.6 | 0.375291 | ||||||||
\(86\) | 152354. | 2.22130 | ||||||||
\(87\) | 39516.3i | 0.559729i | ||||||||
\(88\) | 46582.4i | 0.641232i | ||||||||
\(89\) | 51391.5i | 0.687728i | 0.939020 | + | 0.343864i | \(0.111736\pi\) | ||||
−0.939020 | + | 0.343864i | \(0.888264\pi\) | |||||||
\(90\) | −69954.7 | −0.910354 | ||||||||
\(91\) | − | 13797.9i | − | 0.174666i | ||||||
\(92\) | 192485.i | 2.37098i | ||||||||
\(93\) | 191535.i | 2.29637i | ||||||||
\(94\) | − | 26929.0i | − | 0.314341i | ||||||
\(95\) | −24334.4 | −0.276638 | ||||||||
\(96\) | − | 220209.i | − | 2.43869i | ||||||
\(97\) | − | 100740.i | − | 1.08710i | −0.839376 | − | 0.543551i | \(-0.817079\pi\) | ||
0.839376 | − | 0.543551i | \(-0.182921\pi\) | |||||||
\(98\) | − | 126496.i | − | 1.33049i | ||||||
\(99\) | −262245. | −2.68917 | ||||||||
\(100\) | −127494. | −1.27494 | ||||||||
\(101\) | −31426.0 | −0.306539 | −0.153270 | − | 0.988184i | \(-0.548980\pi\) | ||||
−0.153270 | + | 0.988184i | \(0.548980\pi\) | |||||||
\(102\) | 436776. | 4.15680 | ||||||||
\(103\) | 94967.4i | 0.882027i | 0.897501 | + | 0.441013i | \(0.145381\pi\) | ||||
−0.897501 | + | 0.441013i | \(0.854619\pi\) | |||||||
\(104\) | −29282.0 | −0.265471 | ||||||||
\(105\) | 19175.0i | 0.169732i | ||||||||
\(106\) | − | 57387.2i | − | 0.496079i | ||||||
\(107\) | 179040. | 1.51178 | 0.755892 | − | 0.654696i | \(-0.227203\pi\) | ||||
0.755892 | + | 0.654696i | \(0.227203\pi\) | |||||||
\(108\) | −403215. | −3.32642 | ||||||||
\(109\) | 55763.1i | 0.449553i | 0.974410 | + | 0.224776i | \(0.0721651\pi\) | ||||
−0.974410 | + | 0.224776i | \(0.927835\pi\) | |||||||
\(110\) | 56904.9 | 0.448403 | ||||||||
\(111\) | 108602. | + | 210782.i | 0.836621 | + | 1.62377i | ||||
\(112\) | −24629.9 | −0.185531 | ||||||||
\(113\) | 86748.3i | 0.639095i | 0.947570 | + | 0.319547i | \(0.103531\pi\) | ||||
−0.947570 | + | 0.319547i | \(0.896469\pi\) | |||||||
\(114\) | −425171. | −3.06409 | ||||||||
\(115\) | 62558.3 | 0.441103 | ||||||||
\(116\) | − | 60506.8i | − | 0.417503i | ||||||
\(117\) | − | 164849.i | − | 1.11332i | ||||||
\(118\) | 31192.9 | 0.206229 | ||||||||
\(119\) | − | 83841.3i | − | 0.542738i | ||||||
\(120\) | 40693.6 | 0.257972 | ||||||||
\(121\) | 52273.2 | 0.324575 | ||||||||
\(122\) | 21402.0 | 0.130183 | ||||||||
\(123\) | 71687.1 | 0.427246 | ||||||||
\(124\) | − | 293277.i | − | 1.71287i | ||||||
\(125\) | 85717.4i | 0.490675i | ||||||||
\(126\) | 234617.i | 1.31653i | ||||||||
\(127\) | −282739. | −1.55552 | −0.777760 | − | 0.628561i | \(-0.783644\pi\) | ||||
−0.777760 | + | 0.628561i | \(0.783644\pi\) | |||||||
\(128\) | 192983.i | 1.04110i | ||||||||
\(129\) | − | 498938.i | − | 2.63981i | ||||||
\(130\) | 35770.8i | 0.185640i | ||||||||
\(131\) | 82509.4i | 0.420074i | 0.977693 | + | 0.210037i | \(0.0673584\pi\) | ||||
−0.977693 | + | 0.210037i | \(0.932642\pi\) | |||||||
\(132\) | 573398. | 2.86432 | ||||||||
\(133\) | 81613.5i | 0.400067i | ||||||||
\(134\) | 316282.i | 1.52164i | ||||||||
\(135\) | 131046.i | 0.618857i | ||||||||
\(136\) | −177929. | −0.824898 | ||||||||
\(137\) | 80152.2 | 0.364850 | 0.182425 | − | 0.983220i | \(-0.441605\pi\) | ||||
0.182425 | + | 0.983220i | \(0.441605\pi\) | |||||||
\(138\) | 1.09302e6 | 4.88574 | ||||||||
\(139\) | 91551.6 | 0.401910 | 0.200955 | − | 0.979600i | \(-0.435595\pi\) | ||||
0.200955 | + | 0.979600i | \(0.435595\pi\) | |||||||
\(140\) | − | 29360.6i | − | 0.126603i | ||||||
\(141\) | −88189.0 | −0.373566 | ||||||||
\(142\) | − | 610455.i | − | 2.54058i | ||||||
\(143\) | 134097.i | 0.548377i | ||||||||
\(144\) | −294264. | −1.18258 | ||||||||
\(145\) | −19664.9 | −0.0776734 | ||||||||
\(146\) | − | 431772.i | − | 1.67638i | ||||||
\(147\) | −414258. | −1.58117 | ||||||||
\(148\) | −166289. | − | 322747.i | −0.624037 | − | 1.21118i | ||||
\(149\) | −7264.04 | −0.0268048 | −0.0134024 | − | 0.999910i | \(-0.504266\pi\) | ||||
−0.0134024 | + | 0.999910i | \(0.504266\pi\) | |||||||
\(150\) | 723973.i | 2.62721i | ||||||||
\(151\) | −288159. | −1.02847 | −0.514233 | − | 0.857651i | \(-0.671923\pi\) | ||||
−0.514233 | + | 0.857651i | \(0.671923\pi\) | |||||||
\(152\) | 173202. | 0.608055 | ||||||||
\(153\) | − | 1.00169e6i | − | 3.45942i | ||||||
\(154\) | − | 190850.i | − | 0.648470i | ||||||
\(155\) | −95315.9 | −0.318666 | ||||||||
\(156\) | 360442.i | 1.18583i | ||||||||
\(157\) | 358882. | 1.16199 | 0.580996 | − | 0.813906i | \(-0.302663\pi\) | ||||
0.580996 | + | 0.813906i | \(0.302663\pi\) | |||||||
\(158\) | −543528. | −1.73213 | ||||||||
\(159\) | −187936. | −0.589544 | ||||||||
\(160\) | 109585. | 0.338416 | ||||||||
\(161\) | − | 209810.i | − | 0.637914i | ||||||
\(162\) | 1.09000e6i | 3.26317i | ||||||||
\(163\) | 255867.i | 0.754302i | 0.926152 | + | 0.377151i | \(0.123096\pi\) | ||||
−0.926152 | + | 0.377151i | \(0.876904\pi\) | |||||||
\(164\) | −109766. | −0.318684 | ||||||||
\(165\) | − | 186356.i | − | 0.532886i | ||||||
\(166\) | − | 513831.i | − | 1.44727i | ||||||
\(167\) | − | 279041.i | − | 0.774241i | −0.922029 | − | 0.387120i | \(-0.873470\pi\) | ||
0.922029 | − | 0.387120i | \(-0.126530\pi\) | |||||||
\(168\) | − | 136480.i | − | 0.373074i | ||||||
\(169\) | 286999. | 0.772971 | ||||||||
\(170\) | 217358.i | 0.576837i | ||||||||
\(171\) | 975072.i | 2.55004i | ||||||||
\(172\) | 763968.i | 1.96904i | ||||||||
\(173\) | −322508. | −0.819267 | −0.409633 | − | 0.912250i | \(-0.634343\pi\) | ||||
−0.409633 | + | 0.912250i | \(0.634343\pi\) | |||||||
\(174\) | −343586. | −0.860325 | ||||||||
\(175\) | 138970. | 0.343025 | ||||||||
\(176\) | 239370. | 0.582490 | ||||||||
\(177\) | − | 102153.i | − | 0.245085i | ||||||
\(178\) | −446839. | −1.05706 | ||||||||
\(179\) | 190807.i | 0.445105i | 0.974921 | + | 0.222552i | \(0.0714388\pi\) | ||||
−0.974921 | + | 0.222552i | \(0.928561\pi\) | |||||||
\(180\) | − | 350784.i | − | 0.806971i | ||||||
\(181\) | 616785. | 1.39938 | 0.699692 | − | 0.714444i | \(-0.253320\pi\) | ||||
0.699692 | + | 0.714444i | \(0.253320\pi\) | |||||||
\(182\) | 119970. | 0.268468 | ||||||||
\(183\) | − | 70088.7i | − | 0.154711i | ||||||
\(184\) | −445263. | −0.969554 | ||||||||
\(185\) | −104894. | + | 54044.6i | −0.225331 | + | 0.116098i | ||||
\(186\) | −1.66536e6 | −3.52961 | ||||||||
\(187\) | 814827.i | 1.70397i | ||||||||
\(188\) | 135034. | 0.278643 | ||||||||
\(189\) | 439508. | 0.894978 | ||||||||
\(190\) | − | 211583.i | − | 0.425202i | ||||||
\(191\) | 597918.i | 1.18593i | 0.805229 | + | 0.592964i | \(0.202042\pi\) | ||||
−0.805229 | + | 0.592964i | \(0.797958\pi\) | |||||||
\(192\) | 1.44244e6 | 2.82387 | ||||||||
\(193\) | − | 507806.i | − | 0.981306i | −0.871355 | − | 0.490653i | \(-0.836758\pi\) | ||
0.871355 | − | 0.490653i | \(-0.163242\pi\) | |||||||
\(194\) | 875910. | 1.67092 | ||||||||
\(195\) | 117145. | 0.220616 | ||||||||
\(196\) | 634307. | 1.17940 | ||||||||
\(197\) | −127024. | −0.233196 | −0.116598 | − | 0.993179i | \(-0.537199\pi\) | ||||
−0.116598 | + | 0.993179i | \(0.537199\pi\) | |||||||
