Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.446265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.1 | ||
Root | \(1.86298 + 1.35354i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.r.148.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.711597 | + | 2.19007i | −0.503175 | + | 1.54861i | 0.300642 | + | 0.953737i | \(0.402799\pi\) |
−0.803817 | + | 0.594876i | \(0.797201\pi\) | |||||||
\(3\) | 1.86298 | − | 1.35354i | 1.07559 | − | 0.781465i | 0.0986852 | − | 0.995119i | \(-0.468536\pi\) |
0.976910 | + | 0.213653i | \(0.0685363\pi\) | |||||||
\(4\) | −2.67200 | − | 1.94132i | −1.33600 | − | 0.970661i | ||||
\(5\) | 1.11418 | + | 3.42908i | 0.498275 | + | 1.53353i | 0.811790 | + | 0.583949i | \(0.198493\pi\) |
−0.313515 | + | 0.949583i | \(0.601507\pi\) | |||||||
\(6\) | 1.63865 | + | 5.04324i | 0.668975 | + | 2.05889i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 2.42705 | − | 1.76336i | 0.858092 | − | 0.623440i | ||||
\(9\) | 0.711597 | − | 2.19007i | 0.237199 | − | 0.730023i | ||||
\(10\) | −8.30278 | −2.62557 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −7.60555 | −2.19553 | ||||||||
\(13\) | −2.04123 | + | 6.28225i | −0.566135 | + | 1.74238i | 0.0984213 | + | 0.995145i | \(0.468621\pi\) |
−0.664556 | + | 0.747239i | \(0.731379\pi\) | |||||||
\(14\) | 1.86298 | − | 1.35354i | 0.497904 | − | 0.361748i | ||||
\(15\) | 6.71709 | + | 4.88025i | 1.73434 | + | 1.26007i | ||||
\(16\) | 0.0935628 | + | 0.287957i | 0.0233907 | + | 0.0719892i | ||||
\(17\) | −0.833488 | − | 2.56521i | −0.202151 | − | 0.622155i | −0.999818 | − | 0.0190584i | \(-0.993933\pi\) |
0.797668 | − | 0.603097i | \(-0.206067\pi\) | |||||||
\(18\) | 4.29004 | + | 3.11689i | 1.01117 | + | 0.734659i | ||||
\(19\) | −2.42705 | + | 1.76336i | −0.556804 | + | 0.404542i | −0.830288 | − | 0.557335i | \(-0.811824\pi\) |
0.273484 | + | 0.961877i | \(0.411824\pi\) | |||||||
\(20\) | 3.67988 | − | 11.3255i | 0.822845 | − | 2.53246i | ||||
\(21\) | −2.30278 | −0.502507 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.69722 | −0.562410 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(24\) | 2.13479 | − | 6.57021i | 0.435762 | − | 1.34114i | ||||
\(25\) | −6.47214 | + | 4.70228i | −1.29443 | + | 0.940456i | ||||
\(26\) | −12.3060 | − | 8.94086i | −2.41341 | − | 1.75345i | ||||
\(27\) | 0.496143 | + | 1.52697i | 0.0954827 | + | 0.293866i | ||||
\(28\) | 1.02061 | + | 3.14113i | 0.192878 | + | 0.593617i | ||||
\(29\) | 3.80013 | + | 2.76096i | 0.705667 | + | 0.512697i | 0.881773 | − | 0.471674i | \(-0.156350\pi\) |
−0.176106 | + | 0.984371i | \(0.556350\pi\) | |||||||
\(30\) | −15.4679 | + | 11.2381i | −2.82405 | + | 2.05179i | ||||
\(31\) | 0.309017 | − | 0.951057i | 0.0555011 | − | 0.170815i | −0.919463 | − | 0.393176i | \(-0.871376\pi\) |
0.974964 | + | 0.222361i | \(0.0713764\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.21110 | 1.06520 | ||||||||
\(35\) | 1.11418 | − | 3.42908i | 0.188330 | − | 0.579621i | ||||
\(36\) | −6.15302 | + | 4.47043i | −1.02550 | + | 0.745072i | ||||
\(37\) | 4.21587 | + | 3.06301i | 0.693085 | + | 0.503556i | 0.877673 | − | 0.479260i | \(-0.159095\pi\) |
−0.184588 | + | 0.982816i | \(0.559095\pi\) | |||||||
\(38\) | −2.13479 | − | 6.57021i | −0.346309 | − | 1.06583i | ||||
\(39\) | 4.70049 | + | 14.4666i | 0.752681 | + | 2.31651i | ||||
\(40\) | 8.75086 | + | 6.35787i | 1.38363 | + | 1.00527i | ||||
\(41\) | 5.66312 | − | 4.11450i | 0.884431 | − | 0.642576i | −0.0499893 | − | 0.998750i | \(-0.515919\pi\) |
0.934420 | + | 0.356173i | \(0.115919\pi\) | |||||||
\(42\) | 1.63865 | − | 5.04324i | 0.252849 | − | 0.778189i | ||||
\(43\) | −1.69722 | −0.258824 | −0.129412 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129412 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.30278 | 1.23770 | ||||||||
\(46\) | 1.91934 | − | 5.90711i | 0.282991 | − | 0.870956i | ||||
\(47\) | 1.54387 | − | 1.12169i | 0.225196 | − | 0.163615i | −0.469466 | − | 0.882950i | \(-0.655554\pi\) |
0.694663 | + | 0.719336i | \(0.255554\pi\) | |||||||
\(48\) | 0.564066 | + | 0.409818i | 0.0814160 | + | 0.0591522i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −5.69277 | − | 17.5206i | −0.805080 | − | 2.47778i | ||||
