Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(11,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.8 | ||
Character | \(\chi\) | \(=\) | 60.11 |
Dual form | 60.6.e.a.11.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.53291 | + | 3.38418i | −0.801314 | + | 0.598244i | ||||
\(3\) | 12.7254 | + | 9.00363i | 0.816332 | + | 0.577583i | ||||
\(4\) | 9.09463 | − | 30.6804i | 0.284207 | − | 0.958763i | ||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | −88.1529 | + | 2.25224i | −0.999674 | + | 0.0255409i | ||||
\(7\) | 20.4870i | 0.158027i | 0.996874 | + | 0.0790137i | \(0.0251771\pi\) | ||||
−0.996874 | + | 0.0790137i | \(0.974823\pi\) | |||||||
\(8\) | 62.6029 | + | 169.850i | 0.345835 | + | 0.938295i | ||||
\(9\) | 80.8694 | + | 229.149i | 0.332796 | + | 0.942999i | ||||
\(10\) | −84.6045 | − | 113.323i | −0.267543 | − | 0.358358i | ||||
\(11\) | 681.335 | 1.69777 | 0.848885 | − | 0.528577i | \(-0.177274\pi\) | ||||
0.848885 | + | 0.528577i | \(0.177274\pi\) | |||||||
\(12\) | 391.967 | − | 308.534i | 0.785773 | − | 0.618516i | ||||
\(13\) | −767.277 | −1.25920 | −0.629598 | − | 0.776921i | \(-0.716781\pi\) | ||||
−0.629598 | + | 0.776921i | \(0.716781\pi\) | |||||||
\(14\) | −69.3316 | − | 92.8656i | −0.0945390 | − | 0.126629i | ||||
\(15\) | −225.091 | + | 318.134i | −0.258303 | + | 0.365075i | ||||
\(16\) | −858.575 | − | 558.054i | −0.838452 | − | 0.544975i | ||||
\(17\) | 2038.21i | 1.71051i | 0.518205 | + | 0.855257i | \(0.326601\pi\) | ||||
−0.518205 | + | 0.855257i | \(0.673399\pi\) | |||||||
\(18\) | −1142.05 | − | 765.035i | −0.830818 | − | 0.556545i | ||||
\(19\) | 321.846i | 0.204533i | 0.994757 | + | 0.102267i | \(0.0326095\pi\) | ||||
−0.994757 | + | 0.102267i | \(0.967390\pi\) | |||||||
\(20\) | 767.010 | + | 227.366i | 0.428772 | + | 0.127101i | ||||
\(21\) | −184.457 | + | 260.704i | −0.0912739 | + | 0.129003i | ||||
\(22\) | −3088.43 | + | 2305.76i | −1.36045 | + | 1.01568i | ||||
\(23\) | −3927.07 | −1.54792 | −0.773962 | − | 0.633232i | \(-0.781728\pi\) | ||||
−0.773962 | + | 0.633232i | \(0.781728\pi\) | |||||||
\(24\) | −732.618 | + | 2725.05i | −0.259627 | + | 0.965709i | ||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 3478.00 | − | 2596.60i | 1.00901 | − | 0.753307i | ||||
\(27\) | −1034.08 | + | 3644.12i | −0.272988 | + | 0.962017i | ||||
\(28\) | 628.548 | + | 186.321i | 0.151511 | + | 0.0449125i | ||||
\(29\) | − | 1211.31i | − | 0.267461i | −0.991018 | − | 0.133730i | \(-0.957304\pi\) | ||
0.991018 | − | 0.133730i | \(-0.0426956\pi\) | |||||||
\(30\) | −56.3060 | − | 2203.82i | −0.0114222 | − | 0.447068i | ||||
\(31\) | 2332.43i | 0.435918i | 0.975958 | + | 0.217959i | \(0.0699399\pi\) | ||||
−0.975958 | + | 0.217959i | \(0.930060\pi\) | |||||||
\(32\) | 5780.41 | − | 375.962i | 0.997892 | − | 0.0649036i | ||||
\(33\) | 8670.23 | + | 6134.48i | 1.38594 | + | 0.980603i | ||||
\(34\) | −6897.67 | − | 9239.03i | −1.02330 | − | 1.37066i | ||||
\(35\) | −512.174 | −0.0706720 | ||||||||
\(36\) | 7765.85 | − | 397.083i | 0.998695 | − | 0.0510652i | ||||
\(37\) | 8116.61 | 0.974698 | 0.487349 | − | 0.873207i | \(-0.337964\pi\) | ||||
0.487349 | + | 0.873207i | \(0.337964\pi\) | |||||||
\(38\) | −1089.19 | − | 1458.90i | −0.122361 | − | 0.163895i | ||||
\(39\) | −9763.87 | − | 6908.27i | −1.02792 | − | 0.727291i | ||||
\(40\) | −4246.24 | + | 1565.07i | −0.419618 | + | 0.154662i | ||||
\(41\) | 442.133i | 0.0410765i | 0.999789 | + | 0.0205382i | \(0.00653798\pi\) | ||||
−0.999789 | + | 0.0205382i | \(0.993462\pi\) | |||||||
\(42\) | −46.1415 | − | 1805.98i | −0.00403616 | − | 0.157976i | ||||
\(43\) | − | 11058.4i | − | 0.912058i | −0.889965 | − | 0.456029i | \(-0.849271\pi\) | ||
0.889965 | − | 0.456029i | \(-0.150729\pi\) | |||||||
\(44\) | 6196.49 | − | 20903.6i | 0.482519 | − | 1.62776i | ||||
\(45\) | −5728.72 | + | 2021.74i | −0.421722 | + | 0.148831i | ||||
\(46\) | 17801.1 | − | 13289.9i | 1.24037 | − | 0.926037i | ||||
\(47\) | 19519.2 | 1.28889 | 0.644447 | − | 0.764649i | \(-0.277088\pi\) | ||||
0.644447 | + | 0.764649i | \(0.277088\pi\) | |||||||
\(48\) | −5901.16 | − | 14831.7i | −0.369687 | − | 0.929156i | ||||
\(49\) | 16387.3 | 0.975027 | ||||||||
\(50\) | 2833.07 | − | 2115.11i | 0.160263 | − | 0.119649i | ||||
\(51\) | −18351.3 | + | 25936.9i | −0.987963 | + | 1.39635i | ||||
\(52\) | −6978.10 | + | 23540.4i | −0.357873 | + | 1.20727i | ||||
\(53\) | 16369.3i | 0.800460i | 0.916415 | + | 0.400230i | \(0.131070\pi\) | ||||
−0.916415 | + | 0.400230i | \(0.868930\pi\) | |||||||
\(54\) | −7644.97 | − | 20018.0i | −0.356772 | − | 0.934191i | ||||
\(55\) | 17033.4i | 0.759266i | ||||||||
\(56\) | −3479.70 | + | 1282.54i | −0.148276 | + | 0.0546514i | ||||
\(57\) | −2897.78 | + | 4095.60i | −0.118135 | + | 0.166967i | ||||
\(58\) | 4099.29 | + | 5490.76i | 0.160007 | + | 0.214320i | ||||
\(59\) | −2494.16 | −0.0932814 | −0.0466407 | − | 0.998912i | \(-0.514852\pi\) | ||||
−0.0466407 | + | 0.998912i | \(0.514852\pi\) | |||||||
\(60\) | 7713.36 | + | 9799.19i | 0.276609 | + | 0.351408i | ||||
\(61\) | 14438.4 | 0.496816 | 0.248408 | − | 0.968655i | \(-0.420093\pi\) | ||||
0.248408 | + | 0.968655i | \(0.420093\pi\) | |||||||
\(62\) | −7893.38 | − | 10572.7i | −0.260786 | − | 0.349307i | ||||
\(63\) | −4694.56 | + | 1656.77i | −0.149020 | + | 0.0525909i | ||||
\(64\) | −24929.8 | + | 21266.1i | −0.760796 | + | 0.648991i | ||||
\(65\) | − | 19181.9i | − | 0.563130i | ||||||
\(66\) | −60061.6 | + | 1534.53i | −1.69722 | + | 0.0433626i | ||||
\(67\) | − | 23655.1i | − | 0.643779i | −0.946777 | − | 0.321890i | \(-0.895682\pi\) | ||
0.946777 | − | 0.321890i | \(-0.104318\pi\) | |||||||
\(68\) | 62533.1 | + | 18536.8i | 1.63998 | + | 0.486140i | ||||
\(69\) | −49973.4 | − | 35357.9i | −1.26362 | − | 0.894054i | ||||
\(70\) | 2321.64 | − | 1733.29i | 0.0566304 | − | 0.0422791i | ||||
\(71\) | 20086.3 | 0.472884 | 0.236442 | − | 0.971646i | \(-0.424019\pi\) | ||||
0.236442 | + | 0.971646i | \(0.424019\pi\) | |||||||
\(72\) | −33858.2 | + | 28081.0i | −0.769719 | + | 0.638383i | ||||
\(73\) | −7207.09 | −0.158290 | −0.0791449 | − | 0.996863i | \(-0.525219\pi\) | ||||
−0.0791449 | + | 0.996863i | \(0.525219\pi\) | |||||||
\(74\) | −36791.9 | + | 27468.1i | −0.781039 | + | 0.583108i | ||||
\(75\) | −7953.35 | − | 5627.27i | −0.163266 | − | 0.115517i | ||||
\(76\) | 9874.37 | + | 2927.07i | 0.196099 | + | 0.0581299i | ||||
\(77\) | 13958.5i | 0.268294i | ||||||||
\(78\) | 67637.6 | − | 1728.09i | 1.25879 | − | 0.0321610i | ||||
\(79\) | − | 51621.7i | − | 0.930604i | −0.885152 | − | 0.465302i | \(-0.845946\pi\) | ||
0.885152 | − | 0.465302i | \(-0.154054\pi\) | |||||||
\(80\) | 13951.4 | − | 21464.4i | 0.243720 | − | 0.374967i | ||||
\(81\) | −45969.3 | + | 37062.2i | −0.778494 | + | 0.627652i | ||||
\(82\) | −1496.26 | − | 2004.15i | −0.0245738 | − | 0.0329151i | ||||
\(83\) | 61999.4 | 0.987853 | 0.493927 | − | 0.869504i | \(-0.335561\pi\) | ||||
0.493927 | + | 0.869504i | \(0.335561\pi\) | |||||||
\(84\) | 6320.93 | + | 8030.22i | 0.0977424 | + | 0.124174i | ||||
\(85\) | −50955.2 | −0.764965 | ||||||||
\(86\) | 37423.8 | + | 50126.9i | 0.545634 | + | 0.730845i | ||||
\(87\) | 10906.2 | − | 15414.3i | 0.154481 | − | 0.218337i | ||||
\(88\) | 42653.5 | + | 115724.i | 0.587149 | + | 1.59301i | ||||
\(89\) | − | 97726.8i | − | 1.30779i | −0.756585 | − | 0.653896i | \(-0.773133\pi\) | ||
0.756585 | − | 0.653896i | \(-0.226867\pi\) | |||||||
\(90\) | 19125.9 | − | 28551.4i | 0.248894 | − | 0.371553i | ||||
\(91\) | − | 15719.2i | − | 0.198988i | ||||||
\(92\) | −35715.3 | + | 120484.i | −0.439931 | + | 1.48409i | ||||
\(93\) | −21000.4 | + | 29681.0i | −0.251779 | + | 0.355854i | ||||
\(94\) | −88478.9 | + | 66056.5i | −1.03281 | + | 0.771074i | ||||
\(95\) | −8046.15 | −0.0914701 | ||||||||
\(96\) | 76942.7 | + | 47260.4i | 0.852098 | + | 0.523382i | ||||
\(97\) | 106672. | 1.15112 | 0.575562 | − | 0.817758i | \(-0.304783\pi\) | ||||
0.575562 | + | 0.817758i | \(0.304783\pi\) | |||||||
\(98\) | −74282.2 | + | 55457.5i | −0.781303 | + | 0.583305i | ||||
\(99\) | 55099.2 | + | 156127.i | 0.565011 | + | 1.60100i | ||||
\(100\) | −5684.15 | + | 19175.3i | −0.0568415 | + | 0.191753i | ||||
\(101\) | − | 150535.i | − | 1.46837i | −0.678950 | − | 0.734185i | \(-0.737565\pi\) | ||
0.678950 | − | 0.734185i | \(-0.262435\pi\) | |||||||
\(102\) | −4590.54 | − | 179674.i | −0.0436881 | − | 1.70996i | ||||
\(103\) | − | 135952.i | − | 1.26268i | −0.775506 | − | 0.631340i | \(-0.782505\pi\) | ||
0.775506 | − | 0.631340i | \(-0.217495\pi\) | |||||||
\(104\) | −48033.7 | − | 130322.i | −0.435475 | − | 1.18150i | ||||
\(105\) | −6517.59 | − | 4611.42i | −0.0576918 | − | 0.0408189i | ||||
\(106\) | −55396.6 | − | 74200.5i | −0.478871 | − | 0.641420i | ||||
\(107\) | −76179.0 | −0.643244 | −0.321622 | − | 0.946868i | \(-0.604228\pi\) | ||||
−0.321622 | + | 0.946868i | \(0.604228\pi\) | |||||||
\(108\) | 102398. | + | 64867.8i | 0.844761 | + | 0.535143i | ||||
\(109\) | −162539. | −1.31036 | −0.655180 | − | 0.755473i | \(-0.727407\pi\) | ||||
−0.655180 | + | 0.755473i | \(0.727407\pi\) | |||||||
\(110\) | −57644.0 | − | 77210.8i | −0.454227 | − | 0.608410i | ||||
\(111\) | 103287. | + | 73078.9i | 0.795677 | + | 0.562969i | ||||
\(112\) | 11432.8 | − | 17589.6i | 0.0861209 | − | 0.132498i | ||||
\(113\) | 240171.i | 1.76940i | 0.466164 | + | 0.884698i | \(0.345636\pi\) | ||||
−0.466164 | + | 0.884698i | \(0.654364\pi\) | |||||||
\(114\) | −724.874 | − | 28371.6i | −0.00522397 | − | 0.204467i | ||||
\(115\) | − | 98176.9i | − | 0.692253i | ||||||
\(116\) | −37163.4 | − | 11016.4i | −0.256431 | − | 0.0760142i | ||||
\(117\) | −62049.2 | − | 175820.i | −0.419056 | − | 1.18742i | ||||
\(118\) | 11305.8 | − | 8440.70i | 0.0747477 | − | 0.0558051i | ||||