\(198\) | − | 2.28017e6i | − | 4.13336i | ||||||
\(199\) | 898525.i | 1.60841i | 0.594350 | + | 0.804207i | \(0.297410\pi\) | ||||
−0.594350 | + | 0.804207i | \(0.702590\pi\) | |||||||
\(200\) | − | 294924.i | − | 0.521357i | ||||||
\(201\) | 1.03578e6 | 1.80833 | ||||||||
\(202\) | − | 273243.i | − | 0.471162i | ||||||
\(203\) | 65952.9i | 0.112330i | ||||||||
\(204\) | 2.19019e6i | 3.68474i | ||||||||
\(205\) | 35674.5i | 0.0592888i | ||||||||
\(206\) | −825723. | −1.35571 | ||||||||
\(207\) | − | 2.50669e6i | − | 4.06607i | ||||||
\(208\) | 150470.i | 0.241152i | ||||||||
\(209\) | − | 793177.i | − | 1.25604i | ||||||
\(210\) | −166723. | −0.260884 | ||||||||
\(211\) | 494860. | 0.765202 | 0.382601 | − | 0.923914i | \(-0.375028\pi\) | ||||
0.382601 | + | 0.923914i | \(0.375028\pi\) | |||||||
\(212\) | 287765. | 0.439742 | ||||||||
\(213\) | −1.99916e6 | −3.01925 | ||||||||
\(214\) | 1.55671e6i | 2.32367i | ||||||||
\(215\) | 248292. | 0.366325 | ||||||||
\(216\) | − | 932731.i | − | 1.36026i | ||||||
\(217\) | 319674.i | 0.460849i | ||||||||
\(218\) | −484849. | −0.690980 | ||||||||
\(219\) | −1.41400e6 | −1.99222 | ||||||||
\(220\) | 285347.i | 0.397481i | ||||||||
\(221\) | −512206. | −0.705447 | ||||||||
\(222\) | −1.83271e6 | + | 944269.i | −2.49580 | + | 1.28592i | ||||
\(223\) | 967287. | 1.30255 | 0.651273 | − | 0.758843i | \(-0.274235\pi\) | ||||
0.651273 | + | 0.758843i | \(0.274235\pi\) | |||||||
\(224\) | − | 367531.i | − | 0.489411i | ||||||
\(225\) | 1.66033e6 | 2.18645 | ||||||||
\(226\) | −754260. | −0.982313 | ||||||||
\(227\) | − | 1.25464e6i | − | 1.61605i | −0.589151 | − | 0.808023i | \(-0.700538\pi\) | ||
0.589151 | − | 0.808023i | \(-0.299462\pi\) | |||||||
\(228\) | − | 2.13199e6i | − | 2.71612i | ||||||
\(229\) | −216765. | −0.273149 | −0.136575 | − | 0.990630i | \(-0.543609\pi\) | ||||
−0.136575 | + | 0.990630i | \(0.543609\pi\) | |||||||
\(230\) | 543932.i | 0.677992i | ||||||||
\(231\) | −625009. | −0.770648 | ||||||||
\(232\) | 139966. | 0.170728 | ||||||||
\(233\) | 1.48321e6 | 1.78983 | 0.894916 | − | 0.446234i | \(-0.147235\pi\) | ||||
0.894916 | + | 0.446234i | \(0.147235\pi\) | |||||||
\(234\) | 1.43333e6 | 1.71122 | ||||||||
\(235\) | − | 43886.5i | − | 0.0518396i | ||||||
\(236\) | 156415.i | 0.182809i | ||||||||
\(237\) | 1.77999e6i | 2.05847i | ||||||||
\(238\) | 728983. | 0.834210 | ||||||||
\(239\) | 13603.1i | 0.0154043i | 0.999970 | + | 0.00770216i | \(0.00245170\pi\) | ||||
−0.999970 | + | 0.00770216i | \(0.997548\pi\) | |||||||
\(240\) | − | 209110.i | − | 0.234340i | ||||||
\(241\) | − | 648806.i | − | 0.719568i | −0.933036 | − | 0.359784i | \(-0.882850\pi\) | ||
0.933036 | − | 0.359784i | \(-0.117150\pi\) | |||||||
\(242\) | 454505.i | 0.498885i | ||||||||
\(243\) | 1.32231e6 | 1.43654 | ||||||||
\(244\) | 107319.i | 0.115399i | ||||||||
\(245\) | − | 206152.i | − | 0.219418i | ||||||
\(246\) | 623305.i | 0.656694i | ||||||||
\(247\) | 498596. | 0.520004 | ||||||||
\(248\) | 678418. | 0.700435 | ||||||||
\(249\) | −1.68273e6 | −1.71995 | ||||||||
\(250\) | −745296. | −0.754186 | ||||||||
\(251\) | − | 1.63078e6i | − | 1.63385i | −0.576745 | − | 0.816924i | \(-0.695677\pi\) | ||
0.576745 | − | 0.816924i | \(-0.304323\pi\) | |||||||
\(252\) | −1.17647e6 | −1.16702 | ||||||||
\(253\) | 2.03908e6i | 2.00278i | ||||||||
\(254\) | − | 2.45836e6i | − | 2.39090i | ||||||
\(255\) | 711819. | 0.685519 | ||||||||
\(256\) | −56905.4 | −0.0542692 | ||||||||
\(257\) | − | 680882.i | − | 0.643042i | −0.946903 | − | 0.321521i | \(-0.895806\pi\) | ||
0.946903 | − | 0.321521i | \(-0.104194\pi\) | |||||||
\(258\) | 4.33817e6 | 4.05749 | ||||||||
\(259\) | 181257. | + | 351797.i | 0.167898 | + | 0.325868i | ||||
\(260\) | −179371. | −0.164558 | ||||||||
\(261\) | 787968.i | 0.715991i | ||||||||
\(262\) | −717403. | −0.645669 | ||||||||
\(263\) | −1.05628e6 | −0.941649 | −0.470825 | − | 0.882227i | \(-0.656044\pi\) | ||||
−0.470825 | + | 0.882227i | \(0.656044\pi\) | |||||||
\(264\) | 1.32640e6i | 1.17129i | ||||||||
\(265\) | − | 93524.6i | − | 0.0818109i | ||||||
\(266\) | −709613. | −0.614919 | ||||||||
\(267\) | 1.46334e6i | 1.25622i | ||||||||
\(268\) | −1.58598e6 | −1.34884 | ||||||||
\(269\) | −566463. | −0.477300 | −0.238650 | − | 0.971106i | \(-0.576705\pi\) | ||||
−0.238650 | + | 0.971106i | \(0.576705\pi\) | |||||||
\(270\) | −1.13942e6 | −0.951207 | ||||||||
\(271\) | −616867. | −0.510233 | −0.255116 | − | 0.966910i | \(-0.582114\pi\) | ||||
−0.255116 | + | 0.966910i | \(0.582114\pi\) | |||||||
\(272\) | 914315.i | 0.749331i | ||||||||
\(273\) | − | 392885.i | − | 0.319050i | ||||||
\(274\) | 696907.i | 0.560788i | ||||||||
\(275\) | −1.35061e6 | −1.07695 | ||||||||
\(276\) | 5.48088e6i | 4.33090i | ||||||||
\(277\) | − | 569488.i | − | 0.445949i | −0.974824 | − | 0.222975i | \(-0.928423\pi\) | ||
0.974824 | − | 0.222975i | \(-0.0715767\pi\) | |||||||
\(278\) | 796023.i | 0.617751i | ||||||||
\(279\) | 3.81928e6i | 2.93746i | ||||||||
\(280\) | 67917.9 | 0.0517713 | ||||||||
\(281\) | 366748.i | 0.277078i | 0.990357 | + | 0.138539i | \(0.0442406\pi\) | ||||
−0.990357 | + | 0.138539i | \(0.955759\pi\) | |||||||
\(282\) | − | 766786.i | − | 0.574185i | ||||||
\(283\) | − | 1.60923e6i | − | 1.19441i | −0.802089 | − | 0.597205i | \(-0.796278\pi\) | ||
0.802089 | − | 0.597205i | \(-0.203722\pi\) | |||||||
\(284\) | 3.06109e6 | 2.25206 | ||||||||
\(285\) | −692905. | −0.505314 | ||||||||
\(286\) | −1.16595e6 | −0.842876 | ||||||||
\(287\) | 119646. | 0.0857422 | ||||||||
\(288\) | − | 4.39104e6i | − | 3.11951i | ||||||
\(289\) | −1.69251e6 | −1.19203 | ||||||||
\(290\) | − | 170983.i | − | 0.119387i | ||||||
\(291\) | − | 2.86849e6i | − | 1.98574i | ||||||
\(292\) | 2.16509e6 | 1.48600 | ||||||||
\(293\) | 1.19533e6 | 0.813427 | 0.406714 | − | 0.913556i | \(-0.366675\pi\) | ||||
0.406714 | + | 0.913556i | \(0.366675\pi\) | |||||||
\(294\) | − | 3.60189e6i | − | 2.43032i | ||||||
\(295\) | 50835.4 | 0.0340104 | ||||||||
\(296\) | 746588. | − | 384666.i | 0.495281 | − | 0.255185i | ||||
\(297\) | −4.27144e6 | −2.80985 | ||||||||
\(298\) | − | 63159.4i | − | 0.0412000i | ||||||
\(299\) | −1.28178e6 | −0.829155 | ||||||||
\(300\) | −3.63032e6 | −2.32885 | ||||||||
\(301\) | − | 832732.i | − | 0.529772i | ||||||
\(302\) | − | 2.50548e6i | − | 1.58079i | ||||||
\(303\) | −894835. | −0.559934 | ||||||||
\(304\) | − | 890021.i | − | 0.552352i | ||||||
\(305\) | 34879.0 | 0.0214692 | ||||||||
\(306\) | 8.70948e6 | 5.31727 | ||||||||
\(307\) | −95070.0 | −0.0575702 | −0.0287851 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287851 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(308\) | 957006. | 0.574828 | ||||||||
\(309\) | 2.70414e6i | 1.61114i | ||||||||
\(310\) | − | 828753.i | − | 0.489802i | ||||||
\(311\) | 1.06191e6i | 0.622571i | 0.950317 | + | 0.311285i | \(0.100759\pi\) | ||||
−0.950317 | + | 0.311285i | \(0.899241\pi\) | |||||||
\(312\) | −833787. | −0.484918 | ||||||||
