Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), 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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.17 | ||
Character | \(\chi\) | \(=\) | 43.37 |
Dual form | 43.7.d.a.7.5 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.1559i | 1.26949i | 0.772723 | + | 0.634744i | \(0.218894\pi\) | ||||
−0.772723 | + | 0.634744i | \(0.781106\pi\) | |||||||
\(3\) | 30.5813 | + | 17.6561i | 1.13264 | + | 0.653931i | 0.944598 | − | 0.328230i | \(-0.106452\pi\) |
0.188043 | + | 0.982161i | \(0.439786\pi\) | |||||||
\(4\) | −39.1423 | −0.611599 | ||||||||
\(5\) | 101.658 | + | 58.6923i | 0.813264 | + | 0.469538i | 0.848088 | − | 0.529855i | \(-0.177754\pi\) |
−0.0348238 | + | 0.999393i | \(0.511087\pi\) | |||||||
\(6\) | −179.314 | + | 310.581i | −0.830157 | + | 1.43787i | ||||
\(7\) | 191.878 | − | 110.781i | 0.559411 | − | 0.322976i | −0.193498 | − | 0.981101i | \(-0.561983\pi\) |
0.752909 | + | 0.658125i | \(0.228650\pi\) | |||||||
\(8\) | 252.452i | 0.493070i | ||||||||
\(9\) | 258.977 | + | 448.562i | 0.355250 | + | 0.615312i | ||||
\(10\) | −596.073 | + | 1032.43i | −0.596073 | + | 1.03243i | ||||
\(11\) | 1438.34 | 1.08065 | 0.540323 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540323 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(12\) | −1197.02 | − | 691.102i | −0.692722 | − | 0.399943i | ||||
\(13\) | −661.952 | − | 1146.53i | −0.301298 | − | 0.521864i | 0.675132 | − | 0.737697i | \(-0.264087\pi\) |
−0.976430 | + | 0.215833i | \(0.930753\pi\) | |||||||
\(14\) | 1125.08 | + | 1948.69i | 0.410014 | + | 0.710165i | ||||
\(15\) | 2072.56 | + | 3589.77i | 0.614091 | + | 1.06364i | ||||
\(16\) | −5068.99 | −1.23755 | ||||||||
\(17\) | −3957.19 | − | 6854.06i | −0.805454 | − | 1.39509i | −0.915984 | − | 0.401214i | \(-0.868588\pi\) |
0.110531 | − | 0.993873i | \(-0.464745\pi\) | |||||||
\(18\) | −4555.55 | + | 2630.15i | −0.781130 | + | 0.450986i | ||||
\(19\) | −5836.08 | − | 3369.46i | −0.850864 | − | 0.491247i | 0.0100783 | − | 0.999949i | \(-0.496792\pi\) |
−0.860942 | + | 0.508703i | \(0.830125\pi\) | |||||||
\(20\) | −3979.13 | − | 2297.35i | −0.497392 | − | 0.287169i | ||||
\(21\) | 7823.84 | 0.844816 | ||||||||
\(22\) | 14607.6i | 1.37187i | ||||||||
\(23\) | −7712.75 | + | 13358.9i | −0.633907 | + | 1.09796i | 0.352839 | + | 0.935684i | \(0.385216\pi\) |
−0.986746 | + | 0.162275i | \(0.948117\pi\) | |||||||
\(24\) | −4457.32 | + | 7720.31i | −0.322434 | + | 0.558472i | ||||
\(25\) | −922.926 | − | 1598.55i | −0.0590673 | − | 0.102308i | ||||
\(26\) | 11644.1 | − | 6722.72i | 0.662499 | − | 0.382494i | ||||
\(27\) | − | 7452.48i | − | 0.378625i | ||||||
\(28\) | −7510.55 | + | 4336.22i | −0.342135 | + | 0.197532i | ||||
\(29\) | 11123.1 | − | 6421.92i | 0.456070 | − | 0.263312i | −0.254320 | − | 0.967120i | \(-0.581852\pi\) |
0.710390 | + | 0.703808i | \(0.248518\pi\) | |||||||
\(30\) | −36457.4 | + | 21048.7i | −1.35027 | + | 0.779581i | ||||
\(31\) | 3864.08 | − | 6692.78i | 0.129706 | − | 0.224658i | −0.793857 | − | 0.608105i | \(-0.791930\pi\) |
0.923563 | + | 0.383447i | \(0.125263\pi\) | |||||||
\(32\) | − | 35323.2i | − | 1.07798i | ||||||
\(33\) | 43986.3 | + | 25395.5i | 1.22398 | + | 0.706668i | ||||
\(34\) | 69609.2 | − | 40188.9i | 1.77105 | − | 1.02251i | ||||
\(35\) | 26007.9 | 0.606599 | ||||||||
\(36\) | −10137.0 | − | 17557.8i | −0.217271 | − | 0.376324i | ||||
\(37\) | 12422.5 | + | 7172.14i | 0.245247 | + | 0.141594i | 0.617586 | − | 0.786503i | \(-0.288111\pi\) |
−0.372339 | + | 0.928097i | \(0.621444\pi\) | |||||||
\(38\) | 34219.9 | − | 59270.6i | 0.623631 | − | 1.08016i | ||||
\(39\) | − | 46750.0i | − | 0.788112i | ||||||
\(40\) | −14817.0 | + | 25663.8i | −0.231515 | + | 0.400997i | ||||
\(41\) | 78223.5 | 1.13497 | 0.567487 | − | 0.823383i | \(-0.307916\pi\) | ||||
0.567487 | + | 0.823383i | \(0.307916\pi\) | |||||||
\(42\) | 79458.1i | 1.07248i | ||||||||
\(43\) | −53717.2 | + | 58615.9i | −0.675629 | + | 0.737242i | ||||
\(44\) | −56300.0 | −0.660922 | ||||||||
\(45\) | 60799.9i | 0.667215i | ||||||||
\(46\) | −135671. | − | 78329.9i | −1.39385 | − | 0.804737i | ||||
\(47\) | 104457. | 1.00611 | 0.503055 | − | 0.864254i | \(-0.332209\pi\) | ||||
0.503055 | + | 0.864254i | \(0.332209\pi\) | |||||||
\(48\) | −155016. | − | 89498.7i | −1.40169 | − | 0.809269i | ||||
\(49\) | −34279.7 | + | 59374.2i | −0.291373 | + | 0.504673i | ||||
\(50\) | 16234.8 | − | 9373.15i | 0.129878 | − | 0.0749852i | ||||
\(51\) | − | 279475.i | − | 2.10684i | ||||||
\(52\) | 25910.3 | + | 44878.0i | 0.184274 | + | 0.319171i | ||||
\(53\) | −28184.6 | + | 48817.1i | −0.189315 | + | 0.327902i | −0.945022 | − | 0.327007i | \(-0.893960\pi\) |
0.755707 | + | 0.654909i | \(0.227293\pi\) | |||||||
\(54\) | 75686.6 | 0.480660 | ||||||||
\(55\) | 146219. | + | 84419.5i | 0.878852 | + | 0.507405i | ||||
\(56\) | 27966.8 | + | 48440.0i | 0.159250 | + | 0.275829i | ||||
\(57\) | −118983. | − | 206085.i | −0.642482 | − | 1.11281i | ||||
\(58\) | 65220.4 | + | 112965.i | 0.334271 | + | 0.578975i | ||||
\(59\) | −82703.5 | −0.402687 | −0.201344 | − | 0.979521i | \(-0.564531\pi\) | ||||
−0.201344 | + | 0.979521i | \(0.564531\pi\) | |||||||
\(60\) | −81124.7 | − | 140512.i | −0.375577 | − | 0.650519i | ||||
\(61\) | 133854. | − | 77280.6i | 0.589714 | − | 0.340472i | −0.175270 | − | 0.984520i | \(-0.556080\pi\) |
0.764985 | + | 0.644049i | \(0.222747\pi\) | |||||||
\(62\) | 67971.2 | + | 39243.2i | 0.285200 | + | 0.164660i | ||||
\(63\) | 99384.2 | + | 57379.5i | 0.397462 | + | 0.229475i | ||||
\(64\) | 34323.8 | 0.130935 | ||||||||
\(65\) | − | 155406.i | − | 0.565884i | ||||||
\(66\) | −257914. | + | 446721.i | −0.897106 | + | 1.55383i | ||||
\(67\) | −136307. | + | 236090.i | −0.453203 | + | 0.784971i | −0.998583 | − | 0.0532182i | \(-0.983052\pi\) |
0.545380 | + | 0.838189i | \(0.316385\pi\) | |||||||
\(68\) | 154894. | + | 268284.i | 0.492615 | + | 0.853234i | ||||
\(69\) | −471732. | + | 272354.i | −1.43598 | + | 0.829062i | ||||
\(70\) | 264134.i | 0.770070i | ||||||||
\(71\) | −353197. | + | 203918.i | −0.986829 | + | 0.569746i | −0.904325 | − | 0.426845i | \(-0.859625\pi\) |
−0.0825040 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(72\) | −113240. | + | 65379.4i | −0.303392 | + | 0.175163i | ||||
\(73\) | 240411. | − | 138801.i | 0.617996 | − | 0.356800i | −0.158092 | − | 0.987424i | \(-0.550534\pi\) |
0.776089 | + | 0.630624i | \(0.217201\pi\) | |||||||
\(74\) | −72839.6 | + | 126162.i | −0.179751 | + | 0.311339i | ||||
\(75\) | − | 65181.2i | − | 0.154504i | ||||||
\(76\) | 228438. | + | 131889.i | 0.520387 | + | 0.300446i | ||||
\(77\) | 275986. | − | 159341.i | 0.604526 | − | 0.349023i | ||||
\(78\) | 474789. | 1.00050 | ||||||||
\(79\) | 280774. | + | 486314.i | 0.569476 | + | 0.986361i | 0.996618 | + | 0.0821764i | \(0.0261871\pi\) |
−0.427142 | + | 0.904185i | \(0.640480\pi\) | |||||||
\(80\) | −515303. | − | 297511.i | −1.00645 | − | 0.581075i | ||||
\(81\) | 320376. | − | 554908.i | 0.602845 | − | 1.04416i | ||||
\(82\) | 794430.i | 1.44083i | ||||||||
\(83\) | 383829. | − | 664812.i | 0.671281 | − | 1.16269i | −0.306261 | − | 0.951948i | \(-0.599078\pi\) |
0.977541 | − | 0.210744i | \(-0.0675887\pi\) | |||||||
\(84\) | −306243. | −0.516689 | ||||||||
\(85\) | − | 929027.i | − | 1.51277i | ||||||
\(86\) | −595297. | − | 545547.i | −0.935920 | − | 0.857702i | ||||
\(87\) | 453545. | 0.688751 | ||||||||
\(88\) | 363112.i | 0.532835i | ||||||||
\(89\) | −1.17014e6 | − | 675581.i | −1.65985 | − | 0.958314i | −0.972783 | − | 0.231718i | \(-0.925565\pi\) |
−0.687065 | − | 0.726596i | \(-0.741101\pi\) | |||||||
\(90\) | −617478. | −0.847021 | ||||||||
\(91\) | −254028. | − | 146663.i | −0.337099 | − | 0.194624i | ||||
\(92\) | 301895. | − | 522897.i | 0.387697 | − | 0.671511i | ||||
\(93\) | 236337. | − | 136449.i | 0.293821 | − | 0.169638i | ||||
\(94\) | 1.06086e6i | 1.27724i | ||||||||
\(95\) | −395523. | − | 685065.i | −0.461318 | − | 0.799027i | ||||
\(96\) | 623671. | − | 1.08023e6i | 0.704923 | − | 1.22096i | ||||
\(97\) | 696731. | 0.763396 | 0.381698 | − | 0.924287i | \(-0.375339\pi\) | ||||
0.381698 | + | 0.924287i | \(0.375339\pi\) | |||||||
\(98\) | −602999. | − | 348141.i | −0.640676 | − | 0.369894i | ||||
\(99\) | 372498. | + | 645185.i | 0.383900 | + | 0.664935i | ||||
\(100\) | 36125.5 | + | 62571.2i | 0.0361255 | + | 0.0625712i | ||||
\(101\) | −33336.9 | − | 57741.3i | −0.0323565 | − | 0.0560431i | 0.849394 | − | 0.527760i | \(-0.176968\pi\) |
−0.881750 | + | 0.471717i | \(0.843635\pi\) | |||||||
\(102\) | 2.83832e6 | 2.67461 | ||||||||
\(103\) | −346313. | − | 599831.i | −0.316925 | − | 0.548931i | 0.662920 | − | 0.748691i | \(-0.269317\pi\) |
−0.979845 | + | 0.199760i | \(0.935984\pi\) | |||||||
\(104\) | 289445. | − | 167111.i | 0.257315 | − | 0.148561i | ||||
\(105\) | 795356. | + | 459199.i | 0.687059 | + | 0.396674i | ||||
\(106\) | −495782. | − | 286240.i | −0.416268 | − | 0.240332i | ||||
\(107\) | 574154. | 0.468681 | 0.234340 | − | 0.972155i | \(-0.424707\pi\) | ||||
0.234340 | + | 0.972155i | \(0.424707\pi\) | |||||||
\(108\) | 291707.i | 0.231567i | ||||||||
\(109\) | 125263. | − | 216963.i | 0.0967263 | − | 0.167535i | −0.813601 | − | 0.581423i | \(-0.802496\pi\) |
0.910328 | + | 0.413888i | \(0.135830\pi\) | |||||||
\(110\) | −857357. | + | 1.48499e6i | −0.644145 | + | 1.11569i | ||||
\(111\) | 253265. | + | 438667.i | 0.185185 | + | 0.320750i | ||||
\(112\) | −972627. | + | 561547.i | −0.692297 | + | 0.399698i | ||||
\(113\) | 1.86641e6i | 1.29351i | 0.762696 | + | 0.646757i | \(0.223875\pi\) | ||||
−0.762696 | + | 0.646757i | \(0.776125\pi\) | |||||||
\(114\) | 2.09298e6 | − | 1.20838e6i | 1.41270 | − | 0.815623i | ||||
\(115\) | −1.56813e6 | + | 905358.i | −1.03107 | + | 0.595287i | ||||
\(116\) | −435384. | + | 251369.i | −0.278932 | + | 0.161041i | ||||
