Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.5 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.7.b.a.39.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.73539 | − | 2.04054i | −0.966923 | − | 0.255067i | ||||
\(3\) | 48.2920i | 1.78859i | 0.447476 | + | 0.894296i | \(0.352323\pi\) | ||||
−0.447476 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(4\) | 55.6724 | + | 31.5687i | 0.869881 | + | 0.493261i | ||||
\(5\) | −82.2790 | −0.658232 | −0.329116 | − | 0.944290i | \(-0.606751\pi\) | ||||
−0.329116 | + | 0.944290i | \(0.606751\pi\) | |||||||
\(6\) | 98.5416 | − | 373.557i | 0.456211 | − | 1.72943i | ||||
\(7\) | 359.057i | 1.04681i | 0.852083 | + | 0.523407i | \(0.175339\pi\) | ||||
−0.852083 | + | 0.523407i | \(0.824661\pi\) | |||||||
\(8\) | −366.231 | − | 357.798i | −0.715294 | − | 0.698824i | ||||
\(9\) | −1603.11 | −2.19906 | ||||||||
\(10\) | 636.459 | + | 167.893i | 0.636459 | + | 0.167893i | ||||
\(11\) | 2504.92i | 1.88199i | 0.338427 | + | 0.940993i | \(0.390105\pi\) | ||||
−0.338427 | + | 0.940993i | \(0.609895\pi\) | |||||||
\(12\) | −1524.51 | + | 2688.53i | −0.882242 | + | 1.55586i | ||||
\(13\) | −1511.40 | −0.687936 | −0.343968 | − | 0.938981i | \(-0.611771\pi\) | ||||
−0.343968 | + | 0.938981i | \(0.611771\pi\) | |||||||
\(14\) | 732.669 | − | 2777.45i | 0.267008 | − | 1.01219i | ||||
\(15\) | − | 3973.41i | − | 1.17731i | ||||||
\(16\) | 2102.83 | + | 3515.01i | 0.513387 | + | 0.858157i | ||||
\(17\) | 5229.33 | 1.06439 | 0.532194 | − | 0.846623i | \(-0.321368\pi\) | ||||
0.532194 | + | 0.846623i | \(0.321368\pi\) | |||||||
\(18\) | 12400.7 | + | 3271.22i | 2.12632 | + | 0.560908i | ||||
\(19\) | − | 1573.56i | − | 0.229416i | ||||||
\(20\) | −4580.67 | − | 2597.44i | −0.572583 | − | 0.324680i | ||||
\(21\) | −17339.6 | −1.87232 | ||||||||
\(22\) | 5111.39 | − | 19376.5i | 0.480033 | − | 1.81974i | ||||
\(23\) | 11195.6i | 0.920158i | 0.887878 | + | 0.460079i | \(0.152179\pi\) | ||||
−0.887878 | + | 0.460079i | \(0.847821\pi\) | |||||||
\(24\) | 17278.8 | − | 17686.0i | 1.24991 | − | 1.27937i | ||||
\(25\) | −8855.17 | −0.566731 | ||||||||
\(26\) | 11691.2 | + | 3084.06i | 0.665182 | + | 0.175470i | ||||
\(27\) | − | 42212.7i | − | 2.14463i | ||||||
\(28\) | −11335.0 | + | 19989.6i | −0.516352 | + | 0.910604i | ||||
\(29\) | 33925.0 | 1.39100 | 0.695498 | − | 0.718528i | \(-0.255184\pi\) | ||||
0.695498 | + | 0.718528i | \(0.255184\pi\) | |||||||
\(30\) | −8107.90 | + | 30735.9i | −0.300293 | + | 1.13837i | ||||
\(31\) | − | 19449.1i | − | 0.652850i | −0.945223 | − | 0.326425i | \(-0.894156\pi\) | ||
0.945223 | − | 0.326425i | \(-0.105844\pi\) | |||||||
\(32\) | −9093.73 | − | 31480.9i | −0.277519 | − | 0.960720i | ||||
\(33\) | −120968. | −3.36610 | ||||||||
\(34\) | −40450.9 | − | 10670.7i | −1.02918 | − | 0.271490i | ||||
\(35\) | − | 29542.8i | − | 0.689046i | ||||||
\(36\) | −89249.3 | − | 50608.2i | −1.91292 | − | 1.08471i | ||||
\(37\) | −39956.4 | −0.788826 | −0.394413 | − | 0.918933i | \(-0.629052\pi\) | ||||
−0.394413 | + | 0.918933i | \(0.629052\pi\) | |||||||
\(38\) | −3210.91 | + | 12172.1i | −0.0585164 | + | 0.221827i | ||||
\(39\) | − | 72988.3i | − | 1.23044i | ||||||
\(40\) | 30133.1 | + | 29439.2i | 0.470829 | + | 0.459988i | ||||
\(41\) | 49241.4 | 0.714461 | 0.357230 | − | 0.934016i | \(-0.383721\pi\) | ||||
0.357230 | + | 0.934016i | \(0.383721\pi\) | |||||||
\(42\) | 134128. | + | 35382.1i | 1.81039 | + | 0.477568i | ||||
\(43\) | − | 105511.i | − | 1.32706i | −0.748150 | − | 0.663530i | \(-0.769057\pi\) | ||
0.748150 | − | 0.663530i | \(-0.230943\pi\) | |||||||
\(44\) | −79077.1 | + | 139455.i | −0.928310 | + | 1.63710i | ||||
\(45\) | 131903. | 1.44749 | ||||||||
\(46\) | 22845.0 | − | 86602.0i | 0.234702 | − | 0.889722i | ||||
\(47\) | − | 8104.39i | − | 0.0780597i | −0.999238 | − | 0.0390298i | \(-0.987573\pi\) | ||
0.999238 | − | 0.0390298i | \(-0.0124267\pi\) | |||||||
\(48\) | −169747. | + | 101550.i | −1.53489 | + | 0.918240i | ||||
\(49\) | −11273.0 | −0.0958188 | ||||||||
\(50\) | 68498.2 | + | 18069.3i | 0.547986 | + | 0.144555i | ||||
\(51\) | 252535.i | 1.90375i | ||||||||
\(52\) | −84143.0 | − | 47712.8i | −0.598423 | − | 0.339332i | ||||
\(53\) | 244054. | 1.63930 | 0.819648 | − | 0.572867i | \(-0.194169\pi\) | ||||
0.819648 | + | 0.572867i | \(0.194169\pi\) | |||||||
\(54\) | −86136.7 | + | 326532.i | −0.547024 | + | 2.07369i | ||||
\(55\) | − | 206102.i | − | 1.23878i | ||||||
\(56\) | 128470. | − | 131498.i | 0.731538 | − | 0.748779i | ||||
\(57\) | 75990.4 | 0.410331 | ||||||||
\(58\) | −262423. | − | 69225.3i | −1.34499 | − | 0.354798i | ||||
\(59\) | − | 26040.5i | − | 0.126792i | −0.997988 | − | 0.0633962i | \(-0.979807\pi\) | ||
0.997988 | − | 0.0633962i | \(-0.0201932\pi\) | |||||||
\(60\) | 125435. | − | 221209.i | 0.580720 | − | 1.02412i | ||||
\(61\) | 62773.1 | 0.276556 | 0.138278 | − | 0.990393i | \(-0.455843\pi\) | ||||
0.138278 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(62\) | −39686.6 | + | 150446.i | −0.166521 | + | 0.631256i | ||||
\(63\) | − | 575610.i | − | 2.30201i | ||||||
\(64\) | 6105.59 | + | 262073.i | 0.0232910 | + | 0.999729i | ||||
\(65\) | 124356. | 0.452821 | ||||||||
\(66\) | 935732. | + | 246839.i | 3.25476 | + | 0.858583i | ||||
\(67\) | 473921.i | 1.57573i | 0.615849 | + | 0.787865i | \(0.288813\pi\) | ||||
−0.615849 | + | 0.787865i | \(0.711187\pi\) | |||||||
\(68\) | 291130. | + | 165083.i | 0.925891 | + | 0.525020i | ||||
\(69\) | −540656. | −1.64579 | ||||||||
\(70\) | −60283.3 | + | 228525.i | −0.175753 | + | 0.666254i | ||||
\(71\) | − | 140823.i | − | 0.393458i | −0.980458 | − | 0.196729i | \(-0.936968\pi\) | ||
0.980458 | − | 0.196729i | \(-0.0630320\pi\) | |||||||
\(72\) | 587110. | + | 573591.i | 1.57297 | + | 1.53676i | ||||
\(73\) | −569273. | −1.46336 | −0.731681 | − | 0.681647i | \(-0.761264\pi\) | ||||
−0.731681 | + | 0.681647i | \(0.761264\pi\) | |||||||
\(74\) | 309078. | + | 81532.6i | 0.762735 | + | 0.201204i | ||||
\(75\) | − | 427634.i | − | 1.01365i | ||||||
\(76\) | 49675.3 | − | 87604.0i | 0.113162 | − | 0.199564i | ||||
\(77\) | −899410. | −1.97009 | ||||||||
\(78\) | −148935. | + | 564593.i | −0.313844 | + | 1.18974i | ||||
\(79\) | − | 52609.7i | − | 0.106705i | −0.998576 | − | 0.0533525i | \(-0.983009\pi\) | ||
0.998576 | − | 0.0533525i | \(-0.0169907\pi\) | |||||||
\(80\) | −173019. | − | 289211.i | −0.337928 | − | 0.564866i | ||||
\(81\) | 869865. | 1.63680 | ||||||||
\(82\) | −380901. | − | 100479.i | −0.690829 | − | 0.182236i | ||||
\(83\) | 513228.i | 0.897587i | 0.893636 | + | 0.448793i | \(0.148146\pi\) | ||||
−0.893636 | + | 0.448793i | \(0.851854\pi\) | |||||||
\(84\) | −965336. | − | 547388.i | −1.62870 | − | 0.923543i | ||||
\(85\) | −430264. | −0.700613 | ||||||||
\(86\) | −215298. | + | 816165.i | −0.338490 | + | 1.28317i | ||||
\(87\) | 1.63831e6i | 2.48792i | ||||||||
\(88\) | 896256. | − | 917379.i | 1.31518 | − | 1.34617i | ||||
\(89\) | −700620. | −0.993831 | −0.496915 | − | 0.867799i | \(-0.665534\pi\) | ||||
−0.496915 | + | 0.867799i | \(0.665534\pi\) | |||||||
\(90\) | −1.02032e6 | − | 269152.i | −1.39961 | − | 0.369207i | ||||
\(91\) | − | 542677.i | − | 0.720141i | ||||||
\(92\) | −353429. | + | 623284.i | −0.453878 | + | 0.800428i | ||||
\(93\) | 939234. | 1.16768 | ||||||||
\(94\) | −16537.3 | + | 62690.6i | −0.0199105 | + | 0.0754777i | ||||
\(95\) | 129471.i | 0.151009i | ||||||||
\(96\) | 1.52027e6 | − | 439154.i | 1.71834 | − | 0.496367i | ||||
\(97\) | 337832. | 0.370157 | 0.185078 | − | 0.982724i | \(-0.440746\pi\) | ||||
0.185078 | + | 0.982724i | \(0.440746\pi\) | |||||||
\(98\) | 87200.9 | + | 23002.9i | 0.0926494 | + | 0.0244402i | ||||
\(99\) | − | 4.01568e6i | − | 4.13860i | ||||||
\(100\) | −492989. | − | 279546.i | −0.492989 | − | 0.279546i | ||||
\(101\) | −878050. | −0.852227 | −0.426113 | − | 0.904670i | \(-0.640118\pi\) | ||||
−0.426113 | + | 0.904670i | \(0.640118\pi\) | |||||||
\(102\) | 515307. | − | 1.95345e6i | 0.485585 | − | 1.84078i | ||||
\(103\) | 861088.i | 0.788017i | 0.919107 | + | 0.394009i | \(0.128912\pi\) | ||||
−0.919107 | + | 0.394009i | \(0.871088\pi\) | |||||||
\(104\) | 553519. | + | 540774.i | 0.492077 | + | 0.480746i | ||||
\(105\) | 1.42668e6 | 1.23242 | ||||||||
\(106\) | −1.88785e6 | − | 498001.i | −1.58507 | − | 0.418131i | ||||
\(107\) | 1.31051e6i | 1.06977i | 0.844925 | + | 0.534885i | \(0.179645\pi\) | ||||
−0.844925 | + | 0.534885i | \(0.820355\pi\) | |||||||
\(108\) | 1.33260e6 | − | 2.35008e6i | 1.05786 | − | 1.86557i | ||||
\(109\) | 1.98114e6 | 1.52980 | 0.764901 | − | 0.644148i | \(-0.222788\pi\) | ||||
0.764901 | + | 0.644148i | \(0.222788\pi\) | |||||||
\(110\) | −420560. | + | 1.59428e6i | −0.315973 | + | 1.19781i | ||||
\(111\) | − | 1.92957e6i | − | 1.41089i | ||||||
\(112\) | −1.26209e6 | + | 755038.i | −0.898330 | + | 0.537421i | ||||
\(113\) | −1.82029e6 | −1.26155 | −0.630775 | − | 0.775966i | \(-0.717263\pi\) | ||||
−0.630775 | + | 0.775966i | \(0.717263\pi\) | |||||||
\(114\) | −587815. | − | 155061.i | −0.396759 | − | 0.104662i | ||||
\(115\) | − | 921159.i | − | 0.605677i | ||||||
\(116\) | 1.88869e6 | + | 1.07097e6i | 1.21000 | + | 0.686124i | ||||
\(117\) | 2.42294e6 | 1.51281 | ||||||||
\(118\) | −53136.7 | + | 201433.i | −0.0323406 | + | 0.122599i | ||||