\(313\) | − | 298778.i | − | 0.172380i | −0.996279 | − | 0.0861902i | \(-0.972531\pi\) | ||
0.996279 | − | 0.0861902i | \(-0.0274693\pi\) | |||||||
\(314\) | 3.12041e6i | 1.78603i | ||||||||
\(315\) | 382357.i | 0.217117i | ||||||||
\(316\) | − | 2.72549e6i | − | 1.53542i | ||||||
\(317\) | 766205. | 0.428250 | 0.214125 | − | 0.976806i | \(-0.431310\pi\) | ||||
0.214125 | + | 0.976806i | \(0.431310\pi\) | |||||||
\(318\) | − | 1.63406e6i | − | 0.906152i | ||||||
\(319\) | − | 640976.i | − | 0.352667i | ||||||
\(320\) | 717819.i | 0.391868i | ||||||||
\(321\) | 5.09804e6 | 2.76147 | ||||||||
\(322\) | 1.82426e6 | 0.980498 | ||||||||
\(323\) | 3.02967e6 | 1.61581 | ||||||||
\(324\) | −5.46574e6 | −2.89259 | ||||||||
\(325\) | − | 849001.i | − | 0.445861i | ||||||
\(326\) | −2.22471e6 | −1.15939 | ||||||||
\(327\) | 1.58782e6i | 0.821167i | ||||||||
\(328\) | − | 253915.i | − | 0.130318i | ||||||
\(329\) | −147188. | −0.0749693 | ||||||||
\(330\) | 1.62033e6 | 0.819066 | ||||||||
\(331\) | 2.41648e6i | 1.21231i | 0.795347 | + | 0.606154i | \(0.207289\pi\) | ||||
−0.795347 | + | 0.606154i | \(0.792711\pi\) | |||||||
\(332\) | 2.57658e6 | 1.28291 | ||||||||
\(333\) | 2.16555e6 | + | 4.20306e6i | 1.07018 | + | 2.07709i | ||||
\(334\) | 2.42620e6 | 1.19004 | ||||||||
\(335\) | 515448.i | 0.250942i | ||||||||
\(336\) | −701320. | −0.338897 | ||||||||
\(337\) | −552737. | −0.265121 | −0.132560 | − | 0.991175i | \(-0.542320\pi\) | ||||
−0.132560 | + | 0.991175i | \(0.542320\pi\) | |||||||
\(338\) | 2.49540e6i | 1.18809i | ||||||||
\(339\) | 2.47010e6i | 1.16739i | ||||||||
\(340\) | −1.08993e6 | −0.511330 | ||||||||
\(341\) | − | 3.10681e6i | − | 1.44687i | ||||||
\(342\) | −8.47806e6 | −3.91950 | ||||||||
\(343\) | −1.49014e6 | −0.683897 | ||||||||
\(344\) | −1.76724e6 | −0.805190 | ||||||||
\(345\) | 1.78131e6 | 0.805732 | ||||||||
\(346\) | − | 2.80414e6i | − | 1.25924i | ||||||
\(347\) | − | 2.33460e6i | − | 1.04085i | −0.853907 | − | 0.520426i | \(-0.825773\pi\) | ||
0.853907 | − | 0.520426i | \(-0.174227\pi\) | |||||||
\(348\) | − | 1.72289e6i | − | 0.762623i | ||||||
\(349\) | −1.62677e6 | −0.714930 | −0.357465 | − | 0.933927i | \(-0.616359\pi\) | ||||
−0.357465 | + | 0.933927i | \(0.616359\pi\) | |||||||
\(350\) | 1.20832e6i | 0.527243i | ||||||||
\(351\) | − | 2.68506e6i | − | 1.16329i | ||||||
\(352\) | 3.57192e6i | 1.53654i | ||||||||
\(353\) | − | 2.36096e6i | − | 1.00845i | −0.863574 | − | 0.504223i | \(-0.831779\pi\) | ||
0.863574 | − | 0.504223i | \(-0.168221\pi\) | |||||||
\(354\) | 888198. | 0.376705 | ||||||||
\(355\) | − | 994866.i | − | 0.418980i | ||||||
\(356\) | − | 2.24065e6i | − | 0.937020i | ||||||
\(357\) | − | 2.38733e6i | − | 0.991382i | ||||||
\(358\) | −1.65903e6 | −0.684143 | ||||||||
\(359\) | 3.66248e6 | 1.49982 | 0.749911 | − | 0.661539i | \(-0.230096\pi\) | ||||
0.749911 | + | 0.661539i | \(0.230096\pi\) | |||||||
\(360\) | 811445. | 0.329991 | ||||||||
\(361\) | −473070. | −0.191055 | ||||||||
\(362\) | 5.36282e6i | 2.15091i | ||||||||
\(363\) | 1.48844e6 | 0.592879 | ||||||||
\(364\) | 601581.i | 0.237980i | ||||||||
\(365\) | − | 703663.i | − | 0.276460i | ||||||
\(366\) | 609408. | 0.237796 | ||||||||
\(367\) | 301840. | 0.116980 | 0.0584899 | − | 0.998288i | \(-0.481371\pi\) | ||||
0.0584899 | + | 0.998288i | \(0.481371\pi\) | |||||||
\(368\) | 2.28805e6i | 0.880735i | ||||||||
\(369\) | 1.42947e6 | 0.546522 | ||||||||
\(370\) | −469907. | − | 912030.i | −0.178446 | − | 0.346342i | ||||
\(371\) | −313666. | −0.118313 | ||||||||
\(372\) | − | 8.35086e6i | − | 3.12877i | ||||||
\(373\) | 2.51494e6 | 0.935957 | 0.467979 | − | 0.883740i | \(-0.344982\pi\) | ||||
0.467979 | + | 0.883740i | \(0.344982\pi\) | |||||||
\(374\) | −7.08476e6 | −2.61907 | ||||||||
\(375\) | 2.44075e6i | 0.896282i | ||||||||
\(376\) | 312365.i | 0.113944i | ||||||||
\(377\) | 402922. | 0.146005 | ||||||||
\(378\) | 3.82144e6i | 1.37562i | ||||||||
\(379\) | 3.27388e6 | 1.17075 | 0.585376 | − | 0.810762i | \(-0.300947\pi\) | ||||
0.585376 | + | 0.810762i | \(0.300947\pi\) | |||||||
\(380\) | 1.06097e6 | 0.376915 | ||||||||
\(381\) | −8.05080e6 | −2.84136 | ||||||||
\(382\) | −5.19878e6 | −1.82282 | ||||||||
\(383\) | 2.28037e6i | 0.794345i | 0.917744 | + | 0.397172i | \(0.130009\pi\) | ||||
−0.917744 | + | 0.397172i | \(0.869991\pi\) | |||||||
\(384\) | 5.49506e6i | 1.90171i | ||||||||
\(385\) | − | 311030.i | − | 0.106943i | ||||||
\(386\) | 4.41527e6 | 1.50831 | ||||||||
\(387\) | − | 9.94900e6i | − | 3.37677i | ||||||
\(388\) | 4.39220e6i | 1.48116i | ||||||||
\(389\) | 2.47732e6i | 0.830058i | 0.909808 | + | 0.415029i | \(0.136229\pi\) | ||||
−0.909808 | + | 0.415029i | \(0.863771\pi\) | |||||||
\(390\) | 1.01855e6i | 0.339095i | ||||||||
\(391\) | −7.78861e6 | −2.57643 | ||||||||
\(392\) | 1.46730e6i | 0.482286i | ||||||||
\(393\) | 2.34940e6i | 0.767319i | ||||||||
\(394\) | − | 1.10445e6i | − | 0.358430i | ||||||
\(395\) | −885794. | −0.285654 | ||||||||
\(396\) | 1.14338e7 | 3.66396 | ||||||||
\(397\) | −42062.8 | −0.0133944 | −0.00669718 | − | 0.999978i | \(-0.502132\pi\) | ||||
−0.00669718 | + | 0.999978i | \(0.502132\pi\) | |||||||
\(398\) | −7.81250e6 | −2.47219 | ||||||||
\(399\) | 2.32389e6i | 0.730775i | ||||||||
\(400\) | −1.51551e6 | −0.473597 | ||||||||
\(401\) | − | 1.70554e6i | − | 0.529665i | −0.964294 | − | 0.264832i | \(-0.914683\pi\) | ||
0.964294 | − | 0.264832i | \(-0.0853166\pi\) | |||||||
\(402\) | 9.00592e6i | 2.77947i | ||||||||
\(403\) | 1.95297e6 | 0.599007 | ||||||||
\(404\) | 1.37016e6 | 0.417655 | ||||||||
\(405\) | 1.77639e6i | 0.538145i | ||||||||
\(406\) | −573448. | −0.172655 | ||||||||
\(407\) | −1.76158e6 | − | 3.41900e6i | −0.527128 | − | 1.02309i | ||||
\(408\) | −5.06642e6 | −1.50678 | ||||||||
\(409\) | 4.37126e6i | 1.29211i | 0.763292 | + | 0.646054i | \(0.223582\pi\) | ||||
−0.763292 | + | 0.646054i | \(0.776418\pi\) | |||||||
\(410\) | −310182. | −0.0911292 | ||||||||
\(411\) | 2.28228e6 | 0.666445 | ||||||||
\(412\) | − | 4.14054e6i | − | 1.20175i | ||||||
\(413\) | − | 170494.i | − | 0.0491851i | ||||||
\(414\) | 2.17952e7 | 6.24971 | ||||||||
\(415\) | − | 837396.i | − | 0.238677i | ||||||
\(416\) | −2.24533e6 | −0.636132 | ||||||||
\(417\) | 2.60687e6 | 0.734141 | ||||||||
\(418\) | 6.89651e6 | 1.93058 | ||||||||
\(419\) | 4.55257e6 | 1.26684 | 0.633420 | − | 0.773808i | \(-0.281651\pi\) | ||||
0.633420 | + | 0.773808i | \(0.281651\pi\) | |||||||
\(420\) | − | 836024.i | − | 0.231257i | ||||||
\(421\) | − | 3.21412e6i | − | 0.883804i | −0.897063 | − | 0.441902i | \(-0.854304\pi\) | ||
0.897063 | − | 0.441902i | \(-0.145696\pi\) | |||||||
\(422\) | 4.30271e6i | 1.17614i | ||||||||
\(423\) | −1.75852e6 | −0.477855 | ||||||||
\(424\) | 665667.i | 0.179822i | ||||||||
\(425\) | − | 5.15887e6i | − | 1.38542i | ||||||
\(426\) | − | 1.73823e7i | − | 4.64070i | ||||||
\(427\) | − | 116979.i | − | 0.0310482i | ||||||
\(428\) | −7.80606e6 | −2.05979 | ||||||||
\(429\) | 3.81833e6i | 1.00168i | ||||||||