\(117\) | 342861. | − | 593853.i | 0.214072 | − | 0.370784i | ||||
\(118\) | − | 839929.i | − | 0.511207i | ||||||
\(119\) | −1.51860e6 | − | 876762.i | −0.901159 | − | 0.520285i | ||||
\(120\) | −906246. | + | 523221.i | −0.524448 | + | 0.302790i | ||||
\(121\) | 297264. | 0.167798 | ||||||||
\(122\) | 784854. | + | 1.35941e6i | 0.432225 | + | 0.748635i | ||||
\(123\) | 2.39218e6 | + | 1.38112e6i | 1.28552 | + | 0.742194i | ||||
\(124\) | −151249. | + | 261971.i | −0.0793282 | + | 0.137400i | ||||
\(125\) | − | 2.05081e6i | − | 1.05001i | ||||||
\(126\) | −582740. | + | 1.00934e6i | −0.291315 | + | 0.504573i | ||||
\(127\) | 950924. | 0.464231 | 0.232116 | − | 0.972688i | \(-0.425435\pi\) | ||||
0.232116 | + | 0.972688i | \(0.425435\pi\) | |||||||
\(128\) | − | 1.91210e6i | − | 0.911758i | ||||||
\(129\) | −2.67767e6 | + | 844113.i | −1.24735 | + | 0.393216i | ||||
\(130\) | 1.57829e6 | 0.718383 | ||||||||
\(131\) | 3.90803e6i | 1.73838i | 0.494482 | + | 0.869188i | \(0.335358\pi\) | ||||
−0.494482 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(132\) | −1.72173e6 | − | 994040.i | −0.748588 | − | 0.432197i | ||||
\(133\) | −1.49309e6 | −0.634644 | ||||||||
\(134\) | −2.39771e6 | − | 1.38432e6i | −0.996511 | − | 0.575336i | ||||
\(135\) | 437403. | − | 757604.i | 0.177779 | − | 0.307922i | ||||
\(136\) | 1.73032e6 | − | 999002.i | 0.687876 | − | 0.397145i | ||||
\(137\) | 2.71035e6i | 1.05405i | 0.849848 | + | 0.527027i | \(0.176693\pi\) | ||||
−0.849848 | + | 0.527027i | \(0.823307\pi\) | |||||||
\(138\) | −2.76600e6 | − | 4.79086e6i | −1.05248 | − | 1.82296i | ||||
\(139\) | −1.35135e6 | + | 2.34060e6i | −0.503179 | + | 0.871531i | 0.496814 | + | 0.867857i | \(0.334503\pi\) |
−0.999993 | + | 0.00367447i | \(0.998830\pi\) | |||||||
\(140\) | −1.01801e6 | −0.370995 | ||||||||
\(141\) | 3.19444e6 | + | 1.84431e6i | 1.13956 | + | 0.657926i | ||||
\(142\) | −2.07097e6 | − | 3.58703e6i | −0.723285 | − | 1.25277i | ||||
\(143\) | −952113. | − | 1.64911e6i | −0.325597 | − | 0.563950i | ||||
\(144\) | −1.31275e6 | − | 2.27376e6i | −0.439638 | − | 0.761476i | ||||
\(145\) | 1.50767e6 | 0.494540 | ||||||||
\(146\) | 1.40965e6 | + | 2.44159e6i | 0.452954 | + | 0.784539i | ||||
\(147\) | −2.09664e6 | + | 1.21049e6i | −0.660042 | + | 0.381075i | ||||
\(148\) | −486246. | − | 280734.i | −0.149993 | − | 0.0865985i | ||||
\(149\) | −3.73726e6 | − | 2.15771e6i | −1.12978 | − | 0.652280i | −0.185902 | − | 0.982568i | \(-0.559521\pi\) |
−0.943880 | + | 0.330288i | \(0.892854\pi\) | |||||||
\(150\) | 661974. | 0.196140 | ||||||||
\(151\) | 6.00486e6i | 1.74410i | 0.489415 | + | 0.872051i | \(0.337211\pi\) | ||||
−0.489415 | + | 0.872051i | \(0.662789\pi\) | |||||||
\(152\) | 850627. | − | 1.47333e6i | 0.242219 | − | 0.419536i | ||||
\(153\) | 2.04965e6 | − | 3.55009e6i | 0.572275 | − | 0.991210i | ||||
\(154\) | 1.61825e6 | + | 2.80289e6i | 0.443081 | + | 0.767438i | ||||
\(155\) | 785629. | − | 453583.i | 0.210971 | − | 0.121804i | ||||
\(156\) | 1.82991e6i | 0.482009i | ||||||||
\(157\) | −4.27325e6 | + | 2.46716e6i | −1.10423 | + | 0.637527i | −0.937328 | − | 0.348447i | \(-0.886709\pi\) |
−0.166900 | + | 0.985974i | \(0.553376\pi\) | |||||||
\(158\) | −4.93896e6 | + | 2.85151e6i | −1.25217 | + | 0.722942i | ||||
\(159\) | −1.72384e6 | + | 995261.i | −0.428851 | + | 0.247597i | ||||
\(160\) | 2.07320e6 | − | 3.59089e6i | 0.506152 | − | 0.876682i | ||||
\(161\) | 3.41770e6i | 0.818947i | ||||||||
\(162\) | 5.63559e6 | + | 3.25371e6i | 1.32555 | + | 0.765304i | ||||
\(163\) | 5.44538e6 | − | 3.14389e6i | 1.25738 | − | 0.725947i | 0.284814 | − | 0.958583i | \(-0.408068\pi\) |
0.972564 | + | 0.232636i | \(0.0747350\pi\) | |||||||
\(164\) | −3.06185e6 | −0.694148 | ||||||||
\(165\) | 2.98104e6 | + | 5.16332e6i | 0.663616 | + | 1.14942i | ||||
\(166\) | 6.75177e6 | + | 3.89813e6i | 1.47602 | + | 0.852182i | ||||
\(167\) | 4.53376e6 | − | 7.85271e6i | 0.973440 | − | 1.68605i | 0.288452 | − | 0.957494i | \(-0.406859\pi\) |
0.684989 | − | 0.728554i | \(-0.259807\pi\) | |||||||
\(168\) | 1.97514e6i | 0.416554i | ||||||||
\(169\) | 1.53704e6 | − | 2.66224e6i | 0.318439 | − | 0.551552i | ||||
\(170\) | 9.43511e6 | 1.92044 | ||||||||
\(171\) | − | 3.49046e6i | − | 0.698062i | ||||||
\(172\) | 2.10262e6 | − | 2.29436e6i | 0.413214 | − | 0.450896i | ||||
\(173\) | −9.00093e6 | −1.73840 | −0.869199 | − | 0.494463i | \(-0.835365\pi\) | ||||
−0.869199 | + | 0.494463i | \(0.835365\pi\) | |||||||
\(174\) | 4.60615e6i | 0.874361i | ||||||||
\(175\) | −354178. | − | 204485.i | −0.0660858 | − | 0.0381546i | ||||
\(176\) | −7.29093e6 | −1.33735 | ||||||||
\(177\) | −2.52918e6 | − | 1.46022e6i | −0.456100 | − | 0.263330i | ||||
\(178\) | 6.86114e6 | − | 1.18838e7i | 1.21657 | − | 2.10716i | ||||
\(179\) | −2.38423e6 | + | 1.37654e6i | −0.415709 | + | 0.240010i | −0.693240 | − | 0.720707i | \(-0.743817\pi\) |
0.277531 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(180\) | − | 2.37985e6i | − | 0.408068i | ||||||
\(181\) | 1.71977e6 | + | 2.97873e6i | 0.290025 | + | 0.502337i | 0.973815 | − | 0.227341i | \(-0.0730031\pi\) |
−0.683791 | + | 0.729678i | \(0.739670\pi\) | |||||||
\(182\) | 1.48950e6 | − | 2.57988e6i | 0.247073 | − | 0.427943i | ||||
\(183\) | 5.45790e6 | 0.890579 | ||||||||
\(184\) | −3.37247e6 | − | 1.94710e6i | −0.541371 | − | 0.312561i | ||||
\(185\) | 841899. | + | 1.45821e6i | 0.132967 | + | 0.230306i | ||||
\(186\) | 1.38576e6 | + | 2.40022e6i | 0.215353 | + | 0.373002i | ||||
\(187\) | −5.69179e6 | − | 9.85848e6i | −0.870411 | − | 1.50760i | ||||
\(188\) | −4.08871e6 | −0.615336 | ||||||||
\(189\) | −825591. | − | 1.42997e6i | −0.122287 | − | 0.211807i | ||||
\(190\) | 6.95746e6 | − | 4.01689e6i | 1.01435 | − | 0.585638i | ||||
\(191\) | −3.28426e6 | − | 1.89617e6i | −0.471343 | − | 0.272130i | 0.245458 | − | 0.969407i | \(-0.421062\pi\) |
−0.716802 | + | 0.697277i | \(0.754395\pi\) | |||||||
\(192\) | 1.04967e6 | + | 606025.i | 0.148302 | + | 0.0856223i | ||||
\(193\) | 205647. | 0.0286055 | 0.0143028 | − | 0.999898i | \(-0.495447\pi\) | ||||
0.0143028 | + | 0.999898i | \(0.495447\pi\) | |||||||
\(194\) | 7.07593e6i | 0.969121i | ||||||||
\(195\) | 2.74387e6 | − | 4.75252e6i | 0.370049 | − | 0.640944i | ||||
\(196\) | 1.34179e6 | − | 2.32405e6i | 0.178203 | − | 0.308657i | ||||
\(197\) | 3.52501e6 | + | 6.10549e6i | 0.461064 | + | 0.798586i | 0.999014 | − | 0.0443902i | \(-0.0141345\pi\) |
−0.537950 | + | 0.842977i | \(0.680801\pi\) | |||||||
\(198\) | −6.55244e6 | + | 3.78305e6i | −0.844126 | + | 0.487356i | ||||
\(199\) | − | 1.46553e7i | − | 1.85967i | −0.367982 | − | 0.929833i | \(-0.619951\pi\) | ||
0.367982 | − | 0.929833i | \(-0.380049\pi\) | |||||||
\(200\) | 403558. | − | 232995.i | 0.0504448 | − | 0.0291243i | ||||
\(201\) | −8.33688e6 | + | 4.81330e6i | −1.02663 | + | 0.592727i | ||||
\(202\) | 586415. | − | 338567.i | 0.0711460 | − | 0.0410762i | ||||
\(203\) | 1.42285e6 | − | 2.46445e6i | 0.170087 | − | 0.294599i | ||||
\(204\) | 1.09393e7i | 1.28854i | ||||||||
\(205\) | 7.95205e6 | + | 4.59112e6i | 0.923033 | + | 0.532914i | ||||
\(206\) | 6.09183e6 | − | 3.51712e6i | 0.696861 | − | 0.402333i | ||||
\(207\) | −7.98971e6 | −0.900783 | ||||||||
\(208\) | 3.35543e6 | + | 5.81177e6i | 0.372870 | + | 0.645830i | ||||
\(209\) | −8.39427e6 | − | 4.84643e6i | −0.919483 | − | 0.530864i | ||||
\(210\) | −4.66358e6 | + | 8.07756e6i | −0.503572 | + | 0.872213i | ||||
\(211\) | 5.64350e6i | 0.600761i | 0.953820 | + | 0.300380i | \(0.0971136\pi\) | ||||
−0.953820 | + | 0.300380i | \(0.902886\pi\) | |||||||
\(212\) | 1.10321e6 | − | 1.91082e6i | 0.115785 | − | 0.200545i | ||||
\(213\) | −1.44016e7 | −1.49030 | ||||||||
\(214\) | 5.83105e6i | 0.594985i | ||||||||
\(215\) | −8.90109e6 | + | 2.80599e6i | −0.895628 | + | 0.282339i | ||||
\(216\) | 1.88139e6 | 0.186689 | ||||||||
\(217\) | − | 1.71226e6i | − | 0.167568i | ||||||
\(218\) | 2.20345e6 | + | 1.27216e6i | 0.212683 | + | 0.122793i | ||||
\(219\) | 9.80278e6 | 0.933291 | ||||||||
\(220\) | −5.72335e6 | − | 3.30438e6i | −0.537505 | − | 0.310329i | ||||
\(221\) | −5.23894e6 | + | 9.07412e6i | −0.485363 | + | 0.840674i | ||||
\(222\) | −4.45506e6 | + | 2.57213e6i | −0.407188 | + | 0.235090i | ||||
\(223\) | − | 1.16340e7i | − | 1.04909i | −0.851382 | − | 0.524546i | \(-0.824235\pi\) | ||
0.851382 | − | 0.524546i | \(-0.175765\pi\) | |||||||
\(224\) | −3.91313e6 | − | 6.77775e6i | −0.348161 | − | 0.603033i | ||||
\(225\) | 478034. | − | 827979.i | 0.0419673 | − | 0.0726896i | ||||
\(226\) | −1.89551e7 | −1.64210 | ||||||||
\(227\) | 1.38180e7 | + | 7.97783e6i | 1.18132 | + | 0.682036i | 0.956320 | − | 0.292322i | \(-0.0944280\pi\) |
0.225001 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(228\) | 4.65728e6 | + | 8.06665e6i | 0.392941 | + | 0.680595i | ||||
\(229\) | 8.79463e6 | + | 1.52328e7i | 0.732338 | + | 1.26845i | 0.955882 | + | 0.293752i | \(0.0949040\pi\) |
−0.223544 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(230\) | −9.19472e6 | − | 1.59257e7i | −0.755710 | − | 1.30893i | ||||
\(231\) | 1.12533e7 | 0.912948 | ||||||||
\(232\) | 1.62123e6 | + | 2.80805e6i | 0.129831 | + | 0.224874i | ||||
\(233\) | 275483. | − | 159050.i | 0.0217785 | − | 0.0125738i | −0.489071 | − | 0.872244i | \(-0.662664\pi\) |
0.510850 | + | 0.859670i | \(0.329331\pi\) | |||||||
\(234\) | 6.03111e6 | + | 3.48207e6i | 0.470706 | + | 0.271762i | ||||
\(235\) | 1.06189e7 | + | 6.13084e6i | 0.818234 | + | 0.472407i | ||||
\(236\) | 3.23721e6 | 0.246283 | ||||||||
\(237\) | 1.98295e7i | 1.48959i | ||||||||
\(238\) | 8.90431e6 | − | 1.54227e7i | 0.660495 | − | 1.14401i | ||||
\(239\) | 3.34835e6 | − | 5.79951e6i | 0.245266 | − | 0.424813i | −0.716940 | − | 0.697134i | \(-0.754458\pi\) |
0.962206 | + | 0.272321i | \(0.0877914\pi\) | |||||||
\(240\) | −1.05058e7 | − | 1.81965e7i | −0.759966 | − | 1.31630i | ||||