\(119\) | −41756.7 | −0.270308 | ||||||||
\(120\) | −68126.2 | − | 18315.5i | −0.431878 | − | 0.116109i | ||||
\(121\) | 303166. | 1.88242 | ||||||||
\(122\) | −65448.2 | + | 48862.3i | −0.398106 | + | 0.297218i | ||||
\(123\) | −3980.80 | + | 5626.30i | −0.0237251 | + | 0.0335320i | ||||
\(124\) | 71560.0 | + | 21212.6i | 0.417942 | + | 0.123891i | ||||
\(125\) | − | 15625.0i | − | 0.0894427i | ||||||
\(126\) | 15673.2 | − | 23397.2i | 0.0879493 | − | 0.131292i | ||||
\(127\) | − | 1150.90i | − | 0.00633181i | −0.999995 | − | 0.00316591i | \(-0.998992\pi\) | ||
0.999995 | − | 0.00316591i | \(-0.00100774\pi\) | |||||||
\(128\) | 41036.0 | − | 180764.i | 0.221381 | − | 0.975187i | ||||
\(129\) | 99566.0 | − | 140723.i | 0.526789 | − | 0.744542i | ||||
\(130\) | 64915.1 | + | 86950.0i | 0.336889 | + | 0.451244i | ||||
\(131\) | 138937. | 0.707358 | 0.353679 | − | 0.935367i | \(-0.384930\pi\) | ||||
0.353679 | + | 0.935367i | \(0.384930\pi\) | |||||||
\(132\) | 267061. | − | 210215.i | 1.33406 | − | 1.05010i | ||||
\(133\) | −6593.64 | −0.0323219 | ||||||||
\(134\) | 80053.0 | + | 107226.i | 0.385137 | + | 0.515869i | ||||
\(135\) | −91102.9 | − | 25851.9i | −0.430227 | − | 0.122084i | ||||
\(136\) | −346189. | + | 127598.i | −1.60497 | + | 0.591556i | ||||
\(137\) | 47378.6i | 0.215665i | 0.994169 | + | 0.107833i | \(0.0343911\pi\) | ||||
−0.994169 | + | 0.107833i | \(0.965609\pi\) | |||||||
\(138\) | 346183. | − | 8844.72i | 1.54742 | − | 0.0395354i | ||||
\(139\) | 29701.3i | 0.130388i | 0.997873 | + | 0.0651941i | \(0.0207666\pi\) | ||||
−0.997873 | + | 0.0651941i | \(0.979233\pi\) | |||||||
\(140\) | −4658.03 | + | 15713.7i | −0.0200855 | + | 0.0677577i | ||||
\(141\) | 248389. | + | 175744.i | 1.05217 | + | 0.744443i | ||||
\(142\) | −91049.6 | + | 67975.8i | −0.378929 | + | 0.282900i | ||||
\(143\) | −522772. | −2.13783 | ||||||||
\(144\) | 58444.9 | − | 241871.i | 0.234877 | − | 0.972025i | ||||
\(145\) | 30282.7 | 0.119612 | ||||||||
\(146\) | 32669.1 | − | 24390.1i | 0.126840 | − | 0.0946960i | ||||
\(147\) | 208534. | + | 147545.i | 0.795946 | + | 0.563159i | ||||
\(148\) | 73817.6 | − | 249021.i | 0.277016 | − | 0.934505i | ||||
\(149\) | 263191.i | 0.971194i | 0.874183 | + | 0.485597i | \(0.161398\pi\) | ||||
−0.874183 | + | 0.485597i | \(0.838602\pi\) | |||||||
\(150\) | 55095.5 | − | 1407.65i | 0.199935 | − | 0.00510818i | ||||
\(151\) | 29711.9i | 0.106044i | 0.998593 | + | 0.0530222i | \(0.0168854\pi\) | ||||
−0.998593 | + | 0.0530222i | \(0.983115\pi\) | |||||||
\(152\) | −54665.4 | + | 20148.5i | −0.191913 | + | 0.0707348i | ||||
\(153\) | −467053. | + | 164829.i | −1.61301 | + | 0.569252i | ||||
\(154\) | −47238.0 | − | 63272.6i | −0.160505 | − | 0.214988i | ||||
\(155\) | −58310.8 | −0.194949 | ||||||||
\(156\) | −300747. | + | 236731.i | −0.989442 | + | 0.778833i | ||||
\(157\) | 109319. | 0.353953 | 0.176977 | − | 0.984215i | \(-0.443368\pi\) | ||||
0.176977 | + | 0.984215i | \(0.443368\pi\) | |||||||
\(158\) | 174697. | + | 233997.i | 0.556729 | + | 0.745706i | ||||
\(159\) | −147383. | + | 208305.i | −0.462332 | + | 0.653441i | ||||
\(160\) | 9399.04 | + | 144510.i | 0.0290258 | + | 0.446271i | ||||
\(161\) | − | 80453.8i | − | 0.244614i | ||||||
\(162\) | 82949.5 | − | 323568.i | 0.248328 | − | 0.968676i | ||||
\(163\) | − | 310037.i | − | 0.913997i | −0.889467 | − | 0.456999i | \(-0.848924\pi\) | ||
0.889467 | − | 0.456999i | \(-0.151076\pi\) | |||||||
\(164\) | 13564.8 | + | 4021.04i | 0.0393826 | + | 0.0116742i | ||||
\(165\) | −153362. | + | 216756.i | −0.438539 | + | 0.619813i | ||||
\(166\) | −281038. | + | 209817.i | −0.791580 | + | 0.590978i | ||||
\(167\) | −114004. | −0.316321 | −0.158160 | − | 0.987413i | \(-0.550556\pi\) | ||||
−0.158160 | + | 0.987413i | \(0.550556\pi\) | |||||||
\(168\) | −55828.0 | − | 15009.1i | −0.152608 | − | 0.0410282i | ||||
\(169\) | 217421. | 0.585577 | ||||||||
\(170\) | 230976. | − | 172442.i | 0.612977 | − | 0.457636i | ||||
\(171\) | −73750.6 | + | 26027.5i | −0.192875 | + | 0.0680679i | ||||
\(172\) | −339277. | − | 100572.i | −0.874448 | − | 0.259214i | ||||
\(173\) | 124139.i | 0.315350i | 0.987491 | + | 0.157675i | \(0.0503998\pi\) | ||||
−0.987491 | + | 0.157675i | \(0.949600\pi\) | |||||||
\(174\) | 2728.16 | + | 106780.i | 0.00683119 | + | 0.267373i | ||||
\(175\) | − | 12804.3i | − | 0.0316055i | ||||||
\(176\) | −584977. | − | 380222.i | −1.42350 | − | 0.925242i | ||||
\(177\) | −31739.1 | − | 22456.5i | −0.0761486 | − | 0.0538777i | ||||
\(178\) | 330725. | + | 442987.i | 0.782379 | + | 1.04795i | ||||
\(179\) | 99467.4 | 0.232032 | 0.116016 | − | 0.993247i | \(-0.462988\pi\) | ||||
0.116016 | + | 0.993247i | \(0.462988\pi\) | |||||||
\(180\) | 9927.07 | + | 194146.i | 0.0228370 | + | 0.446630i | ||||
\(181\) | 301984. | 0.685152 | 0.342576 | − | 0.939490i | \(-0.388701\pi\) | ||||
0.342576 | + | 0.939490i | \(0.388701\pi\) | |||||||
\(182\) | 53196.5 | + | 71253.6i | 0.119043 | + | 0.159451i | ||||
\(183\) | 183734. | + | 129998.i | 0.405567 | + | 0.286953i | ||||
\(184\) | −245846. | − | 667012.i | −0.535327 | − | 1.45241i | ||||
\(185\) | 202915.i | 0.435898i | ||||||||
\(186\) | −5253.20 | − | 205611.i | −0.0111338 | − | 0.435776i | ||||
\(187\) | 1.38870e6i | 2.90406i | ||||||||
\(188\) | 177520. | − | 598857.i | 0.366313 | − | 1.23574i | ||||
\(189\) | −74656.9 | − | 21185.1i | −0.152025 | − | 0.0431396i | ||||
\(190\) | 36472.5 | − | 27229.6i | 0.0732962 | − | 0.0547215i | ||||
\(191\) | 153353. | 0.304164 | 0.152082 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152082 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(192\) | −508713. | + | 46161.0i | −0.995908 | + | 0.0903695i | ||||
\(193\) | −705142. | −1.36265 | −0.681323 | − | 0.731983i | \(-0.738595\pi\) | ||||
−0.681323 | + | 0.731983i | \(0.738595\pi\) | |||||||
\(194\) | −483536. | + | 360998.i | −0.922412 | + | 0.688654i | ||||
\(195\) | 172707. | − | 244097.i | 0.325254 | − | 0.459701i | ||||
\(196\) | 149036. | − | 502769.i | 0.277110 | − | 0.934820i | ||||
\(197\) | 210132.i | 0.385768i | 0.981222 | + | 0.192884i | \(0.0617840\pi\) | ||||
−0.981222 | + | 0.192884i | \(0.938216\pi\) | |||||||
\(198\) | −778122. | − | 521245.i | −1.41054 | − | 0.944885i | ||||
\(199\) | − | 747889.i | − | 1.33876i | −0.742918 | − | 0.669382i | \(-0.766559\pi\) | ||
0.742918 | − | 0.669382i | \(-0.233441\pi\) | |||||||
\(200\) | −39126.8 | − | 106156.i | −0.0691670 | − | 0.187659i | ||||
\(201\) | 212981. | − | 301019.i | 0.371836 | − | 0.525538i | ||||
\(202\) | 509439. | + | 682364.i | 0.878444 | + | 1.17662i | ||||
\(203\) | 24816.0 | 0.0422661 | ||||||||
\(204\) | 628858. | + | 798912.i | 1.05798 | + | 1.34407i | ||||
\(205\) | −11053.3 | −0.0183699 | ||||||||
\(206\) | 460087. | + | 616260.i | 0.755391 | + | 1.01180i | ||||
\(207\) | −317580. | − | 899884.i | −0.515143 | − | 1.45969i | ||||
\(208\) | 658765. | + | 428182.i | 1.05578 | + | 0.686231i | ||||
\(209\) | 219285.i | 0.347251i | ||||||||
\(210\) | 45149.6 | − | 1153.54i | 0.0706489 | − | 0.00180503i | ||||
\(211\) | 466221.i | 0.720917i | 0.932775 | + | 0.360459i | \(0.117380\pi\) | ||||
−0.932775 | + | 0.360459i | \(0.882620\pi\) | |||||||
\(212\) | 502216. | + | 148873.i | 0.767451 | + | 0.227497i | ||||
\(213\) | 255606. | + | 180850.i | 0.386030 | + | 0.273130i | ||||
\(214\) | 345313. | − | 257804.i | 0.515441 | − | 0.384817i | ||||
\(215\) | 276461. | 0.407885 | ||||||||
\(216\) | −683688. | + | 52494.6i | −0.997065 | + | 0.0765561i | ||||
\(217\) | −47784.4 | −0.0688870 | ||||||||
\(218\) | 736774. | − | 550061.i | 1.05001 | − | 0.783915i | ||||
\(219\) | −91712.8 | − | 64890.0i | −0.129217 | − | 0.0914255i | ||||
\(220\) | 522591. | + | 154912.i | 0.727956 | + | 0.215789i | ||||
\(221\) | − | 1.56387e6i | − | 2.15387i | ||||||
\(222\) | −715502. | + | 18280.5i | −0.974380 | + | 0.0248947i | ||||
\(223\) | − | 1.31947e6i | − | 1.77679i | −0.459078 | − | 0.888396i | \(-0.651820\pi\) | ||
0.459078 | − | 0.888396i | \(-0.348180\pi\) | |||||||
\(224\) | 7702.31 | + | 118423.i | 0.0102565 | + | 0.157694i | ||||
\(225\) | −50543.4 | − | 143218.i | −0.0665592 | − | 0.188600i | ||||
\(226\) | −812784. | − | 1.08868e6i | −1.05853 | − | 1.41784i | ||||
\(227\) | 865232. | 1.11447 | 0.557235 | − | 0.830355i | \(-0.311862\pi\) | ||||
0.557235 | + | 0.830355i | \(0.311862\pi\) | |||||||
\(228\) | 99300.6 | + | 126153.i | 0.126507 | + | 0.160717i | ||||
\(229\) | 1.01891e6 | 1.28394 | 0.641972 | − | 0.766728i | \(-0.278116\pi\) | ||||
0.641972 | + | 0.766728i | \(0.278116\pi\) | |||||||
\(230\) | 332248. | + | 445027.i | 0.414136 | + | 0.554711i | ||||
\(231\) | −125677. | + | 177627.i | −0.154962 | + | 0.219017i | ||||
\(232\) | 205740. | − | 75831.4i | 0.250957 | − | 0.0924973i | ||||
\(233\) | − | 1.23087e6i | − | 1.48533i | −0.669665 | − | 0.742664i | \(-0.733562\pi\) | ||
0.669665 | − | 0.742664i | \(-0.266438\pi\) | |||||||
\(234\) | 876272. | + | 586993.i | 1.04616 | + | 0.700799i | ||||
\(235\) | 487980.i | 0.576411i | ||||||||
\(236\) | −22683.5 | + | 76522.0i | −0.0265113 | + | 0.0894347i | ||||
\(237\) | 464783. | − | 656905.i | 0.537501 | − | 0.759682i | ||||
\(238\) | 189280. | − | 141312.i | 0.216601 | − | 0.161710i | ||||
\(239\) | 593081. | 0.671613 | 0.335806 | − | 0.941931i | \(-0.390991\pi\) | ||||
0.335806 | + | 0.941931i | \(0.390991\pi\) | |||||||
\(240\) | 370793. | − | 147529.i | 0.415531 | − | 0.165329i | ||||
\(241\) | −872289. | −0.967426 | −0.483713 | − | 0.875227i | \(-0.660712\pi\) | ||||
−0.483713 | + | 0.875227i | \(0.660712\pi\) | |||||||
\(242\) | −1.37423e6 | + | 1.02597e6i | −1.50841 | + | 1.12615i | ||||
\(243\) | −918670. | + | 57740.1i | −0.998031 | + | 0.0627281i | ||||
\(244\) | 131312. | − | 442977.i | 0.141199 | − | 0.476329i | ||||