\(430\) | 2.15885e6i | 0.563056i | ||||||||
\(431\) | 6.25665e6i | 1.62237i | 0.584792 | + | 0.811183i | \(0.301176\pi\) | ||||
−0.584792 | + | 0.811183i | \(0.698824\pi\) | |||||||
\(432\) | −4.79297e6 | −1.23565 | ||||||||
\(433\) | 3.91654e6 | 1.00388 | 0.501942 | − | 0.864902i | \(-0.332619\pi\) | ||||
0.501942 | + | 0.864902i | \(0.332619\pi\) | |||||||
\(434\) | −2.77950e6 | −0.708342 | ||||||||
\(435\) | −559946. | −0.141881 | ||||||||
\(436\) | − | 2.43125e6i | − | 0.612510i | ||||||
\(437\) | 7.58166e6 | 1.89916 | ||||||||
\(438\) | − | 1.22944e7i | − | 3.06212i | ||||||
\(439\) | 3.43312e6i | 0.850212i | 0.905144 | + | 0.425106i | \(0.139763\pi\) | ||||
−0.905144 | + | 0.425106i | \(0.860237\pi\) | |||||||
\(440\) | −660073. | −0.162540 | ||||||||
\(441\) | −8.26046e6 | −2.02259 | ||||||||
\(442\) | − | 4.45353e6i | − | 1.08430i | ||||||
\(443\) | −5.22540e6 | −1.26506 | −0.632528 | − | 0.774537i | \(-0.717983\pi\) | ||||
−0.632528 | + | 0.774537i | \(0.717983\pi\) | |||||||
\(444\) | −4.73498e6 | − | 9.19000e6i | −1.13989 | − | 2.21237i | ||||
\(445\) | −728219. | −0.174326 | ||||||||
\(446\) | 8.41037e6i | 2.00206i | ||||||||
\(447\) | −206839. | −0.0489625 | ||||||||
\(448\) | 2.40745e6 | 0.566711 | ||||||||
\(449\) | − | 6.48272e6i | − | 1.51754i | −0.651357 | − | 0.758772i | \(-0.725800\pi\) | ||
0.651357 | − | 0.758772i | \(-0.274200\pi\) | |||||||
\(450\) | 1.44363e7i | 3.36065i | ||||||||
\(451\) | −1.16281e6 | −0.269194 | ||||||||
\(452\) | − | 3.78219e6i | − | 0.870758i | ||||||
\(453\) | −8.20514e6 | −1.87863 | ||||||||
\(454\) | 1.09088e7 | 2.48392 | ||||||||
\(455\) | 195516. | 0.0442745 | ||||||||
\(456\) | 4.93180e6 | 1.11069 | ||||||||
\(457\) | 506140.i | 0.113365i | 0.998392 | + | 0.0566827i | \(0.0180523\pi\) | ||||
−0.998392 | + | 0.0566827i | \(0.981948\pi\) | |||||||
\(458\) | − | 1.88473e6i | − | 0.419841i | ||||||
\(459\) | − | 1.63155e7i | − | 3.61467i | ||||||
\(460\) | −2.72751e6 | −0.600997 | ||||||||
\(461\) | 600395.i | 0.131578i | 0.997834 | + | 0.0657892i | \(0.0209565\pi\) | ||||
−0.997834 | + | 0.0657892i | \(0.979044\pi\) | |||||||
\(462\) | − | 5.43433e6i | − | 1.18452i | ||||||
\(463\) | − | 4.18675e6i | − | 0.907664i | −0.891087 | − | 0.453832i | \(-0.850057\pi\) | ||
0.891087 | − | 0.453832i | \(-0.149943\pi\) | |||||||
\(464\) | − | 719238.i | − | 0.155088i | ||||||
\(465\) | −2.71406e6 | −0.582086 | ||||||||
\(466\) | 1.28962e7i | 2.75104i | ||||||||
\(467\) | 6.20534e6i | 1.31666i | 0.752730 | + | 0.658329i | \(0.228737\pi\) | ||||
−0.752730 | + | 0.658329i | \(0.771263\pi\) | |||||||
\(468\) | 7.18734e6i | 1.51689i | ||||||||
\(469\) | 1.72873e6 | 0.362906 | ||||||||
\(470\) | 381584. | 0.0796794 | ||||||||
\(471\) | 1.02189e7 | 2.12253 | ||||||||
\(472\) | −361825. | −0.0747555 | ||||||||
\(473\) | 8.09306e6i | 1.66326i | ||||||||
\(474\) | −1.54766e7 | −3.16395 | ||||||||
\(475\) | 5.02179e6i | 1.02123i | ||||||||
\(476\) | 3.65544e6i | 0.739474i | ||||||||
\(477\) | −3.74750e6 | −0.754130 | ||||||||
\(478\) | −118276. | −0.0236770 | ||||||||
\(479\) | − | 1.96601e6i | − | 0.391515i | −0.980652 | − | 0.195757i | \(-0.937284\pi\) | ||
0.980652 | − | 0.195757i | \(-0.0627165\pi\) | |||||||
\(480\) | 3.12036e6 | 0.618162 | ||||||||
\(481\) | 2.14921e6 | − | 1.10734e6i | 0.423561 | − | 0.218232i | ||||
\(482\) | 5.64124e6 | 1.10600 | ||||||||
\(483\) | − | 5.97421e6i | − | 1.16523i | ||||||
\(484\) | −2.27909e6 | −0.442229 | ||||||||
\(485\) | 1.42748e6 | 0.275560 | ||||||||
\(486\) | 1.14972e7i | 2.20802i | ||||||||
\(487\) | − | 6.73550e6i | − | 1.28691i | −0.765485 | − | 0.643454i | \(-0.777501\pi\) | ||
0.765485 | − | 0.643454i | \(-0.222499\pi\) | |||||||
\(488\) | −248254. | −0.0471896 | ||||||||
\(489\) | 7.28565e6i | 1.37783i | ||||||||
\(490\) | 1.79245e6 | 0.337254 | ||||||||
\(491\) | −8.58269e6 | −1.60664 | −0.803322 | − | 0.595545i | \(-0.796936\pi\) | ||||
−0.803322 | + | 0.595545i | \(0.796936\pi\) | |||||||
\(492\) | −3.12553e6 | −0.582117 | ||||||||
\(493\) | 2.44832e6 | 0.453681 | ||||||||
\(494\) | 4.33520e6i | 0.799266i | ||||||||
\(495\) | − | 3.71601e6i | − | 0.681654i | ||||||
\(496\) | − | 3.48615e6i | − | 0.636270i | ||||||
\(497\) | −3.33662e6 | −0.605920 | ||||||||
\(498\) | − | 1.46310e7i | − | 2.64363i | ||||||
\(499\) | 9.02170e6i | 1.62195i | 0.585082 | + | 0.810974i | \(0.301062\pi\) | ||||
−0.585082 | + | 0.810974i | \(0.698938\pi\) | |||||||
\(500\) | − | 3.73724e6i | − | 0.668538i | ||||||
\(501\) | − | 7.94550e6i | − | 1.41425i | ||||||
\(502\) | 1.41793e7 | 2.51129 | ||||||||
\(503\) | 1.72194e6i | 0.303458i | 0.988422 | + | 0.151729i | \(0.0484840\pi\) | ||||
−0.988422 | + | 0.151729i | \(0.951516\pi\) | |||||||
\(504\) | − | 2.72145e6i | − | 0.477227i | ||||||
\(505\) | − | 445307.i | − | 0.0777018i | ||||||
\(506\) | −1.77294e7 | −3.07835 | ||||||||
\(507\) | 8.17210e6 | 1.41193 | ||||||||
\(508\) | 1.23273e7 | 2.11938 | ||||||||
\(509\) | 7.97361e6 | 1.36414 | 0.682072 | − | 0.731285i | \(-0.261079\pi\) | ||||
0.682072 | + | 0.731285i | \(0.261079\pi\) | |||||||
\(510\) | 6.18913e6i | 1.05367i | ||||||||
\(511\) | −2.35997e6 | −0.399811 | ||||||||
\(512\) | 5.68067e6i | 0.957690i | ||||||||
\(513\) | 1.58820e7i | 2.66447i | ||||||||
\(514\) | 5.92013e6 | 0.988379 | ||||||||
\(515\) | −1.34569e6 | −0.223577 | ||||||||
\(516\) | 2.17535e7i | 3.59670i | ||||||||
\(517\) | 1.43048e6 | 0.235372 | ||||||||
\(518\) | −3.05880e6 | + | 1.57599e6i | −0.500872 | + | 0.258066i | ||||
\(519\) | −9.18321e6 | −1.49650 | ||||||||
\(520\) | − | 414927.i | − | 0.0672920i | ||||||
\(521\) | −391196. | −0.0631394 | −0.0315697 | − | 0.999502i | \(-0.510051\pi\) | ||||
−0.0315697 | + | 0.999502i | \(0.510051\pi\) | |||||||
\(522\) | −6.85123e6 | −1.10051 | ||||||||
\(523\) | − | 1.67343e6i | − | 0.267518i | −0.991014 | − | 0.133759i | \(-0.957295\pi\) | ||
0.991014 | − | 0.133759i | \(-0.0427048\pi\) | |||||||
\(524\) | − | 3.59738e6i | − | 0.572345i | ||||||
\(525\) | 3.95708e6 | 0.626580 | ||||||||
\(526\) | − | 9.18414e6i | − | 1.44735i | ||||||
\(527\) | 1.18670e7 | 1.86129 | ||||||||
\(528\) | 6.81592e6 | 1.06399 | ||||||||
\(529\) | −1.30544e7 | −2.02824 | ||||||||
\(530\) | 813177. | 0.125746 | ||||||||
\(531\) | − | 2.03696e6i | − | 0.313506i | ||||||
\(532\) | − | 3.55832e6i | − | 0.545086i | ||||||
\(533\) | − | 730948.i | − | 0.111447i | ||||||
\(534\) | −1.27235e7 | −1.93087 | ||||||||
\(535\) | 2.53699e6i | 0.383208i | ||||||||
\(536\) | − | 3.66873e6i | − | 0.551575i | ||||||
\(537\) | 5.43311e6i | 0.813042i | ||||||||
\(538\) | − | 4.92529e6i | − | 0.733628i | ||||||
\(539\) | 6.71951e6 | 0.996244 | ||||||||
\(540\) | − | 5.71357e6i | − | 0.843185i | ||||||
\(541\) | − | 9.45940e6i | − | 1.38954i | −0.719233 | − | 0.694769i | \(-0.755506\pi\) | ||
0.719233 | − | 0.694769i | \(-0.244494\pi\) | |||||||
\(542\) | − | 5.36354e6i | − | 0.784248i | ||||||
\(543\) | 1.75625e7 | 2.55616 | ||||||||
\(544\) | −1.36435e7 | −1.97665 | ||||||||