\(241\) | −2.09680e7 | + | 1.21059e7i | −1.49798 | + | 0.864857i | −0.999997 | − | 0.00233228i | \(-0.999258\pi\) |
−0.497979 | + | 0.867189i | \(0.665924\pi\) | |||||||
\(242\) | 3.01898e6i | 0.213017i | ||||||||
\(243\) | 1.48901e7 | − | 8.59678e6i | 1.03771 | − | 0.599125i | ||||
\(244\) | −5.23936e6 | + | 3.02494e6i | −0.360669 | + | 0.208232i | ||||
\(245\) | −6.96962e6 | + | 4.02391e6i | −0.473926 | + | 0.273621i | ||||
\(246\) | −1.40266e7 | + | 2.42947e7i | −0.942206 | + | 1.63195i | ||||
\(247\) | 8.92168e6i | 0.592047i | ||||||||
\(248\) | 1.68961e6 | + | 975494.i | 0.110772 | + | 0.0639543i | ||||
\(249\) | 2.34760e7 | − | 1.35539e7i | 1.52064 | − | 0.877942i | ||||
\(250\) | 2.08278e7 | 1.33298 | ||||||||
\(251\) | −7.86861e6 | − | 1.36288e7i | −0.497596 | − | 0.861862i | 0.502400 | − | 0.864635i | \(-0.332450\pi\) |
−0.999996 | + | 0.00277362i | \(0.999117\pi\) | |||||||
\(252\) | −3.89013e6 | − | 2.24597e6i | −0.243087 | − | 0.140347i | ||||
\(253\) | −1.10936e7 | + | 1.92146e7i | −0.685030 | + | 1.18651i | ||||
\(254\) | 9.65749e6i | 0.589336i | ||||||||
\(255\) | 1.64030e7 | − | 2.84109e7i | 0.989244 | − | 1.71342i | ||||
\(256\) | 2.16158e7 | 1.28840 | ||||||||
\(257\) | 7.42651e6i | 0.437507i | 0.975780 | + | 0.218754i | \(0.0701991\pi\) | ||||
−0.975780 | + | 0.218754i | \(0.929801\pi\) | |||||||
\(258\) | −8.57273e6 | − | 2.71942e7i | −0.499183 | − | 1.58350i | ||||
\(259\) | 3.17814e6 | 0.182926 | ||||||||
\(260\) | 6.08295e6i | 0.346094i | ||||||||
\(261\) | 5.76126e6 | + | 3.32626e6i | 0.324038 | + | 0.187083i | ||||
\(262\) | −3.96895e7 | −2.20685 | ||||||||
\(263\) | 5.28004e6 | + | 3.04843e6i | 0.290248 | + | 0.167575i | 0.638054 | − | 0.769992i | \(-0.279740\pi\) |
−0.347805 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(264\) | −6.41115e6 | + | 1.11044e7i | −0.348437 | + | 0.603511i | ||||
\(265\) | −5.73038e6 | + | 3.30844e6i | −0.307926 | + | 0.177781i | ||||
\(266\) | − | 1.51636e7i | − | 0.805672i | ||||||
\(267\) | −2.38563e7 | − | 4.13203e7i | −1.25334 | − | 2.17085i | ||||
\(268\) | 5.33536e6 | − | 9.24112e6i | 0.277179 | − | 0.480087i | ||||
\(269\) | −2.75605e6 | −0.141589 | −0.0707945 | − | 0.997491i | \(-0.522553\pi\) | ||||
−0.0707945 | + | 0.997491i | \(0.522553\pi\) | |||||||
\(270\) | 7.69415e6 | + | 4.44222e6i | 0.390903 | + | 0.225688i | ||||
\(271\) | 5.23944e6 | + | 9.07498e6i | 0.263255 | + | 0.455972i | 0.967105 | − | 0.254377i | \(-0.0818705\pi\) |
−0.703850 | + | 0.710349i | \(0.748537\pi\) | |||||||
\(272\) | 2.00590e7 | + | 3.47431e7i | 0.996786 | + | 1.72648i | ||||
\(273\) | −5.17901e6 | − | 8.97030e6i | −0.254541 | − | 0.440879i | ||||
\(274\) | −2.75260e7 | −1.33811 | ||||||||
\(275\) | −1.32748e6 | − | 2.29927e6i | −0.0638309 | − | 0.110558i | ||||
\(276\) | 1.84647e7 | − | 1.06606e7i | 0.878243 | − | 0.507054i | ||||
\(277\) | −4.80218e6 | − | 2.77254e6i | −0.225943 | − | 0.130448i | 0.382756 | − | 0.923849i | \(-0.374975\pi\) |
−0.608699 | + | 0.793401i | \(0.708308\pi\) | |||||||
\(278\) | −2.37709e7 | − | 1.37241e7i | −1.10640 | − | 0.638779i | ||||
\(279\) | 4.00284e6 | 0.184313 | ||||||||
\(280\) | 6.56575e6i | 0.299096i | ||||||||
\(281\) | 1.83973e7 | − | 3.18651e7i | 0.829155 | − | 1.43614i | −0.0695472 | − | 0.997579i | \(-0.522155\pi\) |
0.898702 | − | 0.438560i | \(-0.144511\pi\) | |||||||
\(282\) | −1.87307e7 | + | 3.24424e7i | −0.835229 | + | 1.44666i | ||||
\(283\) | −2.59431e6 | − | 4.49347e6i | −0.114462 | − | 0.198254i | 0.803102 | − | 0.595841i | \(-0.203181\pi\) |
−0.917565 | + | 0.397587i | \(0.869848\pi\) | |||||||
\(284\) | 1.38250e7 | − | 7.98184e6i | 0.603543 | − | 0.348456i | ||||
\(285\) | − | 2.79336e7i | − | 1.20668i | ||||||
\(286\) | 1.67482e7 | − | 9.66956e6i | 0.715928 | − | 0.413341i | ||||
\(287\) | 1.50094e7 | − | 8.66566e6i | 0.634917 | − | 0.366569i | ||||
\(288\) | 1.58447e7 | − | 9.14791e6i | 0.663293 | − | 0.382952i | ||||
\(289\) | −1.92500e7 | + | 3.33419e7i | −0.797511 | + | 1.38133i | ||||
\(290\) | 1.53117e7i | 0.627813i | ||||||||
\(291\) | 2.13069e7 | + | 1.23016e7i | 0.864653 | + | 0.499208i | ||||
\(292\) | −9.41025e6 | + | 5.43301e6i | −0.377966 | + | 0.218219i | ||||
\(293\) | 4.46231e7 | 1.77401 | 0.887007 | − | 0.461757i | \(-0.152781\pi\) | ||||
0.887007 | + | 0.461757i | \(0.152781\pi\) | |||||||
\(294\) | −1.22937e7 | − | 2.12932e7i | −0.483770 | − | 0.837915i | ||||
\(295\) | −8.40748e6 | − | 4.85406e6i | −0.327491 | − | 0.189077i | ||||
\(296\) | −1.81062e6 | + | 3.13609e6i | −0.0698156 | + | 0.120924i | ||||
\(297\) | − | 1.07192e7i | − | 0.409160i | ||||||
\(298\) | 2.19135e7 | − | 3.79553e7i | 0.828061 | − | 1.43424i | ||||
\(299\) | 2.04219e7 | 0.763980 | ||||||||
\(300\) | 2.55134e6i | 0.0944942i | ||||||||
\(301\) | −3.81363e6 | + | 1.71979e7i | −0.139843 | + | 0.630633i | ||||
\(302\) | −6.09848e7 | −2.21412 | ||||||||
\(303\) | − | 2.35440e6i | − | 0.0846356i | ||||||
\(304\) | 2.95830e7 | + | 1.70797e7i | 1.05298 | + | 0.607940i | ||||
\(305\) | 1.81431e7 | 0.639458 | ||||||||
\(306\) | 3.60544e7 | + | 2.08160e7i | 1.25833 | + | 0.726496i | ||||
\(307\) | −2.38539e7 | + | 4.13162e7i | −0.824412 | + | 1.42792i | 0.0779555 | + | 0.996957i | \(0.475161\pi\) |
−0.902368 | + | 0.430967i | \(0.858173\pi\) | |||||||
\(308\) | −1.08027e7 | + | 6.23696e6i | −0.369727 | + | 0.213462i | ||||
\(309\) | − | 2.44582e7i | − | 0.828988i | ||||||
\(310\) | 4.60655e6 | + | 7.97877e6i | 0.154629 | + | 0.267825i | ||||
\(311\) | 1.73824e7 | − | 3.01072e7i | 0.577867 | − | 1.00090i | −0.417856 | − | 0.908513i | \(-0.637218\pi\) |
0.995724 | − | 0.0923826i | \(-0.0294483\pi\) | |||||||
\(312\) | 1.18021e7 | 0.388595 | ||||||||
\(313\) | −2.95387e7 | − | 1.70542e7i | −0.963294 | − | 0.556158i | −0.0661085 | − | 0.997812i | \(-0.521058\pi\) |
−0.897185 | + | 0.441655i | \(0.854392\pi\) | |||||||
\(314\) | −2.50562e7 | − | 4.33987e7i | −0.809332 | − | 1.40180i | ||||
\(315\) | 6.73547e6 | + | 1.16662e7i | 0.215494 | + | 0.373247i | ||||
\(316\) | −1.09901e7 | − | 1.90355e7i | −0.348291 | − | 0.603257i | ||||
\(317\) | −6.96957e6 | −0.218790 | −0.109395 | − | 0.993998i | \(-0.534891\pi\) | ||||
−0.109395 | + | 0.993998i | \(0.534891\pi\) | |||||||
\(318\) | −1.01078e7 | − | 1.75072e7i | −0.314321 | − | 0.544421i | ||||
\(319\) | 1.59988e7 | − | 9.23691e6i | 0.492850 | − | 0.284547i | ||||
\(320\) | 3.48929e6 | + | 2.01454e6i | 0.106485 | + | 0.0614790i | ||||
\(321\) | 1.75584e7 | + | 1.01373e7i | 0.530847 | + | 0.306485i | ||||
\(322\) | −3.47098e7 | −1.03964 | ||||||||
\(323\) | 5.33344e7i | 1.58271i | ||||||||
\(324\) | −1.25403e7 | + | 2.17204e7i | −0.368699 | + | 0.638606i | ||||
\(325\) | −1.22187e6 | + | 2.11633e6i | −0.0355937 | + | 0.0616501i | ||||
\(326\) | 3.19291e7 | + | 5.53028e7i | 0.921581 | + | 1.59623i | ||||
\(327\) | 7.66143e6 | − | 4.42333e6i | 0.219112 | − | 0.126505i | ||||
\(328\) | 1.97477e7i | 0.559622i | ||||||||
\(329\) | 2.00431e7 | − | 1.15719e7i | 0.562829 | − | 0.324950i | ||||
\(330\) | −5.24382e7 | + | 3.02752e7i | −1.45917 | + | 0.842452i | ||||
\(331\) | −2.88699e6 | + | 1.66680e6i | −0.0796088 | + | 0.0459622i | −0.539276 | − | 0.842129i | \(-0.681302\pi\) |
0.459667 | + | 0.888091i | \(0.347969\pi\) | |||||||
\(332\) | −1.50240e7 | + | 2.60223e7i | −0.410554 | + | 0.711101i | ||||
\(333\) | 7.42970e6i | 0.201205i | ||||||||
\(334\) | 7.97513e7 | + | 4.60444e7i | 2.14042 | + | 1.23577i | ||||
\(335\) | −2.77134e7 | + | 1.60003e7i | −0.737148 | + | 0.425593i | ||||
\(336\) | −3.96589e7 | −1.04550 | ||||||||
\(337\) | −2.99147e6 | − | 5.18137e6i | −0.0781618 | − | 0.135380i | 0.824295 | − | 0.566160i | \(-0.191572\pi\) |
−0.902457 | + | 0.430780i | \(0.858238\pi\) | |||||||
\(338\) | 2.70374e7 | + | 1.56101e7i | 0.700189 | + | 0.404254i | ||||
\(339\) | −3.29535e7 | + | 5.70772e7i | −0.845868 | + | 1.46509i | ||||
\(340\) | 3.63643e7i | 0.925206i | ||||||||
\(341\) | 5.55786e6 | − | 9.62650e6i | 0.140167 | − | 0.242776i | ||||
\(342\) | 3.54487e7 | 0.886181 | ||||||||
\(343\) | 4.12566e7i | 1.02238i | ||||||||
\(344\) | −1.47977e7 | − | 1.35610e7i | −0.363512 | − | 0.333132i | ||||
\(345\) | −6.39404e7 | −1.55711 | ||||||||
\(346\) | − | 9.14126e7i | − | 2.20687i | ||||||
\(347\) | 388377. | + | 224230.i | 0.00929535 | + | 0.00536667i | 0.504640 | − | 0.863330i | \(-0.331625\pi\) |
−0.495345 | + | 0.868696i | \(0.664958\pi\) | |||||||
\(348\) | −1.77528e7 | −0.421239 | ||||||||
\(349\) | −5.71824e7 | − | 3.30143e7i | −1.34520 | − | 0.776650i | −0.357632 | − | 0.933863i | \(-0.616416\pi\) |
−0.987565 | + | 0.157213i | \(0.949749\pi\) | |||||||
\(350\) | 2.07673e6 | − | 3.59700e6i | 0.0484368 | − | 0.0838951i | ||||
\(351\) | −8.54452e6 | + | 4.93318e6i | −0.197591 | + | 0.114079i | ||||
\(352\) | − | 5.08068e7i | − | 1.16491i | ||||||
\(353\) | −1.18380e7 | − | 2.05041e7i | −0.269126 | − | 0.466139i | 0.699511 | − | 0.714622i | \(-0.253401\pi\) |
−0.968636 | + | 0.248483i | \(0.920068\pi\) | |||||||
\(354\) | 1.48299e7 | − | 2.56861e7i | 0.334294 | − | 0.579014i | ||||
\(355\) | −4.78737e7 | −1.07007 | ||||||||
\(356\) | 4.58021e7 | + | 2.64438e7i | 1.01516 | + | 0.586104i | ||||
\(357\) | −3.09605e7 | − | 5.36251e7i | −0.680460 | − | 1.17859i | ||||
\(358\) | −1.39800e7 | − | 2.42140e7i | −0.304690 | − | 0.527738i | ||||
\(359\) | −2.71043e7 | − | 4.69461e7i | −0.585808 | − | 1.01465i | −0.994774 | − | 0.102100i | \(-0.967444\pi\) |
0.408966 | − | 0.912550i | \(-0.365890\pi\) | |||||||
\(360\) | −1.53491e7 | −0.328984 | ||||||||
\(361\) | −816421. | − | 1.41408e6i | −0.0173537 | − | 0.0300575i | ||||
\(362\) | −3.02517e7 | + | 1.74658e7i | −0.637711 | + | 0.368183i | ||||
\(363\) | 9.09071e6 | + | 5.24852e6i | 0.190054 | + | 0.109728i | ||||
\(364\) | 9.94325e6 | + | 5.74074e6i | 0.206169 | + | 0.119032i | ||||
\(365\) | 3.25863e7 | 0.670126 | ||||||||
\(366\) | 5.54299e7i | 1.13058i | ||||||||
\(367\) | 1.21462e7 | − | 2.10378e7i | 0.245721 | − | 0.425601i | −0.716613 | − | 0.697471i | \(-0.754309\pi\) |