\(245\) | 409682.i | 0.436045i | ||||||||
\(246\) | −995.789 | − | 38975.3i | −0.00104913 | − | 0.0410631i | ||||
\(247\) | − | 246945.i | − | 0.257548i | ||||||
\(248\) | −396163. | + | 146017.i | −0.409020 | + | 0.150756i | ||||
\(249\) | 788965. | + | 558220.i | 0.806416 | + | 0.570567i | ||||
\(250\) | 52877.8 | + | 70826.8i | 0.0535086 | + | 0.0716717i | ||||
\(251\) | 581747. | 0.582841 | 0.291421 | − | 0.956595i | \(-0.405872\pi\) | ||||
0.291421 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(252\) | 8135.02 | + | 159099.i | 0.00806969 | + | 0.157821i | ||||
\(253\) | −2.67565e6 | −2.62802 | ||||||||
\(254\) | 3894.85 | + | 5216.93i | 0.00378797 | + | 0.00507377i | ||||
\(255\) | −648423. | − | 458782.i | −0.624465 | − | 0.441831i | ||||
\(256\) | 425727. | + | 958263.i | 0.406005 | + | 0.913871i | ||||
\(257\) | − | 1.32605e6i | − | 1.25236i | −0.779680 | − | 0.626178i | \(-0.784618\pi\) | ||
0.779680 | − | 0.626178i | \(-0.215382\pi\) | |||||||
\(258\) | 24906.3 | + | 974833.i | 0.0232948 | + | 0.911761i | ||||
\(259\) | 166285.i | 0.154029i | ||||||||
\(260\) | −588509. | − | 174453.i | −0.539908 | − | 0.160046i | ||||
\(261\) | 277570. | − | 97957.8i | 0.252215 | − | 0.0890098i | ||||
\(262\) | −629789. | + | 470188.i | −0.566816 | + | 0.423173i | ||||
\(263\) | −696552. | −0.620961 | −0.310480 | − | 0.950580i | \(-0.600490\pi\) | ||||
−0.310480 | + | 0.950580i | \(0.600490\pi\) | |||||||
\(264\) | −499159. | + | 1.85667e6i | −0.440787 | + | 1.63955i | ||||
\(265\) | −409232. | −0.357977 | ||||||||
\(266\) | 29888.4 | − | 22314.1i | 0.0258999 | − | 0.0193364i | ||||
\(267\) | 879895. | − | 1.24361e6i | 0.755358 | − | 1.06759i | ||||
\(268\) | −725747. | − | 215134.i | −0.617232 | − | 0.182967i | ||||
\(269\) | 948575.i | 0.799265i | 0.916675 | + | 0.399633i | \(0.130862\pi\) | ||||
−0.916675 | + | 0.399633i | \(0.869138\pi\) | |||||||
\(270\) | 500449. | − | 191124.i | 0.417783 | − | 0.159553i | ||||
\(271\) | 1.15631e6i | 0.956422i | 0.878245 | + | 0.478211i | \(0.158715\pi\) | ||||
−0.878245 | + | 0.478211i | \(0.841285\pi\) | |||||||
\(272\) | 1.13743e6 | − | 1.74996e6i | 0.932187 | − | 1.43418i | ||||
\(273\) | 141529. | − | 200032.i | 0.114932 | − | 0.162440i | ||||
\(274\) | −160338. | − | 214763.i | −0.129021 | − | 0.172816i | ||||
\(275\) | −425834. | −0.339554 | ||||||||
\(276\) | −1.53929e6 | + | 1.21164e6i | −1.21632 | + | 0.957415i | ||||
\(277\) | 922162. | 0.722118 | 0.361059 | − | 0.932543i | \(-0.382415\pi\) | ||||
0.361059 | + | 0.932543i | \(0.382415\pi\) | |||||||
\(278\) | −100514. | − | 134633.i | −0.0780040 | − | 0.104482i | ||||
\(279\) | −534474. | + | 188622.i | −0.411070 | + | 0.145072i | ||||
\(280\) | −32063.5 | − | 86992.5i | −0.0244409 | − | 0.0663112i | ||||
\(281\) | 895607.i | 0.676631i | 0.941033 | + | 0.338315i | \(0.109857\pi\) | ||||
−0.941033 | + | 0.338315i | \(0.890143\pi\) | |||||||
\(282\) | −1.72067e6 | + | 43961.9i | −1.28847 | + | 0.0329196i | ||||
\(283\) | 1.89178e6i | 1.40412i | 0.712119 | + | 0.702059i | \(0.247736\pi\) | ||||
−0.712119 | + | 0.702059i | \(0.752264\pi\) | |||||||
\(284\) | 182678. | − | 616257.i | 0.134397 | − | 0.453384i | ||||
\(285\) | −102390. | − | 72444.5i | −0.0746700 | − | 0.0528316i | ||||
\(286\) | 2.36968e6 | − | 1.76916e6i | 1.71307 | − | 1.27894i | ||||
\(287\) | −9057.95 | −0.00649120 | ||||||||
\(288\) | 553609. | + | 1.29417e6i | 0.393298 | + | 0.919411i | ||||
\(289\) | −2.73444e6 | −1.92586 | ||||||||
\(290\) | −137269. | + | 102482.i | −0.0958467 | + | 0.0715572i | ||||
\(291\) | 1.35744e6 | + | 960437.i | 0.939700 | + | 0.664870i | ||||
\(292\) | −65545.9 | + | 221117.i | −0.0449871 | + | 0.151762i | ||||
\(293\) | 2.03913e6i | 1.38764i | 0.720151 | + | 0.693818i | \(0.244073\pi\) | ||||
−0.720151 | + | 0.693818i | \(0.755927\pi\) | |||||||
\(294\) | −1.44459e6 | + | 36908.1i | −0.974709 | + | 0.0249031i | ||||
\(295\) | − | 62354.1i | − | 0.0417167i | ||||||
\(296\) | 508123. | + | 1.37860e6i | 0.337085 | + | 0.914555i | ||||
\(297\) | −704553. | + | 2.48286e6i | −0.463471 | + | 1.63328i | ||||
\(298\) | −890687. | − | 1.19302e6i | −0.581011 | − | 0.778231i | ||||
\(299\) | 3.01315e6 | 1.94914 | ||||||||
\(300\) | −244980. | + | 192834.i | −0.157155 | + | 0.123703i | ||||
\(301\) | 226554. | 0.144130 | ||||||||
\(302\) | −100550. | − | 134681.i | −0.0634405 | − | 0.0849748i | ||||
\(303\) | 1.35537e6 | − | 1.91562e6i | 0.848105 | − | 1.19868i | ||||
\(304\) | 179608. | − | 276329.i | 0.111466 | − | 0.171491i | ||||
\(305\) | 360961.i | 0.222183i | ||||||||
\(306\) | 1.55930e6 | − | 2.32775e6i | 0.951977 | − | 1.42112i | ||||
\(307\) | 464992.i | 0.281579i | 0.990040 | + | 0.140789i | \(0.0449640\pi\) | ||||
−0.990040 | + | 0.140789i | \(0.955036\pi\) | |||||||
\(308\) | 428252. | + | 126947.i | 0.257230 | + | 0.0762512i | ||||
\(309\) | 1.22406e6 | − | 1.73004e6i | 0.729302 | − | 1.03077i | ||||
\(310\) | 264318. | − | 197334.i | 0.156215 | − | 0.116627i | ||||
\(311\) | −2.89861e6 | −1.69937 | −0.849686 | − | 0.527289i | \(-0.823208\pi\) | ||||
−0.849686 | + | 0.527289i | \(0.823208\pi\) | |||||||
\(312\) | 562121. | − | 2.09087e6i | 0.326921 | − | 1.21602i | ||||
\(313\) | 2.70104e6 | 1.55837 | 0.779186 | − | 0.626793i | \(-0.215633\pi\) | ||||
0.779186 | + | 0.626793i | \(0.215633\pi\) | |||||||
\(314\) | −495533. | + | 369955.i | −0.283628 | + | 0.211751i | ||||
\(315\) | −41419.2 | − | 117364.i | −0.0235193 | − | 0.0666436i | ||||
\(316\) | −1.58378e6 | − | 469481.i | −0.892229 | − | 0.264485i | ||||
\(317\) | − | 130346.i | − | 0.0728532i | −0.999336 | − | 0.0364266i | \(-0.988402\pi\) | ||
0.999336 | − | 0.0364266i | \(-0.0115975\pi\) | |||||||
\(318\) | −36867.5 | − | 1.44300e6i | −0.0204445 | − | 0.800199i | ||||
\(319\) | − | 825307.i | − | 0.454087i | ||||||
\(320\) | −531654. | − | 623244.i | −0.290238 | − | 0.340238i | ||||
\(321\) | −969406. | − | 685888.i | −0.525101 | − | 0.371527i | ||||
\(322\) | 272270. | + | 364690.i | 0.146339 | + | 0.196013i | ||||
\(323\) | −655989. | −0.349857 | ||||||||
\(324\) | 719011. | + | 1.74742e6i | 0.380516 | + | 0.924774i | ||||
\(325\) | 479548. | 0.251839 | ||||||||
\(326\) | 1.04922e6 | + | 1.40537e6i | 0.546794 | + | 0.732399i | ||||
\(327\) | −2.06836e6 | − | 1.46344e6i | −1.06969 | − | 0.756842i | ||||
\(328\) | −75096.0 | + | 27678.8i | −0.0385418 | + | 0.0142057i | ||||
\(329\) | 399889.i | 0.203681i | ||||||||
\(330\) | −38363.2 | − | 1.50154e6i | −0.0193924 | − | 0.759018i | ||||
\(331\) | 547886.i | 0.274866i | 0.990511 | + | 0.137433i | \(0.0438851\pi\) | ||||
−0.990511 | + | 0.137433i | \(0.956115\pi\) | |||||||
\(332\) | 563862. | − | 1.90217e6i | 0.280755 | − | 0.947117i | ||||
\(333\) | 656385. | + | 1.85991e6i | 0.324376 | + | 0.919139i | ||||
\(334\) | 516769. | − | 385809.i | 0.253472 | − | 0.189237i | ||||
\(335\) | 591376. | 0.287907 | ||||||||
\(336\) | 303857. | − | 120897.i | 0.146832 | − | 0.0584207i | ||||
\(337\) | 1.63196e6 | 0.782772 | 0.391386 | − | 0.920226i | \(-0.371996\pi\) | ||||
0.391386 | + | 0.920226i | \(0.371996\pi\) | |||||||
\(338\) | −985549. | + | 735790.i | −0.469231 | + | 0.350318i | ||||
\(339\) | −2.16241e6 | + | 3.05627e6i | −1.02197 | + | 1.44442i | ||||
\(340\) | −463419. | + | 1.56333e6i | −0.217409 | + | 0.733420i | ||||
\(341\) | 1.58917e6i | 0.740089i | ||||||||
\(342\) | 246223. | − | 367566.i | 0.113832 | − | 0.169930i | ||||
\(343\) | 680050.i | 0.312108i | ||||||||
\(344\) | 1.87827e6 | − | 692290.i | 0.855780 | − | 0.315422i | ||||
\(345\) | 883948. | − | 1.24934e6i | 0.399833 | − | 0.565108i | ||||
\(346\) | −420108. | − | 562711.i | −0.188656 | − | 0.252694i | ||||
\(347\) | −3.73409e6 | −1.66479 | −0.832397 | − | 0.554180i | \(-0.813032\pi\) | ||||
−0.832397 | + | 0.554180i | \(0.813032\pi\) | |||||||
\(348\) | −373730. | − | 474793.i | −0.165428 | − | 0.210163i | ||||
\(349\) | 489164. | 0.214976 | 0.107488 | − | 0.994206i | \(-0.465719\pi\) | ||||
0.107488 | + | 0.994206i | \(0.465719\pi\) | |||||||
\(350\) | 43332.2 | + | 58041.0i | 0.0189078 | + | 0.0253259i | ||||
\(351\) | 793424. | − | 2.79605e6i | 0.343746 | − | 1.21137i | ||||
\(352\) | 3.93839e6 | − | 256156.i | 1.69419 | − | 0.110191i | ||||
\(353\) | − | 3.46900e6i | − | 1.48172i | −0.671658 | − | 0.740861i | \(-0.734418\pi\) | ||
0.671658 | − | 0.740861i | \(-0.265582\pi\) | |||||||
\(354\) | 219868. | − | 5617.46i | 0.0932510 | − | 0.00238249i | ||||
\(355\) | 502158.i | 0.211480i | ||||||||
\(356\) | −2.99830e6 | − | 888789.i | −1.25386 | − | 0.371684i | ||||
\(357\) | −531369. | − | 375962.i | −0.220661 | − | 0.156125i | ||||
\(358\) | −450877. | + | 336616.i | −0.185931 | + | 0.138812i | ||||
\(359\) | −4.42901e6 | −1.81372 | −0.906862 | − | 0.421429i | \(-0.861529\pi\) | ||||
−0.906862 | + | 0.421429i | \(0.861529\pi\) | |||||||
\(360\) | −702025. | − | 846454.i | −0.285494 | − | 0.344229i | ||||
\(361\) | 2.37251e6 | 0.958166 | ||||||||
\(362\) | −1.36887e6 | + | 1.02197e6i | −0.549022 | + | 0.409888i | ||||
\(363\) | 3.85790e6 | + | 2.72960e6i | 1.53668 | + | 1.08726i | ||||
\(364\) | −482270. | − | 142960.i | −0.190782 | − | 0.0565537i | ||||
\(365\) | − | 180177.i | − | 0.0707894i | ||||||
\(366\) | −1.27279e6 | + | 32518.9i | −0.496654 | + | 0.0126891i | ||||
\(367\) | 4.11688e6i | 1.59552i | 0.602974 | + | 0.797761i | \(0.293982\pi\) | ||||
−0.602974 | + | 0.797761i | \(0.706018\pi\) | |||||||
\(368\) | 3.37169e6 | + | 2.19152e6i | 1.29786 | + | 0.843580i | ||||
\(369\) | −101314. | + | 35755.0i | −0.0387351 | + | 0.0136701i | ||||
\(370\) | −686702. | − | 919797.i | −0.260774 | − | 0.349291i | ||||
\(371\) | −335356. | −0.126495 | ||||||||
\(372\) | 719636. | + | 914238.i | 0.269622 | + | 0.342533i | ||||
\(373\) | 1.73214e6 | 0.644630 | 0.322315 | − | 0.946632i | \(-0.395539\pi\) | ||||