\(119\) | 1.87763e6i | 1.11421i | ||||||||
\(120\) | −1.42168e6 | + | 1.45519e6i | −0.822730 | + | 0.842121i | ||||
\(121\) | −4.50308e6 | −2.54187 | ||||||||
\(122\) | −485574. | − | 128091.i | −0.267409 | − | 0.0705405i | ||||
\(123\) | 2.37796e6i | 1.27788i | ||||||||
\(124\) | 613982. | − | 1.08278e6i | 0.322026 | − | 0.567902i | ||||
\(125\) | 2.01420e6 | 1.03127 | ||||||||
\(126\) | −1.17455e6 | + | 4.45256e6i | −0.587166 | + | 2.22586i | ||||
\(127\) | 1.69166e6i | 0.825851i | 0.910765 | + | 0.412926i | \(0.135493\pi\) | ||||
−0.910765 | + | 0.412926i | \(0.864507\pi\) | |||||||
\(128\) | 487540. | − | 2.03969e6i | 0.232477 | − | 0.972602i | ||||
\(129\) | 5.09531e6 | 2.37357 | ||||||||
\(130\) | −961942. | − | 253753.i | −0.437843 | − | 0.115500i | ||||
\(131\) | − | 907898.i | − | 0.403853i | −0.979401 | − | 0.201926i | \(-0.935280\pi\) | ||
0.979401 | − | 0.201926i | \(-0.0647202\pi\) | |||||||
\(132\) | −6.73456e6 | − | 3.81879e6i | −2.92811 | − | 1.66037i | ||||
\(133\) | 564999. | 0.240156 | ||||||||
\(134\) | 967054. | − | 3.66596e6i | 0.401917 | − | 1.52361i | ||||
\(135\) | 3.47322e6i | 1.41166i | ||||||||
\(136\) | −1.91514e6 | − | 1.87104e6i | −0.761350 | − | 0.743819i | ||||
\(137\) | −2.20338e6 | −0.856896 | −0.428448 | − | 0.903566i | \(-0.640940\pi\) | ||||
−0.428448 | + | 0.903566i | \(0.640940\pi\) | |||||||
\(138\) | 4.18218e6 | + | 1.10323e6i | 1.59135 | + | 0.419786i | ||||
\(139\) | 670706.i | 0.249740i | 0.992173 | + | 0.124870i | \(0.0398514\pi\) | ||||
−0.992173 | + | 0.124870i | \(0.960149\pi\) | |||||||
\(140\) | 932629. | − | 1.64472e6i | 0.339879 | − | 0.599388i | ||||
\(141\) | 391377. | 0.139617 | ||||||||
\(142\) | −287355. | + | 1.08932e6i | −0.100358 | + | 0.380444i | ||||
\(143\) | − | 3.78593e6i | − | 1.29469i | ||||||
\(144\) | −3.37109e6 | − | 5.63497e6i | −1.12897 | − | 1.88714i | ||||
\(145\) | −2.79131e6 | −0.915598 | ||||||||
\(146\) | 4.40355e6 | + | 1.16162e6i | 1.41496 | + | 0.373256i | ||||
\(147\) | − | 544395.i | − | 0.171381i | ||||||
\(148\) | −2.22447e6 | − | 1.26137e6i | −0.686185 | − | 0.389097i | ||||
\(149\) | 3.07570e6 | 0.929790 | 0.464895 | − | 0.885366i | \(-0.346092\pi\) | ||||
0.464895 | + | 0.885366i | \(0.346092\pi\) | |||||||
\(150\) | −872603. | + | 3.30791e6i | −0.258549 | + | 0.980122i | ||||
\(151\) | − | 770677.i | − | 0.223842i | −0.993717 | − | 0.111921i | \(-0.964300\pi\) | ||
0.993717 | − | 0.111921i | \(-0.0357004\pi\) | |||||||
\(152\) | −563017. | + | 576287.i | −0.160321 | + | 0.164100i | ||||
\(153\) | −8.38322e6 | −2.34065 | ||||||||
\(154\) | 6.95728e6 | + | 1.83528e6i | 1.90492 | + | 0.502505i | ||||
\(155\) | 1.60025e6i | 0.429727i | ||||||||
\(156\) | 2.30414e6 | − | 4.06343e6i | 0.606926 | − | 1.07033i | ||||
\(157\) | −5.26942e6 | −1.36165 | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(158\) | −107352. | + | 406956.i | −0.0272169 | + | 0.103175i | ||||
\(159\) | 1.17858e7i | 2.93203i | ||||||||
\(160\) | 748223. | + | 2.59021e6i | 0.182672 | + | 0.632376i | ||||
\(161\) | −4.01984e6 | −0.963233 | ||||||||
\(162\) | −6.72874e6 | − | 1.77499e6i | −1.58266 | − | 0.417495i | ||||
\(163\) | − | 4.60269e6i | − | 1.06279i | −0.847123 | − | 0.531397i | \(-0.821667\pi\) | ||
0.847123 | − | 0.531397i | \(-0.178333\pi\) | |||||||
\(164\) | 2.74138e6 | + | 1.55449e6i | 0.621496 | + | 0.352416i | ||||
\(165\) | 9.95309e6 | 2.21568 | ||||||||
\(166\) | 1.04726e6 | − | 3.97002e6i | 0.228945 | − | 0.867898i | ||||
\(167\) | 5.06489e6i | 1.08748i | 0.839254 | + | 0.543739i | \(0.182992\pi\) | ||||
−0.839254 | + | 0.543739i | \(0.817008\pi\) | |||||||
\(168\) | 6.35028e6 | + | 6.20406e6i | 1.33926 | + | 1.30842i | ||||
\(169\) | −2.54249e6 | −0.526744 | ||||||||
\(170\) | 3.32826e6 | + | 877970.i | 0.677439 | + | 0.178703i | ||||
\(171\) | 2.52260e6i | 0.504499i | ||||||||
\(172\) | 3.33083e6 | − | 5.87403e6i | 0.654587 | − | 1.15439i | ||||
\(173\) | 3.89476e6 | 0.752215 | 0.376108 | − | 0.926576i | \(-0.377262\pi\) | ||||
0.376108 | + | 0.926576i | \(0.377262\pi\) | |||||||
\(174\) | 3.34303e6 | − | 1.26729e7i | 0.634588 | − | 2.40563i | ||||
\(175\) | − | 3.17951e6i | − | 0.593262i | ||||||
\(176\) | −8.80483e6 | + | 5.26744e6i | −1.61504 | + | 0.966188i | ||||
\(177\) | 1.25755e6 | 0.226780 | ||||||||
\(178\) | 5.41957e6 | + | 1.42964e6i | 0.960958 | + | 0.253494i | ||||
\(179\) | − | 2.86319e6i | − | 0.499219i | −0.968347 | − | 0.249610i | \(-0.919698\pi\) | ||
0.968347 | − | 0.249610i | \(-0.0803023\pi\) | |||||||
\(180\) | 7.34334e6 | + | 4.16399e6i | 1.25915 | + | 0.713991i | ||||
\(181\) | 2.04811e6 | 0.345396 | 0.172698 | − | 0.984975i | \(-0.444751\pi\) | ||||
0.172698 | + | 0.984975i | \(0.444751\pi\) | |||||||
\(182\) | −1.10735e6 | + | 4.19782e6i | −0.183684 | + | 0.696321i | ||||
\(183\) | 3.03143e6i | 0.494647i | ||||||||
\(184\) | 4.00574e6 | − | 4.10015e6i | 0.643028 | − | 0.658183i | ||||
\(185\) | 3.28757e6 | 0.519230 | ||||||||
\(186\) | −7.26534e6 | − | 1.91654e6i | −1.12906 | − | 0.297838i | ||||
\(187\) | 1.30991e7i | 2.00316i | ||||||||
\(188\) | 255845. | − | 451191.i | 0.0385038 | − | 0.0679027i | ||||
\(189\) | 1.51568e7 | 2.24503 | ||||||||
\(190\) | 264191. | − | 1.00151e6i | 0.0385174 | − | 0.146014i | ||||
\(191\) | − | 8.77547e6i | − | 1.25942i | −0.776830 | − | 0.629710i | \(-0.783174\pi\) | ||
0.776830 | − | 0.629710i | \(-0.216826\pi\) | |||||||
\(192\) | −1.26560e7 | + | 294851.i | −1.78811 | + | 0.0416580i | ||||
\(193\) | −4.12144e6 | −0.573293 | −0.286646 | − | 0.958036i | \(-0.592541\pi\) | ||||
−0.286646 | + | 0.958036i | \(0.592541\pi\) | |||||||
\(194\) | −2.61326e6 | − | 689359.i | −0.357913 | − | 0.0944149i | ||||
\(195\) | 6.00540e6i | 0.809912i | ||||||||
\(196\) | −627594. | − | 355873.i | −0.0833510 | − | 0.0472636i | ||||
\(197\) | 3.10926e6 | 0.406685 | 0.203343 | − | 0.979108i | \(-0.434819\pi\) | ||||
0.203343 | + | 0.979108i | \(0.434819\pi\) | |||||||
\(198\) | −8.19414e6 | + | 3.10628e7i | −1.05562 | + | 4.00171i | ||||
\(199\) | − | 9.11949e6i | − | 1.15721i | −0.815609 | − | 0.578604i | \(-0.803598\pi\) | ||
0.815609 | − | 0.578604i | \(-0.196402\pi\) | |||||||
\(200\) | 3.24304e6 | + | 3.16836e6i | 0.405379 | + | 0.396045i | ||||
\(201\) | −2.28866e7 | −2.81834 | ||||||||
\(202\) | 6.79206e6 | + | 1.79169e6i | 0.824038 | + | 0.217375i | ||||
\(203\) | 1.21810e7i | 1.45611i | ||||||||
\(204\) | −7.97220e6 | + | 1.40592e7i | −0.939047 | + | 1.65604i | ||||
\(205\) | −4.05153e6 | −0.470281 | ||||||||
\(206\) | 1.75708e6 | − | 6.66085e6i | 0.200997 | − | 0.761952i | ||||
\(207\) | − | 1.79478e7i | − | 2.02348i | ||||||
\(208\) | −3.17822e6 | − | 5.31257e6i | −0.353178 | − | 0.590357i | ||||
\(209\) | 3.94165e6 | 0.431757 | ||||||||
\(210\) | −1.10359e7 | − | 2.91120e6i | −1.19166 | − | 0.314350i | ||||
\(211\) | − | 8.39339e6i | − | 0.893491i | −0.894661 | − | 0.446745i | \(-0.852583\pi\) | ||
0.894661 | − | 0.446745i | \(-0.147417\pi\) | |||||||
\(212\) | 1.35871e7 | + | 7.70445e6i | 1.42599 | + | 0.808601i | ||||
\(213\) | 6.80062e6 | 0.703736 | ||||||||
\(214\) | 2.67415e6 | − | 1.01373e7i | 0.272863 | − | 1.03439i | ||||
\(215\) | 8.68130e6i | 0.873513i | ||||||||
\(216\) | −1.51036e7 | + | 1.54596e7i | −1.49872 | + | 1.53404i | ||||
\(217\) | 6.98332e6 | 0.683413 | ||||||||
\(218\) | −1.53249e7 | − | 4.04258e6i | −1.47920 | − | 0.390202i | ||||
\(219\) | − | 2.74913e7i | − | 2.61736i | ||||||
\(220\) | 6.50638e6 | − | 1.14742e7i | 0.611043 | − | 1.07759i | ||||
\(221\) | −7.90359e6 | −0.732230 | ||||||||
\(222\) | −3.93737e6 | + | 1.49260e7i | −0.359871 | + | 1.36422i | ||||
\(223\) | 3.92014e6i | 0.353498i | 0.984256 | + | 0.176749i | \(0.0565581\pi\) | ||||
−0.984256 | + | 0.176749i | \(0.943442\pi\) | |||||||
\(224\) | 1.13034e7 | − | 3.26517e6i | 1.00570 | − | 0.290510i | ||||
\(225\) | 1.41959e7 | 1.24628 | ||||||||
\(226\) | 1.40806e7 | + | 3.71436e6i | 1.21982 | + | 0.321780i | ||||
\(227\) | 82538.0i | 0.00705629i | 0.999994 | + | 0.00352814i | \(0.00112305\pi\) | ||||
−0.999994 | + | 0.00352814i | \(0.998877\pi\) | |||||||
\(228\) | 4.23057e6 | + | 2.39892e6i | 0.356939 | + | 0.202400i | ||||
\(229\) | −1.01294e6 | −0.0843487 | −0.0421743 | − | 0.999110i | \(-0.513428\pi\) | ||||
−0.0421743 | + | 0.999110i | \(0.513428\pi\) | |||||||
\(230\) | −1.87966e6 | + | 7.12552e6i | −0.154488 | + | 0.585643i | ||||
\(231\) | − | 4.34343e7i | − | 3.52368i | ||||||
\(232\) | −1.24244e7 | − | 1.21383e7i | −0.994972 | − | 0.972061i | ||||
\(233\) | 1.68646e7 | 1.33324 | 0.666619 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666619 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(234\) | −1.87424e7 | − | 4.94410e6i | −1.46277 | − | 0.385869i | ||||
\(235\) | 666821.i | 0.0513814i | ||||||||
\(236\) | 822065. | − | 1.44974e6i | 0.0625418 | − | 0.110294i | ||||
\(237\) | 2.54063e6 | 0.190852 | ||||||||
\(238\) | 3.83137e6 | − | 1.45242e7i | 0.284200 | − | 1.07736i | ||||
\(239\) | 1.36074e7i | 0.996742i | 0.866964 | + | 0.498371i | \(0.166068\pi\) | ||||
−0.866964 | + | 0.498371i | \(0.833932\pi\) | |||||||
\(240\) | 1.39666e7 | − | 8.35543e6i | 1.01031 | − | 0.604415i | ||||
\(241\) | 2.21346e6 | 0.158133 | 0.0790663 | − | 0.996869i | \(-0.474806\pi\) | ||||
0.0790663 | + | 0.996869i | \(0.474806\pi\) | |||||||