0.962334 | + | 0.271870i | \(0.0876419\pi\) | |||||||
\(368\) | 3.90958e7 | − | 6.77159e7i | 0.784489 | − | 1.35877i | ||||
\(369\) | 2.02581e7 | + | 3.50881e7i | 0.403200 | + | 0.698362i | ||||
\(370\) | −1.48095e7 | + | 8.55025e6i | −0.292371 | + | 0.168800i | ||||
\(371\) | 1.24892e7i | 0.244576i | ||||||||
\(372\) | −9.25078e6 | + | 5.34094e6i | −0.179701 | + | 0.103750i | ||||
\(373\) | −5.54830e7 | + | 3.20331e7i | −1.06914 | + | 0.617267i | −0.927946 | − | 0.372716i | \(-0.878427\pi\) |
−0.141191 | + | 0.989982i | \(0.545093\pi\) | |||||||
\(374\) | 1.00122e8 | − | 5.78053e7i | 1.91387 | − | 1.10498i | ||||
\(375\) | 3.62093e7 | − | 6.27164e7i | 0.686636 | − | 1.18929i | ||||
\(376\) | 2.63705e7i | 0.496083i | ||||||||
\(377\) | −1.47259e7 | − | 8.50200e6i | −0.274826 | − | 0.158671i | ||||
\(378\) | 1.45226e7 | − | 8.38462e6i | 0.268886 | − | 0.155242i | ||||
\(379\) | −2.15364e7 | −0.395599 | −0.197800 | − | 0.980242i | \(-0.563380\pi\) | ||||
−0.197800 | + | 0.980242i | \(0.563380\pi\) | |||||||
\(380\) | 1.54817e7 | + | 2.68151e7i | 0.282142 | + | 0.488684i | ||||
\(381\) | 2.90805e7 | + | 1.67896e7i | 0.525808 | + | 0.303575i | ||||
\(382\) | 1.92573e7 | − | 3.33546e7i | 0.345466 | − | 0.598365i | ||||
\(383\) | − | 9.47348e7i | − | 1.68622i | −0.537744 | − | 0.843108i | \(-0.680723\pi\) | ||
0.537744 | − | 0.843108i | \(-0.319277\pi\) | |||||||
\(384\) | 3.37602e7 | − | 5.84744e7i | 0.596227 | − | 1.03269i | ||||
\(385\) | 3.74083e7 | 0.655519 | ||||||||
\(386\) | 2.08853e6i | 0.0363144i | ||||||||
\(387\) | −4.02044e7 | − | 8.91531e6i | −0.693651 | − | 0.153817i | ||||
\(388\) | −2.72717e7 | −0.466892 | ||||||||
\(389\) | 1.08224e7i | 0.183854i | 0.995766 | + | 0.0919272i | \(0.0293027\pi\) | ||||
−0.995766 | + | 0.0919272i | \(0.970697\pi\) | |||||||
\(390\) | 4.82661e7 | + | 2.78664e7i | 0.813670 | + | 0.469773i | ||||
\(391\) | 1.22083e8 | 2.04233 | ||||||||
\(392\) | −1.49891e7 | − | 8.65398e6i | −0.248839 | − | 0.143667i | ||||
\(393\) | −6.90006e7 | + | 1.19513e8i | −1.13678 | + | 1.96896i | ||||
\(394\) | −6.20068e7 | + | 3.57996e7i | −1.01380 | + | 0.585315i | ||||
\(395\) | 6.59170e7i | 1.06956i | ||||||||
\(396\) | −1.45804e7 | − | 2.52541e7i | −0.234793 | − | 0.406673i | ||||
\(397\) | −3.97294e7 | + | 6.88134e7i | −0.634952 | + | 1.09977i | 0.351574 | + | 0.936160i | \(0.385647\pi\) |
−0.986525 | + | 0.163608i | \(0.947687\pi\) | |||||||
\(398\) | 1.48838e8 | 2.36082 | ||||||||
\(399\) | −4.56605e7 | − | 2.63621e7i | −0.718823 | − | 0.415013i | ||||
\(400\) | 4.67830e6 | + | 8.10305e6i | 0.0730984 | + | 0.126610i | ||||
\(401\) | 5.82616e7 | + | 1.00912e8i | 0.903544 | + | 1.56498i | 0.822860 | + | 0.568244i | \(0.192377\pi\) |
0.0806833 | + | 0.996740i | \(0.474290\pi\) | |||||||
\(402\) | −4.88834e7 | − | 8.46685e7i | −0.752459 | − | 1.30330i | ||||
\(403\) | −1.02313e7 | −0.156321 | ||||||||
\(404\) | 1.30489e6 | + | 2.26013e6i | 0.0197892 | + | 0.0342759i | ||||
\(405\) | 6.51377e7 | − | 3.76073e7i | 0.980544 | − | 0.566118i | ||||
\(406\) | 2.50287e7 | + | 1.44503e7i | 0.373990 | + | 0.215923i | ||||
\(407\) | 1.78678e7 | + | 1.03160e7i | 0.265026 | + | 0.153013i | ||||
\(408\) | 7.05540e7 | 1.03882 | ||||||||
\(409\) | − | 6.68971e7i | − | 0.977771i | −0.872348 | − | 0.488886i | \(-0.837404\pi\) | ||
0.872348 | − | 0.488886i | \(-0.162596\pi\) | |||||||
\(410\) | −4.66269e7 | + | 8.07602e7i | −0.676527 | + | 1.17178i | ||||
\(411\) | −4.78542e7 | + | 8.28859e7i | −0.689278 | + | 1.19387i | ||||
\(412\) | 1.35555e7 | + | 2.34788e7i | 0.193831 | + | 0.335725i | ||||
\(413\) | −1.58690e7 | + | 9.16197e6i | −0.225268 | + | 0.130058i | ||||
\(414\) | − | 8.11427e7i | − | 1.14353i | ||||||
\(415\) | 7.80387e7 | − | 4.50557e7i | 1.09186 | − | 0.630384i | ||||
\(416\) | −4.04993e7 | + | 2.33823e7i | −0.562558 | + | 0.324793i | ||||
\(417\) | −8.26519e7 | + | 4.77191e7i | −1.13984 | + | 0.658088i | ||||
\(418\) | 4.92199e7 | − | 8.52513e7i | 0.673925 | − | 1.16727i | ||||
\(419\) | 7.35158e7i | 0.999398i | 0.866199 | + | 0.499699i | \(0.166556\pi\) | ||||
−0.866199 | + | 0.499699i | \(0.833444\pi\) | |||||||
\(420\) | −3.11321e7 | − | 1.79741e7i | −0.420204 | − | 0.242605i | ||||
\(421\) | 1.31461e7 | − | 7.58992e6i | 0.176178 | − | 0.101716i | −0.409318 | − | 0.912392i | \(-0.634233\pi\) |
0.585496 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(422\) | −5.73149e7 | −0.762658 | ||||||||
\(423\) | 2.70521e7 | + | 4.68556e7i | 0.357421 | + | 0.619071i | ||||
\(424\) | −1.23240e7 | − | 7.11525e6i | −0.161679 | − | 0.0933454i | ||||
\(425\) | −7.30440e6 | + | 1.26516e7i | −0.0951519 | + | 0.164808i | ||||
\(426\) | − | 1.46262e8i | − | 1.89191i | ||||||
\(427\) | 1.71224e7 | − | 2.96569e7i | 0.219928 | − | 0.380927i | ||||
\(428\) | −2.24737e7 | −0.286645 | ||||||||
\(429\) | − | 6.72425e7i | − | 0.851671i | ||||||
\(430\) | −2.84974e7 | − | 9.03986e7i | −0.358426 | − | 1.13699i | ||||
\(431\) | 8.12140e7 | 1.01438 | 0.507188 | − | 0.861835i | \(-0.330685\pi\) | ||||
0.507188 | + | 0.861835i | \(0.330685\pi\) | |||||||
\(432\) | 3.77765e7i | 0.468566i | ||||||||
\(433\) | 6.19999e7 | + | 3.57956e7i | 0.763708 | + | 0.440927i | 0.830625 | − | 0.556832i | \(-0.187983\pi\) |
−0.0669177 | + | 0.997758i | \(0.521316\pi\) | |||||||
\(434\) | 1.73896e7 | 0.212726 | ||||||||
\(435\) | 4.61065e7 | + | 2.66196e7i | 0.560137 | + | 0.323395i | ||||
\(436\) | −4.90310e6 | + | 8.49242e6i | −0.0591577 | + | 0.102464i | ||||
\(437\) | 9.00243e7 | − | 5.19756e7i | 1.07874 | − | 0.622809i | ||||
\(438\) | 9.95561e7i | 1.18480i | ||||||||
\(439\) | −1.44401e7 | − | 2.50110e7i | −0.170678 | − | 0.295623i | 0.767979 | − | 0.640475i | \(-0.221262\pi\) |
−0.938657 | + | 0.344852i | \(0.887929\pi\) | |||||||
\(440\) | −2.13119e7 | + | 3.69133e7i | −0.250186 | + | 0.433336i | ||||
\(441\) | −3.55107e7 | −0.414041 | ||||||||
\(442\) | −9.21558e7 | − | 5.32062e7i | −1.06723 | − | 0.616163i | ||||
\(443\) | −6.86888e7 | − | 1.18972e8i | −0.790086 | − | 1.36847i | −0.925913 | − | 0.377737i | \(-0.876702\pi\) |
0.135827 | − | 0.990733i | \(-0.456631\pi\) | |||||||
\(444\) | −9.91337e6 | − | 1.71705e7i | −0.113259 | − | 0.196170i | ||||
\(445\) | −7.93029e7 | − | 1.37357e8i | −0.899930 | − | 1.55873i | ||||
\(446\) | 1.18154e8 | 1.33181 | ||||||||
\(447\) | −7.61936e7 | − | 1.31971e8i | −0.853092 | − | 1.47760i | ||||
\(448\) | 6.58598e6 | − | 3.80242e6i | 0.0732465 | − | 0.0422889i | ||||
\(449\) | −3.36568e7 | − | 1.94317e7i | −0.371821 | − | 0.214671i | 0.302433 | − | 0.953171i | \(-0.402201\pi\) |
−0.674254 | + | 0.738500i | \(0.735534\pi\) | |||||||
\(450\) | 8.40888e6 | + | 4.85487e6i | 0.0922785 | + | 0.0532770i | ||||
\(451\) | 1.12512e8 | 1.22651 | ||||||||
\(452\) | − | 7.30555e7i | − | 0.791112i | ||||||
\(453\) | −1.06023e8 | + | 1.83636e8i | −1.14052 | + | 1.97544i | ||||
\(454\) | −8.10221e7 | + | 1.40334e8i | −0.865837 | + | 1.49967i | ||||
\(455\) | −1.72160e7 | − | 2.98190e7i | −0.182767 | − | 0.316562i | ||||
\(456\) | 5.20266e7 | − | 3.00376e7i | 0.548695 | − | 0.316789i | ||||
\(457\) | − | 1.18565e7i | − | 0.124224i | −0.998069 | − | 0.0621122i | \(-0.980216\pi\) | ||
0.998069 | − | 0.0621122i | \(-0.0197837\pi\) | |||||||
\(458\) | −1.54702e8 | + | 8.93174e7i | −1.61028 | + | 0.929693i | ||||
\(459\) | −5.10797e7 | + | 2.94909e7i | −0.528215 | + | 0.304965i | ||||
\(460\) | 6.13801e7 | − | 3.54378e7i | 0.630600 | − | 0.364077i | ||||
\(461\) | 3.36146e7 | − | 5.82222e7i | 0.343104 | − | 0.594273i | −0.641904 | − | 0.766785i | \(-0.721855\pi\) |
0.985007 | + | 0.172512i | \(0.0551885\pi\) | |||||||
\(462\) | 1.14288e8i | 1.15898i | ||||||||
\(463\) | 3.09741e7 | + | 1.78829e7i | 0.312073 | + | 0.180175i | 0.647854 | − | 0.761765i | \(-0.275667\pi\) |
−0.335781 | + | 0.941940i | \(0.609000\pi\) | |||||||
\(464\) | −5.63828e7 | + | 3.25526e7i | −0.564407 | + | 0.325861i | ||||
\(465\) | 3.20341e7 | 0.318606 | ||||||||
\(466\) | 1.61530e6 | + | 2.79778e6i | 0.0159623 | + | 0.0276475i | ||||
\(467\) | 6.76027e7 | + | 3.90304e7i | 0.663764 | + | 0.383224i | 0.793710 | − | 0.608297i | \(-0.208147\pi\) |
−0.129946 | + | 0.991521i | \(0.541480\pi\) | |||||||
\(468\) | −1.34204e7 | + | 2.32448e7i | −0.130927 | + | 0.226771i | ||||
\(469\) | 6.04007e7i | 0.585495i | ||||||||
\(470\) | −6.22643e7 | + | 1.07845e8i | −0.599715 | + | 1.03874i | ||||
\(471\) | −1.74242e8 | −1.66759 | ||||||||
\(472\) | − | 2.08787e7i | − | 0.198553i | ||||||
\(473\) | −7.72637e7 | + | 8.43097e7i | −0.730116 | + | 0.796698i | ||||
\(474\) | −2.01387e8 | −1.89102 | ||||||||
\(475\) | 1.24391e7i | 0.116066i | ||||||||
\(476\) | 5.94414e7 | + | 3.43185e7i | 0.551148 | + | 0.318206i | ||||
\(477\) | −2.91967e7 | −0.269016 | ||||||||
\(478\) | 5.88993e7 | + | 3.40055e7i | 0.539295 | + | 0.311362i | ||||
\(479\) | −5.69000e7 | + | 9.85538e7i | −0.517733 | + | 0.896740i | 0.482055 | + | 0.876141i | \(0.339891\pi\) |
−0.999788 | + | 0.0205991i | \(0.993443\pi\) | |||||||
\(480\) | 1.26802e8 | − | 7.32094e7i | 1.14658 | − | 0.661977i | ||||
\(481\) | − | 1.89905e7i | − | 0.170648i | ||||||
\(482\) | −1.22946e8 | − | 2.12948e8i | −1.09793 | − | 1.90166i | ||||
\(483\) | −6.03433e7 | + | 1.04518e8i | −0.535535 | + | 0.927573i | ||||
\(484\) | −1.16356e7 | −0.102625 | ||||||||
\(485\) | 7.08283e7 | + | 4.08927e7i | 0.620843 | + | 0.358444i | ||||
\(486\) | 8.73081e7 | + | 1.51222e8i | 0.760581 | + | 1.31737i | ||||
\(487\) | 4.84868e6 | + | 8.39816e6i | 0.0419794 | + | 0.0727105i | 0.886252 | − | 0.463204i | \(-0.153300\pi\) |
−0.844272 | + | 0.535914i | \(0.819967\pi\) | |||||||
\(488\) | 1.95096e7 | + | 3.37917e7i | 0.167877 | + | 0.290771i | ||||
\(489\) | 2.22036e8 | 1.89888 | ||||||||
\(490\) | −4.08665e7 | − | 7.07828e7i | −0.347359 | − | 0.601644i | ||||
\(491\) | 1.70411e8 | − | 9.83867e7i | 1.43964 | − | 0.831174i | 0.441811 | − | 0.897108i | \(-0.354336\pi\) |