0.322315 | + | 0.946632i | \(0.395539\pi\) | |||||||
\(374\) | −4.69962e6 | − | 6.29487e6i | −1.73734 | − | 2.32706i | ||||
\(375\) | 140682. | − | 198834.i | 0.0516606 | − | 0.0730150i | ||||
\(376\) | 1.22196e6 | + | 3.31533e6i | 0.445745 | + | 1.20936i | ||||
\(377\) | 929409.i | 0.336785i | ||||||||
\(378\) | 410107. | − | 156622.i | 0.147628 | − | 0.0563798i | ||||
\(379\) | − | 1.16291e6i | − | 0.415863i | −0.978143 | − | 0.207931i | \(-0.933327\pi\) | ||
0.978143 | − | 0.207931i | \(-0.0666730\pi\) | |||||||
\(380\) | −73176.8 | + | 246859.i | −0.0259965 | + | 0.0876981i | ||||
\(381\) | 10362.3 | − | 14645.6i | 0.00365715 | − | 0.00516886i | ||||
\(382\) | −695135. | + | 518973.i | −0.243731 | + | 0.181964i | ||||
\(383\) | −1.86840e6 | −0.650837 | −0.325419 | − | 0.945570i | \(-0.605505\pi\) | ||||
−0.325419 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(384\) | 2.14973e6 | − | 1.93082e6i | 0.743972 | − | 0.668211i | ||||
\(385\) | −348962. | −0.119985 | ||||||||
\(386\) | 3.19635e6 | − | 2.38633e6i | 1.09191 | − | 0.815196i | ||||
\(387\) | 2.53403e6 | − | 894289.i | 0.860070 | − | 0.303529i | ||||
\(388\) | 970145. | − | 3.27275e6i | 0.327158 | − | 1.10366i | ||||
\(389\) | − | 2.03347e6i | − | 0.681341i | −0.940183 | − | 0.340670i | \(-0.889346\pi\) | ||
0.940183 | − | 0.340670i | \(-0.110654\pi\) | |||||||
\(390\) | 43202.3 | + | 1.69094e6i | 0.0143829 | + | 0.562946i | ||||
\(391\) | − | 8.00420e6i | − | 2.64774i | ||||||
\(392\) | 1.02589e6 | + | 2.78337e6i | 0.337199 | + | 0.914864i | ||||
\(393\) | 1.76802e6 | + | 1.25094e6i | 0.577439 | + | 0.408558i | ||||
\(394\) | −711123. | − | 952509.i | −0.230783 | − | 0.309121i | ||||
\(395\) | 1.29054e6 | 0.416179 | ||||||||
\(396\) | 5.29115e6 | − | 270546.i | 1.69556 | − | 0.0866969i | ||||
\(397\) | −4.85163e6 | −1.54494 | −0.772469 | − | 0.635052i | \(-0.780979\pi\) | ||||
−0.772469 | + | 0.635052i | \(0.780979\pi\) | |||||||
\(398\) | 2.53099e6 | + | 3.39012e6i | 0.800909 | + | 1.07277i | ||||
\(399\) | −83906.5 | − | 59366.7i | −0.0263854 | − | 0.0186686i | ||||
\(400\) | 536610. | + | 348784.i | 0.167690 | + | 0.108995i | ||||
\(401\) | 5.92095e6i | 1.83878i | 0.393343 | + | 0.919392i | \(0.371319\pi\) | ||||
−0.393343 | + | 0.919392i | \(0.628681\pi\) | |||||||
\(402\) | 53276.9 | + | 2.08526e6i | 0.0164427 | + | 0.643569i | ||||
\(403\) | − | 1.78962e6i | − | 0.548907i | ||||||
\(404\) | −4.61849e6 | − | 1.36907e6i | −1.40782 | − | 0.417321i | ||||
\(405\) | −926556. | − | 1.14923e6i | −0.280695 | − | 0.348153i | ||||
\(406\) | −112489. | + | 83981.9i | −0.0338684 | + | 0.0252854i | ||||
\(407\) | 5.53013e6 | 1.65481 | ||||||||
\(408\) | −5.55422e6 | − | 1.49323e6i | −1.65186 | − | 0.444095i | ||||
\(409\) | −2.42874e6 | −0.717913 | −0.358957 | − | 0.933354i | \(-0.616867\pi\) | ||||
−0.358957 | + | 0.933354i | \(0.616867\pi\) | |||||||
\(410\) | 50103.7 | − | 37406.4i | 0.0147201 | − | 0.0109897i | ||||
\(411\) | −426579. | + | 602909.i | −0.124565 | + | 0.176055i | ||||
\(412\) | −4.17107e6 | − | 1.23644e6i | −1.21061 | − | 0.358863i | ||||
\(413\) | − | 51097.8i | − | 0.0147410i | ||||||
\(414\) | 4.48494e6 | + | 3.00435e6i | 1.28604 | + | 0.861489i | ||||
\(415\) | 1.54999e6i | 0.441781i | ||||||||
\(416\) | −4.43517e6 | + | 288467.i | −1.25654 | + | 0.0817264i | ||||
\(417\) | −267419. | + | 377959.i | −0.0753100 | + | 0.106440i | ||||
\(418\) | −742100. | − | 994000.i | −0.207741 | − | 0.278257i | ||||
\(419\) | 5.14163e6 | 1.43076 | 0.715378 | − | 0.698738i | \(-0.246255\pi\) | ||||
0.715378 | + | 0.698738i | \(0.246255\pi\) | |||||||
\(420\) | −200755. | + | 158023.i | −0.0555321 | + | 0.0437117i | ||||
\(421\) | −4.22462e6 | −1.16167 | −0.580834 | − | 0.814022i | \(-0.697273\pi\) | ||||
−0.580834 | + | 0.814022i | \(0.697273\pi\) | |||||||
\(422\) | −1.57778e6 | − | 2.11334e6i | −0.431285 | − | 0.577681i | ||||
\(423\) | 1.57851e6 | + | 4.47280e6i | 0.428939 | + | 1.21543i | ||||
\(424\) | −2.78031e6 | + | 1.02476e6i | −0.751068 | + | 0.276827i | ||||
\(425\) | − | 1.27388e6i | − | 0.342103i | ||||||
\(426\) | −1.77067e6 | + | 45239.2i | −0.472730 | + | 0.0120779i | ||||
\(427\) | 295800.i | 0.0785106i | ||||||||
\(428\) | −692821. | + | 2.33720e6i | −0.182815 | + | 0.616719i | ||||
\(429\) | −6.65247e6 | − | 4.70685e6i | −1.74518 | − | 1.23477i | ||||
\(430\) | −1.25317e6 | + | 935594.i | −0.326844 | + | 0.244015i | ||||
\(431\) | −85977.8 | −0.0222943 | −0.0111471 | − | 0.999938i | \(-0.503548\pi\) | ||||
−0.0111471 | + | 0.999938i | \(0.503548\pi\) | |||||||
\(432\) | 2.92145e6 | − | 2.55168e6i | 0.753163 | − | 0.657834i | ||||
\(433\) | 5.57531e6 | 1.42906 | 0.714528 | − | 0.699607i | \(-0.246641\pi\) | ||||
0.714528 | + | 0.699607i | \(0.246641\pi\) | |||||||
\(434\) | 216603. | − | 161711.i | 0.0552001 | − | 0.0412112i | ||||
\(435\) | 385358. | + | 272654.i | 0.0976431 | + | 0.0690858i | ||||
\(436\) | −1.47823e6 | + | 4.98676e6i | −0.372414 | + | 1.25632i | ||||
\(437\) | − | 1.26391e6i | − | 0.316602i | ||||||
\(438\) | 635326. | − | 16232.1i | 0.158238 | − | 0.00404287i | ||||
\(439\) | − | 1.26655e6i | − | 0.313662i | −0.987625 | − | 0.156831i | \(-0.949872\pi\) | ||
0.987625 | − | 0.156831i | \(-0.0501277\pi\) | |||||||
\(440\) | −2.89311e6 | + | 1.06634e6i | −0.712416 | + | 0.262581i | ||||
\(441\) | 1.32523e6 | + | 3.75513e6i | 0.324485 | + | 0.919450i | ||||
\(442\) | 5.29242e6 | + | 7.08889e6i | 1.28854 | + | 1.72593i | ||||
\(443\) | 2.43716e6 | 0.590030 | 0.295015 | − | 0.955493i | \(-0.404675\pi\) | ||||
0.295015 | + | 0.955493i | \(0.404675\pi\) | |||||||
\(444\) | 3.18145e6 | − | 2.50425e6i | 0.765891 | − | 0.602866i | ||||
\(445\) | 2.44317e6 | 0.584862 | ||||||||
\(446\) | 4.46532e6 | + | 5.98103e6i | 1.06296 | + | 1.42377i | ||||
\(447\) | −2.36968e6 | + | 3.34920e6i | −0.560945 | + | 0.792817i | ||||
\(448\) | −435678. | − | 510735.i | −0.102558 | − | 0.120227i | ||||
\(449\) | − | 290528.i | − | 0.0680098i | −0.999422 | − | 0.0340049i | \(-0.989174\pi\) | ||
0.999422 | − | 0.0340049i | \(-0.0108262\pi\) | |||||||
\(450\) | 713784. | + | 478147.i | 0.166164 | + | 0.111309i | ||||
\(451\) | 301240.i | 0.0697384i | ||||||||
\(452\) | 7.36856e6 | + | 2.18427e6i | 1.69643 | + | 0.502876i | ||||
\(453\) | −267515. | + | 378094.i | −0.0612494 | + | 0.0865674i | ||||
\(454\) | −3.92202e6 | + | 2.92810e6i | −0.893040 | + | 0.666725i | ||||
\(455\) | 392979. | 0.0889899 | ||||||||
\(456\) | −877046. | − | 235790.i | −0.197520 | − | 0.0531024i | ||||
\(457\) | −4.43702e6 | −0.993803 | −0.496902 | − | 0.867807i | \(-0.665529\pi\) | ||||
−0.496902 | + | 0.867807i | \(0.665529\pi\) | |||||||
\(458\) | −4.61862e6 | + | 3.44817e6i | −1.02884 | + | 0.768112i | ||||
\(459\) | −7.42747e6 | − | 2.10767e6i | −1.64554 | − | 0.466950i | ||||
\(460\) | −3.01211e6 | − | 892883.i | −0.663706 | − | 0.196743i | ||||
\(461\) | − | 4.88335e6i | − | 1.07020i | −0.844788 | − | 0.535101i | \(-0.820273\pi\) | ||
0.844788 | − | 0.535101i | \(-0.179727\pi\) | |||||||
\(462\) | −31437.8 | − | 1.23048e6i | −0.00685248 | − | 0.268207i | ||||
\(463\) | − | 3.30428e6i | − | 0.716348i | −0.933655 | − | 0.358174i | \(-0.883399\pi\) | ||
0.933655 | − | 0.358174i | \(-0.116601\pi\) | |||||||
\(464\) | −675976. | + | 1.04000e6i | −0.145759 | + | 0.224253i | ||||
\(465\) | −742026. | − | 525009.i | −0.159143 | − | 0.112599i | ||||
\(466\) | 4.16548e6 | + | 5.57943e6i | 0.888589 | + | 1.19021i | ||||
\(467\) | −2.42435e6 | −0.514403 | −0.257202 | − | 0.966358i | \(-0.582800\pi\) | ||||
−0.257202 | + | 0.966358i | \(0.582800\pi\) | |||||||
\(468\) | −5.95856e6 | + | 304672.i | −1.25755 | + | 0.0643011i | ||||
\(469\) | 484620. | 0.101735 | ||||||||
\(470\) | −1.65141e6 | − | 2.21197e6i | −0.344835 | − | 0.461886i | ||||
\(471\) | 1.39112e6 | + | 984266.i | 0.288943 | + | 0.204437i | ||||
\(472\) | −156142. | − | 423633.i | −0.0322600 | − | 0.0875255i | ||||
\(473\) | − | 7.53450e6i | − | 1.54847i | ||||||
\(474\) | 116265. | + | 4.55060e6i | 0.0237685 | + | 0.930300i | ||||
\(475\) | − | 201154.i | − | 0.0409067i | ||||||
\(476\) | −379762. | + | 1.28111e6i | −0.0768235 | + | 0.259161i | ||||
\(477\) | −3.75100e6 | + | 1.32377e6i | −0.754833 | + | 0.266390i | ||||
\(478\) | −2.68838e6 | + | 2.00709e6i | −0.538173 | + | 0.401789i | ||||
\(479\) | 3.29323e6 | 0.655818 | 0.327909 | − | 0.944709i | \(-0.393656\pi\) | ||||
0.327909 | + | 0.944709i | \(0.393656\pi\) | |||||||
\(480\) | −1.18151e6 | + | 1.92357e6i | −0.234064 | + | 0.381070i | ||||
\(481\) | −6.22768e6 | −1.22734 | ||||||||
\(482\) | 3.95401e6 | − | 2.95198e6i | 0.775212 | − | 0.578757i | ||||
\(483\) | 724376. | − | 1.02380e6i | 0.141285 | − | 0.199686i | ||||
\(484\) | 2.75719e6 | − | 9.30126e6i | 0.534999 | − | 1.80480i | ||||
\(485\) | 2.66681e6i | 0.514798i | ||||||||
\(486\) | 3.96885e6 | − | 3.37068e6i | 0.762209 | − | 0.647331i | ||||
\(487\) | − | 9.58600e6i | − | 1.83153i | −0.401710 | − | 0.915767i | \(-0.631584\pi\) | ||
0.401710 | − | 0.915767i | \(-0.368416\pi\) | |||||||
\(488\) | 903888. | + | 2.45236e6i | 0.171817 | + | 0.466160i | ||||
\(489\) | 2.79146e6 | − | 3.94534e6i | 0.527909 | − | 0.746125i | ||||
\(490\) | −1.38644e6 | − | 1.85705e6i | −0.260862 | − | 0.349409i | ||||
\(491\) | −3.42101e6 | −0.640400 | −0.320200 | − | 0.947350i | \(-0.603750\pi\) | ||||
−0.320200 | + | 0.947350i | \(0.603750\pi\) | |||||||
\(492\) | 136413. | + | 173302.i | 0.0254064 | + | 0.0322768i | ||||
\(493\) | 2.46890e6 | 0.457495 | ||||||||
\(494\) | 835706. | + | 1.11938e6i | 0.154076 | + | 0.206377i | ||||
\(495\) | −3.90318e6 | + | 1.37748e6i | −0.715987 | + | 0.252681i | ||||
\(496\) | 1.30162e6 | − | 2.00257e6i | 0.237564 | − | 0.365497i | ||||
\(497\) | 411508.i | 0.0747286i | ||||||||
\(498\) | −5.46543e6 | + | 139638.i | −0.987531 | + | 0.0252307i | ||||