\(51\) | −5.02489 | − | 3.65079i | −0.703625 | − | 0.511213i | ||||
\(52\) | 17.6500 | − | 12.8235i | 2.44762 | − | 1.77830i | ||||
\(53\) | −3.98889 | + | 12.2765i | −0.547917 | + | 1.68631i | 0.166036 | + | 0.986120i | \(0.446903\pi\) |
−0.713953 | + | 0.700194i | \(0.753097\pi\) | |||||||
\(54\) | −3.69722 | −0.503129 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | −2.13479 | + | 6.57021i | −0.282760 | + | 0.870245i | ||||
\(58\) | −8.75086 | + | 6.35787i | −1.14904 | + | 0.834829i | ||||
\(59\) | −5.41817 | − | 3.93653i | −0.705385 | − | 0.512493i | 0.176296 | − | 0.984337i | \(-0.443588\pi\) |
−0.881682 | + | 0.471845i | \(0.843588\pi\) | |||||||
\(60\) | −8.47393 | − | 26.0801i | −1.09398 | − | 3.36692i | ||||
\(61\) | 1.32963 | + | 4.09218i | 0.170242 | + | 0.523950i | 0.999384 | − | 0.0350870i | \(-0.0111708\pi\) |
−0.829142 | + | 0.559037i | \(0.811171\pi\) | |||||||
\(62\) | 1.86298 | + | 1.35354i | 0.236599 | + | 0.171899i | ||||
\(63\) | −1.86298 | + | 1.35354i | −0.234714 | + | 0.170530i | ||||
\(64\) | −3.96056 | + | 12.1894i | −0.495070 | + | 1.52367i | ||||
\(65\) | −23.8167 | −2.95409 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.51388 | 1.04014 | 0.520068 | − | 0.854125i | \(-0.325907\pi\) | ||||
0.520068 | + | 0.854125i | \(0.325907\pi\) | |||||||
\(68\) | −2.75282 | + | 8.47232i | −0.333829 | + | 1.02742i | ||||
\(69\) | −5.02489 | + | 3.65079i | −0.604925 | + | 0.439504i | ||||
\(70\) | 6.71709 | + | 4.88025i | 0.802845 | + | 0.583301i | ||||
\(71\) | −1.32963 | − | 4.09218i | −0.157798 | − | 0.485653i | 0.840636 | − | 0.541601i | \(-0.182182\pi\) |
−0.998434 | + | 0.0559485i | \(0.982182\pi\) | |||||||
\(72\) | −2.13479 | − | 6.57021i | −0.251587 | − | 0.774307i | ||||
\(73\) | −4.04508 | − | 2.93893i | −0.473441 | − | 0.343975i | 0.325340 | − | 0.945597i | \(-0.394521\pi\) |
−0.798781 | + | 0.601622i | \(0.794521\pi\) | |||||||
\(74\) | −9.70820 | + | 7.05342i | −1.12856 | + | 0.819944i | ||||
\(75\) | −5.69277 | + | 17.5206i | −0.657345 | + | 2.02310i | ||||
\(76\) | 9.90833 | 1.13656 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −35.0278 | −3.96611 | ||||||||
\(79\) | 2.56570 | − | 7.89641i | 0.288664 | − | 0.888415i | −0.696613 | − | 0.717447i | \(-0.745310\pi\) |
0.985277 | − | 0.170968i | \(-0.0546895\pi\) | |||||||
\(80\) | −0.883182 | + | 0.641669i | −0.0987428 | + | 0.0717408i | ||||
\(81\) | 8.58007 | + | 6.23379i | 0.953341 | + | 0.692643i | ||||
\(82\) | 4.98118 | + | 15.3305i | 0.550079 | + | 1.69297i | ||||
\(83\) | −0.927051 | − | 2.85317i | −0.101757 | − | 0.313176i | 0.887199 | − | 0.461388i | \(-0.152648\pi\) |
−0.988956 | + | 0.148212i | \(0.952648\pi\) | |||||||
\(84\) | 6.15302 | + | 4.47043i | 0.671350 | + | 0.487764i | ||||
\(85\) | 7.86767 | − | 5.71620i | 0.853369 | − | 0.620009i | ||||
\(86\) | 1.20774 | − | 3.71704i | 0.130234 | − | 0.400819i | ||||
\(87\) | 10.8167 | 1.15967 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7250 | −1.56084 | −0.780422 | − | 0.625253i | \(-0.784996\pi\) | ||||
−0.780422 | + | 0.625253i | \(0.784996\pi\) | |||||||
\(90\) | −5.90823 | + | 18.1837i | −0.622782 | + | 1.91673i | ||||
\(91\) | 5.34400 | − | 3.88265i | 0.560204 | − | 0.407012i | ||||
\(92\) | 7.20699 | + | 5.23618i | 0.751380 | + | 0.545910i | ||||
\(93\) | −0.711597 | − | 2.19007i | −0.0737892 | − | 0.227100i | ||||
\(94\) | 1.35796 | + | 4.17937i | 0.140063 | + | 0.431069i | ||||
\(95\) | −8.75086 | − | 6.35787i | −0.897819 | − | 0.652304i | ||||
\(96\) | 9.87899 | − | 7.17751i | 1.00827 | − | 0.732551i | ||||
\(97\) | −1.11418 | + | 3.42908i | −0.113127 | + | 0.348171i | −0.991552 | − | 0.129711i | \(-0.958595\pi\) |
0.878424 | + | 0.477881i | \(0.158595\pi\) | |||||||
\(98\) | −2.30278 | −0.232615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.4222 | 2.64222 | ||||||||
\(101\) | 1.63865 | − | 5.04324i | 0.163052 | − | 0.501821i | −0.835836 | − | 0.548979i | \(-0.815017\pi\) |
0.998887 | + | 0.0471583i | \(0.0150165\pi\) | |||||||
\(102\) | 11.5712 | − | 8.40696i | 1.14572 | − | 0.832413i | ||||
\(103\) | 11.5712 | + | 8.40696i | 1.14014 | + | 0.828362i | 0.987139 | − | 0.159863i | \(-0.0511053\pi\) |