0.997824 | + | 0.0659341i | \(0.0210027\pi\) | |||||||
\(492\) | −9.36354e7 | − | 5.40604e7i | −0.786221 | − | 0.453925i | ||||
\(493\) | −8.80324e7 | − | 5.08255e7i | −0.734686 | − | 0.424171i | ||||
\(494\) | −9.06077e7 | −0.751596 | ||||||||
\(495\) | 8.74510e7i | 0.721023i | ||||||||
\(496\) | −1.95870e7 | + | 3.39256e7i | −0.160517 | + | 0.278024i | ||||
\(497\) | −4.51805e7 | + | 7.82549e7i | −0.368029 | + | 0.637444i | ||||
\(498\) | 1.37652e8 | + | 2.38420e8i | 1.11454 | + | 1.93043i | ||||
\(499\) | −1.05673e8 | + | 6.10104e7i | −0.850477 | + | 0.491023i | −0.860812 | − | 0.508923i | \(-0.830044\pi\) |
0.0103347 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(500\) | 8.02735e7i | 0.642188i | ||||||||
\(501\) | 2.77297e8 | − | 1.60097e8i | 2.20512 | − | 1.27312i | ||||
\(502\) | 1.38413e8 | − | 7.99128e7i | 1.09412 | − | 0.631692i | ||||
\(503\) | 1.22440e8 | − | 7.06910e7i | 0.962102 | − | 0.555470i | 0.0652826 | − | 0.997867i | \(-0.479205\pi\) |
0.896819 | + | 0.442397i | \(0.145872\pi\) | |||||||
\(504\) | −1.44856e7 | + | 2.50897e7i | −0.113147 | + | 0.195977i | ||||
\(505\) | − | 7.82649e6i | − | 0.0607705i | ||||||
\(506\) | −1.95142e8 | − | 1.12665e8i | −1.50625 | − | 0.869637i | ||||
\(507\) | 9.40096e7 | − | 5.42765e7i | 0.721354 | − | 0.416474i | ||||
\(508\) | −3.72214e7 | −0.283923 | ||||||||
\(509\) | 6.96792e7 | + | 1.20688e8i | 0.528384 | + | 0.915188i | 0.999452 | + | 0.0330916i | \(0.0105353\pi\) |
−0.471068 | + | 0.882097i | \(0.656131\pi\) | |||||||
\(510\) | 2.88538e8 | + | 1.66587e8i | 2.17517 | + | 1.25583i | ||||
\(511\) | 3.07531e7 | − | 5.32659e7i | 0.230476 | − | 0.399196i | ||||
\(512\) | 9.71536e7i | 0.723851i | ||||||||
\(513\) | −2.51108e7 | + | 4.34932e7i | −0.185998 | + | 0.322158i | ||||
\(514\) | −7.54229e7 | −0.555410 | ||||||||
\(515\) | − | 8.13036e7i | − | 0.595234i | ||||||
\(516\) | 1.04810e8 | − | 3.30405e7i | 0.762878 | − | 0.240491i | ||||
\(517\) | 1.50245e8 | 1.08725 | ||||||||
\(518\) | 3.22769e7i | 0.232222i | ||||||||
\(519\) | −2.75260e8 | − | 1.58922e8i | −1.96898 | − | 1.13679i | ||||
\(520\) | 3.92325e7 | 0.279021 | ||||||||
\(521\) | −5.74601e7 | − | 3.31746e7i | −0.406306 | − | 0.234581i | 0.282895 | − | 0.959151i | \(-0.408705\pi\) |
−0.689201 | + | 0.724570i | \(0.742038\pi\) | |||||||
\(522\) | −3.37812e7 | + | 5.85108e7i | −0.237500 | + | 0.411362i | ||||
\(523\) | −3.91943e7 | + | 2.26288e7i | −0.273979 | + | 0.158182i | −0.630695 | − | 0.776031i | \(-0.717230\pi\) |
0.356715 | + | 0.934213i | \(0.383897\pi\) | |||||||
\(524\) | − | 1.52969e8i | − | 1.06319i | ||||||
\(525\) | −7.22083e6 | − | 1.25068e7i | −0.0499010 | − | 0.0864310i | ||||
\(526\) | −3.09596e7 | + | 5.36236e7i | −0.212734 | + | 0.368467i | ||||
\(527\) | −6.11636e7 | −0.417889 | ||||||||
\(528\) | −2.22966e8 | − | 1.28730e8i | −1.51474 | − | 0.874534i | ||||
\(529\) | −4.49549e7 | − | 7.78643e7i | −0.303676 | − | 0.525982i | ||||
\(530\) | −3.36001e7 | − | 5.81972e7i | −0.225691 | − | 0.390908i | ||||
\(531\) | −2.14184e7 | − | 3.70977e7i | −0.143055 | − | 0.247778i | ||||
\(532\) | 5.84429e7 | 0.388147 | ||||||||
\(533\) | −5.17802e7 | − | 8.96859e7i | −0.341965 | − | 0.592301i | ||||
\(534\) | 4.19645e8 | − | 2.42282e8i | 2.75587 | − | 1.59110i | ||||
\(535\) | 5.83674e7 | + | 3.36984e7i | 0.381161 | + | 0.220064i | ||||
\(536\) | −5.96014e7 | − | 3.44109e7i | −0.387046 | − | 0.223461i | ||||
\(537\) | −9.72173e7 | −0.627799 | ||||||||
\(538\) | − | 2.79901e7i | − | 0.179746i | ||||||
\(539\) | −4.93059e7 | + | 8.54004e7i | −0.314871 | + | 0.545373i | ||||
\(540\) | −1.71210e7 | + | 2.96544e7i | −0.108729 | + | 0.188325i | ||||
\(541\) | −9.06542e7 | − | 1.57018e8i | −0.572527 | − | 0.991646i | −0.996305 | − | 0.0858799i | \(-0.972630\pi\) |
0.423779 | − | 0.905766i | \(-0.360703\pi\) | |||||||
\(542\) | −9.21646e7 | + | 5.32113e7i | −0.578851 | + | 0.334200i | ||||
\(543\) | 1.21458e8i | 0.758624i | ||||||||
\(544\) | −2.42107e8 | + | 1.39781e8i | −1.50387 | + | 0.868262i | ||||
\(545\) | 2.54681e7 | − | 1.47040e7i | 0.157328 | − | 0.0908334i | ||||
\(546\) | 9.11015e7 | − | 5.25975e7i | 0.559690 | − | 0.323137i | ||||
\(547\) | 7.75933e7 | − | 1.34396e8i | 0.474092 | − | 0.821151i | −0.525468 | − | 0.850813i | \(-0.676110\pi\) |
0.999560 | + | 0.0296623i | \(0.00944320\pi\) | |||||||
\(548\) | − | 1.06089e8i | − | 0.644659i | ||||||
\(549\) | 6.93303e7 | + | 4.00279e7i | 0.418992 | + | 0.241905i | ||||
\(550\) | 2.33511e7 | − | 1.34818e7i | 0.140352 | − | 0.0810325i | ||||
\(551\) | −8.65536e7 | −0.517404 | ||||||||
\(552\) | −6.87564e7 | − | 1.19090e8i | −0.408786 | − | 0.708038i | ||||
\(553\) | 1.07749e8 | + | 6.22087e7i | 0.637142 | + | 0.367854i | ||||
\(554\) | 2.81576e7 | − | 4.87704e7i | 0.165602 | − | 0.286832i | ||||
\(555\) | 5.94587e7i | 0.347806i | ||||||||
\(556\) | 5.28949e7 | − | 9.16166e7i | 0.307744 | − | 0.533028i | ||||
\(557\) | 2.16954e8 | 1.25546 | 0.627729 | − | 0.778432i | \(-0.283984\pi\) | ||||
0.627729 | + | 0.778432i | \(0.283984\pi\) | |||||||
\(558\) | 4.06524e7i | 0.233983i | ||||||||
\(559\) | 1.02763e8 | + | 2.27877e7i | 0.588305 | + | 0.130456i | ||||
\(560\) | −1.31834e8 | −0.750694 | ||||||||
\(561\) | − | 4.01980e8i | − | 2.27675i | ||||||
\(562\) | 3.23619e8 | + | 1.86841e8i | 1.82316 | + | 1.05260i | ||||
\(563\) | 2.93409e8 | 1.64418 | 0.822089 | − | 0.569359i | \(-0.192809\pi\) | ||||
0.822089 | + | 0.569359i | \(0.192809\pi\) | |||||||
\(564\) | −1.25038e8 | − | 7.21907e7i | −0.696955 | − | 0.402387i | ||||
\(565\) | −1.09544e8 | + | 1.89735e8i | −0.607355 | + | 1.05197i | ||||
\(566\) | 4.56352e7 | − | 2.63475e7i | 0.251681 | − | 0.145308i | ||||
\(567\) | − | 1.41966e8i | − | 0.778818i | ||||||
\(568\) | −5.14796e7 | − | 8.91653e7i | −0.280925 | − | 0.486576i | ||||
\(569\) | −1.08914e8 | + | 1.88645e8i | −0.591219 | + | 1.02402i | 0.402850 | + | 0.915266i | \(0.368020\pi\) |
−0.994069 | + | 0.108755i | \(0.965314\pi\) | |||||||
\(570\) | 2.83691e8 | 1.53187 | ||||||||
\(571\) | −1.72682e8 | − | 9.96982e7i | −0.927555 | − | 0.535524i | −0.0415175 | − | 0.999138i | \(-0.513219\pi\) |
−0.886037 | + | 0.463614i | \(0.846553\pi\) | |||||||
\(572\) | 3.72679e7 | + | 6.45499e7i | 0.199135 | + | 0.344911i | ||||
\(573\) | −6.69580e7 | − | 1.15975e8i | −0.355909 | − | 0.616452i | ||||
\(574\) | 8.80076e7 | + | 1.52434e8i | 0.465355 | + | 0.806019i | ||||
\(575\) | 2.84732e7 | 0.149773 | ||||||||
\(576\) | 8.88909e6 | + | 1.53964e7i | 0.0465147 | + | 0.0805658i | ||||
\(577\) | −1.36232e8 | + | 7.86533e7i | −0.709170 | + | 0.409439i | −0.810753 | − | 0.585388i | \(-0.800942\pi\) |
0.101584 | + | 0.994827i | \(0.467609\pi\) | |||||||
\(578\) | −3.38618e8 | − | 1.95501e8i | −1.75358 | − | 1.01243i | ||||
\(579\) | 6.28895e6 | + | 3.63093e6i | 0.0323998 | + | 0.0187060i | ||||
\(580\) | −5.90137e7 | −0.302460 | ||||||||
\(581\) | − | 1.70084e8i | − | 0.867230i | ||||||
\(582\) | −1.24933e8 | + | 2.16391e8i | −0.633738 | + | 1.09767i | ||||
\(583\) | −4.05390e7 | + | 7.02157e7i | −0.204582 | + | 0.354347i | ||||
\(584\) | 3.50407e7 | + | 6.06923e7i | 0.175928 | + | 0.304716i | ||||
\(585\) | 6.97092e7 | − | 4.02466e7i | 0.348195 | − | 0.201031i | ||||
\(586\) | 4.53188e8i | 2.25209i | ||||||||
\(587\) | −1.87441e8 | + | 1.08219e8i | −0.926726 | + | 0.535045i | −0.885774 | − | 0.464116i | \(-0.846372\pi\) |
−0.0409511 | + | 0.999161i | \(0.513039\pi\) | |||||||
\(588\) | 8.20673e7 | − | 4.73816e7i | 0.403681 | − | 0.233065i | ||||
\(589\) | −4.51021e7 | + | 2.60397e7i | −0.220725 | + | 0.127435i | ||||
\(590\) | 4.92974e7 | − | 8.53855e7i | 0.240031 | − | 0.415746i | ||||
\(591\) | 2.48952e8i | 1.20602i | ||||||||
\(592\) | −6.29696e7 | − | 3.63555e7i | −0.303505 | − | 0.175229i | ||||
\(593\) | −8.73131e7 | + | 5.04102e7i | −0.418712 | + | 0.241743i | −0.694526 | − | 0.719468i | \(-0.744386\pi\) |
0.275814 | + | 0.961211i | \(0.411053\pi\) | |||||||
\(594\) | 1.08863e8 | 0.519423 | ||||||||
\(595\) | −1.02918e8 | − | 1.78260e8i | −0.488587 | − | 0.846258i | ||||
\(596\) | 1.46285e8 | + | 8.44578e7i | 0.690974 | + | 0.398934i | ||||
\(597\) | 2.58755e8 | − | 4.48178e8i | 1.21609 | − | 2.10633i | ||||
\(598\) | 2.07402e8i | 0.969863i | ||||||||
\(599\) | 1.32583e7 | − | 2.29640e7i | 0.0616888 | − | 0.106848i | −0.833532 | − | 0.552472i | \(-0.813685\pi\) |
0.895220 | + | 0.445624i | \(0.147018\pi\) | |||||||
\(600\) | 1.64551e7 | 0.0761811 | ||||||||
\(601\) | 3.34915e8i | 1.54281i | 0.636347 | + | 0.771403i | \(0.280445\pi\) | ||||
−0.636347 | + | 0.771403i | \(0.719555\pi\) | |||||||
\(602\) | −1.74661e8 | − | 3.87309e7i | −0.800581 | − | 0.177529i | ||||
\(603\) | −1.41201e8 | −0.644002 | ||||||||
\(604\) | − | 2.35044e8i | − | 1.06669i | ||||||
\(605\) | 3.02192e7 | + | 1.74471e7i | 0.136464 | + | 0.0787874i | ||||
\(606\) | 2.39111e7 | 0.107444 | ||||||||
\(607\) | 1.22670e8 | + | 7.08236e7i | 0.548495 | + | 0.316674i | 0.748515 | − | 0.663118i | \(-0.230767\pi\) |
−0.200020 | + | 0.979792i | \(0.564101\pi\) | |||||||
\(608\) | −1.19020e8 | + | 2.06149e8i | −0.529553 | + | 0.917213i | ||||
\(609\) | 8.70252e7 | − | 5.02440e7i | 0.385295 | − | 0.222450i | ||||
\(610\) | 1.84260e8i | 0.811784i | ||||||||
\(611\) | −6.91458e7 | − | 1.19764e8i | −0.303139 | − | 0.525052i | ||||
\(612\) | −8.02280e7 | + | 1.38959e8i | −0.350003 | + | 0.606223i | ||||
\(613\) | −8.30587e6 | −0.0360582 | −0.0180291 | − | 0.999837i | \(-0.505739\pi\) | ||||
−0.0180291 | + | 0.999837i | \(0.505739\pi\) | |||||||
\(614\) | −4.19603e8 | − | 2.42258e8i | −1.81273 | − | 1.04658i | ||||
\(615\) | 1.62123e8 | + | 2.80805e8i | 0.696977 | + | 1.20720i | ||||
\(616\) | 4.02259e7 | + | 6.96732e7i | 0.172093 | + | 0.298074i | ||||
\(617\) | 1.32213e8 | + | 2.28999e8i | 0.562882 | + | 0.974940i | 0.997243 | + | 0.0742015i | \(0.0236408\pi\) |
−0.434361 | + | 0.900739i | \(0.643026\pi\) | |||||||
\(618\) | 2.48395e8 | 1.05239 | ||||||||