\(499\) | − | 670965.i | − | 0.120628i | −0.998179 | − | 0.0603140i | \(-0.980790\pi\) | ||
0.998179 | − | 0.0603140i | \(-0.0192102\pi\) | |||||||
\(500\) | −479381. | − | 142104.i | −0.0857544 | − | 0.0254203i | ||||
\(501\) | −1.45074e6 | − | 1.02645e6i | −0.258223 | − | 0.182702i | ||||
\(502\) | −2.63701e6 | + | 1.96874e6i | −0.467039 | + | 0.348681i | ||||
\(503\) | 74144.9 | 0.0130666 | 0.00653328 | − | 0.999979i | \(-0.497920\pi\) | ||||
0.00653328 | + | 0.999979i | \(0.497920\pi\) | |||||||
\(504\) | −575294. | − | 693650.i | −0.100882 | − | 0.121637i | ||||
\(505\) | 3.76339e6 | 0.656675 | ||||||||
\(506\) | 1.21285e7 | − | 9.05489e6i | 2.10587 | − | 1.57220i | ||||
\(507\) | 2.76675e6 | + | 1.95757e6i | 0.478025 | + | 0.338219i | ||||
\(508\) | −35310.1 | − | 10467.0i | −0.00607071 | − | 0.00179955i | ||||
\(509\) | 8.22309e6i | 1.40683i | 0.710781 | + | 0.703414i | \(0.248342\pi\) | ||||
−0.710781 | + | 0.703414i | \(0.751658\pi\) | |||||||
\(510\) | 4.49185e6 | − | 114763.i | 0.764715 | − | 0.0195379i | ||||
\(511\) | − | 147651.i | − | 0.0250141i | ||||||
\(512\) | −5.17272e6 | − | 2.90299e6i | −0.872055 | − | 0.489407i | ||||
\(513\) | −1.17284e6 | − | 332814.i | −0.196765 | − | 0.0558352i | ||||
\(514\) | 4.48760e6 | + | 6.01089e6i | 0.749215 | + | 1.00353i | ||||
\(515\) | 3.39881e6 | 0.564688 | ||||||||
\(516\) | −3.41191e6 | − | 4.33455e6i | −0.564122 | − | 0.716670i | ||||
\(517\) | 1.32991e7 | 2.18825 | ||||||||
\(518\) | −562737. | − | 753754.i | −0.0921470 | − | 0.123426i | ||||
\(519\) | −1.11770e6 | + | 1.57971e6i | −0.182141 | + | 0.257430i | ||||
\(520\) | 3.25804e6 | − | 1.20084e6i | 0.528382 | − | 0.194750i | ||||
\(521\) | − | 6.39310e6i | − | 1.03185i | −0.856633 | − | 0.515925i | \(-0.827448\pi\) | ||
0.856633 | − | 0.515925i | \(-0.172552\pi\) | |||||||
\(522\) | −926693. | + | 1.38338e6i | −0.148854 | + | 0.222211i | ||||
\(523\) | 7.33325e6i | 1.17231i | 0.810199 | + | 0.586155i | \(0.199359\pi\) | ||||
−0.810199 | + | 0.586155i | \(0.800641\pi\) | |||||||
\(524\) | 1.26358e6 | − | 4.26264e6i | 0.201036 | − | 0.678189i | ||||
\(525\) | 115286. | − | 162940.i | 0.0182548 | − | 0.0258006i | ||||
\(526\) | 3.15741e6 | − | 2.35726e6i | 0.497584 | − | 0.371486i | ||||
\(527\) | −4.75399e6 | −0.745644 | ||||||||
\(528\) | −4.02067e6 | − | 1.01054e7i | −0.627644 | − | 1.57749i | ||||
\(529\) | 8.98557e6 | 1.39607 | ||||||||
\(530\) | 1.85501e6 | − | 1.38491e6i | 0.286852 | − | 0.214157i | ||||
\(531\) | −201702. | − | 571535.i | −0.0310437 | − | 0.0879642i | ||||
\(532\) | −59966.8 | + | 202296.i | −0.00918611 | + | 0.0309890i | ||||
\(533\) | − | 339238.i | − | 0.0517233i | ||||||
\(534\) | 220104. | + | 8.61489e6i | 0.0334022 | + | 1.30736i | ||||
\(535\) | − | 1.90448e6i | − | 0.287668i | ||||||
\(536\) | 4.01780e6 | − | 1.48087e6i | 0.604055 | − | 0.222642i | ||||
\(537\) | 1.26576e6 | + | 895567.i | 0.189415 | + | 0.134018i | ||||
\(538\) | −3.21015e6 | − | 4.29981e6i | −0.478156 | − | 0.640462i | ||||
\(539\) | 1.11652e7 | 1.65537 | ||||||||
\(540\) | −1.62170e6 | + | 2.55996e6i | −0.239323 | + | 0.377789i | ||||
\(541\) | 4.28651e6 | 0.629666 | 0.314833 | − | 0.949147i | \(-0.398051\pi\) | ||||
0.314833 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(542\) | −3.91315e6 | − | 5.24144e6i | −0.572174 | − | 0.766394i | ||||
\(543\) | 3.84285e6 | + | 2.71895e6i | 0.559312 | + | 0.395732i | ||||
\(544\) | 766289. | + | 1.17817e7i | 0.111018 | + | 1.70691i | ||||
\(545\) | − | 4.06347e6i | − | 0.586011i | ||||||
\(546\) | 35403.3 | + | 1.38569e6i | 0.00508233 | + | 0.198923i | ||||
\(547\) | − | 6.19383e6i | − | 0.885097i | −0.896744 | − | 0.442549i | \(-0.854074\pi\) | ||
0.896744 | − | 0.442549i | \(-0.145926\pi\) | |||||||
\(548\) | 1.45359e6 | + | 430891.i | 0.206772 | + | 0.0612937i | ||||
\(549\) | 1.16763e6 | + | 3.30855e6i | 0.165338 | + | 0.468497i | ||||
\(550\) | 1.93027e6 | − | 1.44110e6i | 0.272089 | − | 0.203136i | ||||
\(551\) | 389855. | 0.0547046 | ||||||||
\(552\) | 2.87705e6 | − | 1.07015e7i | 0.401883 | − | 1.49484i | ||||
\(553\) | 1.05757e6 | 0.147061 | ||||||||
\(554\) | −4.18008e6 | + | 3.12076e6i | −0.578643 | + | 0.432003i | ||||
\(555\) | −1.82697e6 | + | 2.58217e6i | −0.251767 | + | 0.355838i | ||||
\(556\) | 911247. | + | 270122.i | 0.125011 | + | 0.0370573i | ||||
\(557\) | 4.77647e6i | 0.652333i | 0.945312 | + | 0.326166i | \(0.105757\pi\) | ||||
−0.945312 | + | 0.326166i | \(0.894243\pi\) | |||||||
\(558\) | 1.78439e6 | − | 2.66377e6i | 0.242608 | − | 0.362168i | ||||
\(559\) | 8.48488e6i | 1.14846i | ||||||||
\(560\) | 439740. | + | 285821.i | 0.0592551 | + | 0.0385145i | ||||
\(561\) | −1.25034e7 | + | 1.76717e7i | −1.67733 | + | 2.37068i | ||||
\(562\) | −3.03090e6 | − | 4.05971e6i | −0.404791 | − | 0.542194i | ||||
\(563\) | −1.00423e7 | −1.33525 | −0.667626 | − | 0.744497i | \(-0.732689\pi\) | ||||
−0.667626 | + | 0.744497i | \(0.732689\pi\) | |||||||
\(564\) | 7.65089e6 | − | 6.02235e6i | 1.01278 | − | 0.797201i | ||||
\(565\) | −6.00429e6 | −0.791298 | ||||||||
\(566\) | −6.40211e6 | − | 8.57526e6i | −0.840006 | − | 1.12514i | ||||
\(567\) | −759292. | − | 941770.i | −0.0991862 | − | 0.123023i | ||||
\(568\) | 1.25746e6 | + | 3.41166e6i | 0.163540 | + | 0.443705i | ||||
\(569\) | 1.20533e7i | 1.56072i | 0.625329 | + | 0.780362i | \(0.284965\pi\) | ||||
−0.625329 | + | 0.780362i | \(0.715035\pi\) | |||||||
\(570\) | 709291. | − | 18121.9i | 0.0914402 | − | 0.00233623i | ||||
\(571\) | 1.09626e6i | 0.140709i | 0.997522 | + | 0.0703547i | \(0.0224131\pi\) | ||||
−0.997522 | + | 0.0703547i | \(0.977587\pi\) | |||||||
\(572\) | −4.75442e6 | + | 1.60389e7i | −0.607586 | + | 2.04967i | ||||
\(573\) | 1.95147e6 | + | 1.38073e6i | 0.248299 | + | 0.175680i | ||||
\(574\) | 41058.9 | − | 30653.7i | 0.00520149 | − | 0.00388333i | ||||
\(575\) | 2.45442e6 | 0.309585 | ||||||||
\(576\) | −6.88916e6 | − | 3.99284e6i | −0.865188 | − | 0.501448i | ||||
\(577\) | −2.65691e6 | −0.332228 | −0.166114 | − | 0.986107i | \(-0.553122\pi\) | ||||
−0.166114 | + | 0.986107i | \(0.553122\pi\) | |||||||
\(578\) | 1.23950e7 | − | 9.25384e6i | 1.54321 | − | 1.15213i | ||||
\(579\) | −8.97318e6 | − | 6.34883e6i | −1.11237 | − | 0.787041i | ||||
\(580\) | 275410. | − | 929086.i | 0.0339946 | − | 0.114680i | ||||
\(581\) | 1.27018e6i | 0.156108i | ||||||||
\(582\) | −9.40347e6 | + | 240252.i | −1.15075 | + | 0.0294008i | ||||
\(583\) | 1.11530e7i | 1.35900i | ||||||||
\(584\) | −451185. | − | 1.22412e6i | −0.0547422 | − | 0.148523i | ||||
\(585\) | 4.39551e6 | − | 1.55123e6i | 0.531031 | − | 0.187407i | ||||
\(586\) | −6.90078e6 | − | 9.24319e6i | −0.830145 | − | 1.11193i | ||||
\(587\) | −4.31304e6 | −0.516640 | −0.258320 | − | 0.966059i | \(-0.583169\pi\) | ||||
−0.258320 | + | 0.966059i | \(0.583169\pi\) | |||||||
\(588\) | 6.42328e6 | − | 5.05604e6i | 0.766150 | − | 0.603070i | ||||
\(589\) | −750684. | −0.0891598 | ||||||||
\(590\) | 211018. | + | 282646.i | 0.0249568 | + | 0.0334282i | ||||
\(591\) | −1.89195e6 | + | 2.67400e6i | −0.222813 | + | 0.314914i | ||||
\(592\) | −6.96872e6 | − | 4.52951e6i | −0.817238 | − | 0.531186i | ||||
\(593\) | − | 1.26476e7i | − | 1.47697i | −0.674268 | − | 0.738487i | \(-0.735541\pi\) | ||
0.674268 | − | 0.738487i | \(-0.264459\pi\) | |||||||
\(594\) | −5.20878e6 | − | 1.36389e7i | −0.605718 | − | 1.58604i | ||||
\(595\) | − | 1.04392e6i | − | 0.120885i | ||||||
\(596\) | 8.07482e6 | + | 2.39363e6i | 0.931145 | + | 0.276020i | ||||
\(597\) | 6.73371e6 | − | 9.51715e6i | 0.773248 | − | 1.09288i | ||||
\(598\) | −1.36584e7 | + | 1.01971e7i | −1.56187 | + | 1.16606i | ||||
\(599\) | 940927. | 0.107149 | 0.0535746 | − | 0.998564i | \(-0.482939\pi\) | ||||
0.0535746 | + | 0.998564i | \(0.482939\pi\) | |||||||
\(600\) | 457887. | − | 1.70316e6i | 0.0519254 | − | 0.193142i | ||||
\(601\) | −4.15378e6 | −0.469092 | −0.234546 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234546 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(602\) | −1.02695e6 | + | 766699.i | −0.115493 | + | 0.0862250i | ||||
\(603\) | 5.42053e6 | − | 1.91297e6i | 0.607083 | − | 0.214247i | ||||
\(604\) | 911573. | + | 270219.i | 0.101671 | + | 0.0301386i | ||||
\(605\) | 7.57916e6i | 0.841845i | ||||||||
\(606\) | 339042. | + | 1.32701e7i | 0.0375035 | + | 1.46789i | ||||
\(607\) | − | 6.76513e6i | − | 0.745254i | −0.927981 | − | 0.372627i | \(-0.878457\pi\) | ||
0.927981 | − | 0.372627i | \(-0.121543\pi\) | |||||||
\(608\) | 121002. | + | 1.86040e6i | 0.0132749 | + | 0.204102i | ||||
\(609\) | 315793. | + | 223434.i | 0.0345032 | + | 0.0244122i | ||||
\(610\) | −1.22156e6 | − | 1.63621e6i | −0.132920 | − | 0.178038i | ||||
\(611\) | −1.49766e7 | −1.62297 | ||||||||
\(612\) | 809338. | + | 1.58284e7i | 0.0873477 | + | 1.70828i | ||||
\(613\) | −3.55719e6 | −0.382346 | −0.191173 | − | 0.981556i | \(-0.561229\pi\) | ||||
−0.191173 | + | 0.981556i | \(0.561229\pi\) | |||||||
\(614\) | −1.57362e6 | − | 2.10777e6i | −0.168453 | − | 0.225633i | ||||
\(615\) | −140657. | − | 99519.9i | −0.0149960 | − | 0.0106102i | ||||
\(616\) | −2.37084e6 | + | 873841.i | −0.251739 | + | 0.0927856i | ||||
\(617\) | 9.04265e6i | 0.956275i | 0.878285 | + | 0.478138i | \(0.158688\pi\) | ||||
−0.878285 | + | 0.478138i | \(0.841312\pi\) | |||||||
\(618\) | 306197. | + | 1.19846e7i | 0.0322500 | + | 1.26227i | ||||
\(619\) | − | 5.32981e6i | − | 0.559094i | −0.960132 | − | 0.279547i | \(-0.909816\pi\) | ||
0.960132 | − | 0.279547i | \(-0.0901843\pi\) | |||||||
\(620\) | −530316. | + | 1.78900e6i | −0.0554058 | + | 0.186909i | ||||
\(621\) | 4.06090e6 | − | 1.43107e7i | 0.422565 | − | 1.48913i | ||||
\(622\) | 1.31391e7 | − | 9.80941e6i | 1.36173 | − | 1.01664i | ||||
\(623\) | 2.00212e6 | 0.206667 | ||||||||