\(242\) | 3.48330e7 | + | 9.18869e6i | 2.45779 | + | 0.648347i | ||||
\(243\) | 1.12344e7i | 0.782947i | ||||||||
\(244\) | 3.49473e6 | + | 1.98166e6i | 0.240571 | + | 0.136414i | ||||
\(245\) | 927529. | 0.0630709 | ||||||||
\(246\) | 4.85232e6 | − | 1.83945e7i | 0.325945 | − | 1.23561i | ||||
\(247\) | 2.37828e6i | 0.157823i | ||||||||
\(248\) | −6.95883e6 | + | 7.12284e6i | −0.456227 | + | 0.466980i | ||||
\(249\) | −2.47848e7 | −1.60542 | ||||||||
\(250\) | −1.55806e7 | − | 4.11006e6i | −0.997161 | − | 0.263044i | ||||
\(251\) | − | 1.15827e6i | − | 0.0732466i | −0.999329 | − | 0.0366233i | \(-0.988340\pi\) | ||
0.999329 | − | 0.0366233i | \(-0.0116602\pi\) | |||||||
\(252\) | 1.81712e7 | − | 3.20456e7i | 1.13549 | − | 2.00247i | ||||
\(253\) | −2.80440e7 | −1.73172 | ||||||||
\(254\) | 3.45189e6 | − | 1.30856e7i | 0.210648 | − | 0.798535i | ||||
\(255\) | − | 2.07783e7i | − | 1.25311i | ||||||
\(256\) | −7.93339e6 | + | 1.47830e7i | −0.472867 | + | 0.881134i | ||||
\(257\) | −2.11096e7 | −1.24360 | −0.621801 | − | 0.783175i | \(-0.713599\pi\) | ||||
−0.621801 | + | 0.783175i | \(0.713599\pi\) | |||||||
\(258\) | −3.94142e7 | − | 1.03972e7i | −2.29506 | − | 0.605420i | ||||
\(259\) | − | 1.43466e7i | − | 0.825754i | ||||||
\(260\) | 6.92320e6 | + | 3.92576e6i | 0.393901 | + | 0.223359i | ||||
\(261\) | −5.43857e7 | −3.05889 | ||||||||
\(262\) | −1.85260e6 | + | 7.02294e6i | −0.103010 | + | 0.390495i | ||||
\(263\) | 2.63276e7i | 1.44725i | 0.690193 | + | 0.723625i | \(0.257525\pi\) | ||||
−0.690193 | + | 0.723625i | \(0.742475\pi\) | |||||||
\(264\) | 4.43020e7 | + | 4.32819e7i | 2.40775 | + | 2.35231i | ||||
\(265\) | −2.00805e7 | −1.07904 | ||||||||
\(266\) | −4.37048e6 | − | 1.15290e6i | −0.232212 | − | 0.0612558i | ||||
\(267\) | − | 3.38343e7i | − | 1.77756i | ||||||
\(268\) | −1.49611e7 | + | 2.63843e7i | −0.777245 | + | 1.37070i | ||||
\(269\) | 2.21101e7 | 1.13589 | 0.567943 | − | 0.823068i | \(-0.307739\pi\) | ||||
0.567943 | + | 0.823068i | \(0.307739\pi\) | |||||||
\(270\) | 7.08723e6 | − | 2.68667e7i | 0.360069 | − | 1.36497i | ||||
\(271\) | − | 5.23582e6i | − | 0.263073i | −0.991311 | − | 0.131537i | \(-0.958009\pi\) | ||
0.991311 | − | 0.131537i | \(-0.0419911\pi\) | |||||||
\(272\) | 1.09964e7 | + | 1.83812e7i | 0.546443 | + | 0.913411i | ||||
\(273\) | 2.62070e7 | 1.28804 | ||||||||
\(274\) | 1.70440e7 | + | 4.49609e6i | 0.828553 | + | 0.218566i | ||||
\(275\) | − | 2.21815e7i | − | 1.06658i | ||||||
\(276\) | −3.00996e7 | − | 1.70678e7i | −1.43164 | − | 0.811802i | ||||
\(277\) | 1.18508e7 | 0.557582 | 0.278791 | − | 0.960352i | \(-0.410066\pi\) | ||||
0.278791 | + | 0.960352i | \(0.410066\pi\) | |||||||
\(278\) | 1.36860e6 | − | 5.18817e6i | 0.0637004 | − | 0.241479i | ||||
\(279\) | 3.11791e7i | 1.43566i | ||||||||
\(280\) | −1.05704e7 | + | 1.08195e7i | −0.481522 | + | 0.492870i | ||||
\(281\) | −2.01629e7 | −0.908731 | −0.454365 | − | 0.890815i | \(-0.650134\pi\) | ||||
−0.454365 | + | 0.890815i | \(0.650134\pi\) | |||||||
\(282\) | −3.02745e6 | − | 798620.i | −0.134999 | − | 0.0356117i | ||||
\(283\) | 2.46061e7i | 1.08563i | 0.839851 | + | 0.542817i | \(0.182642\pi\) | ||||
−0.839851 | + | 0.542817i | \(0.817358\pi\) | |||||||
\(284\) | 4.44560e6 | − | 7.83996e6i | 0.194078 | − | 0.342262i | ||||
\(285\) | −6.25241e6 | −0.270093 | ||||||||
\(286\) | −7.72533e6 | + | 2.92856e7i | −0.330232 | + | 1.25186i | ||||
\(287\) | 1.76805e7i | 0.747907i | ||||||||
\(288\) | 1.45783e7 | + | 5.04675e7i | 0.610280 | + | 2.11268i | ||||
\(289\) | 3.20836e6 | 0.132920 | ||||||||
\(290\) | 2.15919e7 | + | 5.69578e6i | 0.885313 | + | 0.233539i | ||||
\(291\) | 1.63146e7i | 0.662059i | ||||||||
\(292\) | −3.16928e7 | − | 1.79712e7i | −1.27295 | − | 0.721819i | ||||
\(293\) | −3.40820e7 | −1.35495 | −0.677474 | − | 0.735547i | \(-0.736925\pi\) | ||||
−0.677474 | + | 0.735547i | \(0.736925\pi\) | |||||||
\(294\) | −1.11086e6 | + | 4.21110e6i | −0.0437136 | + | 0.165712i | ||||
\(295\) | 2.14259e6i | 0.0834588i | ||||||||
\(296\) | 1.46333e7 | + | 1.42963e7i | 0.564243 | + | 0.551251i | ||||
\(297\) | 1.05740e8 | 4.03616 | ||||||||
\(298\) | −2.37917e7 | − | 6.27608e6i | −0.899036 | − | 0.237159i | ||||
\(299\) | − | 1.69209e7i | − | 0.633010i | ||||||
\(300\) | 1.34998e7 | − | 2.38074e7i | 0.499994 | − | 0.881756i | ||||
\(301\) | 3.78843e7 | 1.38918 | ||||||||
\(302\) | −1.57260e6 | + | 5.96148e6i | −0.0570947 | + | 0.216438i | ||||
\(303\) | − | 4.24028e7i | − | 1.52429i | ||||||
\(304\) | 5.53109e6 | − | 3.30894e6i | 0.196875 | − | 0.117779i | ||||
\(305\) | −5.16490e6 | −0.182038 | ||||||||
\(306\) | 6.48475e7 | + | 1.71063e7i | 2.26323 | + | 0.597023i | ||||
\(307\) | − | 2.89285e7i | − | 0.999793i | −0.866085 | − | 0.499897i | \(-0.833371\pi\) | ||
0.866085 | − | 0.499897i | \(-0.166629\pi\) | |||||||
\(308\) | −5.00723e7 | − | 2.83932e7i | −1.71374 | − | 0.971767i | ||||
\(309\) | −4.15836e7 | −1.40944 | ||||||||
\(310\) | 3.26537e6 | − | 1.23785e7i | 0.109609 | − | 0.415513i | ||||
\(311\) | 5.75337e7i | 1.91267i | 0.292265 | + | 0.956337i | \(0.405591\pi\) | ||||
−0.292265 | + | 0.956337i | \(0.594409\pi\) | |||||||
\(312\) | −2.61150e7 | + | 2.67305e7i | −0.859858 | + | 0.880124i | ||||
\(313\) | 4.64530e7 | 1.51489 | 0.757444 | − | 0.652900i | \(-0.226448\pi\) | ||||
0.757444 | + | 0.652900i | \(0.226448\pi\) | |||||||
\(314\) | 4.07610e7 | + | 1.07525e7i | 1.31661 | + | 0.347311i | ||||
\(315\) | 4.73606e7i | 1.51525i | ||||||||
\(316\) | 1.66082e6 | − | 2.92891e6i | 0.0526334 | − | 0.0928206i | ||||
\(317\) | 2.19991e7 | 0.690599 | 0.345300 | − | 0.938492i | \(-0.387777\pi\) | ||||
0.345300 | + | 0.938492i | \(0.387777\pi\) | |||||||
\(318\) | 2.40494e7 | − | 9.11679e7i | 0.747865 | − | 2.83505i | ||||
\(319\) | 8.49795e7i | 2.61784i | ||||||||
\(320\) | −502362. | − | 2.15631e7i | −0.0153309 | − | 0.658053i | ||||
\(321\) | −6.32873e7 | −1.91338 | ||||||||
\(322\) | 3.10950e7 | + | 8.20264e6i | 0.931373 | + | 0.245689i | ||||
\(323\) | − | 8.22868e6i | − | 0.244187i | ||||||
\(324\) | 4.84275e7 | + | 2.74605e7i | 1.42383 | + | 0.807372i | ||||
\(325\) | 1.33837e7 | 0.389875 | ||||||||
\(326\) | −9.39196e6 | + | 3.56036e7i | −0.271084 | + | 1.02764i | ||||
\(327\) | 9.56730e7i | 2.73619i | ||||||||
\(328\) | −1.80337e7 | − | 1.76184e7i | −0.511049 | − | 0.499282i | ||||
\(329\) | 2.90994e6 | 0.0817139 | ||||||||
\(330\) | −7.69910e7 | − | 2.03097e7i | −2.14239 | − | 0.565146i | ||||
\(331\) | 978340.i | 0.0269778i | 0.999909 | + | 0.0134889i | \(0.00429377\pi\) | ||||
−0.999909 | + | 0.0134889i | \(0.995706\pi\) | |||||||
\(332\) | −1.62020e7 | + | 2.85727e7i | −0.442744 | + | 0.780794i | ||||
\(333\) | 6.40547e7 | 1.73468 | ||||||||
\(334\) | 1.03351e7 | − | 3.91789e7i | 0.277380 | − | 1.05151i | ||||
\(335\) | − | 3.89937e7i | − | 1.03719i | ||||||
\(336\) | −3.64623e7 | − | 6.09488e7i | −0.961227 | − | 1.60675i | ||||
\(337\) | 7.26346e7 | 1.89781 | 0.948907 | − | 0.315556i | \(-0.102191\pi\) | ||||
0.948907 | + | 0.315556i | \(0.102191\pi\) | |||||||
\(338\) | 1.96672e7 | + | 5.18805e6i | 0.509321 | + | 0.134355i | ||||
\(339\) | − | 8.79052e7i | − | 2.25640i | ||||||
\(340\) | −2.39538e7 | − | 1.35829e7i | −0.609450 | − | 0.345585i | ||||
\(341\) | 4.87184e7 | 1.22865 | ||||||||
\(342\) | 5.14746e6 | − | 1.95133e7i | 0.128681 | − | 0.487812i | ||||
\(343\) | 3.81951e7i | 0.946509i | ||||||||
\(344\) | −3.77514e7 | + | 3.86412e7i | −0.927381 | + | 0.949238i | ||||
\(345\) | 4.44846e7 | 1.08331 | ||||||||
\(346\) | −3.01274e7 | − | 7.94740e6i | −0.727334 | − | 0.191865i | ||||
\(347\) | 4.28971e6i | 0.102669i | 0.998682 | + | 0.0513345i | \(0.0163475\pi\) | ||||
−0.998682 | + | 0.0513345i | \(0.983653\pi\) | |||||||
\(348\) | −5.17192e7 | + | 9.12085e7i | −1.22720 | + | 2.16420i | ||||
\(349\) | −2.78572e7 | −0.655331 | −0.327666 | − | 0.944794i | \(-0.606262\pi\) | ||||
−0.327666 | + | 0.944794i | \(0.606262\pi\) | |||||||
\(350\) | −6.48792e6 | + | 2.45948e7i | −0.151322 | + | 0.573639i | ||||
\(351\) | 6.38001e7i | 1.47537i | ||||||||
\(352\) | 7.88572e7 | − | 2.27791e7i | 1.80806 | − | 0.522286i | ||||
\(353\) | −2.47434e7 | −0.562516 | −0.281258 | − | 0.959632i | \(-0.590752\pi\) | ||||
−0.281258 | + | 0.959632i | \(0.590752\pi\) | |||||||
\(354\) | −9.72762e6 | − | 2.56607e6i | −0.219279 | − | 0.0578441i | ||||
\(355\) | 1.15868e7i | 0.258987i | ||||||||
\(356\) | −3.90052e7 | − | 2.21177e7i | −0.864515 | − | 0.490218i | ||||
\(357\) | −9.06744e7 | −1.99288 | ||||||||
\(358\) | −5.84245e6 | + | 2.21479e7i | −0.127334 | + | 0.482707i | ||||
\(359\) | − | 3.58715e7i | − | 0.775293i | −0.921808 | − | 0.387647i | \(-0.873288\pi\) | ||
0.921808 | − | 0.387647i | \(-0.126712\pi\) | |||||||
\(360\) | −4.83068e7 | − | 4.71944e7i | −1.03538 | − | 1.01154i | ||||
\(361\) | −2.47610e6 | −0.0526316 | ||||||||
\(362\) | −1.58429e7 | − | 4.17925e6i | −0.333972 | − | 0.0880993i | ||||
\(363\) | − | 2.17462e8i | − | 4.54637i | ||||||
\(364\) | 1.71316e7 | − | 3.02122e7i | 0.355217 | − | 0.626437i | ||||
\(365\) | 4.68392e7 | 0.963231 | ||||||||
\(366\) | 6.18576e6 | − | 2.34493e7i | 0.126168 | − | 0.478285i | ||||
\(367\) | − | 8.44140e7i | − | 1.70772i | −0.520504 | − | 0.853859i | \(-0.674256\pi\) | ||
0.520504 | − | 0.853859i | \(-0.325744\pi\) | |||||||