0.153004 | + | 0.988226i | \(0.451105\pi\) | |||||||
\(104\) | 6.12368 | + | 18.8468i | 0.600477 | + | 1.84808i | ||||
\(105\) | −2.56570 | − | 7.89641i | −0.250387 | − | 0.770611i | ||||
\(106\) | −24.0480 | − | 17.4719i | −2.33575 | − | 1.69702i | ||||
\(107\) | 10.0273 | − | 7.28527i | 0.969378 | − | 0.704294i | 0.0140679 | − | 0.999901i | \(-0.495522\pi\) |
0.955310 | + | 0.295607i | \(0.0955219\pi\) | |||||||
\(108\) | 1.63865 | − | 5.04324i | 0.157679 | − | 0.485286i | ||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 0.0935628 | − | 0.287957i | 0.00884086 | − | 0.0272094i | ||||
\(113\) | 8.65424 | − | 6.28767i | 0.814122 | − | 0.591494i | −0.100901 | − | 0.994897i | \(-0.532172\pi\) |
0.915023 | + | 0.403402i | \(0.132172\pi\) | |||||||
\(114\) | −12.8701 | − | 9.35068i | −1.20540 | − | 0.875771i | ||||
\(115\) | −3.00518 | − | 9.24901i | −0.280235 | − | 0.862474i | ||||
\(116\) | −4.79405 | − | 14.7546i | −0.445117 | − | 1.36993i | ||||
\(117\) | 12.3060 | + | 8.94086i | 1.13769 | + | 0.826583i | ||||
\(118\) | 12.4768 | − | 9.06494i | 1.14858 | − | 0.834496i | ||||
\(119\) | −0.833488 | + | 2.56521i | −0.0764057 | + | 0.235153i | ||||
\(120\) | 24.9083 | 2.27381 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.90833 | −0.897058 | ||||||||
\(123\) | 4.98118 | − | 15.3305i | 0.449138 | − | 1.38230i | ||||
\(124\) | −2.67200 | + | 1.94132i | −0.239953 | + | 0.174336i | ||||
\(125\) | −8.75086 | − | 6.35787i | −0.782700 | − | 0.568665i | ||||
\(126\) | −1.63865 | − | 5.04324i | −0.145982 | − | 0.449287i | ||||
\(127\) | −0.618034 | − | 1.90211i | −0.0548416 | − | 0.168785i | 0.919884 | − | 0.392191i | \(-0.128283\pi\) |
−0.974726 | + | 0.223405i | \(0.928283\pi\) | |||||||
\(128\) | −15.2972 | − | 11.1140i | −1.35209 | − | 0.982351i | ||||
\(129\) | −3.16190 | + | 2.29726i | −0.278390 | + | 0.202262i | ||||
\(130\) | 16.9479 | − | 52.1601i | 1.48643 | − | 4.57475i | ||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | −6.05845 | + | 18.6460i | −0.523370 | + | 1.61077i | ||||
\(135\) | −4.68332 | + | 3.40263i | −0.403076 | + | 0.292852i | ||||
\(136\) | −6.54630 | − | 4.75617i | −0.561341 | − | 0.407838i | ||||
\(137\) | −3.12708 | − | 9.62415i | −0.267164 | − | 0.822247i | −0.991187 | − | 0.132471i | \(-0.957709\pi\) |
0.724023 | − | 0.689776i | \(-0.242291\pi\) | |||||||
\(138\) | −4.41980 | − | 13.6027i | −0.376238 | − | 1.15794i | ||||
\(139\) | 17.4793 | + | 12.6994i | 1.48257 | + | 1.07715i | 0.976717 | + | 0.214532i | \(0.0688227\pi\) |
0.505854 | + | 0.862619i | \(0.331177\pi\) | |||||||
\(140\) | −9.63404 | + | 6.99954i | −0.814225 | + | 0.591569i | ||||
\(141\) | 1.35796 | − | 4.17937i | 0.114361 | − | 0.351966i | ||||
\(142\) | 9.90833 | 0.831488 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.697224 | 0.0581020 | ||||||||
\(145\) | −5.23354 | + | 16.1072i | −0.434622 | + | 1.33763i | ||||
\(146\) | 9.31492 | − | 6.76769i | 0.770909 | − | 0.560098i | ||||
\(147\) | 1.86298 | + | 1.35354i | 0.153656 | + | 0.111638i | ||||
\(148\) | −5.31852 | − | 16.3687i | −0.437180 | − | 1.34550i | ||||
\(149\) | 1.51676 | + | 4.66810i | 0.124258 | + | 0.382425i | 0.993765 | − | 0.111494i | \(-0.0355637\pi\) |
−0.869508 | + | 0.493920i | \(0.835564\pi\) | |||||||
\(150\) | −34.3203 | − | 24.9351i | −2.80224 | − | 2.03595i | ||||
\(151\) | −0.170786 | + | 0.124083i | −0.0138983 | + | 0.0100977i | −0.594713 | − | 0.803938i | \(-0.702734\pi\) |
0.580814 | + | 0.814036i | \(0.302734\pi\) | |||||||
\(152\) | −2.78115 | + | 8.55951i | −0.225581 | + | 0.694268i | ||||
\(153\) | −6.21110 | −0.502138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60555 | 0.289605 | ||||||||
\(156\) | 15.5247 | − | 47.7800i | 1.24297 | − | 3.82546i | ||||
\(157\) | −5.83390 | + | 4.23858i | −0.465596 | + | 0.338275i | −0.795723 | − | 0.605661i | \(-0.792909\pi\) |
0.330126 | + | 0.943937i | \(0.392909\pi\) | |||||||
\(158\) | 15.4679 | + | 11.2381i | 1.23056 | + | 0.894057i | ||||
\(159\) | 9.18552 | + | 28.2701i | 0.728459 | + | 2.24197i | ||||
\(160\) | 5.90823 | + | 18.1837i | 0.467086 | + | 1.43754i | ||||
\(161\) | 2.18210 | + | 1.58539i | 0.171974 | + | 0.124946i | ||||