\(624\) | 4.52783e6 | + | 1.13800e7i | 0.465509 | + | 1.16999i | ||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.22436e7 | + | 9.14082e6i | −1.24874 | + | 0.932287i | ||||
\(627\) | −1.97436e6 | + | 2.79048e6i | −0.200566 | + | 0.283472i | ||||
\(628\) | 994215. | − | 3.35395e6i | 0.100596 | − | 0.339357i | ||||
\(629\) | 1.65433e7i | 1.66723i | ||||||||
\(630\) | 584931. | + | 391831.i | 0.0587155 | + | 0.0393321i | ||||
\(631\) | 1.65389e7i | 1.65361i | 0.562486 | + | 0.826807i | \(0.309845\pi\) | ||||
−0.562486 | + | 0.826807i | \(0.690155\pi\) | |||||||
\(632\) | 8.76793e6 | − | 3.23167e6i | 0.873181 | − | 0.321836i | ||||
\(633\) | −4.19768e6 | + | 5.93283e6i | −0.416390 | + | 0.588508i | ||||
\(634\) | 441114. | + | 590846.i | 0.0435840 | + | 0.0583783i | ||||
\(635\) | 28772.5 | 0.00283167 | ||||||||
\(636\) | 5.05048e6 | + | 6.41622e6i | 0.495097 | + | 0.628980i | ||||
\(637\) | −1.25736e7 | −1.22775 | ||||||||
\(638\) | 2.79299e6 | + | 3.74104e6i | 0.271655 | + | 0.363866i | ||||
\(639\) | 1.62437e6 | + | 4.60276e6i | 0.157374 | + | 0.445929i | ||||
\(640\) | 4.51911e6 | + | 1.02590e6i | 0.436117 | + | 0.0990046i | ||||
\(641\) | − | 1.16495e7i | − | 1.11985i | −0.828542 | − | 0.559927i | \(-0.810829\pi\) | ||
0.828542 | − | 0.559927i | \(-0.189171\pi\) | |||||||
\(642\) | 6.71540e6 | − | 171574.i | 0.643035 | − | 0.0164291i | ||||
\(643\) | − | 5.98124e6i | − | 0.570511i | −0.958452 | − | 0.285255i | \(-0.907922\pi\) | ||
0.958452 | − | 0.285255i | \(-0.0920784\pi\) | |||||||
\(644\) | −2.46836e6 | − | 731698.i | −0.234527 | − | 0.0695212i | ||||
\(645\) | 3.51806e6 | + | 2.48915e6i | 0.332969 | + | 0.235587i | ||||
\(646\) | 2.97354e6 | − | 2.21999e6i | 0.280345 | − | 0.209300i | ||||
\(647\) | 3.64629e6 | 0.342444 | 0.171222 | − | 0.985232i | \(-0.445228\pi\) | ||||
0.171222 | + | 0.985232i | \(0.445228\pi\) | |||||||
\(648\) | −9.17282e6 | − | 5.48766e6i | −0.858154 | − | 0.513393i | ||||
\(649\) | −1.69936e6 | −0.158370 | ||||||||
\(650\) | −2.17375e6 | + | 1.62288e6i | −0.201802 | + | 0.150661i | ||||
\(651\) | −608074. | − | 430233.i | −0.0562346 | − | 0.0397879i | ||||
\(652\) | −9.51207e6 | − | 2.81968e6i | −0.876307 | − | 0.259765i | ||||
\(653\) | 4.43691e6i | 0.407190i | 0.979055 | + | 0.203595i | \(0.0652626\pi\) | ||||
−0.979055 | + | 0.203595i | \(0.934737\pi\) | |||||||
\(654\) | 1.43283e7 | − | 366076.i | 1.30993 | − | 0.0334678i | ||||
\(655\) | 3.47342e6i | 0.316340i | ||||||||
\(656\) | 246734. | − | 379604.i | 0.0223856 | − | 0.0344407i | ||||
\(657\) | −582833. | − | 1.65150e6i | −0.0526782 | − | 0.149267i | ||||
\(658\) | −1.35330e6 | − | 1.81266e6i | −0.121851 | − | 0.163212i | ||||
\(659\) | 2.98319e6 | 0.267589 | 0.133794 | − | 0.991009i | \(-0.457284\pi\) | ||||
0.133794 | + | 0.991009i | \(0.457284\pi\) | |||||||
\(660\) | 5.25538e6 | + | 6.67653e6i | 0.469618 | + | 0.596610i | ||||
\(661\) | 7.43256e6 | 0.661660 | 0.330830 | − | 0.943690i | \(-0.392671\pi\) | ||||
0.330830 | + | 0.943690i | \(0.392671\pi\) | |||||||
\(662\) | −1.85415e6 | − | 2.48352e6i | −0.164437 | − | 0.220254i | ||||
\(663\) | 1.40805e7 | − | 1.99008e7i | 1.24404 | − | 1.75828i | ||||
\(664\) | 3.88134e6 | + | 1.05306e7i | 0.341634 | + | 0.926898i | ||||
\(665\) | − | 164841.i | − | 0.0144548i | ||||||
\(666\) | −9.26961e6 | − | 6.20949e6i | −0.809797 | − | 0.542463i | ||||
\(667\) | 4.75690e6i | 0.414009i | ||||||||
\(668\) | −1.03682e6 | + | 3.49768e6i | −0.0899007 | + | 0.303277i | ||||
\(669\) | 1.18800e7 | − | 1.67907e7i | 1.02624 | − | 1.45045i | ||||
\(670\) | −2.68066e6 | + | 2.00132e6i | −0.230704 | + | 0.172239i | ||||
\(671\) | 9.83742e6 | 0.843480 | ||||||||
\(672\) | −968221. | + | 1.57632e6i | −0.0827087 | + | 0.134655i | ||||
\(673\) | −1.68280e7 | −1.43217 | −0.716085 | − | 0.698013i | \(-0.754068\pi\) | ||||
−0.716085 | + | 0.698013i | \(0.754068\pi\) | |||||||
\(674\) | −7.39755e6 | + | 5.52286e6i | −0.627246 | + | 0.468289i | ||||
\(675\) | 646298. | − | 2.27757e6i | 0.0545976 | − | 0.192403i | ||||
\(676\) | 1.97736e6 | − | 6.67055e6i | 0.166425 | − | 0.561429i | ||||
\(677\) | − | 9.53318e6i | − | 0.799404i | −0.916645 | − | 0.399702i | \(-0.869114\pi\) | ||
0.916645 | − | 0.399702i | \(-0.130886\pi\) | |||||||
\(678\) | −540924. | − | 2.11718e7i | −0.0451920 | − | 1.76882i | ||||
\(679\) | 2.18539e6i | 0.181909i | ||||||||
\(680\) | −3.18994e6 | − | 8.65472e6i | −0.264552 | − | 0.717763i | ||||
\(681\) | 1.10104e7 | + | 7.79023e6i | 0.909777 | + | 0.643698i | ||||
\(682\) | −5.37803e6 | − | 7.20356e6i | −0.442754 | − | 0.593043i | ||||
\(683\) | −2.22827e7 | −1.82774 | −0.913872 | − | 0.406002i | \(-0.866923\pi\) | ||||
−0.913872 | + | 0.406002i | \(0.866923\pi\) | |||||||
\(684\) | 127800. | + | 2.49941e6i | 0.0104445 | + | 0.204266i | ||||
\(685\) | −1.18446e6 | −0.0964485 | ||||||||
\(686\) | −2.30141e6 | − | 3.08261e6i | −0.186717 | − | 0.250097i | ||||
\(687\) | 1.29660e7 | + | 9.17386e6i | 1.04812 | + | 0.741584i | ||||
\(688\) | −6.17121e6 | + | 9.49450e6i | −0.497049 | + | 0.764717i | ||||
\(689\) | − | 1.25598e7i | − | 1.00794i | ||||||
\(690\) | 221118. | + | 8.65457e6i | 0.0176808 | + | 0.692027i | ||||
\(691\) | − | 1.73408e7i | − | 1.38158i | −0.723058 | − | 0.690788i | \(-0.757264\pi\) | ||
0.723058 | − | 0.690788i | \(-0.242736\pi\) | |||||||
\(692\) | 3.80863e6 | + | 1.12900e6i | 0.302345 | + | 0.0896247i | ||||
\(693\) | −3.19857e6 | + | 1.12881e6i | −0.253001 | + | 0.0892872i | ||||
\(694\) | 1.69263e7 | − | 1.26368e7i | 1.33402 | − | 0.995954i | ||||
\(695\) | −742532. | −0.0583113 | ||||||||
\(696\) | 3.30088e6 | + | 887427.i | 0.258289 | + | 0.0694400i | ||||
\(697\) | −901159. | −0.0702618 | ||||||||
\(698\) | −2.21734e6 | + | 1.65542e6i | −0.172264 | + | 0.128608i | ||||
\(699\) | 1.10823e7 | − | 1.56633e7i | 0.857900 | − | 1.21252i | ||||
\(700\) | −392843. | − | 116451.i | −0.0303021 | − | 0.00898251i | ||||
\(701\) | − | 3.41026e6i | − | 0.262115i | −0.991375 | − | 0.131058i | \(-0.958163\pi\) | ||
0.991375 | − | 0.131058i | \(-0.0418373\pi\) | |||||||
\(702\) | 5.86581e6 | + | 1.53593e7i | 0.449247 | + | 1.17633i | ||||
\(703\) | 2.61230e6i | 0.199358i | ||||||||
\(704\) | −1.69855e7 | + | 1.44894e7i | −1.29166 | + | 1.10184i | ||||
\(705\) | −4.39359e6 | + | 6.20972e6i | −0.332925 | + | 0.470543i | ||||
\(706\) | 1.17397e7 | + | 1.57247e7i | 0.886432 | + | 1.18732i | ||||
\(707\) | 3.08401e6 | 0.232043 | ||||||||
\(708\) | −977631. | + | 769536.i | −0.0732980 | + | 0.0576960i | ||||
\(709\) | −1.52586e6 | −0.113999 | −0.0569994 | − | 0.998374i | \(-0.518153\pi\) | ||||
−0.0569994 | + | 0.998374i | \(0.518153\pi\) | |||||||
\(710\) | −1.69939e6 | − | 2.27624e6i | −0.126517 | − | 0.169462i | ||||
\(711\) | 1.18291e7 | − | 4.17462e6i | 0.877559 | − | 0.309701i | ||||
\(712\) | 1.65989e7 | − | 6.11798e6i | 1.22709 | − | 0.452280i | ||||
\(713\) | − | 9.15964e6i | − | 0.674768i | ||||||
\(714\) | 3.68097e6 | − | 94046.1i | 0.270220 | − | 0.00690391i | ||||
\(715\) | − | 1.30693e7i | − | 0.956065i | ||||||
\(716\) | 904620. | − | 3.05170e6i | 0.0659453 | − | 0.222464i | ||||
\(717\) | 7.54716e6 | + | 5.33988e6i | 0.548259 | + | 0.387912i | ||||
\(718\) | 2.00763e7 | − | 1.49886e7i | 1.45336 | − | 1.08505i | ||||
\(719\) | 1.49038e6 | 0.107517 | 0.0537583 | − | 0.998554i | \(-0.482880\pi\) | ||||
0.0537583 | + | 0.998554i | \(0.482880\pi\) | |||||||
\(720\) | 6.04677e6 | + | 1.46112e6i | 0.434703 | + | 0.105040i | ||||
\(721\) | 2.78525e6 | 0.199538 | ||||||||
\(722\) | −1.07544e7 | + | 8.02902e6i | −0.767792 | + | 0.573217i | ||||
\(723\) | −1.11002e7 | − | 7.85376e6i | −0.789741 | − | 0.558769i | ||||
\(724\) | 2.74643e6 | − | 9.26498e6i | 0.194725 | − | 0.656898i | ||||
\(725\) | 757068.i | 0.0534921i | ||||||||
\(726\) | −2.67250e7 | + | 682803.i | −1.88181 | + | 0.0480788i | ||||
\(727\) | 2.01845e7i | 1.41639i | 0.706017 | + | 0.708194i | \(0.250490\pi\) | ||||
−0.706017 | + | 0.708194i | \(0.749510\pi\) | |||||||
\(728\) | 2.66989e6 | − | 984064.i | 0.186709 | − | 0.0688169i | ||||
\(729\) | −1.22103e7 | − | 7.53660e6i | −0.850955 | − | 0.525239i | ||||
\(730\) | 609753. | + | 816729.i | 0.0423493 | + | 0.0567245i | ||||
\(731\) | 2.25394e7 | 1.56009 | ||||||||
\(732\) | 5.65940e6 | − | 4.45476e6i | 0.390385 | − | 0.307289i | ||||
\(733\) | −6.38127e6 | −0.438679 | −0.219340 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219340 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(734\) | −1.39323e7 | − | 1.86614e7i | −0.954512 | − | 1.27851i | ||||
\(735\) | −3.68862e6 | + | 5.21335e6i | −0.251852 | + | 0.355958i | ||||
\(736\) | −2.27001e7 | + | 1.47643e6i | −1.54466 | + | 0.100466i | ||||
\(737\) | − | 1.61170e7i | − | 1.09299i | ||||||
\(738\) | 338247. | − | 504940.i | 0.0228609 | − | 0.0341270i | ||||
\(739\) | 1.62657e7i | 1.09562i | 0.836602 | + | 0.547812i | \(0.184539\pi\) | ||||
−0.836602 | + | 0.547812i | \(0.815461\pi\) | |||||||
\(740\) | 6.22552e6 | + | 1.84544e6i | 0.417923 | + | 0.123886i | ||||
\(741\) | 2.22340e6 | − | 3.14246e6i | 0.148755 | − | 0.210244i | ||||
\(742\) | 1.52014e6 | − | 1.13491e6i | 0.101362 | − | 0.0756747i | ||||
\(743\) | −1.19714e7 | −0.795557 | −0.397778 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397778 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(744\) | −6.35599e6 | − | 1.70878e6i | −0.420970 | − | 0.113176i | ||||
\(745\) | −6.57978e6 | −0.434331 | ||||||||
\(746\) | −7.85164e6 | + | 5.86187e6i | −0.516551 | + | 0.385646i | ||||
\(747\) | 5.01386e6 | + | 1.42071e7i | 0.328754 | + | 0.931545i | ||||
\(748\) | 4.26060e7 | + | 1.26297e7i | 2.78430 | + | 0.825355i | ||||
\(749\) | − | 1.56068e6i | − | 0.101650i | ||||||
\(750\) | 35191.3 | + | 1.37739e6i | 0.00228445 | + | 0.0894135i | ||||
\(751\) | 9.93487e6i | 0.642780i | 0.946947 | + | 0.321390i | \(0.104150\pi\) | ||||