\(368\) | −3.93525e7 | + | 2.35424e7i | −0.789640 | + | 0.472397i | ||||
\(369\) | −7.89395e7 | −1.57114 | ||||||||
\(370\) | −2.54306e7 | − | 6.70842e6i | −0.502056 | − | 0.132439i | ||||
\(371\) | 8.76292e7i | 1.71604i | ||||||||
\(372\) | 5.22894e7 | + | 2.96504e7i | 1.01575 | + | 0.575972i | ||||
\(373\) | −7.87938e7 | −1.51833 | −0.759164 | − | 0.650900i | \(-0.774392\pi\) | ||||
−0.759164 | + | 0.650900i | \(0.774392\pi\) | |||||||
\(374\) | 2.67292e7 | − | 1.01326e8i | 0.510941 | − | 1.93690i | ||||
\(375\) | 9.72698e7i | 1.84452i | ||||||||
\(376\) | −2.89973e6 | + | 2.96808e6i | −0.0545500 | + | 0.0558356i | ||||
\(377\) | −5.12741e7 | −0.956917 | ||||||||
\(378\) | −1.17244e8 | − | 3.09280e7i | −2.17077 | − | 0.572633i | ||||
\(379\) | 7.03334e7i | 1.29195i | 0.763360 | + | 0.645973i | \(0.223548\pi\) | ||||
−0.763360 | + | 0.645973i | \(0.776452\pi\) | |||||||
\(380\) | −4.08723e6 | + | 7.20797e6i | −0.0744867 | + | 0.131360i | ||||
\(381\) | −8.16936e7 | −1.47711 | ||||||||
\(382\) | −1.79067e7 | + | 6.78817e7i | −0.321237 | + | 1.21776i | ||||
\(383\) | − | 4.60539e7i | − | 0.819728i | −0.912147 | − | 0.409864i | \(-0.865576\pi\) | ||
0.912147 | − | 0.409864i | \(-0.134424\pi\) | |||||||
\(384\) | 9.85008e7 | + | 2.35443e7i | 1.73959 | + | 0.415807i | ||||
\(385\) | 7.40025e7 | 1.29677 | ||||||||
\(386\) | 3.18809e7 | + | 8.40994e6i | 0.554330 | + | 0.146228i | ||||
\(387\) | 1.69146e8i | 2.91829i | ||||||||
\(388\) | 1.88079e7 | + | 1.06649e7i | 0.321993 | + | 0.182584i | ||||
\(389\) | 3.81887e7 | 0.648763 | 0.324381 | − | 0.945926i | \(-0.394844\pi\) | ||||
0.324381 | + | 0.945926i | \(0.394844\pi\) | |||||||
\(390\) | 1.22542e7 | − | 4.64541e7i | 0.206582 | − | 0.783123i | ||||
\(391\) | 5.85453e7i | 0.979404i | ||||||||
\(392\) | 4.12851e6 | + | 4.03345e6i | 0.0685386 | + | 0.0669604i | ||||
\(393\) | 4.38442e7 | 0.722328 | ||||||||
\(394\) | −2.40513e7 | − | 6.34456e6i | −0.393234 | − | 0.103732i | ||||
\(395\) | 4.32867e6i | 0.0702366i | ||||||||
\(396\) | 1.26770e8 | − | 2.23562e8i | 2.04141 | − | 3.60009i | ||||
\(397\) | −8.28073e7 | −1.32342 | −0.661709 | − | 0.749761i | \(-0.730168\pi\) | ||||
−0.661709 | + | 0.749761i | \(0.730168\pi\) | |||||||
\(398\) | −1.86087e7 | + | 7.05428e7i | −0.295166 | + | 1.11893i | ||||
\(399\) | 2.72849e7i | 0.429540i | ||||||||
\(400\) | −1.86210e7 | − | 3.11260e7i | −0.290953 | − | 0.486344i | ||||
\(401\) | −1.18588e7 | −0.183911 | −0.0919555 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919555 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(402\) | 1.77037e8 | + | 4.67009e7i | 2.72511 | + | 0.718865i | ||||
\(403\) | 2.93952e7i | 0.449119i | ||||||||
\(404\) | −4.88832e7 | − | 2.77189e7i | −0.741336 | − | 0.420370i | ||||
\(405\) | −7.15716e7 | −1.07740 | ||||||||
\(406\) | 2.48558e7 | − | 9.42249e7i | 0.371407 | − | 1.40795i | ||||
\(407\) | − | 1.00088e8i | − | 1.48456i | ||||||
\(408\) | 9.03564e7 | − | 9.24860e7i | 1.33039 | − | 1.36174i | ||||
\(409\) | 1.34754e7 | 0.196957 | 0.0984787 | − | 0.995139i | \(-0.468602\pi\) | ||||
0.0984787 | + | 0.995139i | \(0.468602\pi\) | |||||||
\(410\) | 3.13401e7 | + | 8.26729e6i | 0.454725 | + | 0.119953i | ||||
\(411\) | − | 1.06406e8i | − | 1.53264i | ||||||
\(412\) | −2.71834e7 | + | 4.79388e7i | −0.388698 | + | 0.685482i | ||||
\(413\) | 9.35003e6 | 0.132728 | ||||||||
\(414\) | −3.66231e7 | + | 1.38833e8i | −0.516124 | + | 1.95655i | ||||
\(415\) | − | 4.22279e7i | − | 0.590820i | ||||||
\(416\) | 1.37442e7 | + | 4.75801e7i | 0.190915 | + | 0.660914i | ||||
\(417\) | −3.23897e7 | −0.446683 | ||||||||
\(418\) | −3.04902e7 | − | 8.04309e6i | −0.417476 | − | 0.110127i | ||||
\(419\) | − | 1.18620e8i | − | 1.61256i | −0.591534 | − | 0.806280i | \(-0.701477\pi\) | ||
0.591534 | − | 0.806280i | \(-0.298523\pi\) | |||||||
\(420\) | 7.94268e7 | + | 4.50385e7i | 1.07206 | + | 0.607905i | ||||
\(421\) | −2.48333e7 | −0.332803 | −0.166402 | − | 0.986058i | \(-0.553215\pi\) | ||||
−0.166402 | + | 0.986058i | \(0.553215\pi\) | |||||||
\(422\) | −1.71270e7 | + | 6.49261e7i | −0.227900 | + | 0.863937i | ||||
\(423\) | 1.29923e7i | 0.171658i | ||||||||
\(424\) | −8.93799e7 | − | 8.73218e7i | −1.17258 | − | 1.14558i | ||||
\(425\) | −4.63067e7 | −0.603221 | ||||||||
\(426\) | −5.26055e7 | − | 1.38769e7i | −0.680459 | − | 0.179500i | ||||
\(427\) | 2.25391e7i | 0.289503i | ||||||||
\(428\) | −4.13712e7 | + | 7.29595e7i | −0.527676 | + | 0.930573i | ||||
\(429\) | 1.82830e8 | 2.31566 | ||||||||
\(430\) | 1.77145e7 | − | 6.71532e7i | 0.222805 | − | 0.844620i | ||||
\(431\) | − | 4.23106e7i | − | 0.528466i | −0.964459 | − | 0.264233i | \(-0.914881\pi\) | ||
0.964459 | − | 0.264233i | \(-0.0851189\pi\) | |||||||
\(432\) | 1.48378e8 | − | 8.87664e7i | 1.84043 | − | 1.10103i | ||||
\(433\) | 7.59981e7 | 0.936136 | 0.468068 | − | 0.883692i | \(-0.344950\pi\) | ||||
0.468068 | + | 0.883692i | \(0.344950\pi\) | |||||||
\(434\) | −5.40187e7 | − | 1.42497e7i | −0.660808 | − | 0.174316i | ||||
\(435\) | − | 1.34798e8i | − | 1.63763i | ||||||
\(436\) | 1.10295e8 | + | 6.25419e7i | 1.33075 | + | 0.754591i | ||||
\(437\) | 1.76169e7 | 0.211099 | ||||||||
\(438\) | −5.60971e7 | + | 2.12656e8i | −0.667602 | + | 2.53078i | ||||
\(439\) | − | 6.66957e7i | − | 0.788324i | −0.919041 | − | 0.394162i | \(-0.871035\pi\) | ||
0.919041 | − | 0.394162i | \(-0.128965\pi\) | |||||||
\(440\) | −7.37430e7 | + | 7.54810e7i | −0.865690 | + | 0.886093i | ||||
\(441\) | 1.80719e7 | 0.210711 | ||||||||
\(442\) | 6.11373e7 | + | 1.61276e7i | 0.708011 | + | 0.186768i | ||||
\(443\) | 2.25074e7i | 0.258889i | 0.991587 | + | 0.129445i | \(0.0413194\pi\) | ||||
−0.991587 | + | 0.129445i | \(0.958681\pi\) | |||||||
\(444\) | 6.09141e7 | − | 1.07424e8i | 0.695936 | − | 1.22731i | ||||
\(445\) | 5.76463e7 | 0.654171 | ||||||||
\(446\) | 7.99920e6 | − | 3.03238e7i | 0.0901658 | − | 0.341806i | ||||
\(447\) | 1.48532e8i | 1.66302i | ||||||||
\(448\) | −9.40991e7 | + | 2.19226e6i | −1.04653 | + | 0.0243813i | ||||
\(449\) | −9.29233e7 | −1.02656 | −0.513281 | − | 0.858220i | \(-0.671570\pi\) | ||||
−0.513281 | + | 0.858220i | \(0.671570\pi\) | |||||||
\(450\) | −1.09810e8 | − | 2.89672e7i | −1.20505 | − | 0.317884i | ||||
\(451\) | 1.23346e8i | 1.34460i | ||||||||
\(452\) | −1.01340e8 | − | 5.74640e7i | −1.09740 | − | 0.622273i | ||||
\(453\) | 3.72175e7 | 0.400362 | ||||||||
\(454\) | 168422. | − | 638463.i | 0.00179983 | − | 0.00682289i | ||||
\(455\) | 4.46509e7i | 0.474020i | ||||||||
\(456\) | −2.78300e7 | − | 2.71892e7i | −0.293507 | − | 0.286749i | ||||
\(457\) | −1.57094e7 | −0.164593 | −0.0822964 | − | 0.996608i | \(-0.526225\pi\) | ||||
−0.0822964 | + | 0.996608i | \(0.526225\pi\) | |||||||
\(458\) | 7.83550e6 | + | 2.06695e6i | 0.0815587 | + | 0.0215146i | ||||
\(459\) | − | 2.20744e8i | − | 2.28271i | ||||||
\(460\) | 2.90798e7 | − | 5.12831e7i | 0.298757 | − | 0.526867i | ||||
\(461\) | 9.56746e7 | 0.976549 | 0.488274 | − | 0.872690i | \(-0.337627\pi\) | ||||
0.488274 | + | 0.872690i | \(0.337627\pi\) | |||||||
\(462\) | −8.86293e7 | + | 3.35981e8i | −0.898776 | + | 3.40713i | ||||
\(463\) | 1.41181e8i | 1.42244i | 0.702968 | + | 0.711221i | \(0.251857\pi\) | ||||
−0.702968 | + | 0.711221i | \(0.748143\pi\) | |||||||
\(464\) | 7.13387e7 | + | 1.19247e8i | 0.714120 | + | 1.19369i | ||||
\(465\) | −7.72792e7 | −0.768606 | ||||||||
\(466\) | −1.30454e8 | − | 3.44128e7i | −1.28914 | − | 0.340065i | ||||
\(467\) | 2.20137e7i | 0.216144i | 0.994143 | + | 0.108072i | \(0.0344677\pi\) | ||||
−0.994143 | + | 0.108072i | \(0.965532\pi\) | |||||||
\(468\) | 1.34891e8 | + | 7.64891e7i | 1.31597 | + | 0.746211i | ||||
\(469\) | −1.70165e8 | −1.64949 | ||||||||
\(470\) | 1.36067e6 | − | 5.15812e6i | 0.0131057 | − | 0.0496818i | ||||
\(471\) | − | 2.54471e8i | − | 2.43543i | ||||||
\(472\) | −9.31724e6 | + | 9.53683e6i | −0.0886056 | + | 0.0906939i | ||||
\(473\) | 2.64296e8 | 2.49751 | ||||||||
\(474\) | −1.96527e7 | − | 5.18424e6i | −0.184539 | − | 0.0486800i | ||||
\(475\) | 1.39342e7i | 0.130017i | ||||||||
\(476\) | −5.92743e7 | + | 1.04532e8i | −0.549599 | + | 0.969235i | ||||
\(477\) | −3.91246e8 | −3.60491 | ||||||||
\(478\) | 2.77665e7 | − | 1.05259e8i | 0.254236 | − | 0.963773i | ||||
\(479\) | 1.11880e8i | 1.01800i | 0.860768 | + | 0.508998i | \(0.169984\pi\) | ||||
−0.860768 | + | 0.508998i | \(0.830016\pi\) | |||||||
\(480\) | −1.25087e8 | + | 3.61331e7i | −1.13106 | + | 0.326725i | ||||
\(481\) | 6.03900e7 | 0.542662 | ||||||||
\(482\) | −1.71220e7 | − | 4.51666e6i | −0.152902 | − | 0.0403344i | ||||
\(483\) | − | 1.94126e8i | − | 1.72283i | ||||||
\(484\) | −2.50697e8 | − | 1.42156e8i | −2.21112 | − | 1.25380i | ||||
\(485\) | −2.77965e7 | −0.243649 | ||||||||
\(486\) | 2.29243e7 | − | 8.69027e7i | 0.199704 | − | 0.757049i | ||||
\(487\) | 3.79408e7i | 0.328488i | 0.986420 | + | 0.164244i | \(0.0525184\pi\) | ||||
−0.986420 | + | 0.164244i | \(0.947482\pi\) | |||||||
\(488\) | −2.29894e7 | − | 2.24601e7i | −0.197819 | − | 0.193264i | ||||
\(489\) | 2.22273e8 | 1.90090 | ||||||||
\(490\) | −7.17480e6 | − | 1.89266e6i | −0.0609848 | − | 0.0160873i | ||||
\(491\) | − | 5.44109e7i | − | 0.459665i | −0.973230 | − | 0.229833i | \(-0.926182\pi\) | ||
0.973230 | − | 0.229833i | \(-0.0738178\pi\) | |||||||