\(619\) | 1.03558e8 | + | 1.79368e8i | 0.436629 | + | 0.756264i | 0.997427 | − | 0.0716887i | \(-0.0228388\pi\) |
−0.560798 | + | 0.827953i | \(0.689505\pi\) | |||||||
\(620\) | −3.07514e7 | + | 1.77543e7i | −0.129030 | + | 0.0744952i | ||||
\(621\) | 9.95566e7 | + | 5.74790e7i | 0.415715 | + | 0.240013i | ||||
\(622\) | 3.05766e8 | + | 1.76534e8i | 1.27062 | + | 0.733596i | ||||
\(623\) | −2.99366e8 | −1.23805 | ||||||||
\(624\) | 2.36975e8i | 0.975325i | ||||||||
\(625\) | 1.05946e8 | − | 1.83504e8i | 0.433955 | − | 0.751632i | ||||
\(626\) | 1.73201e8 | − | 2.99992e8i | 0.706036 | − | 1.22289i | ||||
\(627\) | −1.71138e8 | − | 2.96420e8i | −0.694296 | − | 1.20256i | ||||
\(628\) | 1.67265e8 | − | 9.65704e7i | 0.675345 | − | 0.389911i | ||||
\(629\) | − | 1.13526e8i | − | 0.456189i | ||||||
\(630\) | −1.18480e8 | + | 6.84047e7i | −0.473833 | + | 0.273568i | ||||
\(631\) | 2.34018e8 | − | 1.35110e8i | 0.931454 | − | 0.537775i | 0.0441826 | − | 0.999023i | \(-0.485932\pi\) |
0.887271 | + | 0.461248i | \(0.152598\pi\) | |||||||
\(632\) | −1.22771e8 | + | 7.08819e7i | −0.486345 | + | 0.280792i | ||||
\(633\) | −9.96424e7 | + | 1.72586e8i | −0.392856 | + | 0.680446i | ||||
\(634\) | − | 7.07823e7i | − | 0.277752i | ||||||
\(635\) | 9.66691e7 | + | 5.58119e7i | 0.377543 | + | 0.217975i | ||||
\(636\) | 6.74752e7 | − | 3.89568e7i | 0.262285 | − | 0.151430i | ||||
\(637\) | 9.07661e7 | 0.351160 | ||||||||
\(638\) | 9.38091e7 | + | 1.62482e8i | 0.361229 | + | 0.625668i | ||||
\(639\) | −1.82940e8 | − | 1.05621e8i | −0.701142 | − | 0.404805i | ||||
\(640\) | 1.12225e8 | − | 1.94380e8i | 0.428106 | − | 0.741501i | ||||
\(641\) | − | 2.70921e8i | − | 1.02865i | −0.857595 | − | 0.514326i | \(-0.828042\pi\) | ||
0.857595 | − | 0.514326i | \(-0.171958\pi\) | |||||||
\(642\) | −1.02954e8 | + | 1.78321e8i | −0.389079 | + | 0.673904i | ||||
\(643\) | −1.15803e8 | −0.435598 | −0.217799 | − | 0.975994i | \(-0.569888\pi\) | ||||
−0.217799 | + | 0.975994i | \(0.569888\pi\) | |||||||
\(644\) | − | 1.33777e8i | − | 0.500867i | ||||||
\(645\) | −3.21750e8 | − | 7.13479e7i | −1.19906 | − | 0.265890i | ||||
\(646\) | −5.41659e8 | −2.00922 | ||||||||
\(647\) | − | 2.24081e8i | − | 0.827354i | −0.910424 | − | 0.413677i | \(-0.864244\pi\) | ||
0.910424 | − | 0.413677i | \(-0.135756\pi\) | |||||||
\(648\) | 1.40088e8 | + | 8.08797e7i | 0.514843 | + | 0.297245i | ||||
\(649\) | −1.18956e8 | −0.435163 | ||||||||
\(650\) | −2.14933e7 | − | 1.24091e7i | −0.0782641 | − | 0.0451858i | ||||
\(651\) | 3.02319e7 | − | 5.23632e7i | 0.109578 | − | 0.189794i | ||||
\(652\) | −2.13145e8 | + | 1.23059e8i | −0.769011 | + | 0.443989i | ||||
\(653\) | − | 1.52001e8i | − | 0.545893i | −0.962029 | − | 0.272947i | \(-0.912002\pi\) | ||
0.962029 | − | 0.272947i | \(-0.0879983\pi\) | |||||||
\(654\) | 4.49229e7 | + | 7.78088e7i | 0.160596 | + | 0.278160i | ||||
\(655\) | −2.29371e8 | + | 3.97282e8i | −0.816234 | + | 1.41376i | ||||
\(656\) | −3.96514e8 | −1.40458 | ||||||||
\(657\) | 1.24522e8 | + | 7.18929e7i | 0.439087 | + | 0.253507i | ||||
\(658\) | 1.17523e8 | + | 2.03555e8i | 0.412520 | + | 0.714505i | ||||
\(659\) | 2.85772e8 | + | 4.94972e8i | 0.998537 | + | 1.72952i | 0.546099 | + | 0.837721i | \(0.316112\pi\) |
0.452438 | + | 0.891796i | \(0.350554\pi\) | |||||||
\(660\) | −1.16685e8 | − | 2.02104e8i | −0.405867 | − | 0.702982i | ||||
\(661\) | 1.01945e8 | 0.352989 | 0.176495 | − | 0.984302i | \(-0.443524\pi\) | ||||
0.176495 | + | 0.984302i | \(0.443524\pi\) | |||||||
\(662\) | −1.69279e7 | − | 2.93200e7i | −0.0583484 | − | 0.101062i | ||||
\(663\) | −3.20428e8 | + | 1.84999e8i | −1.09948 | + | 0.634788i | ||||
\(664\) | 1.67833e8 | + | 9.68985e7i | 0.573289 | + | 0.330989i | ||||
\(665\) | −1.51784e8 | − | 8.76327e7i | −0.516133 | − | 0.297990i | ||||
\(666\) | −7.54553e7 | −0.255427 | ||||||||
\(667\) | 1.98122e8i | 0.667661i | ||||||||
\(668\) | −1.77462e8 | + | 3.07373e8i | −0.595355 | + | 1.03119i | ||||
\(669\) | 2.05411e8 | − | 3.55783e8i | 0.686034 | − | 1.18825i | ||||
\(670\) | −1.62498e8 | − | 2.81454e8i | −0.540285 | − | 0.935800i | ||||
\(671\) | 1.92528e8 | − | 1.11156e8i | 0.637273 | − | 0.367930i | ||||
\(672\) | − | 2.76363e8i | − | 0.910693i | ||||||
\(673\) | 1.29678e8 | − | 7.48697e7i | 0.425423 | − | 0.245618i | −0.271972 | − | 0.962305i | \(-0.587676\pi\) |
0.697395 | + | 0.716687i | \(0.254342\pi\) | |||||||
\(674\) | 5.26215e7 | − | 3.03810e7i | 0.171863 | − | 0.0992254i | ||||
\(675\) | −1.19132e7 | + | 6.87808e6i | −0.0387362 | + | 0.0223643i | ||||
\(676\) | −6.01635e7 | + | 1.04206e8i | −0.194757 | + | 0.337329i | ||||
\(677\) | − | 4.69587e8i | − | 1.51339i | −0.653771 | − | 0.756693i | \(-0.726814\pi\) | ||
0.653771 | − | 0.756693i | \(-0.273186\pi\) | |||||||
\(678\) | −5.79670e8 | − | 3.34673e8i | −1.85991 | − | 1.07382i | ||||
\(679\) | 1.33687e8 | − | 7.71844e7i | 0.427052 | − | 0.246559i | ||||
\(680\) | 2.34535e8 | 0.745900 | ||||||||
\(681\) | 2.81715e8 | + | 4.87945e8i | 0.892009 | + | 1.54500i | ||||
\(682\) | 9.77657e7 | + | 5.64451e7i | 0.308201 | + | 0.177940i | ||||
\(683\) | 8.33942e7 | − | 1.44443e8i | 0.261742 | − | 0.453351i | −0.704963 | − | 0.709244i | \(-0.749036\pi\) |
0.966705 | + | 0.255893i | \(0.0823696\pi\) | |||||||
\(684\) | 1.36625e8i | 0.426934i | ||||||||
\(685\) | −1.59076e8 | + | 2.75529e8i | −0.494919 | + | 0.857225i | ||||
\(686\) | −4.18998e8 | −1.29790 | ||||||||
\(687\) | 6.21117e8i | 1.91559i | ||||||||
\(688\) | 2.72292e8 | − | 2.97123e8i | 0.836121 | − | 0.912371i | ||||
\(689\) | 7.46273e7 | 0.228160 | ||||||||
\(690\) | − | 6.49373e8i | − | 1.97673i | ||||||
\(691\) | 2.23152e8 | + | 1.28837e8i | 0.676343 | + | 0.390487i | 0.798476 | − | 0.602027i | \(-0.205640\pi\) |
−0.122133 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(692\) | 3.52317e8 | 1.06320 | ||||||||
\(693\) | 1.42948e8 | + | 8.25312e7i | 0.429516 | + | 0.247981i | ||||
\(694\) | −2.27726e6 | + | 3.94432e6i | −0.00681292 | + | 0.0118003i | ||||
\(695\) | −2.74751e8 | + | 1.58627e8i | −0.818435 | + | 0.472524i | ||||
\(696\) | 1.14498e8i | 0.339603i | ||||||||
\(697\) | −3.09546e8 | − | 5.36149e8i | −0.914168 | − | 1.58339i | ||||
\(698\) | 3.35290e8 | − | 5.80738e8i | 0.985947 | − | 1.70771i | ||||
\(699\) | 1.12328e7 | 0.0328896 | ||||||||
\(700\) | 1.38634e7 | + | 8.00402e6i | 0.0404180 | + | 0.0233353i | ||||
\(701\) | 3.25912e8 | + | 5.64496e8i | 0.946120 | + | 1.63873i | 0.753493 | + | 0.657456i | \(0.228368\pi\) |
0.192628 | + | 0.981272i | \(0.438299\pi\) | |||||||
\(702\) | −5.01009e7 | − | 8.67773e7i | −0.144822 | − | 0.250839i | ||||
\(703\) | −4.83325e7 | − | 8.37144e7i | −0.139115 | − | 0.240954i | ||||
\(704\) | 4.93693e7 | 0.141494 | ||||||||
\(705\) | 2.16494e8 | + | 3.74978e8i | 0.617843 | + | 1.07014i | ||||
\(706\) | 2.08237e8 | − | 1.20226e8i | 0.591758 | − | 0.341652i | ||||
\(707\) | −1.27933e7 | − | 7.38619e6i | −0.0362012 | − | 0.0209008i | ||||
\(708\) | 9.89981e7 | + | 5.71566e7i | 0.278950 | + | 0.161052i | ||||
\(709\) | −9.85959e7 | −0.276643 | −0.138322 | − | 0.990387i | \(-0.544171\pi\) | ||||
−0.138322 | + | 0.990387i | \(0.544171\pi\) | |||||||
\(710\) | − | 4.86201e8i | − | 1.35844i | ||||||
\(711\) | −1.45428e8 | + | 2.51889e8i | −0.404613 | + | 0.700810i | ||||
\(712\) | 1.70552e8 | − | 2.95405e8i | 0.472516 | − | 0.818422i | ||||
\(713\) | 5.96053e7 | + | 1.03239e8i | 0.164443 | + | 0.284824i | ||||
\(714\) | 5.44611e8 | − | 3.14431e8i | 1.49621 | − | 0.863836i | ||||
\(715\) | − | 2.23527e8i | − | 0.611521i | ||||||
\(716\) | 9.33245e7 | − | 5.38809e7i | 0.254247 | − | 0.146790i | ||||
\(717\) | 2.04794e8 | − | 1.18238e8i | 0.555597 | − | 0.320774i | ||||
\(718\) | 4.76780e8 | − | 2.75269e8i | 1.28809 | − | 0.743676i | ||||
\(719\) | −2.06868e8 | + | 3.58306e8i | −0.556554 | + | 0.963979i | 0.441227 | + | 0.897395i | \(0.354543\pi\) |
−0.997781 | + | 0.0665838i | \(0.978790\pi\) | |||||||
\(720\) | − | 3.08194e8i | − | 0.825709i | ||||||
\(721\) | −1.32900e8 | − | 7.67296e7i | −0.354583 | − | 0.204719i | ||||
\(722\) | 1.43613e7 | − | 8.29149e6i | 0.0381576 | − | 0.0220303i | ||||
\(723\) | −8.54970e8 | −2.26223 | ||||||||
\(724\) | −6.73159e7 | − | 1.16594e8i | −0.177379 | − | 0.307229i | ||||
\(725\) | −2.05316e7 | − | 1.18539e7i | −0.0538776 | − | 0.0311062i | ||||
\(726\) | −5.33035e7 | + | 9.23244e7i | −0.139298 | + | 0.241272i | ||||
\(727\) | − | 5.17844e8i | − | 1.34771i | −0.738865 | − | 0.673854i | \(-0.764638\pi\) | ||
0.738865 | − | 0.673854i | \(-0.235362\pi\) | |||||||
\(728\) | 3.70254e7 | − | 6.41299e7i | 0.0959634 | − | 0.166214i | ||||
\(729\) | 1.40035e8 | 0.361454 | ||||||||
\(730\) | 3.30943e8i | 0.850717i | ||||||||
\(731\) | 6.14326e8 | + | 1.36227e8i | 1.57270 | + | 0.348746i | ||||
\(732\) | −2.13635e8 | −0.544677 | ||||||||
\(733\) | − | 4.80474e8i | − | 1.22000i | −0.792403 | − | 0.609998i | \(-0.791170\pi\) | ||
0.792403 | − | 0.609998i | \(-0.208830\pi\) | |||||||
\(734\) | 2.13658e8 | + | 1.23356e8i | 0.540296 | + | 0.311940i | ||||
\(735\) | −2.84187e8 | −0.715718 | ||||||||
\(736\) | 4.71878e8 | + | 2.72439e8i | 1.18358 | + | 0.683338i | ||||
\(737\) | −1.96056e8 | + | 3.39578e8i | −0.489753 | + | 0.848276i | ||||
\(738\) | −3.56351e8 | + | 2.05739e8i | −0.886562 | + | 0.511857i | ||||
\(739\) | 3.41996e8i | 0.847399i | 0.905803 | + | 0.423700i | \(0.139269\pi\) | ||||
−0.905803 | + | 0.423700i | \(0.860731\pi\) | |||||||
\(740\) | −3.29539e7 | − | 5.70778e7i | −0.0813227 | − | 0.140855i | ||||
\(741\) | −1.57522e8 | + | 2.72837e8i | −0.387157 | + | 0.670576i | ||||
\(742\) | −1.26840e8 | −0.310487 | ||||||||
\(743\) | 5.19730e8 | + | 3.00066e8i | 1.26710 | + | 0.731561i | 0.974438 | − | 0.224654i | \(-0.0721253\pi\) |
0.292663 | + | 0.956216i | \(0.405459\pi\) | |||||||
\(744\) | 3.44469e7 | + | 5.96638e7i | 0.0836433 | + | 0.144874i | ||||
\(745\) | −2.53282e8 | − | 4.38697e8i | −0.612541 | − | 1.06095i | ||||