−0.946947 | + | 0.321390i | \(0.895850\pi\) | |||||||
\(752\) | −1.67587e7 | − | 1.08928e7i | −1.08068 | − | 0.702415i | ||||
\(753\) | 7.40294e6 | + | 5.23784e6i | 0.475792 | + | 0.336639i | ||||
\(754\) | −3.14529e6 | − | 4.21293e6i | −0.201480 | − | 0.269871i | ||||
\(755\) | −742797. | −0.0474245 | ||||||||
\(756\) | −1.32894e6 | + | 2.09783e6i | −0.0845673 | + | 0.133495i | ||||
\(757\) | −2.53967e6 | −0.161079 | −0.0805393 | − | 0.996751i | \(-0.525664\pi\) | ||||
−0.0805393 | + | 0.996751i | \(0.525664\pi\) | |||||||
\(758\) | 3.93551e6 | + | 5.27139e6i | 0.248787 | + | 0.333236i | ||||
\(759\) | −3.40486e7 | − | 2.40906e7i | −2.14534 | − | 1.51790i | ||||
\(760\) | −503712. | − | 1.36664e6i | −0.0316336 | − | 0.0858259i | ||||
\(761\) | − | 1.19650e7i | − | 0.748950i | −0.927237 | − | 0.374475i | \(-0.877823\pi\) | ||
0.927237 | − | 0.374475i | \(-0.122177\pi\) | |||||||
\(762\) | 2592.10 | + | 101455.i | 0.000161720 | + | 0.00632975i | ||||
\(763\) | − | 3.32992e6i | − | 0.207073i | ||||||
\(764\) | 1.39469e6 | − | 4.70492e6i | 0.0864457 | − | 0.291621i | ||||
\(765\) | −4.12072e6 | − | 1.16763e7i | −0.254577 | − | 0.721361i | ||||
\(766\) | 8.46929e6 | − | 6.32300e6i | 0.521525 | − | 0.389360i | ||||
\(767\) | 1.91371e6 | 0.117460 | ||||||||
\(768\) | −3.21032e6 | + | 1.60273e7i | −0.196402 | + | 0.980524i | ||||
\(769\) | 7.59430e6 | 0.463097 | 0.231548 | − | 0.972823i | \(-0.425621\pi\) | ||||
0.231548 | + | 0.972823i | \(0.425621\pi\) | |||||||
\(770\) | 1.58181e6 | − | 1.18095e6i | 0.0961454 | − | 0.0717802i | ||||
\(771\) | 1.19393e7 | − | 1.68745e7i | 0.723340 | − | 1.02234i | ||||
\(772\) | −6.41301e6 | + | 2.16340e7i | −0.387274 | + | 1.30645i | ||||
\(773\) | 1.90915e7i | 1.14919i | 0.818439 | + | 0.574593i | \(0.194840\pi\) | ||||
−0.818439 | + | 0.574593i | \(0.805160\pi\) | |||||||
\(774\) | −8.46009e6 | + | 1.26293e7i | −0.507601 | + | 0.757754i | ||||
\(775\) | − | 1.45777e6i | − | 0.0871836i | ||||||
\(776\) | 6.67799e6 | + | 1.81182e7i | 0.398099 | + | 1.08009i | ||||
\(777\) | −1.49716e6 | + | 2.11603e6i | −0.0889645 | + | 0.125739i | ||||
\(778\) | 6.88164e6 | + | 9.21756e6i | 0.407608 | + | 0.545968i | ||||
\(779\) | −142299. | −0.00840150 | ||||||||
\(780\) | −5.91828e6 | − | 7.51869e6i | −0.348305 | − | 0.442492i | ||||
\(781\) | 1.36855e7 | 0.802849 | ||||||||
\(782\) | 2.70877e7 | + | 3.62824e7i | 1.58400 | + | 2.12167i | ||||
\(783\) | 4.41415e6 | + | 1.25259e6i | 0.257302 | + | 0.0730135i | ||||
\(784\) | −1.40697e7 | − | 9.14499e6i | −0.817514 | − | 0.531365i | ||||
\(785\) | 2.73297e6i | 0.158293i | ||||||||
\(786\) | −1.22477e7 | + | 312919.i | −0.707127 | + | 0.0180666i | ||||
\(787\) | − | 2.01262e7i | − | 1.15831i | −0.815218 | − | 0.579155i | \(-0.803383\pi\) | ||
0.815218 | − | 0.579155i | \(-0.196617\pi\) | |||||||
\(788\) | 6.44692e6 | + | 1.91107e6i | 0.369860 | + | 0.109638i | ||||
\(789\) | −8.86387e6 | − | 6.27149e6i | −0.506910 | − | 0.358656i | ||||
\(790\) | −5.84992e6 | + | 4.36743e6i | −0.333490 | + | 0.248977i | ||||
\(791\) | −4.92038e6 | −0.279613 | ||||||||
\(792\) | −2.30687e7 | + | 1.91326e7i | −1.30681 | + | 1.08383i | ||||
\(793\) | −1.10783e7 | −0.625590 | ||||||||
\(794\) | 2.19920e7 | − | 1.64188e7i | 1.23798 | − | 0.924251i | ||||
\(795\) | −5.20762e6 | − | 3.68457e6i | −0.292228 | − | 0.206761i | ||||
\(796\) | −2.29455e7 | − | 6.80177e6i | −1.28356 | − | 0.380487i | ||||
\(797\) | 5.17898e6i | 0.288801i | 0.989519 | + | 0.144400i | \(0.0461253\pi\) | ||||
−0.989519 | + | 0.144400i | \(0.953875\pi\) | |||||||
\(798\) | 581249. | − | 14850.5i | 0.0323113 | − | 0.000825530i | ||||
\(799\) | 3.97842e7i | 2.20467i | ||||||||
\(800\) | −3.61275e6 | + | 234976.i | −0.199578 | + | 0.0129807i | ||||
\(801\) | 2.23940e7 | − | 7.90311e6i | 1.23325 | − | 0.435228i | ||||
\(802\) | −2.00376e7 | − | 2.68392e7i | −1.10004 | − | 1.47344i | ||||
\(803\) | −4.91044e6 | −0.268740 | ||||||||
\(804\) | −7.29840e6 | − | 9.27201e6i | −0.398187 | − | 0.505864i | ||||
\(805\) | 2.01134e6 | 0.109395 | ||||||||
\(806\) | 6.05640e6 | + | 8.11220e6i | 0.328380 | + | 0.439846i | ||||
\(807\) | −8.54062e6 | + | 1.20710e7i | −0.461642 | + | 0.652466i | ||||
\(808\) | 2.55684e7 | − | 9.42395e6i | 1.37776 | − | 0.507814i | ||||
\(809\) | 359839.i | 0.0193302i | 0.999953 | + | 0.00966511i | \(0.00307655\pi\) | ||||
−0.999953 | + | 0.00966511i | \(0.996923\pi\) | |||||||
\(810\) | 8.08921e6 | + | 2.07374e6i | 0.433205 | + | 0.111056i | ||||
\(811\) | 1.11026e7i | 0.592750i | 0.955072 | + | 0.296375i | \(0.0957778\pi\) | ||||
−0.955072 | + | 0.296375i | \(0.904222\pi\) | |||||||
\(812\) | 225693. | − | 761366.i | 0.0120123 | − | 0.0405231i | ||||
\(813\) | −1.04109e7 | + | 1.47144e7i | −0.552413 | + | 0.780758i | ||||
\(814\) | −2.50676e7 | + | 1.87150e7i | −1.32602 | + | 0.989983i | ||||
\(815\) | 7.75093e6 | 0.408752 | ||||||||
\(816\) | 3.02302e7 | − | 1.20278e7i | 1.58933 | − | 0.632355i | ||||
\(817\) | 3.55911e6 | 0.186546 | ||||||||
\(818\) | 1.10092e7 | − | 8.21928e6i | 0.575274 | − | 0.429487i | ||||
\(819\) | 3.60203e6 | − | 1.27120e6i | 0.187645 | − | 0.0662222i | ||||
\(820\) | −100526. | + | 339120.i | −0.00522087 | + | 0.0176124i | ||||
\(821\) | 2.09829e7i | 1.08644i | 0.839589 | + | 0.543222i | \(0.182796\pi\) | ||||
−0.839589 | + | 0.543222i | \(0.817204\pi\) | |||||||
\(822\) | −106708. | − | 4.17656e6i | −0.00550829 | − | 0.215595i | ||||
\(823\) | − | 3.50985e7i | − | 1.80630i | −0.429330 | − | 0.903148i | \(-0.641250\pi\) | ||
0.429330 | − | 0.903148i | \(-0.358750\pi\) | |||||||
\(824\) | 2.30914e7 | − | 8.51100e6i | 1.18477 | − | 0.436679i | ||||
\(825\) | −5.41889e6 | − | 3.83405e6i | −0.277189 | − | 0.196121i | ||||
\(826\) | 172924. | + | 231622.i | 0.00881873 | + | 0.0118122i | ||||
\(827\) | 4.52044e6 | 0.229836 | 0.114918 | − | 0.993375i | \(-0.463340\pi\) | ||||
0.114918 | + | 0.993375i | \(0.463340\pi\) | |||||||
\(828\) | −3.04971e7 | + | 1.55937e6i | −1.54590 | + | 0.0790450i | ||||
\(829\) | −1.51914e7 | −0.767735 | −0.383867 | − | 0.923388i | \(-0.625408\pi\) | ||||
−0.383867 | + | 0.923388i | \(0.625408\pi\) | |||||||
\(830\) | −5.24543e6 | − | 7.02595e6i | −0.264293 | − | 0.354006i | ||||
\(831\) | 1.17348e7 | + | 8.30281e6i | 0.589488 | + | 0.417083i | ||||
\(832\) | 1.91280e7 | − | 1.63170e7i | 0.957992 | − | 0.817208i | ||||
\(833\) | 3.34007e7i | 1.66780i | ||||||||
\(834\) | −66894.4 | − | 2.61825e6i | −0.00333023 | − | 0.130346i | ||||
\(835\) | − | 2.85009e6i | − | 0.141463i | ||||||
\(836\) | 6.72775e6 | + | 1.99432e6i | 0.332931 | + | 0.0986912i | ||||
\(837\) | −8.49966e6 | − | 2.41192e6i | −0.419361 | − | 0.119000i | ||||
\(838\) | −2.33065e7 | + | 1.74002e7i | −1.14648 | + | 0.855941i | ||||
\(839\) | 1.66391e7 | 0.816068 | 0.408034 | − | 0.912967i | \(-0.366215\pi\) | ||||
0.408034 | + | 0.912967i | \(0.366215\pi\) | |||||||
\(840\) | 375228. | − | 1.39570e6i | 0.0183483 | − | 0.0682486i | ||||
\(841\) | 1.90439e7 | 0.928465 | ||||||||
\(842\) | 1.91498e7 | − | 1.42969e7i | 0.930860 | − | 0.694961i | ||||
\(843\) | −8.06371e6 | + | 1.13969e7i | −0.390810 | + | 0.552355i | ||||
\(844\) | 1.43038e7 | + | 4.24011e6i | 0.691189 | + | 0.204890i | ||||
\(845\) | 5.43551e6i | 0.261878i | ||||||||
\(846\) | −2.22920e7 | − | 1.49329e7i | −1.07084 | − | 0.717327i | ||||
\(847\) | 6.21095e6i | 0.297474i | ||||||||
\(848\) | 9.13494e6 | − | 1.40543e7i | 0.436231 | − | 0.671148i | ||||
\(849\) | −1.70328e7 | + | 2.40735e7i | −0.810995 | + | 1.14623i | ||||
\(850\) | 4.31104e6 | + | 5.77439e6i | 0.204661 | + | 0.274132i | ||||
\(851\) | −3.18745e7 | −1.50876 | ||||||||
\(852\) | 7.87319e6 | − | 6.19733e6i | 0.371579 | − | 0.292486i | ||||
\(853\) | −757984. | −0.0356687 | −0.0178344 | − | 0.999841i | \(-0.505677\pi\) | ||||
−0.0178344 | + | 0.999841i | \(0.505677\pi\) | |||||||
\(854\) | −1.00104e6 | − | 1.34084e6i | −0.0469685 | − | 0.0629116i | ||||
\(855\) | −650687. | − | 1.84376e6i | −0.0304409 | − | 0.0862562i | ||||
\(856\) | −4.76903e6 | − | 1.29390e7i | −0.222457 | − | 0.603553i | ||||
\(857\) | − | 6.79216e6i | − | 0.315905i | −0.987447 | − | 0.157952i | \(-0.949511\pi\) | ||
0.987447 | − | 0.157952i | \(-0.0504892\pi\) | |||||||
\(858\) | 4.60839e7 | − | 1.17741e6i | 2.13713 | − | 0.0546021i | ||||
\(859\) | − | 1.34595e7i | − | 0.622367i | −0.950350 | − | 0.311184i | \(-0.899275\pi\) | ||
0.950350 | − | 0.311184i | \(-0.100725\pi\) | |||||||
\(860\) | 2.51431e6 | − | 8.48193e6i | 0.115924 | − | 0.391065i | ||||
\(861\) | −115266. | − | 81554.4i | −0.00529898 | − | 0.00374921i | ||||
\(862\) | 389730. | − | 290964.i | 0.0178647 | − | 0.0133374i | ||||
\(863\) | 4.32536e7 | 1.97695 | 0.988474 | − | 0.151390i | \(-0.0483751\pi\) | ||||
0.988474 | + | 0.151390i | \(0.0483751\pi\) | |||||||
\(864\) | −4.60734e6 | + | 2.14532e7i | −0.209974 | + | 0.977707i | ||||
\(865\) | −3.10347e6 | −0.141029 | ||||||||
\(866\) | −2.52724e7 | + | 1.88679e7i | −1.14512 | + | 0.854925i | ||||
\(867\) | −3.47967e7 | − | 2.46199e7i | −1.57214 | − | 1.11234i | ||||
\(868\) | −434582. | + | 1.46605e6i | −0.0195782 | + | 0.0660463i | ||||
\(869\) | − | 3.51717e7i | − | 1.57995i | ||||||
\(870\) | −2.66951e6 | + | 68203.9i | −0.119573 | + | 0.00305500i | ||||
\(871\) | 1.81500e7i | 0.810645i | ||||||||
\(872\) | −1.01754e7 | − | 2.76071e7i | −0.453169 | − | 1.22950i | ||||
\(873\) | 8.62652e6 | + | 2.44438e7i | 0.383089 | + | 1.08551i | ||||
\(874\) | 4.27731e6 | + | 5.72921e6i | 0.189405 | + | 0.253698i | ||||
\(875\) | 320109. | 0.0141344 | ||||||||
\(876\) | −2.82495e6 | + | 2.22364e6i | −0.124380 | + | 0.0979047i | ||||
\(877\) | 1.00835e7 | 0.442703 | 0.221351 | − | 0.975194i | \(-0.428953\pi\) | ||||
0.221351 | + | 0.975194i | \(0.428953\pi\) | |||||||
\(878\) | 4.28624e6 | + | 5.74117e6i | 0.187646 | + | 0.251341i | ||||