\(545\) | −790164. | −0.113953 | ||||||||
\(546\) | 3.41606e6 | 0.490392 | ||||||||
\(547\) | 441408.i | 0.0630771i | 0.999503 | + | 0.0315386i | \(0.0100407\pi\) | ||||
−0.999503 | + | 0.0315386i | \(0.989959\pi\) | |||||||
\(548\) | −3.49460e6 | −0.497103 | ||||||||
\(549\) | − | 1.39759e6i | − | 0.197902i | ||||||
\(550\) | − | 1.17433e7i | − | 1.65532i | ||||||
\(551\) | −2.38326e6 | −0.334420 | ||||||||
\(552\) | −1.26786e7 | −1.77102 | ||||||||
\(553\) | 2.97081e6i | 0.413106i | ||||||||
\(554\) | 4.95159e6 | 0.685441 | ||||||||
\(555\) | −2.98678e6 | + | 1.53889e6i | −0.411596 | + | 0.212067i | ||||
\(556\) | −3.99161e6 | −0.547597 | ||||||||
\(557\) | − | 3.74743e6i | − | 0.511795i | −0.966704 | − | 0.255897i | \(-0.917629\pi\) | ||
0.966704 | − | 0.255897i | \(-0.0823710\pi\) | |||||||
\(558\) | −3.32079e7 | −4.51498 | ||||||||
\(559\) | −5.08736e6 | −0.688593 | ||||||||
\(560\) | − | 349006.i | − | 0.0470287i | ||||||
\(561\) | 2.32017e7i | 3.11252i | ||||||||
\(562\) | −3.18880e6 | −0.425879 | ||||||||
\(563\) | 2.07672e6i | 0.276126i | 0.990423 | + | 0.138063i | \(0.0440877\pi\) | ||||
−0.990423 | + | 0.138063i | \(0.955912\pi\) | |||||||
\(564\) | 3.84501e6 | 0.508978 | ||||||||
\(565\) | −1.22923e6 | −0.161998 | ||||||||
\(566\) | 1.39920e7 | 1.83585 | ||||||||
\(567\) | 5.95771e6 | 0.778254 | ||||||||
\(568\) | 7.08103e6i | 0.920927i | ||||||||
\(569\) | − | 5.04942e6i | − | 0.653824i | −0.945055 | − | 0.326912i | \(-0.893992\pi\) | ||
0.945055 | − | 0.326912i | \(-0.106008\pi\) | |||||||
\(570\) | − | 6.02467e6i | − | 0.776688i | ||||||
\(571\) | −4.82893e6 | −0.619812 | −0.309906 | − | 0.950767i | \(-0.600298\pi\) | ||||
−0.309906 | + | 0.950767i | \(0.600298\pi\) | |||||||
\(572\) | − | 5.84658e6i | − | 0.747156i | ||||||
\(573\) | 1.70253e7i | 2.16625i | ||||||||
\(574\) | 1.04030e6i | 0.131789i | ||||||||
\(575\) | − | 1.29099e7i | − | 1.62837i | ||||||
\(576\) | 2.87628e7 | 3.61223 | ||||||||
\(577\) | 5.22766e6i | 0.653684i | 0.945079 | + | 0.326842i | \(0.105984\pi\) | ||||
−0.945079 | + | 0.326842i | \(0.894016\pi\) | |||||||
\(578\) | − | 1.47161e7i | − | 1.83220i | ||||||
\(579\) | − | 1.44594e7i | − | 1.79248i | ||||||
\(580\) | 857382. | 0.105829 | ||||||||
\(581\) | −2.80849e6 | −0.345170 | ||||||||
\(582\) | 2.49410e7 | 3.05215 | ||||||||
\(583\) | 3.04842e6 | 0.371453 | ||||||||
\(584\) | 5.00837e6i | 0.607665i | ||||||||
\(585\) | 2.33591e6 | 0.282206 | ||||||||
\(586\) | 1.03932e7i | 1.25027i | ||||||||
\(587\) | 1.82439e6i | 0.218536i | 0.994012 | + | 0.109268i | \(0.0348507\pi\) | ||||
−0.994012 | + | 0.109268i | \(0.965149\pi\) | |||||||
\(588\) | 1.80615e7 | 2.15432 | ||||||||
\(589\) | −1.15517e7 | −1.37201 | ||||||||
\(590\) | 442004.i | 0.0522752i | ||||||||
\(591\) | −3.61693e6 | −0.425962 | ||||||||
\(592\) | −1.97666e6 | − | 3.83645e6i | −0.231808 | − | 0.449910i | ||||
\(593\) | −1.01857e7 | −1.18947 | −0.594736 | − | 0.803921i | \(-0.702744\pi\) | ||||
−0.594736 | + | 0.803921i | \(0.702744\pi\) | |||||||
\(594\) | − | 3.71394e7i | − | 4.31885i | ||||||
\(595\) | 1.18803e6 | 0.137574 | ||||||||
\(596\) | 316709. | 0.0365212 | ||||||||
\(597\) | 2.55849e7i | 2.93798i | ||||||||
\(598\) | − | 1.11448e7i | − | 1.27444i | ||||||
\(599\) | −6.34368e6 | −0.722395 | −0.361197 | − | 0.932489i | \(-0.617632\pi\) | ||||
−0.361197 | + | 0.932489i | \(0.617632\pi\) | |||||||
\(600\) | − | 8.39778e6i | − | 0.952327i | ||||||
\(601\) | −1.51876e7 | −1.71515 | −0.857575 | − | 0.514359i | \(-0.828030\pi\) | ||||
−0.857575 | + | 0.514359i | \(0.828030\pi\) | |||||||
\(602\) | 7.24044e6 | 0.814280 | ||||||||
\(603\) | 2.06539e7 | 2.31317 | ||||||||
\(604\) | 1.25636e7 | 1.40127 | ||||||||
\(605\) | 740711.i | 0.0822736i | ||||||||
\(606\) | − | 7.78041e6i | − | 0.860639i | ||||||
\(607\) | 9.62724e6i | 1.06055i | 0.847827 | + | 0.530274i | \(0.177911\pi\) | ||||
−0.847827 | + | 0.530274i | \(0.822089\pi\) | |||||||
\(608\) | 1.32810e7 | 1.45704 | ||||||||
\(609\) | 1.87797e6i | 0.205185i | ||||||||
\(610\) | 303266.i | 0.0329989i | ||||||||
\(611\) | 899208.i | 0.0974444i | ||||||||
\(612\) | 4.36732e7i | 4.71342i | ||||||||
\(613\) | −2.24848e6 | −0.241678 | −0.120839 | − | 0.992672i | \(-0.538559\pi\) | ||||
−0.120839 | + | 0.992672i | \(0.538559\pi\) | |||||||
\(614\) | − | 826615.i | − | 0.0884876i | ||||||
\(615\) | 1.01581e6i | 0.108299i | ||||||||
\(616\) | 2.21378e6i | 0.235062i | ||||||||
\(617\) | −4.22918e6 | −0.447243 | −0.223622 | − | 0.974676i | \(-0.571788\pi\) | ||||
−0.223622 | + | 0.974676i | \(0.571788\pi\) | |||||||
\(618\) | −2.35119e7 | −2.47638 | ||||||||
\(619\) | −9.60617e6 | −1.00768 | −0.503841 | − | 0.863796i | \(-0.668080\pi\) | ||||
−0.503841 | + | 0.863796i | \(0.668080\pi\) | |||||||
\(620\) | 4.15573e6 | 0.434179 | ||||||||
\(621\) | − | 4.08290e7i | − | 4.24854i | ||||||
\(622\) | −9.23314e6 | −0.956915 | ||||||||
\(623\) | 2.44233e6i | 0.252106i | ||||||||
\(624\) | 4.28453e6i | 0.440496i | ||||||||
\(625\) | 7.92354e6 | 0.811371 | ||||||||
\(626\) | 2.59782e6 | 0.264955 | ||||||||
\(627\) | − | 2.25852e7i | − | 2.29432i | ||||||
\(628\) | −1.56471e7 | −1.58320 | ||||||||
\(629\) | 1.30595e7 | − | 6.72865e6i | 1.31613 | − | 0.678112i | ||||
\(630\) | −3.32452e6 | −0.333716 | ||||||||
\(631\) | 1.22895e7i | 1.22874i | 0.789019 | + | 0.614369i | \(0.210589\pi\) | ||||
−0.789019 | + | 0.614369i | \(0.789411\pi\) | |||||||
\(632\) | 6.30470e6 | 0.627873 | ||||||||
\(633\) | 1.40908e7 | 1.39774 | ||||||||
\(634\) | 6.66200e6i | 0.658236i | ||||||||
\(635\) | − | 4.00641e6i | − | 0.394295i | ||||||
\(636\) | 8.19392e6 | 0.803246 | ||||||||
\(637\) | 4.22393e6i | 0.412447i | ||||||||
\(638\) | 5.57316e6 | 0.542063 | ||||||||
\(639\) | −3.98640e7 | −3.86215 | ||||||||
\(640\) | −2.73457e6 | −0.263900 | ||||||||
\(641\) | 1.31532e7 | 1.26441 | 0.632203 | − | 0.774803i | \(-0.282151\pi\) | ||||
0.632203 | + | 0.774803i | \(0.282151\pi\) | |||||||
\(642\) | 4.43264e7i | 4.24449i | ||||||||
\(643\) | − | 1.14463e7i | − | 1.09179i | −0.837855 | − | 0.545893i | \(-0.816191\pi\) | ||
0.837855 | − | 0.545893i | \(-0.183809\pi\) | |||||||
\(644\) | 9.14764e6i | 0.869149i | ||||||||
\(645\) | 7.06996e6 | 0.669141 | ||||||||
\(646\) | 2.63424e7i | 2.48356i | ||||||||
\(647\) | 1.97923e7i | 1.85882i | 0.369054 | + | 0.929408i | \(0.379682\pi\) | ||||
−0.369054 | + | 0.929408i | \(0.620318\pi\) | |||||||
\(648\) | − | 1.26435e7i | − | 1.18285i | ||||||
\(649\) | 1.65698e6i | 0.154420i | ||||||||
\(650\) | 7.38189e6 | 0.685306 | ||||||||
\(651\) | 9.10252e6i | 0.841800i | ||||||||
\(652\) | − | 1.11557e7i | − | 1.02773i | ||||||
\(653\) | − | 9.62504e6i | − | 0.883323i | −0.897182 | − | 0.441661i | \(-0.854389\pi\) | ||
0.897182 | − | 0.441661i | \(-0.145611\pi\) | |||||||
\(654\) | −1.38058e7 | −1.26216 | ||||||||
\(655\) | −1.16916e6 | −0.106481 | ||||||||
\(656\) | −1.30478e6 | −0.118380 | ||||||||
\(657\) | −2.81956e7 | −2.54840 | ||||||||
\(658\) | − | 1.27977e6i | − | 0.115231i | ||||||