\(746\) | −3.25325e8 | − | 5.63480e8i | −0.783612 | − | 1.35726i | ||||
\(747\) | 3.97613e8 | 0.953890 | ||||||||
\(748\) | 2.22790e8 | + | 3.85884e8i | 0.532342 | + | 0.922044i | ||||
\(749\) | 1.10168e8 | − | 6.36053e7i | 0.262185 | − | 0.151373i | ||||
\(750\) | 6.36942e8 | + | 3.67739e8i | 1.50979 | + | 0.871677i | ||||
\(751\) | 2.26931e7 | + | 1.31019e7i | 0.0535766 | + | 0.0309324i | 0.526549 | − | 0.850145i | \(-0.323486\pi\) |
−0.472972 | + | 0.881077i | \(0.656819\pi\) | |||||||
\(752\) | −5.29493e8 | −1.24511 | ||||||||
\(753\) | − | 5.55717e8i | − | 1.30157i | ||||||
\(754\) | 8.63455e7 | − | 1.49555e8i | 0.201431 | − | 0.348888i | ||||
\(755\) | −3.52439e8 | + | 6.10442e8i | −0.818923 | + | 1.41842i | ||||
\(756\) | 3.23156e7 | + | 5.59722e7i | 0.0747905 | + | 0.129541i | ||||
\(757\) | 1.95459e8 | − | 1.12849e8i | 0.450577 | − | 0.260141i | −0.257497 | − | 0.966279i | \(-0.582898\pi\) |
0.708074 | + | 0.706138i | \(0.249564\pi\) | |||||||
\(758\) | − | 2.18722e8i | − | 0.502209i | ||||||
\(759\) | −6.78511e8 | + | 3.91738e8i | −1.55178 | + | 0.895923i | ||||
\(760\) | 1.72946e8 | − | 9.98505e7i | 0.393976 | − | 0.227462i | ||||
\(761\) | −1.31405e8 | + | 7.58669e7i | −0.298167 | + | 0.172147i | −0.641619 | − | 0.767023i | \(-0.721737\pi\) |
0.343452 | + | 0.939170i | \(0.388404\pi\) | |||||||
\(762\) | −1.70514e8 | + | 2.95339e8i | −0.385385 | + | 0.667506i | ||||
\(763\) | − | 5.55071e7i | − | 0.124961i | ||||||
\(764\) | 1.28554e8 | + | 7.42205e7i | 0.288273 | + | 0.166435i | ||||
\(765\) | 4.16727e8 | − | 2.40597e8i | 0.930822 | − | 0.537411i | ||||
\(766\) | 9.62118e8 | 2.14063 | ||||||||
\(767\) | 5.47458e7 | + | 9.48224e7i | 0.121329 | + | 0.210148i | ||||
\(768\) | 6.61039e8 | + | 3.81651e8i | 1.45930 | + | 0.842525i | ||||
\(769\) | −2.31730e8 | + | 4.01367e8i | −0.509568 | + | 0.882598i | 0.490370 | + | 0.871514i | \(0.336862\pi\) |
−0.999939 | + | 0.0110840i | \(0.996472\pi\) | |||||||
\(770\) | 3.79915e8i | 0.832174i | ||||||||
\(771\) | −1.31123e8 | + | 2.27112e8i | −0.286099 | + | 0.495539i | ||||
\(772\) | −8.04950e6 | −0.0174951 | ||||||||
\(773\) | − | 3.30973e8i | − | 0.716563i | −0.933614 | − | 0.358281i | \(-0.883363\pi\) | ||
0.933614 | − | 0.358281i | \(-0.116637\pi\) | |||||||
\(774\) | 9.05430e7 | − | 4.08312e8i | 0.195268 | − | 0.880581i | ||||
\(775\) | −1.42650e7 | −0.0306456 | ||||||||
\(776\) | 1.75891e8i | 0.376408i | ||||||||
\(777\) | 9.71918e7 | + | 5.61137e7i | 0.207189 | + | 0.119621i | ||||
\(778\) | −1.09911e8 | −0.233401 | ||||||||
\(779\) | −4.56518e8 | − | 2.63571e8i | −0.965708 | − | 0.557552i | ||||
\(780\) | −1.07401e8 | + | 1.86025e8i | −0.226322 | + | 0.392000i | ||||
\(781\) | −5.08018e8 | + | 2.93304e8i | −1.06641 | + | 0.615694i | ||||
\(782\) | 1.23987e9i | 2.59271i | ||||||||
\(783\) | −4.78592e7 | − | 8.28945e7i | −0.0996965 | − | 0.172679i | ||||
\(784\) | 1.73763e8 | − | 3.00967e8i | 0.360587 | − | 0.624555i | ||||
\(785\) | −5.79213e8 | −1.19737 | ||||||||
\(786\) | −1.21376e9 | − | 7.00763e8i | −2.49956 | − | 1.44312i | ||||
\(787\) | −2.10526e8 | − | 3.64642e8i | −0.431899 | − | 0.748071i | 0.565138 | − | 0.824996i | \(-0.308823\pi\) |
−0.997037 | + | 0.0769256i | \(0.975490\pi\) | |||||||
\(788\) | −1.37977e8 | − | 2.38983e8i | −0.281986 | − | 0.488415i | ||||
\(789\) | 1.07647e8 | + | 1.86450e8i | 0.219165 | + | 0.379605i | ||||
\(790\) | −6.69447e8 | −1.35780 | ||||||||
\(791\) | 2.06762e8 | + | 3.58123e8i | 0.417774 | + | 0.723606i | ||||
\(792\) | −1.62878e8 | + | 9.40378e7i | −0.327859 | + | 0.189290i | ||||
\(793\) | −1.77210e8 | − | 1.02312e8i | −0.355360 | − | 0.205167i | ||||
\(794\) | −6.98862e8 | − | 4.03488e8i | −1.39614 | − | 0.806063i | ||||
\(795\) | −2.33657e8 | −0.465025 | ||||||||
\(796\) | 5.73642e8i | 1.13737i | ||||||||
\(797\) | 2.39325e8 | − | 4.14523e8i | 0.472730 | − | 0.818792i | −0.526783 | − | 0.850000i | \(-0.676602\pi\) |
0.999513 | + | 0.0312074i | \(0.00993524\pi\) | |||||||
\(798\) | 2.67731e8 | − | 4.63724e8i | 0.526854 | − | 0.912537i | ||||
\(799\) | −4.13358e8 | − | 7.15957e8i | −0.810375 | − | 1.40361i | ||||
\(800\) | −5.64661e7 | + | 3.26007e7i | −0.110285 | + | 0.0636733i | ||||
\(801\) | − | 6.99842e8i | − | 1.36177i | ||||||
\(802\) | −1.02485e9 | + | 5.91699e8i | −1.98673 | + | 1.14704i | ||||
\(803\) | 3.45793e8 | − | 1.99644e8i | 0.667836 | − | 0.385575i | ||||
\(804\) | 3.26325e8 | − | 1.88404e8i | 0.627888 | − | 0.362511i | ||||
\(805\) | −2.00593e8 | + | 3.47436e8i | −0.384527 | + | 0.666021i | ||||
\(806\) | − | 1.03908e8i | − | 0.198447i | ||||||
\(807\) | −8.42835e7 | − | 4.86611e7i | −0.160370 | − | 0.0925894i | ||||
\(808\) | 1.45769e7 | − | 8.41598e6i | 0.0276332 | − | 0.0159540i | ||||
\(809\) | 2.24024e8 | 0.423107 | 0.211553 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(810\) | 3.81936e8 | + | 6.61532e8i | 0.718679 | + | 1.24479i | ||||
\(811\) | −6.94632e8 | − | 4.01046e8i | −1.30224 | − | 0.751850i | −0.321454 | − | 0.946925i | \(-0.604172\pi\) |
−0.980788 | + | 0.195075i | \(0.937505\pi\) | |||||||
\(812\) | −5.56937e7 | + | 9.64643e7i | −0.104025 | + | 0.180177i | ||||
\(813\) | 3.70033e8i | 0.688603i | ||||||||
\(814\) | −1.04768e8 | + | 1.81464e8i | −0.194248 | + | 0.336447i | ||||
\(815\) | 7.38090e8 | 1.36344 | ||||||||
\(816\) | 1.41665e9i | 2.60731i | ||||||||
\(817\) | 5.11002e8 | − | 1.61089e8i | 0.937036 | − | 0.295392i | ||||
\(818\) | 6.79400e8 | 1.24127 | ||||||||
\(819\) | − | 1.51930e8i | − | 0.276561i | ||||||
\(820\) | −3.11262e8 | − | 1.79707e8i | −0.564526 | − | 0.325929i | ||||
\(821\) | −3.65354e8 | −0.660214 | −0.330107 | − | 0.943943i | \(-0.607085\pi\) | ||||
−0.330107 | + | 0.943943i | \(0.607085\pi\) | |||||||
\(822\) | −8.41781e8 | − | 4.86003e8i | −1.51560 | − | 0.875030i | ||||
\(823\) | 1.64426e8 | − | 2.84794e8i | 0.294965 | − | 0.510895i | −0.680012 | − | 0.733201i | \(-0.738025\pi\) |
0.974977 | + | 0.222307i | \(0.0713586\pi\) | |||||||
\(824\) | 1.51429e8 | − | 8.74273e7i | 0.270661 | − | 0.156266i | ||||
\(825\) | − | 9.37528e7i | − | 0.166964i | ||||||
\(826\) | −9.30480e7 | − | 1.61164e8i | −0.165108 | − | 0.285975i | ||||
\(827\) | 5.97002e7 | − | 1.03404e8i | 0.105550 | − | 0.182818i | −0.808413 | − | 0.588616i | \(-0.799673\pi\) |
0.913963 | + | 0.405798i | \(0.133006\pi\) | |||||||
\(828\) | 3.12736e8 | 0.550918 | ||||||||
\(829\) | 1.63931e8 | + | 9.46456e7i | 0.287738 | + | 0.166126i | 0.636921 | − | 0.770929i | \(-0.280208\pi\) |
−0.349183 | + | 0.937054i | \(0.613541\pi\) | |||||||
\(830\) | 4.57581e8 | + | 7.92554e8i | 0.800265 | + | 1.38610i | ||||
\(831\) | −9.79045e7 | − | 1.69576e8i | −0.170608 | − | 0.295502i | ||||
\(832\) | −2.27207e7 | − | 3.93534e7i | −0.0394504 | − | 0.0683302i | ||||
\(833\) | 5.42606e8 | 0.938749 | ||||||||
\(834\) | −4.84630e8 | − | 8.39404e8i | −0.835435 | − | 1.44702i | ||||
\(835\) | 9.21787e8 | − | 5.32194e8i | 1.58333 | − | 0.914135i | ||||
\(836\) | 3.28571e8 | + | 1.89701e8i | 0.562355 | + | 0.324676i | ||||
\(837\) | −4.98778e7 | − | 2.87969e7i | −0.0850610 | − | 0.0491100i | ||||
\(838\) | −7.46619e8 | −1.26872 | ||||||||
\(839\) | 8.91962e8i | 1.51029i | 0.655557 | + | 0.755145i | \(0.272434\pi\) | ||||
−0.655557 | + | 0.755145i | \(0.727566\pi\) | |||||||
\(840\) | −1.15926e8 | + | 2.00789e8i | −0.195588 | + | 0.338768i | ||||
\(841\) | −2.14930e8 | + | 3.72269e8i | −0.361334 | + | 0.625848i | ||||
\(842\) | 7.70824e7 | + | 1.33511e8i | 0.129128 | + | 0.223656i | ||||
\(843\) | 1.12523e9 | − | 6.49651e8i | 1.87827 | − | 1.08442i | ||||
\(844\) | − | 2.20900e8i | − | 0.367425i | ||||||
\(845\) | 3.12506e8 | − | 1.80425e8i | 0.517950 | − | 0.299039i | ||||
\(846\) | −4.75861e8 | + | 2.74739e8i | −0.785903 | + | 0.453742i | ||||
\(847\) | 5.70384e7 | − | 3.29311e7i | 0.0938678 | − | 0.0541946i | ||||
\(848\) | 1.42867e8 | − | 2.47453e8i | 0.234285 | − | 0.405794i | ||||
\(849\) | − | 1.83222e8i | − | 0.299401i | ||||||
\(850\) | −1.28488e8 | − | 7.41827e7i | −0.209222 | − | 0.120794i | ||||
\(851\) | −1.91623e8 | + | 1.10634e8i | −0.310928 | + | 0.179514i | ||||
\(852\) | 5.63713e8 | 0.911464 | ||||||||
\(853\) | 2.84838e8 | + | 4.93354e8i | 0.458935 | + | 0.794899i | 0.998905 | − | 0.0467855i | \(-0.0148977\pi\) |
−0.539970 | + | 0.841684i | \(0.681564\pi\) | |||||||
\(854\) | 3.01193e8 | + | 1.73894e8i | 0.483583 | + | 0.279197i | ||||
\(855\) | 2.04863e8 | − | 3.54833e8i | 0.327767 | − | 0.567709i | ||||
\(856\) | 1.44946e8i | 0.231093i | ||||||||
\(857\) | −8.98225e6 | + | 1.55577e7i | −0.0142706 | + | 0.0247174i | −0.873073 | − | 0.487590i | \(-0.837876\pi\) |
0.858802 | + | 0.512308i | \(0.171209\pi\) | |||||||
\(858\) | 6.82908e8 | 1.08119 | ||||||||
\(859\) | − | 1.50399e8i | − | 0.237283i | −0.992937 | − | 0.118641i | \(-0.962146\pi\) | ||
0.992937 | − | 0.118641i | \(-0.0378539\pi\) | |||||||
\(860\) | 3.48409e8 | − | 1.09833e8i | 0.547765 | − | 0.172678i | ||||
\(861\) | 6.12008e8 | 0.958843 | ||||||||
\(862\) | 8.24802e8i | 1.28774i | ||||||||
\(863\) | −7.61547e8 | − | 4.39680e8i | −1.18485 | − | 0.684075i | −0.227721 | − | 0.973726i | \(-0.573127\pi\) |
−0.957132 | + | 0.289651i | \(0.906461\pi\) | |||||||
\(864\) | −2.63245e8 | −0.408150 | ||||||||
\(865\) | −9.15017e8 | − | 5.28285e8i | −1.41378 | − | 0.816244i | ||||
\(866\) | −3.63537e8 | + | 6.29665e8i | −0.559751 | + | 0.969517i | ||||
\(867\) | −1.17738e9 | + | 6.79760e8i | −1.80659 | + | 1.04303i | ||||
\(868\) | 6.70219e7i | 0.102484i | ||||||||
\(869\) | 4.03848e8 | + | 6.99486e8i | 0.615402 | + | 1.06591i | ||||
\(870\) | −2.70346e8 | + | 4.68253e8i | −0.410546 | + | 0.711087i | ||||
\(871\) | 3.60914e8 | 0.546197 | ||||||||
\(872\) | 5.47726e7 | + | 3.16230e7i | 0.0826065 | + | 0.0476929i | ||||
\(873\) | 1.80438e8 | + | 3.12527e8i | 0.271197 | + | 0.469726i | ||||
\(874\) | 5.27859e8 | + | 9.14278e8i | 0.790649 | + | 1.36944i | ||||