\(879\) | −1.83595e7 | + | 2.59486e7i | −0.801474 | + | 1.13277i | ||||
\(880\) | 9.50555e6 | − | 1.46244e7i | 0.413781 | − | 0.636608i | ||||
\(881\) | 5.34970e6i | 0.232215i | 0.993237 | + | 0.116107i | \(0.0370416\pi\) | ||||
−0.993237 | + | 0.116107i | \(0.962958\pi\) | |||||||
\(882\) | −1.87152e7 | − | 1.25368e7i | −0.810070 | − | 0.542646i | ||||
\(883\) | 1.63008e7i | 0.703572i | 0.936080 | + | 0.351786i | \(0.114426\pi\) | ||||
−0.936080 | + | 0.351786i | \(0.885574\pi\) | |||||||
\(884\) | −4.79802e7 | − | 1.42228e7i | −2.06505 | − | 0.612146i | ||||
\(885\) | 561413. | − | 793478.i | 0.0240949 | − | 0.0340547i | ||||
\(886\) | −1.10474e7 | + | 8.24778e6i | −0.472799 | + | 0.352982i | ||||
\(887\) | 690733. | 0.0294782 | 0.0147391 | − | 0.999891i | \(-0.495308\pi\) | ||||
0.0147391 | + | 0.999891i | \(0.495308\pi\) | |||||||
\(888\) | −5.94638e6 | + | 2.21182e7i | −0.253058 | + | 0.941275i | ||||
\(889\) | 23578.4 | 0.00100060 | ||||||||
\(890\) | −1.10747e7 | + | 8.26813e6i | −0.468658 | + | 0.349891i | ||||
\(891\) | −3.13205e7 | + | 2.52518e7i | −1.32170 | + | 1.06561i | ||||
\(892\) | −4.04818e7 | − | 1.20001e7i | −1.70352 | − | 0.504977i | ||||
\(893\) | 6.28218e6i | 0.263622i | ||||||||
\(894\) | −592770. | − | 2.32011e7i | −0.0248052 | − | 0.970877i | ||||
\(895\) | 2.48669e6i | 0.103768i | ||||||||
\(896\) | 3.70331e6 | + | 840703.i | 0.154106 | + | 0.0349842i | ||||
\(897\) | 3.83434e7 | + | 2.71293e7i | 1.59115 | + | 1.12579i | ||||
\(898\) | 983198. | + | 1.31694e6i | 0.0406865 | + | 0.0544972i | ||||
\(899\) | 2.82530e6 | 0.116591 | ||||||||
\(900\) | −4.85366e6 | + | 248177.i | −0.199739 | + | 0.0102130i | ||||
\(901\) | −3.33640e7 | −1.36920 | ||||||||
\(902\) | −1.01945e6 | − | 1.36550e6i | −0.0417206 | − | 0.0558823i | ||||
\(903\) | 2.88298e6 | + | 2.03980e6i | 0.117658 | + | 0.0832471i | ||||
\(904\) | −4.07930e7 | + | 1.50354e7i | −1.66022 | + | 0.611920i | ||||
\(905\) | 7.54959e6i | 0.306409i | ||||||||
\(906\) | −66918.3 | − | 2.61919e6i | −0.00270847 | − | 0.106010i | ||||
\(907\) | − | 552634.i | − | 0.0223059i | −0.999938 | − | 0.0111529i | \(-0.996450\pi\) | ||
0.999938 | − | 0.0111529i | \(-0.00355017\pi\) | |||||||
\(908\) | 7.86897e6 | − | 2.65457e7i | 0.316740 | − | 1.06851i | ||||
\(909\) | 3.44950e7 | − | 1.21737e7i | 1.38467 | − | 0.488667i | ||||
\(910\) | −1.78134e6 | + | 1.32991e6i | −0.0713088 | + | 0.0532377i | ||||
\(911\) | 7.62450e6 | 0.304380 | 0.152190 | − | 0.988351i | \(-0.451367\pi\) | ||||
0.152190 | + | 0.988351i | \(0.451367\pi\) | |||||||
\(912\) | 4.77353e6 | − | 1.89927e6i | 0.190043 | − | 0.0756134i | ||||
\(913\) | 4.22424e7 | 1.67715 | ||||||||
\(914\) | 2.01126e7 | − | 1.50157e7i | 0.796348 | − | 0.594537i | ||||
\(915\) | −3.24996e6 | + | 4.59336e6i | −0.128329 | + | 0.181375i | ||||
\(916\) | 9.26659e6 | − | 3.12605e7i | 0.364906 | − | 1.23100i | ||||
\(917\) | 2.84639e6i | 0.111782i | ||||||||
\(918\) | 4.08008e7 | − | 1.55820e7i | 1.59795 | − | 0.610264i | ||||
\(919\) | − | 9.45535e6i | − | 0.369308i | −0.982804 | − | 0.184654i | \(-0.940884\pi\) | ||
0.982804 | − | 0.184654i | \(-0.0591165\pi\) | |||||||
\(920\) | 1.66753e7 | − | 6.14615e6i | 0.649537 | − | 0.239405i | ||||
\(921\) | −4.18662e6 | + | 5.91719e6i | −0.162635 | + | 0.229862i | ||||
\(922\) | 1.65262e7 | + | 2.21358e7i | 0.640243 | + | 0.857568i | ||||
\(923\) | −1.54118e7 | −0.595454 | ||||||||
\(924\) | 4.30667e6 | + | 5.47127e6i | 0.165944 | + | 0.210818i | ||||
\(925\) | −5.07288e6 | −0.194940 | ||||||||
\(926\) | 1.11823e7 | + | 1.49780e7i | 0.428551 | + | 0.574020i | ||||
\(927\) | 3.11533e7 | − | 1.09944e7i | 1.19071 | − | 0.420215i | ||||
\(928\) | −455406. | − | 7.00185e6i | −0.0173591 | − | 0.266897i | ||||
\(929\) | 172428.i | 0.00655493i | 0.999995 | + | 0.00327746i | \(0.00104325\pi\) | ||||
−0.999995 | + | 0.00327746i | \(0.998957\pi\) | |||||||
\(930\) | 5.14027e6 | − | 131330.i | 0.194885 | − | 0.00497916i | ||||
\(931\) | 5.27418e6i | 0.199426i | ||||||||
\(932\) | −3.77636e7 | − | 1.11943e7i | −1.42408 | − | 0.422141i | ||||
\(933\) | −3.68858e7 | − | 2.60980e7i | −1.38725 | − | 0.981528i | ||||
\(934\) | 1.09894e7 | − | 8.20445e6i | 0.412198 | − | 0.307739i | ||||
\(935\) | −3.47176e7 | −1.29873 | ||||||||
\(936\) | 2.59786e7 | − | 2.15459e7i | 0.969227 | − | 0.803850i | ||||
\(937\) | 1.83653e7 | 0.683360 | 0.341680 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341680 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(938\) | −2.19674e6 | + | 1.64004e6i | −0.0815214 | + | 0.0608622i | ||||
\(939\) | 3.43718e7 | + | 2.43192e7i | 1.27215 | + | 0.900089i | ||||
\(940\) | 1.49714e7 | + | 4.43800e6i | 0.552642 | + | 0.163820i | ||||
\(941\) | 1.27692e7i | 0.470100i | 0.971983 | + | 0.235050i | \(0.0755253\pi\) | ||||
−0.971983 | + | 0.235050i | \(0.924475\pi\) | |||||||
\(942\) | −9.63677e6 | + | 246212.i | −0.353838 | + | 0.00904029i | ||||
\(943\) | − | 1.73629e6i | − | 0.0635832i | ||||||
\(944\) | 2.14143e6 | + | 1.39188e6i | 0.0782120 | + | 0.0508360i | ||||
\(945\) | 529627. | − | 1.86642e6i | 0.0192926 | − | 0.0679877i | ||||
\(946\) | 2.54981e7 | + | 3.41532e7i | 0.926361 | + | 1.24081i | ||||
\(947\) | −6.19053e6 | −0.224312 | −0.112156 | − | 0.993691i | \(-0.535776\pi\) | ||||
−0.112156 | + | 0.993691i | \(0.535776\pi\) | |||||||
\(948\) | −1.59271e7 | − | 2.02340e7i | −0.575593 | − | 0.731243i | ||||
\(949\) | 5.52984e6 | 0.199318 | ||||||||
\(950\) | 680741. | + | 911813.i | 0.0244722 | + | 0.0327791i | ||||
\(951\) | 1.17358e6 | − | 1.65870e6i | 0.0420788 | − | 0.0594724i | ||||
\(952\) | −2.61409e6 | − | 7.09236e6i | −0.0934820 | − | 0.253629i | ||||
\(953\) | − | 4.37797e7i | − | 1.56149i | −0.624847 | − | 0.780747i | \(-0.714839\pi\) | ||
0.624847 | − | 0.780747i | \(-0.285161\pi\) | |||||||
\(954\) | 1.25231e7 | − | 1.86946e7i | 0.445492 | − | 0.665036i | ||||
\(955\) | 3.83382e6i | 0.136026i | ||||||||
\(956\) | 5.39385e6 | − | 1.81960e7i | 0.190877 | − | 0.643918i | ||||
\(957\) | 7.43075e6 | − | 1.05023e7i | 0.262273 | − | 0.370685i | ||||
\(958\) | −1.49279e7 | + | 1.11449e7i | −0.525516 | + | 0.392339i | ||||
\(959\) | −970643. | −0.0340810 | ||||||||
\(960\) | −1.15402e6 | − | 1.27178e7i | −0.0404145 | − | 0.445384i | ||||
\(961\) | 2.31889e7 | 0.809975 | ||||||||
\(962\) | 2.82296e7 | − | 2.10756e7i | 0.983482 | − | 0.734247i | ||||
\(963\) | −6.16055e6 | − | 1.74563e7i | −0.214069 | − | 0.606579i | ||||
\(964\) | −7.93315e6 | + | 2.67622e7i | −0.274950 | + | 0.927532i | ||||
\(965\) | − | 1.76285e7i | − | 0.609394i | ||||||
\(966\) | 181201. | + | 7.09223e6i | 0.00624767 | + | 0.244534i | ||||
\(967\) | − | 5.06463e7i | − | 1.74173i | −0.491521 | − | 0.870866i | \(-0.663559\pi\) | ||
0.491521 | − | 0.870866i | \(-0.336441\pi\) | |||||||
\(968\) | 1.89791e7 | + | 5.14927e7i | 0.651008 | + | 1.76627i | ||||
\(969\) | −8.34770e6 | − | 5.90628e6i | −0.285599 | − | 0.202071i | ||||
\(970\) | −9.02496e6 | − | 1.20884e7i | −0.307975 | − | 0.412515i | ||||
\(971\) | 2.44809e7 | 0.833257 | 0.416628 | − | 0.909077i | \(-0.363212\pi\) | ||||
0.416628 | + | 0.909077i | \(0.363212\pi\) | |||||||
\(972\) | −6.58348e6 | + | 2.87103e7i | −0.223506 | + | 0.974702i | ||||
\(973\) | −608489. | −0.0206049 | ||||||||
\(974\) | 3.24408e7 | + | 4.34525e7i | 1.09570 | + | 1.46763i | ||||
\(975\) | 6.10242e6 | + | 4.31767e6i | 0.205585 | + | 0.145458i | ||||
\(976\) | −1.23965e7 | − | 8.05744e6i | −0.416557 | − | 0.270752i | ||||
\(977\) | − | 3.11204e7i | − | 1.04306i | −0.853233 | − | 0.521529i | \(-0.825362\pi\) | ||
0.853233 | − | 0.521529i | \(-0.174638\pi\) | |||||||
\(978\) | 698278. | + | 2.73307e7i | 0.0233443 | + | 0.913699i | ||||
\(979\) | − | 6.65847e7i | − | 2.22033i | ||||||
\(980\) | 1.25692e7 | + | 3.72591e6i | 0.418064 | + | 0.123927i | ||||
\(981\) | −1.31444e7 | − | 3.72455e7i | −0.436082 | − | 1.23567i | ||||
\(982\) | 1.55072e7 | − | 1.15773e7i | 0.513161 | − | 0.383116i | ||||
\(983\) | −1.97896e7 | −0.653209 | −0.326605 | − | 0.945161i | \(-0.605905\pi\) | ||||
−0.326605 | + | 0.945161i | \(0.605905\pi\) | |||||||
\(984\) | −1.20483e6 | − | 323915.i | −0.0396679 | − | 0.0106646i | ||||
\(985\) | −5.25329e6 | −0.172521 | ||||||||
\(986\) | −1.11913e7 | + | 8.35520e6i | −0.366597 | + | 0.273694i | ||||
\(987\) | −3.60045e6 | + | 5.08873e6i | −0.117642 | + | 0.166271i | ||||
\(988\) | −7.57637e6 | − | 2.24587e6i | −0.246927 | − | 0.0731970i | ||||
\(989\) | 4.34273e7i | 1.41180i | ||||||||
\(990\) | 1.30311e7 | − | 1.94530e7i | 0.422565 | − | 0.630812i | ||||
\(991\) | − | 4.81206e7i | − | 1.55649i | −0.627960 | − | 0.778246i | \(-0.716110\pi\) | ||
0.627960 | − | 0.778246i | \(-0.283890\pi\) | |||||||
\(992\) | 876905. | + | 1.34824e7i | 0.0282926 | + | 0.434999i | ||||
\(993\) | −4.93296e6 | + | 6.97205e6i | −0.158758 | + | 0.224382i | ||||
\(994\) | −1.39262e6 | − | 1.86533e6i | −0.0447060 | − | 0.0598811i | ||||
\(995\) | 1.86972e7 | 0.598714 | ||||||||
\(996\) | 2.43018e7 | − | 1.91290e7i | 0.776228 | − | 0.611003i | ||||
\(997\) | 2.32964e6 | 0.0742250 | 0.0371125 | − | 0.999311i | \(-0.488184\pi\) | ||||
0.0371125 | + | 0.999311i | \(0.488184\pi\) | |||||||
\(998\) | 2.27067e6 | + | 3.04143e6i | 0.0721650 | + | 0.0966609i | ||||
\(999\) | −8.39320e6 | + | 2.95779e7i | −0.266081 | + | 0.937677i |
(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 | 60.6.e.a.11.8 | yes | 40 | |
3.2 | odd | 2 | inner | 60.6.e.a.11.33 | yes | 40 | |
4.3 | odd | 2 | inner | 60.6.e.a.11.34 | yes | 40 | |
12.11 | even | 2 | inner | 60.6.e.a.11.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.e.a.11.7 | ✓ | 40 | 12.11 | even | 2 | inner | |
60.6.e.a.11.8 | yes | 40 | 1.1 | even | 1 | trivial | |
60.6.e.a.11.33 | yes | 40 | 3.2 | odd | 2 | inner | |
60.6.e.a.11.34 | yes | 40 | 4.3 | odd | 2 | inner |