\(492\) | −7.50692e7 | + | 1.32387e8i | −0.630327 | + | 1.11160i | ||||
\(493\) | 1.77405e8 | 1.48056 | ||||||||
\(494\) | 4.85296e6 | − | 1.83969e7i | 0.0402556 | − | 0.152603i | ||||
\(495\) | 3.30406e8i | 2.72416i | ||||||||
\(496\) | 6.83637e7 | − | 4.08982e7i | 0.560248 | − | 0.335165i | ||||
\(497\) | 5.05635e7 | 0.411878 | ||||||||
\(498\) | 1.91720e8 | + | 5.05743e7i | 1.55231 | + | 0.409489i | ||||
\(499\) | 8.64804e7i | 0.696011i | 0.937492 | + | 0.348006i | \(0.113141\pi\) | ||||
−0.937492 | + | 0.348006i | \(0.886859\pi\) | |||||||
\(500\) | 1.12136e8 | + | 6.35858e7i | 0.897084 | + | 0.508686i | ||||
\(501\) | −2.44594e8 | −1.94505 | ||||||||
\(502\) | −2.36349e6 | + | 8.95964e6i | −0.0186828 | + | 0.0708238i | ||||
\(503\) | − | 1.63899e8i | − | 1.28787i | −0.765080 | − | 0.643935i | \(-0.777301\pi\) | ||
0.765080 | − | 0.643935i | \(-0.222699\pi\) | |||||||
\(504\) | −2.05952e8 | + | 2.10806e8i | −1.60870 | + | 1.64661i | ||||
\(505\) | 7.22450e7 | 0.560963 | ||||||||
\(506\) | 2.16931e8 | + | 5.72248e7i | 1.67444 | + | 0.441706i | ||||
\(507\) | − | 1.22782e8i | − | 0.942130i | ||||||
\(508\) | −5.34035e7 | + | 9.41788e7i | −0.407360 | + | 0.718393i | ||||
\(509\) | 2.04007e8 | 1.54700 | 0.773501 | − | 0.633795i | \(-0.218504\pi\) | ||||
0.773501 | + | 0.633795i | \(0.218504\pi\) | |||||||
\(510\) | −4.23989e7 | + | 1.60728e8i | −0.319627 | + | 1.21166i | ||||
\(511\) | − | 2.04401e8i | − | 1.53187i | ||||||
\(512\) | 9.15330e7 | − | 9.81637e7i | 0.681974 | − | 0.731376i | ||||
\(513\) | −6.64244e7 | −0.492012 | ||||||||
\(514\) | 1.63291e8 | + | 4.30750e7i | 1.20247 | + | 0.317202i | ||||
\(515\) | − | 7.08494e7i | − | 0.518698i | ||||||
\(516\) | 2.83668e8 | + | 1.60852e8i | 2.06472 | + | 1.17079i | ||||
\(517\) | 2.03009e7 | 0.146907 | ||||||||
\(518\) | −2.92748e7 | + | 1.10977e8i | −0.210623 | + | 0.798441i | ||||
\(519\) | 1.88085e8i | 1.34541i | ||||||||
\(520\) | −4.55430e7 | − | 4.44943e7i | −0.323900 | − | 0.316442i | ||||
\(521\) | −2.05591e8 | −1.45376 | −0.726878 | − | 0.686767i | \(-0.759029\pi\) | ||||
−0.726878 | + | 0.686767i | \(0.759029\pi\) | |||||||
\(522\) | 4.20694e8 | + | 1.10976e8i | 2.95771 | + | 0.780221i | ||||
\(523\) | − | 1.50208e8i | − | 1.04999i | −0.851104 | − | 0.524997i | \(-0.824067\pi\) | ||
0.851104 | − | 0.524997i | \(-0.175933\pi\) | |||||||
\(524\) | 2.86612e7 | − | 5.05449e7i | 0.199205 | − | 0.351304i | ||||
\(525\) | 1.53545e8 | 1.06110 | ||||||||
\(526\) | 5.37224e7 | − | 2.03654e8i | 0.369146 | − | 1.39938i | ||||
\(527\) | − | 1.01706e8i | − | 0.694886i | ||||||
\(528\) | −2.54375e8 | − | 4.25203e8i | −1.72812 | − | 2.88864i | ||||
\(529\) | 2.26954e7 | 0.153310 | ||||||||
\(530\) | 1.55330e8 | + | 4.09750e7i | 1.04335 | + | 0.275227i | ||||
\(531\) | 4.17459e7i | 0.278824i | ||||||||
\(532\) | 3.14548e7 | + | 1.78363e7i | 0.208907 | + | 0.118459i | ||||
\(533\) | −7.44232e7 | −0.491503 | ||||||||
\(534\) | −6.90402e7 | + | 2.61722e8i | −0.453397 | + | 1.71876i | ||||
\(535\) | − | 1.07828e8i | − | 0.704156i | ||||||
\(536\) | 1.69568e8 | − | 1.73564e8i | 1.10116 | − | 1.12711i | ||||
\(537\) | 1.38269e8 | 0.892899 | ||||||||
\(538\) | −1.71030e8 | − | 4.51166e7i | −1.09831 | − | 0.289727i | ||||
\(539\) | − | 2.82379e7i | − | 0.180330i | ||||||
\(540\) | −1.09645e8 | + | 1.93362e8i | −0.696318 | + | 1.22798i | ||||
\(541\) | −4.39712e7 | −0.277701 | −0.138850 | − | 0.990313i | \(-0.544341\pi\) | ||||
−0.138850 | + | 0.990313i | \(0.544341\pi\) | |||||||
\(542\) | −1.06839e7 | + | 4.05011e7i | −0.0671013 | + | 0.254372i | ||||
\(543\) | 9.89073e7i | 0.617773i | ||||||||
\(544\) | −4.75541e7 | − | 1.64624e8i | −0.295387 | − | 1.02258i | ||||
\(545\) | −1.63006e8 | −1.00696 | ||||||||
\(546\) | −2.02721e8 | − | 5.34763e7i | −1.24543 | − | 0.328536i | ||||
\(547\) | 1.66991e8i | 1.02030i | 0.860084 | + | 0.510152i | \(0.170411\pi\) | ||||
−0.860084 | + | 0.510152i | \(0.829589\pi\) | |||||||
\(548\) | −1.22668e8 | − | 6.95579e7i | −0.745398 | − | 0.422673i | ||||
\(549\) | −1.00632e8 | −0.608164 | ||||||||
\(550\) | −4.52622e7 | + | 1.71583e8i | −0.272050 | + | 1.03130i | ||||
\(551\) | − | 5.33831e7i | − | 0.319117i | ||||||
\(552\) | 1.98005e8 | + | 1.93445e8i | 1.17722 | + | 1.15011i | ||||
\(553\) | 1.88899e7 | 0.111700 | ||||||||
\(554\) | −9.16705e7 | − | 2.41820e7i | −0.539139 | − | 0.142221i | ||||
\(555\) | 1.58763e8i | 0.928691i | ||||||||
\(556\) | −2.11733e7 | + | 3.73398e7i | −0.123187 | + | 0.217244i | ||||
\(557\) | −1.23329e8 | −0.713672 | −0.356836 | − | 0.934167i | \(-0.616145\pi\) | ||||
−0.356836 | + | 0.934167i | \(0.616145\pi\) | |||||||
\(558\) | 6.36221e7 | − | 2.41182e8i | 0.366189 | − | 1.38817i | ||||
\(559\) | 1.59468e8i | 0.912933i | ||||||||
\(560\) | 1.03843e8 | − | 6.21237e7i | 0.591309 | − | 0.353747i | ||||
\(561\) | −6.32580e8 | −3.58284 | ||||||||
\(562\) | 1.55968e8 | + | 4.11433e7i | 0.878673 | + | 0.231787i | ||||
\(563\) | − | 1.82847e8i | − | 1.02462i | −0.858800 | − | 0.512311i | \(-0.828790\pi\) | ||
0.858800 | − | 0.512311i | \(-0.171210\pi\) | |||||||
\(564\) | 2.17889e7 | + | 1.23553e7i | 0.121450 | + | 0.0688675i | ||||
\(565\) | 1.49771e8 | 0.830392 | ||||||||
\(566\) | 5.02097e7 | − | 1.90338e8i | 0.276910 | − | 1.04972i | ||||
\(567\) | 3.12331e8i | 1.71343i | ||||||||
\(568\) | −5.03862e7 | + | 5.15737e7i | −0.274958 | + | 0.281438i | ||||
\(569\) | 1.60414e8 | 0.870774 | 0.435387 | − | 0.900243i | \(-0.356611\pi\) | ||||
0.435387 | + | 0.900243i | \(0.356611\pi\) | |||||||
\(570\) | 4.83648e7 | + | 1.27583e7i | 0.261159 | + | 0.0688918i | ||||
\(571\) | 2.93526e7i | 0.157666i | 0.996888 | + | 0.0788331i | \(0.0251194\pi\) | ||||
−0.996888 | + | 0.0788331i | \(0.974881\pi\) | |||||||
\(572\) | 1.19517e8 | − | 2.10772e8i | 0.638618 | − | 1.12622i | ||||
\(573\) | 4.23785e8 | 2.25259 | ||||||||
\(574\) | 3.60776e7 | − | 1.36765e8i | 0.190767 | − | 0.723169i | ||||
\(575\) | − | 9.91386e7i | − | 0.521482i | ||||||
\(576\) | −9.78796e6 | − | 4.20133e8i | −0.0512183 | − | 2.19846i | ||||
\(577\) | 4.45013e7 | 0.231657 | 0.115829 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115829 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(578\) | −2.48179e7 | − | 6.54678e6i | −0.128523 | − | 0.0339035i | ||||
\(579\) | − | 1.99032e8i | − | 1.02539i | ||||||
\(580\) | −1.55399e8 | − | 8.81182e7i | −0.796462 | − | 0.451629i | ||||
\(581\) | −1.84278e8 | −0.939606 | ||||||||
\(582\) | 3.32905e7 | − | 1.26200e8i | 0.168870 | − | 0.640161i | ||||
\(583\) | 6.11335e8i | 3.08513i | ||||||||
\(584\) | 2.08485e8 | + | 2.03685e8i | 1.04673 | + | 1.02263i | ||||
\(585\) | −1.99357e8 | −0.995781 | ||||||||
\(586\) | 2.63638e8 | + | 6.95456e7i | 1.31013 | + | 0.345603i | ||||
\(587\) | 3.64234e8i | 1.80080i | 0.435062 | + | 0.900400i | \(0.356726\pi\) | ||||
−0.435062 | + | 0.900400i | \(0.643274\pi\) | |||||||
\(588\) | 1.71858e7 | − | 3.03078e7i | 0.0845354 | − | 0.149081i | ||||
\(589\) | −3.06043e7 | −0.149774 | ||||||||
\(590\) | 4.37203e6 | − | 1.65737e7i | 0.0212876 | − | 0.0806983i | ||||
\(591\) | 1.50152e8i | 0.727394i | ||||||||
\(592\) | −8.40218e7 | − | 1.40447e8i | −0.404974 | − | 0.676937i | ||||
\(593\) | −6.07879e7 | −0.291510 | −0.145755 | − | 0.989321i | \(-0.546561\pi\) | ||||
−0.145755 | + | 0.989321i | \(0.546561\pi\) | |||||||
\(594\) | −8.17937e8 | − | 2.15766e8i | −3.90266 | − | 1.02949i | ||||
\(595\) | − | 1.54489e8i | − | 0.733411i | ||||||
\(596\) | 1.71232e8 | + | 9.70958e7i | 0.808807 | + | 0.458629i | ||||
\(597\) | 4.40398e8 | 2.06977 | ||||||||
\(598\) | −3.45278e7 | + | 1.30890e8i | −0.161460 | + | 0.612072i | ||||
\(599\) | 5.82355e7i | 0.270962i | 0.990780 | + | 0.135481i | \(0.0432579\pi\) | ||||
−0.990780 | + | 0.135481i | \(0.956742\pi\) | |||||||
\(600\) | −1.53006e8 | + | 1.56613e8i | −0.708363 | + | 0.725058i | ||||
\(601\) | −4.01876e7 | −0.185127 | −0.0925633 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925633 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(602\) | −2.93050e8 | − | 7.73044e7i | −1.34324 | − | 0.354335i | ||||
\(603\) | − | 7.59750e8i | − | 3.46512i | ||||||
\(604\) | 2.43293e7 | − | 4.29054e7i | 0.110412 | − | 0.194716i | ||||
\(605\) | 3.70508e8 | 1.67314 | ||||||||
\(606\) | −8.65244e7 | + | 3.28002e8i | −0.388795 | + | 1.47387i | ||||
\(607\) | 9.92257e7i | 0.443668i | 0.975084 | + | 0.221834i | \(0.0712043\pi\) | ||||
−0.975084 | + | 0.221834i | \(0.928796\pi\) | |||||||
\(608\) | −4.95371e7 | + | 1.43096e7i | −0.220404 | + | 0.0636671i | ||||
\(609\) | −5.88245e8 | −2.60439 | ||||||||
\(610\) | 3.99525e7 | + | 1.05392e7i | 0.176017 | + | 0.0464320i | ||||
\(611\) | 1.22489e7i | 0.0537001i | ||||||||
\(612\) | −4.66714e8 | − | 2.64647e8i | −2.03609 | − | 1.15455i | ||||
\(613\) | −2.11691e8 | −0.919010 | −0.459505 | − | 0.888175i | \(-0.651973\pi\) | ||||
−0.459505 | + | 0.888175i | \(0.651973\pi\) | |||||||
\(614\) | −5.90296e7 | + | 2.23773e8i | −0.255014 | + | 0.966723i | ||||
\(615\) | − | 1.95656e8i | − | 0.841140i | ||||||
\(616\) | 3.29391e8 | + | 3.21807e8i | 1.40919 | + | 1.37674i | ||||
\(617\) | −2.82765e8 | −1.20385 | −0.601923 | − | 0.798554i | \(-0.705599\pi\) | ||||
−0.601923 | + | 0.798554i | \(0.705599\pi\) | |||||||
\(618\) | 3.21665e8 | + | 8.48530e7i | 1.36282 | + | 0.359502i | ||||