\(659\) | −4.95277e6 | −0.444257 | −0.222129 | − | 0.975017i | \(-0.571301\pi\) | ||||
−0.222129 | + | 0.975017i | \(0.571301\pi\) | |||||||
\(660\) | 8.12506e6i | 0.726050i | ||||||||
\(661\) | − | 1.59938e7i | − | 1.42379i | −0.702284 | − | 0.711897i | \(-0.747836\pi\) | ||
0.702284 | − | 0.711897i | \(-0.252164\pi\) | |||||||
\(662\) | −2.10108e7 | −1.86336 | ||||||||
\(663\) | −1.45847e7 | −1.28859 | ||||||||
\(664\) | 5.96022e6i | 0.524617i | ||||||||
\(665\) | −1.15646e6 | −0.101409 | ||||||||
\(666\) | −3.65448e7 | + | 1.88291e7i | −3.19257 | + | 1.64491i | ||||
\(667\) | 6.12684e6 | 0.533239 | ||||||||
\(668\) | 1.21661e7i | 1.05489i | ||||||||
\(669\) | 2.75429e7 | 2.37927 | ||||||||
\(670\) | −4.48172e6 | −0.385707 | ||||||||
\(671\) | 1.13688e6i | 0.0974783i | ||||||||
\(672\) | − | 1.04652e7i | − | 0.893972i | ||||||
\(673\) | 6.85466e6 | 0.583376 | 0.291688 | − | 0.956514i | \(-0.405783\pi\) | ||||
0.291688 | + | 0.956514i | \(0.405783\pi\) | |||||||
\(674\) | − | 4.80594e6i | − | 0.407501i | ||||||
\(675\) | 2.70435e7 | 2.28457 | ||||||||
\(676\) | −1.25130e7 | −1.05316 | ||||||||
\(677\) | −5.43592e6 | −0.455829 | −0.227914 | − | 0.973681i | \(-0.573191\pi\) | ||||
−0.227914 | + | 0.973681i | \(0.573191\pi\) | |||||||
\(678\) | −2.14771e7 | −1.79432 | ||||||||
\(679\) | − | 4.78754e6i | − | 0.398509i | ||||||
\(680\) | − | 2.52126e6i | − | 0.209096i | ||||||
\(681\) | − | 3.57250e7i | − | 2.95192i | ||||||
\(682\) | 2.70131e7 | 2.22389 | ||||||||
\(683\) | 1.59391e7i | 1.30741i | 0.756749 | + | 0.653706i | \(0.226787\pi\) | ||||
−0.756749 | + | 0.653706i | \(0.773213\pi\) | |||||||
\(684\) | − | 4.25127e7i | − | 3.47439i | ||||||
\(685\) | 1.13576e6i | 0.0924824i | ||||||||
\(686\) | − | 1.29564e7i | − | 1.05118i | ||||||
\(687\) | −6.17224e6 | −0.498943 | ||||||||
\(688\) | 9.08120e6i | 0.731429i | ||||||||
\(689\) | 1.91626e6i | 0.153782i | ||||||||
\(690\) | 1.54881e7i | 1.23844i | ||||||||
\(691\) | −1.36355e6 | −0.108636 | −0.0543181 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543181 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(692\) | 1.40612e7 | 1.11624 | ||||||||
\(693\) | −1.24629e7 | −0.985793 | ||||||||
\(694\) | 2.02989e7 | 1.59983 | ||||||||
\(695\) | 1.29729e6i | 0.101877i | ||||||||
\(696\) | 3.98545e6 | 0.311856 | ||||||||
\(697\) | − | 4.44153e6i | − | 0.346299i | ||||||
\(698\) | − | 1.41445e7i | − | 1.09887i | ||||||
\(699\) | 4.22334e7 | 3.26936 | ||||||||
\(700\) | −6.05903e6 | −0.467367 | ||||||||
\(701\) | − | 1.03807e7i | − | 0.797867i | −0.916980 | − | 0.398934i | \(-0.869380\pi\) | ||
0.916980 | − | 0.398934i | \(-0.130620\pi\) | |||||||
\(702\) | 2.33461e7 | 1.78801 | ||||||||
\(703\) | −1.27124e7 | + | 6.54986e6i | −0.970154 | + | 0.499855i | ||||
\(704\) | −2.33972e7 | −1.77923 | ||||||||
\(705\) | − | 1.24964e6i | − | 0.0946917i | ||||||
\(706\) | 2.05281e7 | 1.55002 | ||||||||
\(707\) | −1.49349e6 | −0.112371 | ||||||||
\(708\) | 4.45382e6i | 0.333925i | ||||||||
\(709\) | − | 1.48434e7i | − | 1.10896i | −0.832196 | − | 0.554481i | \(-0.812917\pi\) | ||
0.832196 | − | 0.554481i | \(-0.187083\pi\) | |||||||
\(710\) | 8.65016e6 | 0.643989 | ||||||||
\(711\) | 3.54935e7i | 2.63315i | ||||||||
\(712\) | 5.18315e6 | 0.383172 | ||||||||
\(713\) | 2.96968e7 | 2.18769 | ||||||||
\(714\) | 2.07573e7 | 1.52379 | ||||||||
\(715\) | −1.90016e6 | −0.139003 | ||||||||
\(716\) | − | 8.31911e6i | − | 0.606449i | ||||||
\(717\) | 387339.i | 0.0281380i | ||||||||
\(718\) | 3.18446e7i | 2.30528i | ||||||||
\(719\) | 7.41307e6 | 0.534781 | 0.267391 | − | 0.963588i | \(-0.413839\pi\) | ||||
0.267391 | + | 0.963588i | \(0.413839\pi\) | |||||||
\(720\) | − | 4.16972e6i | − | 0.299762i | ||||||
\(721\) | 4.51323e6i | 0.323332i | ||||||||
\(722\) | − | 4.11325e6i | − | 0.293658i | ||||||
\(723\) | − | 1.84743e7i | − | 1.31439i | ||||||
\(724\) | −2.68915e7 | −1.90664 | ||||||||
\(725\) | 4.05817e6i | 0.286738i | ||||||||
\(726\) | 1.29417e7i | 0.911278i | ||||||||
\(727\) | − | 807655.i | − | 0.0566748i | −0.999598 | − | 0.0283374i | \(-0.990979\pi\) | ||
0.999598 | − | 0.0283374i | \(-0.00902128\pi\) | |||||||
\(728\) | −1.39160e6 | −0.0973162 | ||||||||
\(729\) | 7.18890e6 | 0.501007 | ||||||||
\(730\) | 6.11821e6 | 0.424930 | ||||||||
\(731\) | −3.09128e7 | −2.13966 | ||||||||
\(732\) | 3.05584e6i | 0.210791i | ||||||||
\(733\) | 1.29072e7 | 0.887306 | 0.443653 | − | 0.896199i | \(-0.353682\pi\) | ||||
0.443653 | + | 0.896199i | \(0.353682\pi\) | |||||||
\(734\) | 2.62444e6i | 0.179803i | ||||||||
\(735\) | − | 5.87005e6i | − | 0.400796i | ||||||
\(736\) | −3.41425e7 | −2.32328 | ||||||||
\(737\) | −1.68010e7 | −1.13937 | ||||||||
\(738\) | 1.24289e7i | 0.840026i | ||||||||
\(739\) | −5.36335e6 | −0.361265 | −0.180632 | − | 0.983551i | \(-0.557814\pi\) | ||||
−0.180632 | + | 0.983551i | \(0.557814\pi\) | |||||||
\(740\) | 4.57332e6 | − | 2.35632e6i | 0.307010 | − | 0.158181i | ||||
\(741\) | 1.41972e7 | 0.949855 | ||||||||
\(742\) | − | 2.72727e6i | − | 0.181852i | ||||||
\(743\) | −1.71956e7 | −1.14274 | −0.571369 | − | 0.820693i | \(-0.693587\pi\) | ||||
−0.571369 | + | 0.820693i | \(0.693587\pi\) | |||||||
\(744\) | 1.93175e7 | 1.27944 | ||||||||
\(745\) | − | 102932.i | − | 0.00679450i | ||||||
\(746\) | 2.18669e7i | 1.43860i | ||||||||
\(747\) | −3.35542e7 | −2.20012 | ||||||||
\(748\) | − | 3.55261e7i | − | 2.32164i | ||||||
\(749\) | 8.50867e6 | 0.554188 | ||||||||
\(750\) | −2.12218e7 | −1.37762 | ||||||||
\(751\) | 1.95976e7 | 1.26795 | 0.633976 | − | 0.773353i | \(-0.281422\pi\) | ||||
0.633976 | + | 0.773353i | \(0.281422\pi\) | |||||||
\(752\) | 1.60513e6 | 0.103506 | ||||||||
\(753\) | − | 4.64355e7i | − | 2.98444i | ||||||
\(754\) | 3.50333e6i | 0.224415i | ||||||||
\(755\) | − | 4.08321e6i | − | 0.260696i | ||||||
\(756\) | −1.91624e7 | −1.21940 | ||||||||
\(757\) | − | 2.38291e7i | − | 1.51136i | −0.654941 | − | 0.755680i | \(-0.727306\pi\) | ||
0.654941 | − | 0.755680i | \(-0.272694\pi\) | |||||||
\(758\) | 2.84658e7i | 1.79949i | ||||||||
\(759\) | 5.80615e7i | 3.65834i | ||||||||
\(760\) | 2.45427e6i | 0.154130i | ||||||||
\(761\) | 1.78221e7 | 1.11557 | 0.557784 | − | 0.829986i | \(-0.311652\pi\) | ||||
0.557784 | + | 0.829986i | \(0.311652\pi\) | |||||||
\(762\) | − | 7.00001e7i | − | 4.36728i | ||||||
\(763\) | 2.65008e6i | 0.164796i | ||||||||
\(764\) | − | 2.60690e7i | − | 1.61581i | ||||||
\(765\) | 1.41939e7 | 0.876898 | ||||||||
\(766\) | −1.98274e7 | −1.22094 | ||||||||
\(767\) | −1.04159e6 | −0.0639303 | ||||||||
\(768\) | −1.62034e6 | −0.0991297 | ||||||||
\(769\) | 2.34202e7i | 1.42815i | 0.700069 | + | 0.714075i | \(0.253152\pi\) | ||||
−0.700069 | + | 0.714075i | \(0.746848\pi\) | |||||||
\(770\) | 2.70435e6 | 0.164375 | ||||||||
\(771\) | − | 1.93877e7i | − | 1.17460i | ||||||
\(772\) | 2.21401e7i | 1.33702i | ||||||||
\(773\) | −3.01305e7 | −1.81367 | −0.906834 | − | 0.421488i | \(-0.861508\pi\) | ||||
−0.906834 | + | 0.421488i | \(0.861508\pi\) | |||||||