\(162\) | −19.7580 | + | 14.3550i | −1.55233 | + | 1.12784i | ||||
\(163\) | 0.870394 | − | 2.67880i | 0.0681745 | − | 0.209820i | −0.911165 | − | 0.412041i | \(-0.864816\pi\) |
0.979340 | + | 0.202221i | \(0.0648161\pi\) | |||||||
\(164\) | −23.1194 | −1.80532 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.90833 | 0.536190 | ||||||||
\(167\) | 1.61032 | − | 4.95605i | 0.124610 | − | 0.383511i | −0.869220 | − | 0.494426i | \(-0.835378\pi\) |
0.993830 | + | 0.110915i | \(0.0353782\pi\) | |||||||
\(168\) | −5.58895 | + | 4.06061i | −0.431197 | + | 0.313283i | ||||
\(169\) | −24.7829 | − | 18.0058i | −1.90637 | − | 1.38506i | ||||
\(170\) | 6.92027 | + | 21.2984i | 0.530760 | + | 1.63351i | ||||
\(171\) | 2.13479 | + | 6.57021i | 0.163252 | + | 0.502436i | ||||
\(172\) | 4.53499 | + | 3.29486i | 0.345789 | + | 0.251231i | ||||
\(173\) | −1.05397 | + | 0.765752i | −0.0801317 | + | 0.0582191i | −0.627130 | − | 0.778915i | \(-0.715770\pi\) |
0.546998 | + | 0.837134i | \(0.315770\pi\) | |||||||
\(174\) | −7.69710 | + | 23.6892i | −0.583515 | + | 1.79588i | ||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.4222 | −1.15920 | ||||||||
\(178\) | 10.4782 | − | 32.2487i | 0.785378 | − | 2.41714i | ||||
\(179\) | 5.17322 | − | 3.75856i | 0.386664 | − | 0.280928i | −0.377423 | − | 0.926041i | \(-0.623190\pi\) |
0.764087 | + | 0.645113i | \(0.223190\pi\) | |||||||
\(180\) | −22.1850 | − | 16.1184i | −1.65357 | − | 1.20139i | ||||
\(181\) | −7.79066 | − | 23.9772i | −0.579075 | − | 1.78221i | −0.621863 | − | 0.783126i | \(-0.713624\pi\) |
0.0427881 | − | 0.999084i | \(-0.486376\pi\) | |||||||
\(182\) | 4.70049 | + | 14.4666i | 0.348423 | + | 1.07234i | ||||
\(183\) | 8.01600 | + | 5.82397i | 0.592560 | + | 0.430520i | ||||
\(184\) | −6.54630 | + | 4.75617i | −0.482600 | + | 0.350629i | ||||
\(185\) | −5.80609 | + | 17.8693i | −0.426872 | + | 1.31378i | ||||
\(186\) | 5.30278 | 0.388818 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.30278 | −0.459677 | ||||||||
\(189\) | 0.496143 | − | 1.52697i | 0.0360891 | − | 0.111071i | ||||
\(190\) | 20.1513 | − | 14.6407i | 1.46193 | − | 1.06215i | ||||
\(191\) | 21.6951 | + | 15.7624i | 1.56980 | + | 1.14053i | 0.927343 | + | 0.374211i | \(0.122086\pi\) |
0.642461 | + | 0.766318i | \(0.277914\pi\) | |||||||
\(192\) | 9.12029 | + | 28.0694i | 0.658200 | + | 2.02573i | ||||
\(193\) | 0.654940 | + | 2.01570i | 0.0471436 | + | 0.145093i | 0.971857 | − | 0.235570i | \(-0.0756957\pi\) |
−0.924714 | + | 0.380663i | \(0.875696\pi\) | |||||||
\(194\) | −6.71709 | − | 4.88025i | −0.482259 | − | 0.350381i | ||||
\(195\) | −44.3701 | + | 32.2367i | −3.17741 | + | 2.30852i | ||||
\(196\) | 1.02061 | − | 3.14113i | 0.0729010 | − | 0.224366i | ||||
\(197\) | 10.6056 | 0.755614 | 0.377807 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377807 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4222 | 1.37680 | 0.688402 | − | 0.725330i | \(-0.258313\pi\) | ||||
0.688402 | + | 0.725330i | \(0.258313\pi\) | |||||||
\(200\) | −7.41641 | + | 22.8254i | −0.524419 | + | 1.61400i | ||||
\(201\) | 15.8612 | − | 11.5239i | 1.11876 | − | 0.812830i | ||||
\(202\) | 9.87899 | + | 7.17751i | 0.695083 | + | 0.505008i | ||||
\(203\) | −1.45152 | − | 4.46733i | −0.101877 | − | 0.313545i | ||||
\(204\) | 6.33914 | + | 19.5099i | 0.443828 | + | 1.36596i | ||||
\(205\) | 20.4187 | + | 14.8350i | 1.42610 | + | 1.03612i | ||||
\(206\) | −26.6459 | + | 19.3593i | −1.85650 | + | 1.34883i | ||||
\(207\) | −1.91934 | + | 5.90711i | −0.133403 | + | 0.410572i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 19.1194 | 1.31937 | ||||||||
\(211\) | −4.79405 | + | 14.7546i | −0.330036 | + | 1.01575i | 0.639080 | + | 0.769141i | \(0.279315\pi\) |
−0.969116 | + | 0.246606i | \(0.920685\pi\) | |||||||
\(212\) | 34.4911 | − | 25.0592i | 2.36886 | − | 1.72107i | ||||
\(213\) | −8.01600 | − | 5.82397i | −0.549248 | − | 0.399052i | ||||
\(214\) | 8.81985 | + | 27.1447i | 0.602913 | + | 1.85557i | ||||
\(215\) | −1.89101 | − | 5.81992i | −0.128966 | − | 0.396915i | ||||
\(216\) | 3.89675 | + | 2.83116i | 0.265141 | + | 0.192636i | ||||