\(875\) | −2.27190e8 | − | 3.93505e8i | −0.339130 | − | 0.587390i | ||||
\(876\) | −3.83704e8 | −0.570800 | ||||||||
\(877\) | −2.70605e8 | − | 4.68702e8i | −0.401178 | − | 0.694860i | 0.592690 | − | 0.805430i | \(-0.298066\pi\) |
−0.993868 | + | 0.110570i | \(0.964732\pi\) | |||||||
\(878\) | 2.54010e8 | − | 1.46652e8i | 0.375290 | − | 0.216673i | ||||
\(879\) | 1.36463e9 | + | 7.87871e8i | 2.00932 | + | 1.16008i | ||||
\(880\) | −7.41182e8 | − | 4.27922e8i | −1.08762 | − | 0.627937i | ||||
\(881\) | −1.17750e9 | −1.72199 | −0.860997 | − | 0.508610i | \(-0.830160\pi\) | ||||
−0.860997 | + | 0.508610i | \(0.830160\pi\) | |||||||
\(882\) | − | 3.60643e8i | − | 0.525620i | ||||||
\(883\) | −3.10519e8 | + | 5.37835e8i | −0.451031 | + | 0.781209i | −0.998450 | − | 0.0556498i | \(-0.982277\pi\) |
0.547419 | + | 0.836858i | \(0.315610\pi\) | |||||||
\(884\) | 2.05065e8 | − | 3.55182e8i | 0.296848 | − | 0.514155i | ||||
\(885\) | −1.71408e8 | − | 2.96887e8i | −0.247287 | − | 0.428313i | ||||
\(886\) | 1.20827e9 | − | 6.97596e8i | 1.73726 | − | 1.00300i | ||||
\(887\) | − | 2.54948e8i | − | 0.365327i | −0.983176 | − | 0.182663i | \(-0.941528\pi\) | ||
0.983176 | − | 0.182663i | \(-0.0584718\pi\) | |||||||
\(888\) | −1.10742e8 | + | 6.39371e7i | −0.158152 | + | 0.0913092i | ||||
\(889\) | 1.82461e8 | − | 1.05344e8i | 0.259696 | − | 0.149936i | ||||
\(890\) | 1.39498e9 | − | 8.05392e8i | 1.97878 | − | 1.14245i | ||||
\(891\) | 4.60811e8 | − | 7.98147e8i | 0.651462 | − | 1.12837i | ||||
\(892\) | 4.55381e8i | 0.641624i | ||||||||
\(893\) | −6.09621e8 | − | 3.51965e8i | −0.856063 | − | 0.494248i | ||||
\(894\) | 1.34029e9 | − | 7.73814e8i | 1.87579 | − | 1.08299i | ||||
\(895\) | −3.23169e8 | −0.450776 | ||||||||
\(896\) | −2.11824e8 | − | 3.66889e8i | −0.294476 | − | 0.510048i | ||||
\(897\) | 6.24527e8 | + | 3.60571e8i | 0.865315 | + | 0.499590i | ||||
\(898\) | 1.97347e8 | − | 3.41815e8i | 0.272522 | − | 0.472022i | ||||
\(899\) | − | 9.92591e7i | − | 0.136613i | ||||||
\(900\) | −1.87114e7 | + | 3.24090e7i | −0.0256672 | + | 0.0444569i | ||||
\(901\) | 4.46127e8 | 0.609936 | ||||||||
\(902\) | 1.14266e9i | 1.55703i | ||||||||
\(903\) | −4.20275e8 | + | 4.58601e8i | −0.570782 | + | 0.622834i | ||||
\(904\) | −4.71178e8 | −0.637793 | ||||||||
\(905\) | 4.03749e8i | 0.544711i | ||||||||
\(906\) | −1.86499e9 | − | 1.07675e9i | −2.50780 | − | 1.44788i | ||||
\(907\) | −7.61186e8 | −1.02016 | −0.510081 | − | 0.860127i | \(-0.670384\pi\) | ||||
−0.510081 | + | 0.860127i | \(0.670384\pi\) | |||||||
\(908\) | −5.40869e8 | − | 3.12271e8i | −0.722495 | − | 0.417133i | ||||
\(909\) | 1.72670e7 | − | 2.99074e7i | 0.0229893 | − | 0.0398187i | ||||
\(910\) | 3.02839e8 | − | 1.74844e8i | 0.401871 | − | 0.232021i | ||||
\(911\) | − | 7.47823e6i | − | 0.00989107i | −0.999988 | − | 0.00494554i | \(-0.998426\pi\) | ||
0.999988 | − | 0.00494554i | \(-0.00157422\pi\) | |||||||
\(912\) | 6.03124e8 | + | 1.04464e9i | 0.795101 | + | 1.37716i | ||||
\(913\) | 5.52078e8 | − | 9.56227e8i | 0.725417 | − | 1.25646i | ||||
\(914\) | 1.20413e8 | 0.157701 | ||||||||
\(915\) | 5.54840e8 | + | 3.20337e8i | 0.724277 | + | 0.418161i | ||||
\(916\) | −3.44242e8 | − | 5.96245e8i | −0.447897 | − | 0.775780i | ||||
\(917\) | 4.32934e8 | + | 7.49864e8i | 0.561454 | + | 0.972467i | ||||
\(918\) | −2.99507e8 | − | 5.18761e8i | −0.387149 | − | 0.670562i | ||||
\(919\) | 1.12173e9 | 1.44524 | 0.722620 | − | 0.691245i | \(-0.242938\pi\) | ||||
0.722620 | + | 0.691245i | \(0.242938\pi\) | |||||||
\(920\) | −2.28559e8 | − | 3.95876e8i | −0.293519 | − | 0.508389i | ||||
\(921\) | −1.45897e9 | + | 8.42335e8i | −1.86753 | + | 1.07822i | ||||
\(922\) | 5.91299e8 | + | 3.41387e8i | 0.754422 | + | 0.435566i | ||||
\(923\) | 4.67599e8 | + | 2.69968e8i | 0.594659 | + | 0.343327i | ||||
\(924\) | −4.40482e8 | −0.558358 | ||||||||
\(925\) | − | 2.64774e7i | − | 0.0334542i | ||||||
\(926\) | −1.81617e8 | + | 3.14570e8i | −0.228730 | + | 0.396173i | ||||
\(927\) | 1.79374e8 | − | 3.10686e8i | 0.225176 | − | 0.390015i | ||||
\(928\) | −2.26843e8 | − | 3.92903e8i | −0.283845 | − | 0.491634i | ||||
\(929\) | −3.07905e7 | + | 1.77769e7i | −0.0384034 | + | 0.0221722i | −0.519079 | − | 0.854726i | \(-0.673725\pi\) |
0.480675 | + | 0.876899i | \(0.340392\pi\) | |||||||
\(930\) | 3.25335e8i | 0.404466i | ||||||||
\(931\) | 4.00118e8 | − | 2.31008e8i | 0.495837 | − | 0.286272i | ||||
\(932\) | −1.07830e7 | + | 6.22560e6i | −0.0133197 | + | 0.00769012i | ||||
\(933\) | 1.06315e9 | − | 6.13811e8i | 1.30903 | − | 0.755770i | ||||
\(934\) | −3.96389e8 | + | 6.86566e8i | −0.486498 | + | 0.842640i | ||||
\(935\) | − | 1.33626e9i | − | 1.63477i | ||||||
\(936\) | 1.49919e8 | + | 8.65560e7i | 0.182823 | + | 0.105553i | ||||
\(937\) | −1.51076e8 | + | 8.72237e7i | −0.183644 | + | 0.106027i | −0.589004 | − | 0.808130i | \(-0.700480\pi\) |
0.405360 | + | 0.914157i | \(0.367146\pi\) | |||||||
\(938\) | −6.13423e8 | −0.743279 | ||||||||
\(939\) | −6.02222e8 | − | 1.04308e9i | −0.727377 | − | 1.25985i | ||||
\(940\) | −4.15650e8 | − | 2.39976e8i | −0.500431 | − | 0.288924i | ||||
\(941\) | 5.72580e8 | − | 9.91737e8i | 0.687174 | − | 1.19022i | −0.285574 | − | 0.958357i | \(-0.592184\pi\) |
0.972748 | − | 0.231864i | \(-0.0744825\pi\) | |||||||
\(942\) | − | 1.76958e9i | − | 2.11699i | ||||||
\(943\) | −6.03318e8 | + | 1.04498e9i | −0.719467 | + | 1.24615i | ||||
\(944\) | 4.19223e8 | 0.498344 | ||||||||
\(945\) | − | 1.93823e8i | − | 0.229673i | ||||||
\(946\) | −8.56240e8 | − | 7.84682e8i | −1.01140 | − | 0.926873i | ||||
\(947\) | 1.51800e9 | 1.78741 | 0.893703 | − | 0.448659i | \(-0.148098\pi\) | ||||
0.893703 | + | 0.448659i | \(0.148098\pi\) | |||||||
\(948\) | − | 7.76173e8i | − | 0.911032i | ||||||
\(949\) | −3.18281e8 | − | 1.83760e8i | −0.372402 | − | 0.215007i | ||||
\(950\) | −1.26330e8 | −0.147345 | ||||||||
\(951\) | −2.13139e8 | − | 1.23056e8i | −0.247811 | − | 0.143074i | ||||
\(952\) | 2.21340e8 | − | 3.83373e8i | 0.256537 | − | 0.444335i | ||||
\(953\) | −5.27716e8 | + | 3.04677e8i | −0.609708 | + | 0.352015i | −0.772851 | − | 0.634587i | \(-0.781170\pi\) |
0.163143 | + | 0.986602i | \(0.447837\pi\) | |||||||
\(954\) | − | 2.96519e8i | − | 0.341513i | ||||||
\(955\) | −2.22581e8 | − | 3.85522e8i | −0.255551 | − | 0.442628i | ||||
\(956\) | −1.31062e8 | + | 2.27007e8i | −0.150004 | + | 0.259815i | ||||
\(957\) | 6.52352e8 | 0.744297 | ||||||||
\(958\) | −1.00090e9 | − | 5.77871e8i | −1.13840 | − | 0.657256i | ||||
\(959\) | 3.00254e8 | + | 5.20056e8i | 0.340434 | + | 0.589650i | ||||
\(960\) | 7.11381e7 | + | 1.23215e8i | 0.0804060 | + | 0.139267i | ||||
\(961\) | 4.13890e8 | + | 7.16878e8i | 0.466353 | + | 0.807746i | ||||
\(962\) | 1.92865e8 | 0.216635 | ||||||||
\(963\) | 1.48693e8 | + | 2.57544e8i | 0.166499 | + | 0.288385i | ||||
\(964\) | 8.20735e8 | − | 4.73851e8i | 0.916161 | − | 0.528946i | ||||
\(965\) | 2.09057e7 | + | 1.20699e7i | 0.0232639 | + | 0.0134314i | ||||
\(966\) | −1.06147e9 | − | 6.12840e8i | −1.17754 | − | 0.679855i | ||||
\(967\) | 6.32569e8 | 0.699566 | 0.349783 | − | 0.936831i | \(-0.386255\pi\) | ||||
0.349783 | + | 0.936831i | \(0.386255\pi\) | |||||||
\(968\) | 7.50448e7i | 0.0827360i | ||||||||
\(969\) | −9.41679e8 | + | 1.63104e9i | −1.03498 | + | 1.79264i | ||||
\(970\) | −4.15303e8 | + | 7.19325e8i | −0.455040 | + | 0.788152i | ||||
\(971\) | 1.15448e8 | + | 1.99962e8i | 0.126104 | + | 0.218418i | 0.922164 | − | 0.386799i | \(-0.126419\pi\) |
−0.796060 | + | 0.605218i | \(0.793086\pi\) | |||||||
\(972\) | −5.82832e8 | + | 3.36498e8i | −0.634665 | + | 0.366424i | ||||
\(973\) | 5.98813e8i | 0.650059i | ||||||||
\(974\) | −8.52909e7 | + | 4.92427e7i | −0.0923051 | + | 0.0532924i | ||||
\(975\) | −7.47325e7 | + | 4.31468e7i | −0.0806298 | + | 0.0465516i | ||||
\(976\) | −6.78504e8 | + | 3.91734e8i | −0.729798 | + | 0.421349i | ||||
\(977\) | −6.27123e8 | + | 1.08621e9i | −0.672464 | + | 1.16474i | 0.304739 | + | 0.952436i | \(0.401431\pi\) |
−0.977203 | + | 0.212306i | \(0.931903\pi\) | |||||||
\(978\) | 2.25498e9i | 2.41060i | ||||||||
\(979\) | −1.68306e9 | − | 9.71716e8i | −1.79371 | − | 1.03560i | ||||
\(980\) | 2.72807e8 | − | 1.57505e8i | 0.289853 | − | 0.167347i | ||||
\(981\) | 1.29762e8 | 0.137448 | ||||||||
\(982\) | 9.99206e8 | + | 1.73067e9i | 1.05516 | + | 1.82760i | ||||
\(983\) | 1.13500e9 | + | 6.55292e8i | 1.19491 | + | 0.689881i | 0.959416 | − | 0.281995i | \(-0.0909961\pi\) |
0.235493 | + | 0.971876i | \(0.424329\pi\) | |||||||
\(984\) | −3.48667e8 | + | 6.03910e8i | −0.365954 | + | 0.633850i | ||||
\(985\) | 8.27563e8i | 0.865949i | ||||||||
\(986\) | 5.16179e8 | − | 8.94049e8i | 0.538480 | − | 0.932675i | ||||
\(987\) | 8.17258e8 | 0.849978 | ||||||||
\(988\) | − | 3.49215e8i | − | 0.362095i | ||||||
\(989\) | −3.68735e8 | − | 1.16969e9i | −0.381176 | − | 1.20916i | ||||
\(990\) | −8.88144e8 | −0.915330 | ||||||||
\(991\) | 1.40751e9i | 1.44620i | 0.690741 | + | 0.723102i | \(0.257284\pi\) | ||||
−0.690741 | + | 0.723102i | \(0.742716\pi\) | |||||||
\(992\) | −2.36410e8 | − | 1.36492e8i | −0.242176 | − | 0.139820i | ||||
\(993\) | −1.17717e8 | −0.120224 | ||||||||
\(994\) | −7.94749e8 | − | 4.58848e8i | −0.809228 | − | 0.467208i | ||||
\(995\) | 8.60152e8 | − | 1.48983e9i | 0.873185 | − | 1.51240i | ||||
\(996\) | −9.18906e8 | + | 5.30531e8i | −0.930022 | + | 0.536948i | ||||
\(997\) | 3.05962e8i | 0.308732i | 0.988014 | + | 0.154366i | \(0.0493335\pi\) | ||||
−0.988014 | + | 0.154366i | \(0.950667\pi\) | |||||||
\(998\) | −6.19615e8 | − | 1.07321e9i | −0.623348 | − | 1.07967i | ||||
\(999\) | 5.34502e7 | − | 9.25785e7i | 0.0536109 | − | 0.0928568i |
(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 | 43.7.d.a.37.17 | yes | 42 | |
43.7 | odd | 6 | inner | 43.7.d.a.7.5 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.5 | ✓ | 42 | 43.7 | odd | 6 | inner | |
43.7.d.a.37.17 | yes | 42 | 1.1 | even | 1 | trivial |