\(774\) | 8.65046e7 | 5.19023 | ||||||||
\(775\) | 1.96700e7i | 1.17639i | ||||||||
\(776\) | −1.01602e7 | −0.605686 | ||||||||
\(777\) | 5.16117e6 | + | 1.00172e7i | 0.306687 | + | 0.595241i | ||||
\(778\) | −2.15398e7 | −1.27583 | ||||||||
\(779\) | 4.32351e6i | 0.255266i | ||||||||
\(780\) | −5.10747e6 | −0.300586 | ||||||||
\(781\) | 3.24276e7 | 1.90233 | ||||||||
\(782\) | − | 6.77204e7i | − | 3.96007i | ||||||
\(783\) | 1.28344e7i | 0.748122i | ||||||||
\(784\) | 7.53994e6 | 0.438105 | ||||||||
\(785\) | 5.08537e6i | 0.294543i | ||||||||
\(786\) | −2.04276e7 | −1.17940 | ||||||||
\(787\) | 1.11009e7 | 0.638884 | 0.319442 | − | 0.947606i | \(-0.396505\pi\) | ||||
0.319442 | + | 0.947606i | \(0.396505\pi\) | |||||||
\(788\) | 5.53819e6 | 0.317726 | ||||||||
\(789\) | −3.00769e7 | −1.72005 | ||||||||
\(790\) | − | 7.70180e6i | − | 0.439061i | ||||||
\(791\) | 4.12262e6i | 0.234278i | ||||||||
\(792\) | 2.64490e7i | 1.49829i | ||||||||
\(793\) | −714650. | −0.0403562 | ||||||||
\(794\) | − | 365728.i | − | 0.0205877i | ||||||
\(795\) | − | 2.66305e6i | − | 0.149438i | ||||||
\(796\) | − | 3.91753e7i | − | 2.19144i | ||||||
\(797\) | − | 1.27525e7i | − | 0.711130i | −0.934652 | − | 0.355565i | \(-0.884288\pi\) | ||
0.934652 | − | 0.355565i | \(-0.115712\pi\) | |||||||
\(798\) | −2.02058e7 | −1.12323 | ||||||||
\(799\) | 5.46395e6i | 0.302789i | ||||||||
\(800\) | − | 2.26146e7i | − | 1.24929i | ||||||
\(801\) | 2.91795e7i | 1.60693i | ||||||||
\(802\) | 1.48293e7 | 0.814115 | ||||||||
\(803\) | 2.29358e7 | 1.25524 | ||||||||
\(804\) | −4.51596e7 | −2.46383 | ||||||||
\(805\) | 2.97301e6 | 0.161699 | ||||||||
\(806\) | 1.69806e7i | 0.920697i | ||||||||
\(807\) | −1.61297e7 | −0.871850 | ||||||||
\(808\) | 3.16950e6i | 0.170790i | ||||||||
\(809\) | − | 1.44917e6i | − | 0.0778480i | −0.999242 | − | 0.0389240i | \(-0.987607\pi\) | ||
0.999242 | − | 0.0389240i | \(-0.0123930\pi\) | |||||||
\(810\) | −1.54453e7 | −0.827150 | ||||||||
\(811\) | 1.18481e7 | 0.632554 | 0.316277 | − | 0.948667i | \(-0.397567\pi\) | ||||
0.316277 | + | 0.948667i | \(0.397567\pi\) | |||||||
\(812\) | − | 2.87552e6i | − | 0.153048i | ||||||
\(813\) | −1.75649e7 | −0.932007 | ||||||||
\(814\) | 2.97275e7 | − | 1.53166e7i | 1.57253 | − | 0.810217i | ||||
\(815\) | −3.62564e6 | −0.191201 | ||||||||
\(816\) | 2.60345e7i | 1.36875i | ||||||||
\(817\) | 3.00914e7 | 1.57720 | ||||||||
\(818\) | −3.80073e7 | −1.98602 | ||||||||
\(819\) | − | 7.83427e6i | − | 0.408121i | ||||||
\(820\) | − | 1.55539e6i | − | 0.0807802i | ||||||
\(821\) | −1.26759e7 | −0.656328 | −0.328164 | − | 0.944621i | \(-0.606430\pi\) | ||||
−0.328164 | + | 0.944621i | \(0.606430\pi\) | |||||||
\(822\) | 1.98440e7i | 1.02435i | ||||||||
\(823\) | 8.00608e6 | 0.412022 | 0.206011 | − | 0.978550i | \(-0.433952\pi\) | ||||
0.206011 | + | 0.978550i | \(0.433952\pi\) | |||||||
\(824\) | 9.57804e6 | 0.491427 | ||||||||
\(825\) | −3.84576e7 | −1.96720 | ||||||||
\(826\) | 1.48241e6 | 0.0755993 | ||||||||
\(827\) | 2.11433e6i | 0.107500i | 0.998554 | + | 0.0537501i | \(0.0171174\pi\) | ||||
−0.998554 | + | 0.0537501i | \(0.982883\pi\) | |||||||
\(828\) | 1.09291e8i | 5.53997i | ||||||||
\(829\) | − | 3.78313e6i | − | 0.191190i | −0.995420 | − | 0.0955949i | \(-0.969525\pi\) | ||
0.995420 | − | 0.0955949i | \(-0.0304753\pi\) | |||||||
\(830\) | 7.28099e6 | 0.366856 | ||||||||
\(831\) | − | 1.62158e7i | − | 0.814585i | ||||||
\(832\) | − | 1.47077e7i | − | 0.736607i | ||||||
\(833\) | 2.56663e7i | 1.28159i | ||||||||
\(834\) | 2.26662e7i | 1.12840i | ||||||||
\(835\) | 3.95401e6 | 0.196255 | ||||||||
\(836\) | 3.45822e7i | 1.71134i | ||||||||
\(837\) | 6.22085e7i | 3.06928i | ||||||||
\(838\) | 3.95837e7i | 1.94718i | ||||||||
\(839\) | −2.05721e7 | −1.00896 | −0.504481 | − | 0.863423i | \(-0.668316\pi\) | ||||
−0.504481 | + | 0.863423i | \(0.668316\pi\) | |||||||
\(840\) | 1.93392e6 | 0.0945671 | ||||||||
\(841\) | 1.85852e7 | 0.906103 | ||||||||
\(842\) | 2.79461e7 | 1.35844 | ||||||||
\(843\) | 1.04429e7i | 0.506119i | ||||||||
\(844\) | −2.15757e7 | −1.04258 | ||||||||
\(845\) | 4.06677e6i | 0.195933i | ||||||||
\(846\) | − | 1.52900e7i | − | 0.734482i | ||||||
\(847\) | 2.48423e6 | 0.118982 | ||||||||
\(848\) | 3.42063e6 | 0.163349 | ||||||||
\(849\) | − | 4.58219e7i | − | 2.18174i | ||||||
\(850\) | 4.48553e7 | 2.12945 | ||||||||
\(851\) | 3.26809e7 | − | 1.68382e7i | 1.54693 | − | 0.797027i | ||||
\(852\) | 8.71626e7 | 4.11369 | ||||||||
\(853\) | 2.89651e7i | 1.36302i | 0.731809 | + | 0.681509i | \(0.238676\pi\) | ||||
−0.731809 | + | 0.681509i | \(0.761324\pi\) | |||||||
\(854\) | 1.01711e6 | 0.0477223 | ||||||||
\(855\) | −1.38168e7 | −0.646385 | ||||||||
\(856\) | − | 1.80572e7i | − | 0.842300i | ||||||
\(857\) | − | 3.44820e7i | − | 1.60376i | −0.597483 | − | 0.801881i | \(-0.703833\pi\) | ||
0.597483 | − | 0.801881i | \(-0.296167\pi\) | |||||||
\(858\) | −3.31996e7 | −1.53962 | ||||||||
\(859\) | − | 2.20350e7i | − | 1.01890i | −0.860501 | − | 0.509449i | \(-0.829849\pi\) | ||
0.860501 | − | 0.509449i | \(-0.170151\pi\) | |||||||
\(860\) | −1.08254e7 | −0.499113 | ||||||||
\(861\) | 3.40685e6 | 0.156619 | ||||||||
\(862\) | −5.44004e7 | −2.49364 | ||||||||
\(863\) | 1.42747e7 | 0.652439 | 0.326219 | − | 0.945294i | \(-0.394225\pi\) | ||||
0.326219 | + | 0.945294i | \(0.394225\pi\) | |||||||
\(864\) | − | 7.15214e7i | − | 3.25950i | ||||||
\(865\) | − | 4.56994e6i | − | 0.207669i | ||||||
\(866\) | 3.40536e7i | 1.54301i | ||||||||
\(867\) | −4.81932e7 | −2.17740 | ||||||||
\(868\) | − | 1.39377e7i | − | 0.627900i | ||||||
\(869\) | − | 2.88724e7i | − | 1.29698i | ||||||
\(870\) | − | 4.86862e6i | − | 0.218076i | ||||||
\(871\) | − | 1.05612e7i | − | 0.471703i | ||||||
\(872\) | 5.62404e6 | 0.250471 | ||||||||
\(873\) | − | 5.71988e7i | − | 2.54010i | ||||||
\(874\) | 6.59210e7i | 2.91908i | ||||||||
\(875\) | 4.07363e6i | 0.179871i | ||||||||
\(876\) | 6.16497e7 | 2.71438 | ||||||||
\(877\) | −2.53596e7 | −1.11338 | −0.556689 | − | 0.830721i | \(-0.687928\pi\) | ||||
−0.556689 | + | 0.830721i | \(0.687928\pi\) | |||||||
\(878\) | −2.98503e7 | −1.30681 | ||||||||
\(879\) | 3.40362e7 | 1.48583 | ||||||||
\(880\) | 3.39188e6i | 0.147650i | ||||||||
\(881\) | 4.97673e6 | 0.216025 | 0.108012 | − | 0.994150i | \(-0.465551\pi\) | ||||
0.108012 | + | 0.994150i | \(0.465551\pi\) | |||||||
\(882\) | − | 7.18231e7i | − | 3.10880i | ||||||
\(883\) | 1.36078e7i | 0.587337i | 0.955907 | + | 0.293669i | \(0.0948762\pi\) | ||||
−0.955907 | + | 0.293669i | \(0.905124\pi\) | |||||||
\(884\) | 2.23320e7 | 0.961162 | ||||||||
\(885\) | 1.44751e6 | 0.0621244 | ||||||||
\(886\) | − | 4.54338e7i | − | 1.94444i | ||||||
\(887\) | −6.45258e6 | −0.275375 | −0.137688 | − | 0.990476i | \(-0.543967\pi\) | ||||
−0.137688 | + | 0.990476i | \(0.543967\pi\) | |||||||
\(888\) | 2.12586e7 | − | 1.09531e7i | 0.904696 | − | 0.466129i | ||||
\(889\) | −1.34368e7 | −0.570221 | ||||||||
\(890\) | − | 6.33172e6i | − | 0.267945i | ||||||