\(217\) | −0.809017 | + | 0.587785i | −0.0549197 | + | 0.0399015i | ||||
\(218\) | −5.69277 | + | 17.5206i | −0.385563 | + | 1.18664i | ||||
\(219\) | −11.5139 | −0.778036 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8167 | 1.19848 | ||||||||
\(222\) | −8.53916 | + | 26.2808i | −0.573111 | + | 1.76385i | ||||
\(223\) | −11.2521 | + | 8.17511i | −0.753495 | + | 0.547446i | −0.896908 | − | 0.442217i | \(-0.854192\pi\) |
0.143414 | + | 0.989663i | \(0.454192\pi\) | |||||||
\(224\) | −4.29004 | − | 3.11689i | −0.286640 | − | 0.208256i | ||||
\(225\) | 5.69277 | + | 17.5206i | 0.379518 | + | 1.16804i | ||||
\(226\) | 7.61211 | + | 23.4277i | 0.506350 | + | 1.55839i | ||||
\(227\) | 5.26984 | + | 3.82876i | 0.349771 | + | 0.254124i | 0.748773 | − | 0.662826i | \(-0.230643\pi\) |
−0.399002 | + | 0.916950i | \(0.630643\pi\) | |||||||
\(228\) | 18.4591 | − | 13.4113i | 1.22248 | − | 0.888185i | ||||
\(229\) | −0.805160 | + | 2.47803i | −0.0532064 | + | 0.163753i | −0.974129 | − | 0.225993i | \(-0.927437\pi\) |
0.920922 | + | 0.389746i | \(0.127437\pi\) | |||||||
\(230\) | 22.3944 | 1.47665 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0917 | 0.925164 | ||||||||
\(233\) | −5.56231 | + | 17.1190i | −0.364399 | + | 1.12150i | 0.585958 | + | 0.810341i | \(0.300718\pi\) |
−0.950357 | + | 0.311163i | \(0.899282\pi\) | |||||||
\(234\) | −28.3381 | + | 20.5888i | −1.85252 | + | 1.34593i | ||||
\(235\) | 5.56650 | + | 4.04430i | 0.363118 | + | 0.263821i | ||||
\(236\) | 6.83528 | + | 21.0368i | 0.444939 | + | 1.36938i | ||||
\(237\) | −5.90823 | − | 18.1837i | −0.383781 | − | 1.18116i | ||||
\(238\) | −5.02489 | − | 3.65079i | −0.325715 | − | 0.236646i | ||||
\(239\) | 21.3018 | − | 15.4767i | 1.37790 | − | 1.00110i | 0.380829 | − | 0.924645i | \(-0.375639\pi\) |
0.997073 | − | 0.0764590i | \(-0.0243614\pi\) | |||||||
\(240\) | −0.776831 | + | 2.39084i | −0.0501442 | + | 0.154328i | ||||
\(241\) | −0.486122 | −0.0313139 | −0.0156569 | − | 0.999877i | \(-0.504984\pi\) | ||||
−0.0156569 | + | 0.999877i | \(0.504984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6056 | 1.25770 | ||||||||
\(244\) | 4.39147 | − | 13.5156i | 0.281135 | − | 0.865245i | ||||
\(245\) | −2.91695 | + | 2.11929i | −0.186357 | + | 0.135396i | ||||
\(246\) | 30.0302 | + | 21.8183i | 1.91466 | + | 1.39108i | ||||
\(247\) | −6.12368 | − | 18.8468i | −0.389641 | − | 1.19919i | ||||
\(248\) | −0.927051 | − | 2.85317i | −0.0588678 | − | 0.181176i | ||||
\(249\) | −5.58895 | − | 4.06061i | −0.354186 | − | 0.257331i | ||||
\(250\) | 20.1513 | − | 14.6407i | 1.27448 | − | 0.925962i | ||||
\(251\) | 1.35796 | − | 4.17937i | 0.0857136 | − | 0.263799i | −0.899009 | − | 0.437930i | \(-0.855712\pi\) |
0.984722 | + | 0.174131i | \(0.0557116\pi\) | |||||||
\(252\) | 7.60555 | 0.479105 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.60555 | 0.288978 | ||||||||
\(255\) | 6.92027 | − | 21.2984i | 0.433364 | − | 1.33376i | ||||
\(256\) | 14.4881 | − | 10.5263i | 0.905509 | − | 0.657891i | ||||
\(257\) | −5.24738 | − | 3.81245i | −0.327323 | − | 0.237814i | 0.411971 | − | 0.911197i | \(-0.364840\pi\) |
−0.739294 | + | 0.673383i | \(0.764840\pi\) | |||||||
\(258\) | −2.78115 | − | 8.55951i | −0.173147 | − | 0.532892i | ||||
\(259\) | −1.61032 | − | 4.95605i | −0.100060 | − | 0.307954i | ||||
\(260\) | 63.6381 | + | 46.2358i | 3.94667 | + | 2.86742i | ||||
\(261\) | 8.75086 | − | 6.35787i | 0.541664 | − | 0.393542i | ||||
\(262\) | −4.26958 | + | 13.1404i | −0.263776 | + | 0.811818i | ||||
\(263\) | −20.2389 | −1.24798 | −0.623991 | − | 0.781432i | \(-0.714490\pi\) | ||||
−0.623991 | + | 0.781432i | \(0.714490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −46.5416 | −2.85903 | ||||||||
\(266\) | −2.13479 | + | 6.57021i | −0.130892 | + | 0.402845i | ||||
\(267\) | −27.4324 | + | 19.9308i | −1.67884 | + | 1.21975i | ||||
\(268\) | −22.7491 | − | 16.5282i | −1.38962 | − | 1.00962i | ||||
\(269\) | 4.98118 | + | 15.3305i | 0.303708 | + | 0.934716i | 0.980156 | + | 0.198226i | \(0.0635181\pi\) |
−0.676448 | + | 0.736490i | \(0.736482\pi\) | |||||||
\(270\) | −4.11936 | − | 12.6781i | −0.250696 | − | 0.771564i | ||||