\(619\) | − | 1.81094e8i | − | 0.763539i | −0.924258 | − | 0.381770i | \(-0.875315\pi\) | ||
0.924258 | − | 0.381770i | \(-0.124685\pi\) | |||||||
\(620\) | −5.05178e7 | + | 8.90897e7i | −0.211967 | + | 0.373811i | ||||
\(621\) | 4.72595e8 | 1.97340 | ||||||||
\(622\) | 1.17400e8 | − | 4.45045e8i | 0.487861 | − | 1.84941i | ||||
\(623\) | − | 2.51563e8i | − | 1.04036i | ||||||
\(624\) | 2.56555e8 | − | 1.53482e8i | 1.05591 | − | 0.631691i | ||||
\(625\) | −2.73644e7 | −0.112085 | ||||||||
\(626\) | −3.59332e8 | − | 9.47891e7i | −1.46478 | − | 0.386398i | ||||
\(627\) | 1.90350e8i | 0.772237i | ||||||||
\(628\) | −2.93362e8 | − | 1.66349e8i | −1.18447 | − | 0.671647i | ||||
\(629\) | −2.08945e8 | −0.839617 | ||||||||
\(630\) | 9.66410e7 | − | 3.66352e8i | 0.386491 | − | 1.46513i | ||||
\(631\) | − | 4.76664e7i | − | 0.189725i | −0.995490 | − | 0.0948624i | \(-0.969759\pi\) | ||
0.995490 | − | 0.0948624i | \(-0.0302411\pi\) | |||||||
\(632\) | −1.88236e7 | + | 1.92673e7i | −0.0745679 | + | 0.0763254i | ||||
\(633\) | 4.05333e8 | 1.59809 | ||||||||
\(634\) | −1.70171e8 | − | 4.48899e7i | −0.667757 | − | 0.176149i | ||||
\(635\) | − | 1.39188e8i | − | 0.543601i | ||||||
\(636\) | −3.72063e8 | + | 6.56146e8i | −1.44626 | + | 2.55052i | ||||
\(637\) | 1.70379e7 | 0.0659172 | ||||||||
\(638\) | 1.73404e8 | − | 6.57350e8i | 0.667724 | − | 2.53125i | ||||
\(639\) | 2.25756e8i | 0.865239i | ||||||||
\(640\) | −4.01143e7 | + | 1.67824e8i | −0.153024 | + | 0.640197i | ||||
\(641\) | 2.34991e7 | 0.0892231 | 0.0446115 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446115 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(642\) | 4.89552e8 | + | 1.29140e8i | 1.85009 | + | 0.488041i | ||||
\(643\) | 176446.i | 0.000663710i | 1.00000 | 0.000331855i | \(0.000105633\pi\) | |||||
−1.00000 | 0.000331855i | \(0.999894\pi\) | ||||||||
\(644\) | −2.23794e8 | − | 1.26901e8i | −0.837899 | − | 0.475125i | ||||
\(645\) | −4.19237e8 | −1.56236 | ||||||||
\(646\) | −1.67909e7 | + | 6.36520e7i | −0.0622841 | + | 0.236110i | ||||
\(647\) | − | 9.23923e7i | − | 0.341132i | −0.985346 | − | 0.170566i | \(-0.945440\pi\) | ||
0.985346 | − | 0.170566i | \(-0.0545597\pi\) | |||||||
\(648\) | −3.18571e8 | − | 3.11236e8i | −1.17080 | − | 1.14384i | ||||
\(649\) | 6.52295e7 | 0.238622 | ||||||||
\(650\) | −1.03528e8 | − | 2.73099e7i | −0.376979 | − | 0.0994443i | ||||
\(651\) | 3.37239e8i | 1.22235i | ||||||||
\(652\) | 1.45301e8 | − | 2.56243e8i | 0.524234 | − | 0.924504i | ||||
\(653\) | 2.44394e7 | 0.0877710 | 0.0438855 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438855 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(654\) | 1.95224e8 | − | 7.40068e8i | 0.697912 | − | 2.64569i | ||||
\(655\) | 7.47009e7i | 0.265829i | ||||||||
\(656\) | 1.03546e8 | + | 1.73084e8i | 0.366795 | + | 0.613119i | ||||
\(657\) | 9.12610e8 | 3.21802 | ||||||||
\(658\) | −2.25095e7 | − | 5.93784e6i | −0.0790111 | − | 0.0208425i | ||||
\(659\) | − | 2.63308e8i | − | 0.920042i | −0.887908 | − | 0.460021i | \(-0.847842\pi\) | ||
0.887908 | − | 0.460021i | \(-0.152158\pi\) | |||||||
\(660\) | 5.54113e8 | + | 3.14206e8i | 1.92737 | + | 1.09291i | ||||
\(661\) | 4.02712e8 | 1.39441 | 0.697205 | − | 0.716871i | \(-0.254427\pi\) | ||||
0.697205 | + | 0.716871i | \(0.254427\pi\) | |||||||
\(662\) | 1.99634e6 | − | 7.56784e6i | 0.00688114 | − | 0.0260854i | ||||
\(663\) | − | 3.81680e8i | − | 1.30966i | ||||||
\(664\) | 1.83632e8 | − | 1.87960e8i | 0.627255 | − | 0.642038i | ||||
\(665\) | −4.64875e7 | −0.158078 | ||||||||
\(666\) | −4.95488e8 | − | 1.30706e8i | −1.67730 | − | 0.442459i | ||||
\(667\) | 3.79809e8i | 1.27994i | ||||||||
\(668\) | −1.59892e8 | + | 2.81975e8i | −0.536410 | + | 0.945977i | ||||
\(669\) | −1.89311e8 | −0.632264 | ||||||||
\(670\) | −7.95682e7 | + | 3.01632e8i | −0.264554 | + | 1.00289i | ||||
\(671\) | 1.57242e8i | 0.520475i | ||||||||
\(672\) | 1.57681e8 | + | 5.45865e8i | 0.519604 | + | 1.79878i | ||||
\(673\) | −4.34441e8 | −1.42523 | −0.712616 | − | 0.701555i | \(-0.752490\pi\) | ||||
−0.712616 | + | 0.701555i | \(0.752490\pi\) | |||||||
\(674\) | −5.61856e8 | − | 1.48214e8i | −1.83504 | − | 0.484070i | ||||
\(675\) | 3.73801e8i | 1.21543i | ||||||||
\(676\) | −1.41547e8 | − | 8.02632e7i | −0.458205 | − | 0.259822i | ||||
\(677\) | 4.81073e8 | 1.55040 | 0.775202 | − | 0.631713i | \(-0.217648\pi\) | ||||
0.775202 | + | 0.631713i | \(0.217648\pi\) | |||||||
\(678\) | −1.79374e8 | + | 6.79981e8i | −0.575533 | + | 2.18176i | ||||
\(679\) | 1.21301e8i | 0.387485i | ||||||||
\(680\) | 1.57576e8 | + | 1.53948e8i | 0.501144 | + | 0.489605i | ||||
\(681\) | −3.98592e6 | −0.0126208 | ||||||||
\(682\) | −3.76856e8 | − | 9.94117e7i | −1.18802 | − | 0.313390i | ||||
\(683\) | 2.18383e8i | 0.685418i | 0.939442 | + | 0.342709i | \(0.111345\pi\) | ||||
−0.939442 | + | 0.342709i | \(0.888655\pi\) | |||||||
\(684\) | −7.96352e7 | + | 1.40439e8i | −0.248850 | + | 0.438854i | ||||
\(685\) | 1.81292e8 | 0.564036 | ||||||||
\(686\) | 7.79385e7 | − | 2.95454e8i | 0.241423 | − | 0.915202i | ||||
\(687\) | − | 4.89170e7i | − | 0.150865i | ||||||
\(688\) | 3.70871e8 | − | 2.21871e8i | 1.13883 | − | 0.681296i | ||||
\(689\) | −3.68862e8 | −1.12773 | ||||||||
\(690\) | −3.44105e8 | − | 9.07724e7i | −1.04748 | − | 0.276316i | ||||
\(691\) | − | 7.88603e7i | − | 0.239015i | −0.992833 | − | 0.119507i | \(-0.961869\pi\) | ||
0.992833 | − | 0.119507i | \(-0.0381315\pi\) | |||||||
\(692\) | 2.16830e8 | + | 1.22952e8i | 0.654338 | + | 0.371038i | ||||
\(693\) | 1.44186e9 | 4.33234 | ||||||||
\(694\) | 8.75332e6 | − | 3.31826e7i | 0.0261875 | − | 0.0992731i | ||||
\(695\) | − | 5.51850e7i | − | 0.164387i | ||||||
\(696\) | 5.86182e8 | − | 5.99998e8i | 1.73862 | − | 1.77960i | ||||
\(697\) | 2.57499e8 | 0.760463 | ||||||||
\(698\) | 2.15486e8 | + | 5.68436e7i | 0.633655 | + | 0.167153i | ||||
\(699\) | 8.14423e8i | 2.38462i | ||||||||
\(700\) | 1.00373e8 | − | 1.77011e8i | 0.292633 | − | 0.516068i | ||||
\(701\) | −5.62633e8 | −1.63332 | −0.816659 | − | 0.577120i | \(-0.804176\pi\) | ||||
−0.816659 | + | 0.577120i | \(0.804176\pi\) | |||||||
\(702\) | 1.30187e8 | − | 4.93519e8i | 0.376318 | − | 1.42657i | ||||
\(703\) | 6.28739e7i | 0.180969i | ||||||||
\(704\) | −6.56472e8 | + | 1.52940e7i | −1.88147 | + | 0.0438333i | ||||
\(705\) | −3.22021e7 | −0.0919003 | ||||||||
\(706\) | 1.91400e8 | + | 5.04898e7i | 0.543910 | + | 0.143479i | ||||
\(707\) | − | 3.15270e8i | − | 0.892123i | ||||||
\(708\) | 7.00107e7 | + | 3.96991e7i | 0.197272 | + | 0.111862i | ||||
\(709\) | 2.78449e8 | 0.781280 | 0.390640 | − | 0.920544i | \(-0.372254\pi\) | ||||
0.390640 | + | 0.920544i | \(0.372254\pi\) | |||||||
\(710\) | 2.36433e7 | − | 8.96282e7i | 0.0660590 | − | 0.250420i | ||||
\(711\) | 8.43394e7i | 0.234651i | ||||||||
\(712\) | 2.56588e8 | + | 2.50680e8i | 0.710881 | + | 0.694513i | ||||
\(713\) | 2.17743e8 | 0.600725 | ||||||||
\(714\) | 7.01402e8 | + | 1.85025e8i | 1.92696 | + | 0.508317i | ||||
\(715\) | 3.11502e8i | 0.852203i | ||||||||
\(716\) | 9.03872e7 | − | 1.59401e8i | 0.246245 | − | 0.434262i | ||||
\(717\) | −6.57130e8 | −1.78276 | ||||||||
\(718\) | −7.31971e7 | + | 2.77480e8i | −0.197752 | + | 0.749649i | ||||
\(719\) | 1.29123e8i | 0.347388i | 0.984800 | + | 0.173694i | \(0.0555704\pi\) | ||||
−0.984800 | + | 0.173694i | \(0.944430\pi\) | |||||||
\(720\) | 2.77369e8 | + | 4.63639e8i | 0.743124 | + | 1.24217i | ||||
\(721\) | −3.09180e8 | −0.824907 | ||||||||
\(722\) | 1.91536e7 | + | 5.05257e6i | 0.0508907 | + | 0.0134246i | ||||
\(723\) | 1.06893e8i | 0.282835i | ||||||||
\(724\) | 1.14023e8 | + | 6.46562e7i | 0.300454 | + | 0.170371i | ||||
\(725\) | −3.00412e8 | −0.788321 | ||||||||
\(726\) | −4.43740e8 | + | 1.68216e9i | −1.15963 | + | 4.39599i | ||||
\(727\) | 6.69981e8i | 1.74365i | 0.489817 | + | 0.871826i | \(0.337064\pi\) | ||||
−0.489817 | + | 0.871826i | \(0.662936\pi\) | |||||||
\(728\) | −1.94169e8 | + | 1.98745e8i | −0.503252 | + | 0.515112i | ||||
\(729\) | 9.15989e7 | 0.236433 | ||||||||
\(730\) | −3.62319e8 | − | 9.55771e7i | −0.931371 | − | 0.245689i | ||||
\(731\) | − | 5.51750e8i | − | 1.41251i | ||||||
\(732\) | −9.56984e7 | + | 1.68767e8i | −0.243990 | + | 0.430284i | ||||
\(733\) | −6.18110e8 | −1.56947 | −0.784737 | − | 0.619829i | \(-0.787202\pi\) | ||||
−0.784737 | + | 0.619829i | \(0.787202\pi\) | |||||||
\(734\) | −1.72250e8 | + | 6.52975e8i | −0.435583 | + | 1.65123i | ||||
\(735\) | 4.47922e7i | 0.112808i | ||||||||
\(736\) | 3.52446e8 | − | 1.01809e8i | 0.884014 | − | 0.255361i | ||||
\(737\) | −1.18714e9 | −2.96550 | ||||||||
\(738\) | 6.10628e8 | + | 1.61079e8i | 1.51917 | + | 0.400747i | ||||
\(739\) | 4.24026e8i | 1.05065i | 0.850901 | + | 0.525327i | \(0.176057\pi\) | ||||
−0.850901 | + | 0.525327i | \(0.823943\pi\) | |||||||
\(740\) | 1.83027e8 | + | 1.03784e8i | 0.451669 | + | 0.256116i | ||||
\(741\) | −1.14852e8 | −0.282282 | ||||||||
\(742\) | 1.78811e8 | − | 6.77845e8i | 0.437705 | − | 1.65928i | ||||
\(743\) | 6.24199e8i | 1.52180i | 0.648871 | + | 0.760898i | \(0.275241\pi\) | ||||
−0.648871 | + | 0.760898i | \(0.724759\pi\) | |||||||
\(744\) | −3.43976e8 | − | 3.36056e8i | −0.835236 | − | 0.816004i | ||||
\(745\) | −2.53065e8 | −0.612017 | ||||||||