\(891\) | −5.79011e7 | −2.44339 | ||||||||
\(892\) | −4.21733e7 | −1.77470 | ||||||||
\(893\) | − | 5.31876e6i | − | 0.223194i | ||||||
\(894\) | − | 1.79842e6i | − | 0.0752572i | ||||||
\(895\) | −2.70374e6 | −0.112826 | ||||||||
\(896\) | 9.17131e6i | 0.381646i | ||||||||
\(897\) | −3.64979e7 | −1.51456 | ||||||||
\(898\) | 5.63659e7 | 2.33252 | ||||||||
\(899\) | −9.33506e6 | −0.385228 | ||||||||
\(900\) | −7.23898e7 | −2.97901 | ||||||||
\(901\) | 1.16440e7i | 0.477847i | ||||||||
\(902\) | − | 1.01104e7i | − | 0.413762i | ||||||
\(903\) | − | 2.37115e7i | − | 0.967697i | ||||||
\(904\) | 8.74910e6 | 0.356075 | ||||||||
\(905\) | 8.73985e6i | 0.354717i | ||||||||
\(906\) | − | 7.13420e7i | − | 2.88752i | ||||||
\(907\) | − | 4.02195e6i | − | 0.162337i | −0.996700 | − | 0.0811687i | \(-0.974135\pi\) | ||
0.996700 | − | 0.0811687i | \(-0.0258653\pi\) | |||||||
\(908\) | 5.47017e7i | 2.20184i | ||||||||
\(909\) | −1.78433e7 | −0.716253 | ||||||||
\(910\) | 1.69997e6i | 0.0680516i | ||||||||
\(911\) | 3.83319e7i | 1.53026i | 0.643876 | + | 0.765129i | \(0.277325\pi\) | ||||
−0.643876 | + | 0.765129i | \(0.722675\pi\) | |||||||
\(912\) | − | 2.53428e7i | − | 1.00894i | ||||||
\(913\) | 2.72948e7 | 1.08369 | ||||||||
\(914\) | −4.40079e6 | −0.174247 | ||||||||
\(915\) | 993158. | 0.0392162 | ||||||||
\(916\) | 9.45085e6 | 0.372162 | ||||||||
\(917\) | 3.92117e6i | 0.153990i | ||||||||
\(918\) | 1.41860e8 | 5.55589 | ||||||||
\(919\) | − | 4.19419e6i | − | 0.163817i | −0.996640 | − | 0.0819085i | \(-0.973898\pi\) | ||
0.996640 | − | 0.0819085i | \(-0.0261015\pi\) | |||||||
\(920\) | − | 6.30938e6i | − | 0.245763i | ||||||
\(921\) | −2.70706e6 | −0.105159 | ||||||||
\(922\) | −5.22032e6 | −0.202241 | ||||||||
\(923\) | 2.03842e7i | 0.787570i | ||||||||
\(924\) | 2.72501e7 | 1.05000 | ||||||||
\(925\) | 1.11530e7 | + | 2.16465e7i | 0.428585 | + | 0.831828i | ||||
\(926\) | 3.64030e7 | 1.39511 | ||||||||
\(927\) | 5.39214e7i | 2.06092i | ||||||||
\(928\) | 1.07326e7 | 0.409103 | ||||||||
\(929\) | −922581. | −0.0350724 | −0.0175362 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175362 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(930\) | − | 2.35982e7i | − | 0.894688i | ||||||
\(931\) | − | 2.49843e7i | − | 0.944698i | ||||||
\(932\) | −6.46673e7 | −2.43862 | ||||||||
\(933\) | 3.02373e7i | 1.13721i | ||||||||
\(934\) | −5.39542e7 | −2.02376 | ||||||||
\(935\) | −1.15461e7 | −0.431924 | ||||||||
\(936\) | −1.66260e7 | −0.620295 | ||||||||
\(937\) | −5.51331e6 | −0.205146 | −0.102573 | − | 0.994725i | \(-0.532708\pi\) | ||||
−0.102573 | + | 0.994725i | \(0.532708\pi\) | |||||||
\(938\) | 1.50309e7i | 0.557801i | ||||||||
\(939\) | − | 8.50751e6i | − | 0.314875i | ||||||
\(940\) | 1.91343e6i | 0.0706307i | ||||||||
\(941\) | 4.10357e7 | 1.51073 | 0.755366 | − | 0.655303i | \(-0.227459\pi\) | ||||
0.755366 | + | 0.655303i | \(0.227459\pi\) | |||||||
\(942\) | 8.88517e7i | 3.26241i | ||||||||
\(943\) | − | 1.11148e7i | − | 0.407026i | ||||||
\(944\) | 1.85929e6i | 0.0679073i | ||||||||
\(945\) | 6.22784e6i | 0.226860i | ||||||||
\(946\) | −7.03676e7 | −2.55649 | ||||||||
\(947\) | 2.34797e7i | 0.850781i | 0.905010 | + | 0.425390i | \(0.139863\pi\) | ||||
−0.905010 | + | 0.425390i | \(0.860137\pi\) | |||||||
\(948\) | − | 7.76066e7i | − | 2.80464i | ||||||
\(949\) | 1.44176e7i | 0.519671i | ||||||||
\(950\) | −4.36635e7 | −1.56967 | ||||||||
\(951\) | 2.18172e7 | 0.782254 | ||||||||
\(952\) | −8.45590e6 | −0.302390 | ||||||||
\(953\) | −2.94523e7 | −1.05048 | −0.525238 | − | 0.850955i | \(-0.676024\pi\) | ||||
−0.525238 | + | 0.850955i | \(0.676024\pi\) | |||||||
\(954\) | − | 3.25838e7i | − | 1.15913i | ||||||
\(955\) | −8.47251e6 | −0.300610 | ||||||||
\(956\) | − | 593088.i | − | 0.0209882i | ||||||
\(957\) | − | 1.82514e7i | − | 0.644193i | ||||||
\(958\) | 1.70941e7 | 0.601773 | ||||||||
\(959\) | 3.80915e6 | 0.133746 | ||||||||
\(960\) | 2.04394e7i | 0.715798i | ||||||||
\(961\) | −1.66179e7 | −0.580455 | ||||||||
\(962\) | 9.62812e6 | + | 1.86869e7i | 0.335431 | + | 0.651030i | ||||
\(963\) | 1.01657e8 | 3.53240 | ||||||||
\(964\) | 2.82877e7i | 0.980403i | ||||||||
\(965\) | 7.19562e6 | 0.248742 | ||||||||
\(966\) | 5.19446e7 | 1.79101 | ||||||||
\(967\) | − | 2.02726e7i | − | 0.697179i | −0.937276 | − | 0.348589i | \(-0.886661\pi\) | ||
0.937276 | − | 0.348589i | \(-0.113339\pi\) | |||||||
\(968\) | − | 5.27206e6i | − | 0.180839i | ||||||
\(969\) | 8.62679e7 | 2.95148 | ||||||||
\(970\) | 1.24117e7i | 0.423546i | ||||||||
\(971\) | 8.07665e6 | 0.274905 | 0.137453 | − | 0.990508i | \(-0.456109\pi\) | ||||
0.137453 | + | 0.990508i | \(0.456109\pi\) | |||||||
\(972\) | −5.76522e7 | −1.95727 | ||||||||
\(973\) | 4.35089e6 | 0.147332 | ||||||||
\(974\) | 5.85638e7 | 1.97803 | ||||||||
\(975\) | − | 2.41747e7i | − | 0.814423i | ||||||
\(976\) | 1.27569e6i | 0.0428667i | ||||||||
\(977\) | − | 1.45675e7i | − | 0.488257i | −0.969743 | − | 0.244129i | \(-0.921498\pi\) | ||
0.969743 | − | 0.244129i | \(-0.0785019\pi\) | |||||||
\(978\) | −6.33473e7 | −2.11778 | ||||||||
\(979\) | − | 2.37362e7i | − | 0.791507i | ||||||
\(980\) | 8.98814e6i | 0.298954i | ||||||||
\(981\) | 3.16616e7i | 1.05042i | ||||||||
\(982\) | − | 7.46248e7i | − | 2.46947i | ||||||
\(983\) | −2.94115e7 | −0.970808 | −0.485404 | − | 0.874290i | \(-0.661327\pi\) | ||||
−0.485404 | + | 0.874290i | \(0.661327\pi\) | |||||||
\(984\) | − | 7.23008e6i | − | 0.238043i | ||||||
\(985\) | − | 1.79993e6i | − | 0.0591106i | ||||||
\(986\) | 2.12876e7i | 0.697325i | ||||||||
\(987\) | −4.19109e6 | −0.136941 | ||||||||
\(988\) | −2.17386e7 | −0.708499 | ||||||||
\(989\) | −7.73584e7 | −2.51488 | ||||||||
\(990\) | 3.23100e7 | 1.04773 | ||||||||
\(991\) | − | 5.95225e7i | − | 1.92529i | −0.270762 | − | 0.962646i | \(-0.587276\pi\) | ||
0.270762 | − | 0.962646i | \(-0.412724\pi\) | |||||||
\(992\) | 5.20207e7 | 1.67841 | ||||||||
\(993\) | 6.88077e7i | 2.21444i | ||||||||
\(994\) | − | 2.90112e7i | − | 0.931323i | ||||||
\(995\) | −1.27321e7 | −0.407702 | ||||||||
\(996\) | 7.33663e7 | 2.34341 | ||||||||
\(997\) | 3.48734e6i | 0.111111i | 0.998456 | + | 0.0555553i | \(0.0176929\pi\) | ||||
−0.998456 | + | 0.0555553i | \(0.982307\pi\) | |||||||
\(998\) | −7.84419e7 | −2.49300 | ||||||||
\(999\) | 3.52726e7 | + | 6.84596e7i | 1.11821 | + | 2.17030i |
(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 | 37.6.b.a.36.14 | yes | 16 | |
3.2 | odd | 2 | 333.6.c.d.73.3 | 16 | |||
4.3 | odd | 2 | 592.6.g.c.369.2 | 16 | |||
37.36 | even | 2 | inner | 37.6.b.a.36.3 | ✓ | 16 | |
111.110 | odd | 2 | 333.6.c.d.73.14 | 16 | |||
148.147 | odd | 2 | 592.6.g.c.369.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.b.a.36.3 | ✓ | 16 | 37.36 | even | 2 | inner | |
37.6.b.a.36.14 | yes | 16 | 1.1 | even | 1 | trivial | |
333.6.c.d.73.3 | 16 | 3.2 | odd | 2 | |||
333.6.c.d.73.14 | 16 | 111.110 | odd | 2 | |||
592.6.g.c.369.1 | 16 | 148.147 | odd | 2 | |||
592.6.g.c.369.2 | 16 | 4.3 | odd | 2 |