\(271\) | −23.0682 | − | 16.7600i | −1.40129 | − | 1.01810i | −0.994517 | − | 0.104572i | \(-0.966653\pi\) |
−0.406777 | − | 0.913528i | \(-0.633347\pi\) | |||||||
\(272\) | 0.660687 | − | 0.480017i | 0.0400600 | − | 0.0291053i | ||||
\(273\) | 4.70049 | − | 14.4666i | 0.284487 | − | 0.875560i | ||||
\(274\) | 23.3028 | 1.40777 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 20.5139 | 1.23479 | ||||||||
\(277\) | −9.25076 | + | 28.4709i | −0.555824 | + | 1.71065i | 0.137933 | + | 0.990442i | \(0.455954\pi\) |
−0.693757 | + | 0.720209i | \(0.744046\pi\) | |||||||
\(278\) | −40.2508 | + | 29.2439i | −2.41408 | + | 1.75393i | ||||
\(279\) | −1.86298 | − | 1.35354i | −0.111534 | − | 0.0810342i | ||||
\(280\) | −3.34253 | − | 10.2872i | −0.199754 | − | 0.614781i | ||||
\(281\) | −1.97599 | − | 6.08148i | −0.117878 | − | 0.362791i | 0.874659 | − | 0.484740i | \(-0.161086\pi\) |
−0.992536 | + | 0.121949i | \(0.961086\pi\) | |||||||
\(282\) | 8.18679 | + | 5.94805i | 0.487516 | + | 0.354201i | ||||
\(283\) | 3.55518 | − | 2.58299i | 0.211334 | − | 0.153543i | −0.477083 | − | 0.878858i | \(-0.658306\pi\) |
0.688417 | + | 0.725315i | \(0.258306\pi\) | |||||||
\(284\) | −4.39147 | + | 13.5156i | −0.260586 | + | 0.802001i | ||||
\(285\) | −24.9083 | −1.47544 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.00000 | −0.413197 | ||||||||
\(288\) | 3.77344 | − | 11.6134i | 0.222352 | − | 0.684329i | ||||
\(289\) | 7.86767 | − | 5.71620i | 0.462804 | − | 0.336247i | ||||
\(290\) | −31.5517 | − | 22.9236i | −1.85278 | − | 1.34612i | ||||
\(291\) | 2.56570 | + | 7.89641i | 0.150404 | + | 0.462896i | ||||
\(292\) | 5.10307 | + | 15.7056i | 0.298635 | + | 0.919103i | ||||
\(293\) | 3.89675 | + | 2.83116i | 0.227651 | + | 0.165398i | 0.695764 | − | 0.718271i | \(-0.255066\pi\) |
−0.468113 | + | 0.883669i | \(0.655066\pi\) | |||||||
\(294\) | −4.29004 | + | 3.11689i | −0.250200 | + | 0.181781i | ||||
\(295\) | 7.46189 | − | 22.9653i | 0.434448 | − | 1.33709i | ||||
\(296\) | 15.6333 | 0.908668 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.3028 | −0.654752 | ||||||||
\(299\) | 5.50565 | − | 16.9446i | 0.318400 | − | 0.979934i | ||||
\(300\) | 49.2242 | − | 35.7634i | 2.84196 | − | 2.06480i | ||||
\(301\) | 1.37308 | + | 0.997603i | 0.0791432 | + | 0.0575009i | ||||
\(302\) | −0.150220 | − | 0.462329i | −0.00864418 | − | 0.0266041i | ||||
\(303\) | −3.77344 | − | 11.6134i | −0.216778 | − | 0.667175i | ||||
\(304\) | −0.734852 | − | 0.533901i | −0.0421466 | − | 0.0306213i | ||||
\(305\) | −12.5510 | + | 9.11883i | −0.718668 | + | 0.522143i | ||||
\(306\) | 4.41980 | − | 13.6027i | 0.252663 | − | 0.777617i | ||||
\(307\) | 16.6333 | 0.949313 | 0.474657 | − | 0.880171i | \(-0.342572\pi\) | ||||
0.474657 | + | 0.880171i | \(0.342572\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.9361 | 1.87367 | ||||||||
\(310\) | −2.56570 | + | 7.89641i | −0.145722 | + | 0.448486i | ||||
\(311\) | −5.17322 | + | 3.75856i | −0.293346 | + | 0.213129i | −0.724718 | − | 0.689046i | \(-0.758030\pi\) |
0.431371 | + | 0.902174i | \(0.358030\pi\) | |||||||
\(312\) | 36.9181 | + | 26.8226i | 2.09008 | + | 1.51853i | ||||
\(313\) | 4.72882 | + | 14.5538i | 0.267289 | + | 0.822630i | 0.991157 | + | 0.132692i | \(0.0423621\pi\) |
−0.723869 | + | 0.689938i | \(0.757638\pi\) | |||||||
\(314\) | −5.13140 | − | 15.7928i | −0.289582 | − | 0.891240i | ||||
\(315\) | −6.71709 | − | 4.88025i | −0.378465 | − | 0.274971i | ||||
\(316\) | −22.1850 | + | 16.1184i | −1.24801 | + | 0.906729i | ||||
\(317\) | 5.34685 | − | 16.4559i | 0.300309 | − | 0.924256i | −0.681077 | − | 0.732212i | \(-0.738488\pi\) |
0.981386 | − | 0.192045i | \(-0.0615119\pi\) | |||||||
\(318\) | −68.4500 | −3.83848 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −46.2111 | −2.58328 | ||||||||
\(321\) | 8.81985 | − | 27.1447i | 0.492276 | − | 1.51507i | ||||
\(322\) | −5.02489 | + | 3.65079i | −0.280026 | + | 0.203451i | ||||
\(323\) | 6.54630 | + | 4.75617i | 0.364246 | + | 0.264640i | ||||
\(324\) | −10.8242 | − | 33.3134i | −0.601343 | − | 1.85074i | ||||
\(325\) | −16.3298 | − | 50.2580i | −0.905815 | − | 2.78781i | ||||
\(326\) | 5.24738 | + | 3.81245i | 0.290626 | + | 0.211152i | ||||