\(746\) | 6.09500e8 | + | 1.60782e8i | 1.46811 | + | 0.387276i | ||||
\(747\) | − | 8.22764e8i | − | 1.97385i | ||||||
\(748\) | −4.13521e8 | + | 7.29257e8i | −0.988081 | + | 1.74251i | ||||
\(749\) | −4.70549e8 | −1.11985 | ||||||||
\(750\) | 1.98483e8 | − | 7.52420e8i | 0.470478 | − | 1.78351i | ||||
\(751\) | − | 1.82866e8i | − | 0.431732i | −0.976423 | − | 0.215866i | \(-0.930743\pi\) | ||
0.976423 | − | 0.215866i | \(-0.0692574\pi\) | |||||||
\(752\) | 2.84870e7 | − | 1.70422e7i | 0.0669875 | − | 0.0400749i | ||||
\(753\) | 5.59350e7 | 0.131008 | ||||||||
\(754\) | 3.96625e8 | + | 1.04627e8i | 0.925265 | + | 0.244078i | ||||
\(755\) | 6.34105e7i | 0.147340i | ||||||||
\(756\) | 8.43814e8 | + | 4.78480e8i | 1.95291 | + | 1.10738i | ||||
\(757\) | −6.57939e8 | −1.51669 | −0.758347 | − | 0.651851i | \(-0.773993\pi\) | ||||
−0.758347 | + | 0.651851i | \(0.773993\pi\) | |||||||
\(758\) | 1.43518e8 | − | 5.44056e8i | 0.329533 | − | 1.24921i | ||||
\(759\) | − | 1.35430e9i | − | 3.09735i | ||||||
\(760\) | 4.63245e7 | − | 4.74163e7i | 0.105528 | − | 0.108016i | ||||
\(761\) | −5.74786e8 | −1.30422 | −0.652112 | − | 0.758123i | \(-0.726117\pi\) | ||||
−0.652112 | + | 0.758123i | \(0.726117\pi\) | |||||||
\(762\) | 6.31931e8 | + | 1.66699e8i | 1.42825 | + | 0.376762i | ||||
\(763\) | 7.11341e8i | 1.60142i | ||||||||
\(764\) | 2.77030e8 | − | 4.88552e8i | 0.621222 | − | 1.09555i | ||||
\(765\) | 6.89763e8 | 1.54069 | ||||||||
\(766\) | −9.39746e7 | + | 3.56244e8i | −0.209086 | + | 0.792614i | ||||
\(767\) | 3.93575e7i | 0.0872251i | ||||||||
\(768\) | −7.13899e8 | − | 3.83119e8i | −1.57599 | − | 0.845765i | ||||
\(769\) | 3.75438e8 | 0.825581 | 0.412790 | − | 0.910826i | \(-0.364554\pi\) | ||||
0.412790 | + | 0.910826i | \(0.364554\pi\) | |||||||
\(770\) | −5.72438e8 | − | 1.51005e8i | −1.25388 | − | 0.330765i | ||||
\(771\) | − | 1.01943e9i | − | 2.22430i | ||||||
\(772\) | −2.29450e8 | − | 1.30108e8i | −0.498697 | − | 0.282783i | ||||
\(773\) | 4.91185e8 | 1.06342 | 0.531712 | − | 0.846925i | \(-0.321549\pi\) | ||||
0.531712 | + | 0.846925i | \(0.321549\pi\) | |||||||
\(774\) | 3.45148e8 | − | 1.30841e9i | 0.744359 | − | 2.82176i | ||||
\(775\) | 1.72225e8i | 0.369991i | ||||||||
\(776\) | −1.23724e8 | − | 1.20876e8i | −0.264771 | − | 0.258674i | ||||
\(777\) | 6.92827e8 | 1.47694 | ||||||||
\(778\) | −2.95404e8 | − | 7.79255e7i | −0.627304 | − | 0.165478i | ||||
\(779\) | − | 7.74843e7i | − | 0.163909i | ||||||
\(780\) | −1.89583e8 | + | 3.34335e8i | −0.399498 | + | 0.704528i | ||||
\(781\) | 3.52751e8 | 0.740483 | ||||||||
\(782\) | 1.19464e8 | − | 4.52871e8i | 0.249814 | − | 0.947008i | ||||
\(783\) | − | 1.43207e9i | − | 2.98317i | ||||||
\(784\) | −2.37052e7 | − | 3.96247e7i | −0.0491921 | − | 0.0822275i | ||||
\(785\) | 4.33563e8 | 0.896278 | ||||||||
\(786\) | −3.39152e8 | − | 8.94657e7i | −0.698436 | − | 0.184242i | ||||
\(787\) | 3.93360e8i | 0.806987i | 0.914983 | + | 0.403493i | \(0.132204\pi\) | ||||
−0.914983 | + | 0.403493i | \(0.867796\pi\) | |||||||
\(788\) | 1.73100e8 | + | 9.81553e7i | 0.353768 | + | 0.200602i | ||||
\(789\) | −1.27141e9 | −2.58854 | ||||||||
\(790\) | 8.83281e6 | − | 3.34839e7i | 0.0179150 | − | 0.0679134i | ||||
\(791\) | − | 6.53586e8i | − | 1.32061i | ||||||
\(792\) | −1.43680e9 | + | 1.47066e9i | −2.89215 | + | 2.96031i | ||||
\(793\) | −9.48749e7 | −0.190253 | ||||||||
\(794\) | 6.40546e8 | + | 1.68971e8i | 1.27964 | + | 0.337560i | ||||
\(795\) | − | 9.69726e8i | − | 1.92996i | ||||||
\(796\) | 2.87891e8 | − | 5.07704e8i | 0.570806 | − | 1.00663i | ||||
\(797\) | 9.32022e8 | 1.84099 | 0.920494 | − | 0.390757i | \(-0.127787\pi\) | ||||
0.920494 | + | 0.390757i | \(0.127787\pi\) | |||||||
\(798\) | 5.56759e7 | − | 2.11059e8i | 0.109562 | − | 0.415332i | ||||
\(799\) | − | 4.23806e7i | − | 0.0830857i | ||||||
\(800\) | 8.05266e7 | + | 2.78769e8i | 0.157278 | + | 0.544470i | ||||
\(801\) | 1.12317e9 | 2.18549 | ||||||||
\(802\) | 9.17324e7 | + | 2.41983e7i | 0.177828 | + | 0.0469097i | ||||
\(803\) | − | 1.42598e9i | − | 2.75403i | ||||||
\(804\) | −1.27415e9 | − | 7.22499e8i | −2.45162 | − | 1.39017i | ||||
\(805\) | 3.30749e8 | 0.634031 | ||||||||
\(806\) | 5.99821e7 | − | 2.27384e8i | 0.114556 | − | 0.434264i | ||||
\(807\) | 1.06774e9i | 2.03164i | ||||||||
\(808\) | 3.21569e8 | + | 3.14164e8i | 0.609593 | + | 0.595556i | ||||
\(809\) | −4.21370e8 | −0.795826 | −0.397913 | − | 0.917423i | \(-0.630265\pi\) | ||||
−0.397913 | + | 0.917423i | \(0.630265\pi\) | |||||||
\(810\) | 5.53634e8 | + | 1.46045e8i | 1.04176 | + | 0.274809i | ||||
\(811\) | − | 1.33493e8i | − | 0.250262i | −0.992140 | − | 0.125131i | \(-0.960065\pi\) | ||
0.992140 | − | 0.125131i | \(-0.0399351\pi\) | |||||||
\(812\) | −3.84539e8 | + | 6.78147e8i | −0.718244 | + | 1.26665i | ||||
\(813\) | 2.52848e8 | 0.470531 | ||||||||
\(814\) | −2.04233e8 | + | 7.74217e8i | −0.378662 | + | 1.43546i | ||||
\(815\) | 3.78704e8i | 0.699564i | ||||||||
\(816\) | −8.87663e8 | + | 5.31039e8i | −1.63372 | + | 0.977363i | ||||
\(817\) | −1.66027e8 | −0.304448 | ||||||||
\(818\) | −1.04238e8 | − | 2.74971e7i | −0.190443 | − | 0.0502374i | ||||
\(819\) | 8.69974e8i | 1.58363i | ||||||||
\(820\) | −2.25558e8 | − | 1.27901e8i | −0.409088 | − | 0.231971i | ||||
\(821\) | −9.43811e8 | −1.70552 | −0.852758 | − | 0.522306i | \(-0.825072\pi\) | ||||
−0.852758 | + | 0.522306i | \(0.825072\pi\) | |||||||
\(822\) | −2.17125e8 | + | 8.23089e8i | −0.390926 | + | 1.48194i | ||||
\(823\) | 5.97602e8i | 1.07204i | 0.844204 | + | 0.536022i | \(0.180074\pi\) | ||||
−0.844204 | + | 0.536022i | \(0.819926\pi\) | |||||||
\(824\) | 3.08095e8 | − | 3.15357e8i | 0.550685 | − | 0.563664i | ||||
\(825\) | 1.07119e9 | 1.90768 | ||||||||
\(826\) | −7.23261e7 | − | 1.90791e7i | −0.128338 | − | 0.0338546i | ||||
\(827\) | − | 5.02109e8i | − | 0.887731i | −0.896093 | − | 0.443865i | \(-0.853607\pi\) | ||
0.896093 | − | 0.443865i | \(-0.146393\pi\) | |||||||
\(828\) | 5.66587e8 | − | 9.99195e8i | 0.998104 | − | 1.76019i | ||||
\(829\) | −1.37713e8 | −0.241720 | −0.120860 | − | 0.992670i | \(-0.538565\pi\) | ||||
−0.120860 | + | 0.992670i | \(0.538565\pi\) | |||||||
\(830\) | −8.61676e7 | + | 3.26649e8i | −0.150699 | + | 0.571278i | ||||
\(831\) | 5.72299e8i | 0.997286i | ||||||||
\(832\) | −9.22796e6 | − | 3.96096e8i | −0.0160227 | − | 0.687750i | ||||
\(833\) | −5.89502e7 | −0.101988 | ||||||||
\(834\) | 2.50547e8 | + | 6.60924e7i | 0.431908 | + | 0.113934i | ||||
\(835\) | − | 4.16734e8i | − | 0.715813i | ||||||
\(836\) | 2.19441e8 | + | 1.24433e8i | 0.375577 | + | 0.212969i | ||||
\(837\) | −8.20998e8 | −1.40012 | ||||||||
\(838\) | −2.42049e8 | + | 9.17572e8i | −0.411311 | + | 1.55922i | ||||
\(839\) | 6.49417e8i | 1.09961i | 0.835294 | + | 0.549804i | \(0.185298\pi\) | ||||
−0.835294 | + | 0.549804i | \(0.814702\pi\) | |||||||
\(840\) | −5.22494e8 | − | 5.10464e8i | −0.881544 | − | 0.861245i | ||||
\(841\) | 5.56084e8 | 0.934872 | ||||||||
\(842\) | 1.92095e8 | + | 5.06732e7i | 0.321795 | + | 0.0848871i | ||||
\(843\) | − | 9.73709e8i | − | 1.62535i | ||||||
\(844\) | 2.64968e8 | − | 4.67280e8i | 0.440724 | − | 0.777231i | ||||
\(845\) | 2.09194e8 | 0.346719 | ||||||||
\(846\) | 2.65112e7 | − | 1.00500e8i | 0.0437843 | − | 0.165980i | ||||
\(847\) | − | 1.61686e9i | − | 2.66086i | ||||||
\(848\) | 5.13204e8 | + | 8.57851e8i | 0.841594 | + | 1.40677i | ||||
\(849\) | −1.18828e9 | −1.94176 | ||||||||
\(850\) | 3.58200e8 | + | 9.44905e7i | 0.583269 | + | 0.153862i | ||||
\(851\) | − | 4.47334e8i | − | 0.725845i | ||||||
\(852\) | 3.78607e8 | + | 2.14687e8i | 0.612167 | + | 0.347126i | ||||
\(853\) | −3.15563e8 | −0.508439 | −0.254219 | − | 0.967147i | \(-0.581819\pi\) | ||||
−0.254219 | + | 0.967147i | \(0.581819\pi\) | |||||||
\(854\) | 4.59919e7 | − | 1.74349e8i | 0.0738427 | − | 0.279927i | ||||
\(855\) | − | 2.07557e8i | − | 0.332077i | ||||||
\(856\) | 4.68899e8 | − | 4.79950e8i | 0.747581 | − | 0.765200i | ||||
\(857\) | 3.07046e8 | 0.487822 | 0.243911 | − | 0.969798i | \(-0.421570\pi\) | ||||
0.243911 | + | 0.969798i | \(0.421570\pi\) | |||||||
\(858\) | −1.41426e9 | − | 3.73071e8i | −2.23907 | − | 0.590650i | ||||
\(859\) | − | 2.35602e7i | − | 0.0371705i | −0.999827 | − | 0.0185853i | \(-0.994084\pi\) | ||
0.999827 | − | 0.0185853i | \(-0.00591622\pi\) | |||||||
\(860\) | −2.74057e8 | + | 4.83309e8i | −0.430870 | + | 0.759853i | ||||
\(861\) | −8.53824e8 | −1.33770 | ||||||||
\(862\) | −8.63364e7 | + | 3.27289e8i | −0.134794 | + | 0.510986i | ||||
\(863\) | 5.55471e8i | 0.864229i | 0.901819 | + | 0.432114i | \(0.142232\pi\) | ||||
−0.901819 | + | 0.432114i | \(0.857768\pi\) | |||||||
\(864\) | −1.32889e9 | + | 3.83871e8i | −2.06039 | + | 0.595174i | ||||
\(865\) | −3.20456e8 | −0.495132 | ||||||||
\(866\) | −5.87875e8 | − | 1.55077e8i | −0.905172 | − | 0.238778i | ||||
\(867\) | 1.54938e8i | 0.237739i | ||||||||
\(868\) | 3.88779e8 | + | 2.20454e8i | 0.594488 | + | 0.337101i | ||||
\(869\) | 1.31783e8 | 0.200817 | ||||||||
\(870\) | −2.75061e8 | + | 1.04272e9i | −0.417706 | + | 1.58346i | ||||
\(871\) | − | 7.16282e8i | − | 1.08400i | ||||||
\(872\) | −7.25553e8 | − | 7.08846e8i | −1.09426 | − | 1.06906i | ||||
\(873\) | −5.41584e8 | −0.813997 | ||||||||
\(874\) | −1.36274e8 | − | 3.59480e7i | −0.204116 | − | 0.0538443i | ||||