\(327\) | 14.9039 | − | 10.8283i | 0.824186 | − | 0.598806i | ||||
\(328\) | 6.48936 | − | 19.9722i | 0.358315 | − | 1.10278i | ||||
\(329\) | −1.90833 | −0.105209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8167 | 1.30908 | 0.654541 | − | 0.756027i | \(-0.272862\pi\) | ||||
0.654541 | + | 0.756027i | \(0.272862\pi\) | |||||||
\(332\) | −3.06184 | + | 9.42338i | −0.168040 | + | 0.517175i | ||||
\(333\) | 9.70820 | − | 7.05342i | 0.532006 | − | 0.386525i | ||||
\(334\) | 9.70820 | + | 7.05342i | 0.531209 | + | 0.385946i | ||||
\(335\) | 9.48596 | + | 29.1948i | 0.518274 | + | 1.59508i | ||||
\(336\) | −0.215454 | − | 0.663100i | −0.0117540 | − | 0.0361751i | ||||
\(337\) | 9.53742 | + | 6.92934i | 0.519536 | + | 0.377465i | 0.816429 | − | 0.577446i | \(-0.195950\pi\) |
−0.296893 | + | 0.954911i | \(0.595950\pi\) | |||||||
\(338\) | 57.0694 | − | 41.4633i | 3.10417 | − | 2.25531i | ||||
\(339\) | 7.61211 | − | 23.4277i | 0.413433 | − | 1.27242i | ||||
\(340\) | −32.1194 | −1.74192 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −15.9083 | −0.860224 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | −4.11925 | + | 2.99281i | −0.222095 | + | 0.161362i | ||||
\(345\) | −18.1175 | − | 13.1631i | −0.975413 | − | 0.708679i | ||||
\(346\) | −0.927051 | − | 2.85317i | −0.0498386 | − | 0.153387i | ||||
\(347\) | −2.96828 | − | 9.13542i | −0.159346 | − | 0.490415i | 0.839230 | − | 0.543777i | \(-0.183006\pi\) |
−0.998575 | + | 0.0533619i | \(0.983006\pi\) | |||||||
\(348\) | −28.9021 | − | 20.9986i | −1.54932 | − | 1.12564i | ||||
\(349\) | −3.80013 | + | 2.76096i | −0.203417 | + | 0.147791i | −0.684830 | − | 0.728703i | \(-0.740124\pi\) |
0.481413 | + | 0.876494i | \(0.340124\pi\) | |||||||
\(350\) | −5.69277 | + | 17.5206i | −0.304292 | + | 0.936513i | ||||
\(351\) | −10.6056 | −0.566082 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.09167 | 0.271002 | 0.135501 | − | 0.990777i | \(-0.456736\pi\) | ||||
0.135501 | + | 0.990777i | \(0.456736\pi\) | |||||||
\(354\) | 10.9744 | − | 33.7757i | 0.583282 | − | 1.79516i | ||||
\(355\) | 12.5510 | − | 9.11883i | 0.666137 | − | 0.483977i | ||||
\(356\) | 39.3452 | + | 28.5859i | 2.08529 | + | 1.51505i | ||||
\(357\) | 1.91934 | + | 5.90711i | 0.101582 | + | 0.312637i | ||||
\(358\) | 4.55027 | + | 14.0043i | 0.240489 | + | 0.740150i | ||||
\(359\) | −27.4549 | − | 19.9471i | −1.44901 | − | 1.05277i | −0.986061 | − | 0.166386i | \(-0.946790\pi\) |
−0.462952 | − | 0.886383i | \(-0.653210\pi\) | |||||||
\(360\) | 20.1513 | − | 14.6407i | 1.06206 | − | 0.771635i | ||||
\(361\) | −3.09017 | + | 9.51057i | −0.162641 | + | 0.500556i | ||||
\(362\) | 58.0555 | 3.05133 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.8167 | −1.14350 | ||||||||
\(365\) | 5.57088 | − | 17.1454i | 0.291593 | − | 0.897432i | ||||
\(366\) | −18.4591 | + | 13.4113i | −0.964871 | + | 0.701019i | ||||
\(367\) | 14.2656 | + | 10.3646i | 0.744661 | + | 0.541028i | 0.894167 | − | 0.447733i | \(-0.147769\pi\) |
−0.149507 | + | 0.988761i | \(0.547769\pi\) | |||||||
\(368\) | −0.252360 | − | 0.776684i | −0.0131552 | − | 0.0404874i | ||||
\(369\) | −4.98118 | − | 15.3305i | −0.259310 | − | 0.798073i | ||||
\(370\) | −35.0034 | − | 25.4315i | −1.81974 | − | 1.32212i | ||||
\(371\) | 10.4431 | − | 7.58732i | 0.542176 | − | 0.393914i | ||||
\(372\) | −2.35024 | + | 7.23331i | −0.121855 | + | 0.375030i | ||||
\(373\) | 20.1194 | 1.04174 | 0.520872 | − | 0.853635i | \(-0.325607\pi\) | ||||
0.520872 | + | 0.853635i | \(0.325607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.9083 | −1.28626 | ||||||||
\(376\) | 1.76912 | − | 5.44478i | 0.0912352 | − | 0.280793i | ||||
\(377\) | −25.1020 | + | 18.2377i | −1.29282 | + | 0.939287i | ||||
\(378\) | 2.99112 | + | 2.17317i | 0.153846 | + | 0.111776i | ||||
\(379\) | −4.88761 | − | 15.0425i | −0.251060 | − | 0.772683i | −0.994580 | − | 0.103970i | \(-0.966845\pi\) |
0.743521 | − | 0.668713i | \(-0.233155\pi\) | |||||||
\(380\) | 11.0396 | + | 33.9765i | 0.566321 | + | 1.74296i | ||||
\(381\) | −3.72597 | − | 2.70708i | −0.190887 | − | 0.138688i | ||||
\(382\) | −49.9590 | + | 36.2973i | −2.55613 | + | 1.85713i | ||||