\(875\) | 7.23214e8i | 1.07955i | ||||||||
\(876\) | 8.67865e8 | − | 1.53051e9i | 1.29104 | − | 2.27679i | ||||
\(877\) | 6.78056e8 | 1.00523 | 0.502617 | − | 0.864509i | \(-0.332371\pi\) | ||||
0.502617 | + | 0.864509i | \(0.332371\pi\) | |||||||
\(878\) | −1.36095e8 | + | 5.15917e8i | −0.201075 | + | 0.762248i | ||||
\(879\) | − | 1.64589e9i | − | 2.42345i | ||||||
\(880\) | 7.24452e8 | − | 4.33399e8i | 1.06307 | − | 0.635975i | ||||
\(881\) | 5.69424e8 | 0.832737 | 0.416369 | − | 0.909196i | \(-0.363303\pi\) | ||||
0.416369 | + | 0.909196i | \(0.363303\pi\) | |||||||
\(882\) | −1.39793e8 | − | 3.68764e7i | −0.203742 | − | 0.0537455i | ||||
\(883\) | − | 2.57956e8i | − | 0.374682i | −0.982295 | − | 0.187341i | \(-0.940013\pi\) | ||
0.982295 | − | 0.187341i | \(-0.0599870\pi\) | |||||||
\(884\) | −4.40012e8 | − | 2.49506e8i | −0.636954 | − | 0.361181i | ||||
\(885\) | −1.03470e8 | −0.149274 | ||||||||
\(886\) | 4.59272e7 | − | 1.74103e8i | 0.0660341 | − | 0.250326i | ||||
\(887\) | 4.77476e8i | 0.684196i | 0.939664 | + | 0.342098i | \(0.111137\pi\) | ||||
−0.939664 | + | 0.342098i | \(0.888863\pi\) | |||||||
\(888\) | −6.90397e8 | + | 7.06669e8i | −0.985962 | + | 1.00920i | ||||
\(889\) | −6.07402e8 | −0.864512 | ||||||||
\(890\) | −4.45916e8 | − | 1.17629e8i | −0.632533 | − | 0.166858i | ||||
\(891\) | 2.17894e9i | 3.08044i | ||||||||
\(892\) | −1.23754e8 | + | 2.18244e8i | −0.174367 | + | 0.307502i | ||||
\(893\) | −1.27528e7 | −0.0179081 | ||||||||
\(894\) | 3.03084e8 | − | 1.14895e9i | 0.424181 | − | 1.60801i | ||||
\(895\) | 2.35580e8i | 0.328602i | ||||||||
\(896\) | 7.32366e8 | + | 1.75055e8i | 1.01813 | + | 0.243361i | ||||
\(897\) | 8.17144e8 | 1.13220 | ||||||||
\(898\) | 7.18797e8 | + | 1.89613e8i | 0.992607 | + | 0.261842i | ||||
\(899\) | − | 6.59810e8i | − | 0.908113i | ||||||
\(900\) | 7.90318e8 | + | 4.48145e8i | 1.08411 | + | 0.614739i | ||||
\(901\) | 1.27624e9 | 1.74485 | ||||||||
\(902\) | 2.51692e8 | − | 9.54127e8i | 0.342965 | − | 1.30013i | ||||
\(903\) | 1.82951e9i | 2.48468i | ||||||||
\(904\) | 6.66644e8 | + | 6.51294e8i | 0.902379 | + | 0.881600i | ||||
\(905\) | −1.68516e8 | −0.227351 | ||||||||
\(906\) | −2.87892e8 | − | 7.59437e7i | −0.387119 | − | 0.102119i | ||||
\(907\) | 9.69290e8i | 1.29907i | 0.760333 | + | 0.649534i | \(0.225036\pi\) | ||||
−0.760333 | + | 0.649534i | \(0.774964\pi\) | |||||||
\(908\) | −2.60562e6 | + | 4.59509e6i | −0.00348059 | + | 0.00613813i | ||||
\(909\) | 1.40761e9 | 1.87410 | ||||||||
\(910\) | 9.11119e7 | − | 3.45392e8i | 0.120907 | − | 0.458341i | ||||
\(911\) | 9.65924e8i | 1.27758i | 0.769382 | + | 0.638789i | \(0.220564\pi\) | ||||
−0.769382 | + | 0.638789i | \(0.779436\pi\) | |||||||
\(912\) | 1.59795e8 | + | 2.67107e8i | 0.210659 | + | 0.352128i | ||||
\(913\) | −1.28560e9 | −1.68925 | ||||||||
\(914\) | 1.21518e8 | + | 3.20556e7i | 0.159149 | + | 0.0419822i | ||||
\(915\) | − | 2.49423e8i | − | 0.325592i | ||||||
\(916\) | −5.63929e7 | − | 3.19773e7i | −0.0733733 | − | 0.0416059i | ||||
\(917\) | 3.25987e8 | 0.422759 | ||||||||
\(918\) | −4.50437e8 | + | 1.70754e9i | −0.582246 | + | 2.20721i | ||||
\(919\) | − | 1.81018e8i | − | 0.233225i | −0.993178 | − | 0.116612i | \(-0.962796\pi\) | ||
0.993178 | − | 0.116612i | \(-0.0372035\pi\) | |||||||
\(920\) | −3.29588e8 | + | 3.37356e8i | −0.423261 | + | 0.433237i | ||||
\(921\) | 1.39701e9 | 1.78822 | ||||||||
\(922\) | −7.40080e8 | − | 1.95228e8i | −0.944248 | − | 0.249086i | ||||
\(923\) | 2.12839e8i | 0.270674i | ||||||||
\(924\) | 1.37116e9 | − | 2.41809e9i | 1.73809 | − | 3.06519i | ||||
\(925\) | 3.53821e8 | 0.447052 | ||||||||
\(926\) | 2.88086e8 | − | 1.09209e9i | 0.362818 | − | 1.37539i | ||||
\(927\) | − | 1.38042e9i | − | 1.73290i | ||||||
\(928\) | −3.08505e8 | − | 1.06799e9i | −0.386027 | − | 1.33636i | ||||
\(929\) | −1.78665e8 | −0.222839 | −0.111420 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111420 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(930\) | 5.97784e8 | + | 1.57691e8i | 0.743183 | + | 0.196046i | ||||
\(931\) | 1.77387e7i | 0.0219823i | ||||||||
\(932\) | 9.38891e8 | + | 5.32392e8i | 1.15976 | + | 0.657634i | ||||
\(933\) | −2.77842e9 | −3.42099 | ||||||||
\(934\) | 4.49199e7 | − | 1.70285e8i | 0.0551313 | − | 0.208995i | ||||
\(935\) | − | 1.07778e9i | − | 1.31854i | ||||||
\(936\) | −8.87355e8 | − | 8.66923e8i | −1.08211 | − | 1.05719i | ||||
\(937\) | 1.27982e9 | 1.55571 | 0.777857 | − | 0.628442i | \(-0.216307\pi\) | ||||
0.777857 | + | 0.628442i | \(0.216307\pi\) | |||||||
\(938\) | 1.31629e9 | + | 3.47227e8i | 1.59493 | + | 0.420732i | ||||
\(939\) | 2.24331e9i | 2.70952i | ||||||||
\(940\) | −2.10507e7 | + | 3.71235e7i | −0.0253444 | + | 0.0446957i | ||||
\(941\) | 3.45454e8 | 0.414592 | 0.207296 | − | 0.978278i | \(-0.433534\pi\) | ||||
0.207296 | + | 0.978278i | \(0.433534\pi\) | |||||||
\(942\) | −5.19257e8 | + | 1.96843e9i | −0.621198 | + | 2.35487i | ||||
\(943\) | 5.51284e8i | 0.657416i | ||||||||
\(944\) | 9.15327e7 | − | 5.47589e7i | 0.108808 | − | 0.0650937i | ||||
\(945\) | −1.24708e9 | −1.47775 | ||||||||
\(946\) | −2.04443e9 | − | 5.39306e8i | −2.41490 | − | 0.637032i | ||||
\(947\) | 5.09568e8i | 0.600001i | 0.953939 | + | 0.300001i | \(0.0969869\pi\) | ||||
−0.953939 | + | 0.300001i | \(0.903013\pi\) | |||||||
\(948\) | 1.41443e8 | + | 8.02042e7i | 0.166018 | + | 0.0941396i | ||||
\(949\) | 8.60397e8 | 1.00670 | ||||||||
\(950\) | 2.84332e7 | − | 1.07786e8i | 0.0331631 | − | 0.125717i | ||||
\(951\) | 1.06238e9i | 1.23520i | ||||||||
\(952\) | 6.71811e8 | − | 6.87645e8i | 0.778640 | − | 0.796991i | ||||
\(953\) | 1.13954e9 | 1.31659 | 0.658295 | − | 0.752760i | \(-0.271278\pi\) | ||||
0.658295 | + | 0.752760i | \(0.271278\pi\) | |||||||
\(954\) | 3.02644e9 | + | 7.98352e8i | 3.48567 | + | 0.919495i | ||||
\(955\) | 7.22037e8i | 0.828990i | ||||||||
\(956\) | −4.29569e8 | + | 7.57559e8i | −0.491654 | + | 0.867047i | ||||
\(957\) | −4.10383e9 | −4.68224 | ||||||||
\(958\) | 2.28295e8 | − | 8.65435e8i | 0.259657 | − | 0.984323i | ||||
\(959\) | − | 7.91140e8i | − | 0.897011i | ||||||
\(960\) | 1.04132e9 | − | 2.42600e7i | 1.17699 | − | 0.0274206i | ||||
\(961\) | 5.09238e8 | 0.573786 | ||||||||
\(962\) | −4.67140e8 | − | 1.23228e8i | −0.524713 | − | 0.138415i | ||||
\(963\) | − | 2.10090e9i | − | 2.35249i | ||||||
\(964\) | 1.23229e8 | + | 6.98761e7i | 0.137557 | + | 0.0780006i | ||||
\(965\) | 3.39107e8 | 0.377360 | ||||||||
\(966\) | −3.96122e8 | + | 1.50164e9i | −0.439438 | + | 1.66585i | ||||
\(967\) | − | 9.15673e7i | − | 0.101265i | −0.998717 | − | 0.0506327i | \(-0.983876\pi\) | ||
0.998717 | − | 0.0506327i | \(-0.0161238\pi\) | |||||||
\(968\) | 1.64916e9 | + | 1.61119e9i | 1.81818 | + | 1.77632i | ||||
\(969\) | 3.97379e8 | 0.436751 | ||||||||
\(970\) | 2.15016e8 | + | 5.67198e7i | 0.235590 | + | 0.0621469i | ||||
\(971\) | 1.45596e9i | 1.59034i | 0.606384 | + | 0.795172i | \(0.292619\pi\) | ||||
−0.606384 | + | 0.795172i | \(0.707381\pi\) | |||||||
\(972\) | −3.54656e8 | + | 6.25448e8i | −0.386197 | + | 0.681071i | ||||
\(973\) | −2.40822e8 | −0.261431 | ||||||||
\(974\) | 7.74196e7 | − | 2.93486e8i | 0.0837865 | − | 0.317622i | ||||
\(975\) | 6.46324e8i | 0.697327i | ||||||||
\(976\) | 1.32001e8 | + | 2.20648e8i | 0.141981 | + | 0.237329i | ||||
\(977\) | 1.39700e9 | 1.49800 | 0.749000 | − | 0.662571i | \(-0.230535\pi\) | ||||
0.749000 | + | 0.662571i | \(0.230535\pi\) | |||||||
\(978\) | −1.71937e9 | − | 4.53556e8i | −1.83803 | − | 0.484858i | ||||
\(979\) | − | 1.75500e9i | − | 1.87038i | ||||||
\(980\) | 5.16378e7 | + | 2.92809e7i | 0.0548642 | + | 0.0311104i | ||||
\(981\) | −3.17599e9 | −3.36412 | ||||||||
\(982\) | −1.11027e8 | + | 4.20889e8i | −0.117245 | + | 0.444461i | ||||
\(983\) | − | 1.52689e9i | − | 1.60749i | −0.594977 | − | 0.803743i | \(-0.702839\pi\) | ||
0.594977 | − | 0.803743i | \(-0.297161\pi\) | |||||||
\(984\) | 8.50829e8 | − | 8.70882e8i | 0.893012 | − | 0.914059i | ||||
\(985\) | −2.55827e8 | −0.267693 | ||||||||
\(986\) | −1.37230e9 | − | 3.62002e8i | −1.43159 | − | 0.377642i | ||||
\(987\) | 1.40527e8i | 0.146153i | ||||||||
\(988\) | −7.50791e7 | + | 1.32404e8i | −0.0778481 | + | 0.137288i | ||||
\(989\) | 1.18125e9 | 1.22110 | ||||||||
\(990\) | 6.74205e8 | − | 2.55582e9i | 0.694843 | − | 2.63405i | ||||
\(991\) | − | 5.72594e8i | − | 0.588337i | −0.955754 | − | 0.294168i | \(-0.904957\pi\) | ||
0.955754 | − | 0.294168i | \(-0.0950427\pi\) | |||||||
\(992\) | −6.12274e8 | + | 1.76865e8i | −0.627207 | + | 0.181178i | ||||
\(993\) | −4.72460e7 | −0.0482522 | ||||||||
\(994\) | −3.91128e8 | − | 1.03177e8i | −0.398254 | − | 0.105056i | ||||
\(995\) | 7.50342e8i | 0.761711i | ||||||||
\(996\) | −1.37983e9 | − | 7.82424e8i | −1.39652 | − | 0.791889i | ||||
\(997\) | −1.39206e9 | −1.40466 | −0.702332 | − | 0.711850i | \(-0.747858\pi\) | ||||
−0.702332 | + | 0.711850i | \(0.747858\pi\) | |||||||
\(998\) | 1.76467e8 | − | 6.68960e8i | 0.177530 | − | 0.672990i | ||||
\(999\) | 1.68667e9i | 1.69174i |
(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 | 76.7.b.a.39.5 | ✓ | 54 | |
4.3 | odd | 2 | inner | 76.7.b.a.39.6 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.b.a.39.5 | ✓ | 54 | 1.1 | even | 1 | trivial | |
76.7.b.a.39.6 | yes | 54 | 4.3 | odd | 2 | inner |