\(383\) | 11.9383 | − | 36.7425i | 0.610021 | − | 1.87745i | 0.152361 | − | 0.988325i | \(-0.451313\pi\) |
0.457661 | − | 0.889127i | \(-0.348687\pi\) | |||||||
\(384\) | −43.5416 | −2.22197 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.88057 | −0.248414 | ||||||||
\(387\) | −1.20774 | + | 3.71704i | −0.0613928 | + | 0.188948i | ||||
\(388\) | 9.63404 | − | 6.99954i | 0.489094 | − | 0.355348i | ||||
\(389\) | 6.32381 | + | 4.59451i | 0.320630 | + | 0.232951i | 0.736444 | − | 0.676498i | \(-0.236503\pi\) |
−0.415814 | + | 0.909449i | \(0.636503\pi\) | |||||||
\(390\) | −39.0271 | − | 120.113i | −1.97621 | − | 6.08216i | ||||
\(391\) | 2.24810 | + | 6.91895i | 0.113692 | + | 0.349907i | ||||
\(392\) | 2.42705 | + | 1.76336i | 0.122585 | + | 0.0890629i | ||||
\(393\) | 11.1779 | − | 8.12123i | 0.563851 | − | 0.409662i | ||||
\(394\) | −7.54688 | + | 23.2269i | −0.380206 | + | 1.17015i | ||||
\(395\) | 29.9361 | 1.50625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2111 | 1.51625 | 0.758126 | − | 0.652108i | \(-0.226115\pi\) | ||||
0.758126 | + | 0.652108i | \(0.226115\pi\) | |||||||
\(398\) | −13.8208 | + | 42.5360i | −0.692773 | + | 2.13214i | ||||
\(399\) | 5.58895 | − | 4.06061i | 0.279798 | − | 0.203285i | ||||
\(400\) | −1.95961 | − | 1.42374i | −0.0979803 | − | 0.0711868i | ||||
\(401\) | −6.55459 | − | 20.1730i | −0.327321 | − | 1.00739i | −0.970382 | − | 0.241575i | \(-0.922336\pi\) |
0.643062 | − | 0.765815i | \(-0.277664\pi\) | |||||||
\(402\) | 13.9512 | + | 42.9375i | 0.695825 | + | 2.14153i | ||||
\(403\) | 5.34400 | + | 3.88265i | 0.266204 | + | 0.193408i | ||||
\(404\) | −14.1690 | + | 10.2944i | −0.704935 | + | 0.512166i | ||||
\(405\) | −11.8165 | + | 36.3673i | −0.587164 | + | 1.80711i | ||||
\(406\) | 10.8167 | 0.536822 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.6333 | −0.922486 | ||||||||
\(409\) | −6.36747 | + | 19.5970i | −0.314851 | + | 0.969011i | 0.660965 | + | 0.750417i | \(0.270147\pi\) |
−0.975816 | + | 0.218595i | \(0.929853\pi\) | |||||||
\(410\) | −47.0196 | + | 34.1617i | −2.32213 | + | 1.68713i | ||||
\(411\) | −18.8523 | − | 13.6970i | −0.929917 | − | 0.675625i | ||||
\(412\) | −14.5976 | − | 44.9268i | −0.719173 | − | 2.21339i | ||||
\(413\) | 2.06956 | + | 6.36944i | 0.101836 | + | 0.313420i | ||||
\(414\) | −11.5712 | − | 8.40696i | −0.568693 | − | 0.413180i | ||||
\(415\) | 8.75086 | − | 6.35787i | 0.429563 | − | 0.312096i | ||||
\(416\) | −10.8242 | + | 33.3134i | −0.530699 | + | 1.63332i | ||||
\(417\) | 49.7527 | 2.43640 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.4222 | −1.87705 | −0.938524 | − | 0.345215i | \(-0.887806\pi\) | ||||
−0.938524 | + | 0.345215i | \(0.887806\pi\) | |||||||
\(420\) | −8.47393 | + | 26.0801i | −0.413485 | + | 1.27258i | ||||
\(421\) | 17.6500 | − | 12.8235i | 0.860210 | − | 0.624980i | −0.0677317 | − | 0.997704i | \(-0.521576\pi\) |
0.927942 | + | 0.372724i | \(0.121576\pi\) | |||||||
\(422\) | −28.9021 | − | 20.9986i | −1.40693 | − | 1.02220i | ||||
\(423\) | −1.35796 | − | 4.17937i | −0.0660262 | − | 0.203208i | ||||
\(424\) | 11.9667 | + | 36.8296i | 0.581153 | + | 1.78861i | ||||
\(425\) | 17.4568 | + | 12.6831i | 0.846779 | + | 0.615221i | ||||
\(426\) | 18.4591 | − | 13.4113i | 0.894344 | − | 0.649779i | ||||
\(427\) | 1.32963 | − | 4.09218i | 0.0643453 | − | 0.198035i | ||||
\(428\) | −40.9361 | −1.97872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0917 | 0.679561 | ||||||||
\(431\) | 0.963957 | − | 2.96675i | 0.0464322 | − | 0.142903i | −0.925153 | − | 0.379595i | \(-0.876063\pi\) |
0.971585 | + | 0.236692i | \(0.0760632\pi\) | |||||||
\(432\) | −0.393281 | + | 0.285735i | −0.0189217 | + | 0.0137474i | ||||
\(433\) | −23.5806 | − | 17.1323i | −1.13321 | − | 0.823325i | −0.147051 | − | 0.989129i | \(-0.546978\pi\) |
−0.986159 | + | 0.165804i | \(0.946978\pi\) | |||||||
\(434\) | −0.711597 | − | 2.19007i | −0.0341577 | − | 0.105127i | ||||
\(435\) | 12.0517 | + | 37.0912i | 0.577833 | + | 1.77839i | ||||
\(436\) | −21.3760 | − | 15.5306i | −1.02373 | − | 0.743780i | ||||
\(437\) | 6.54630 | − | 4.75617i | 0.313152 | − | 0.227518i | ||||
\(438\) | 8.19324 | − | 25.2162i | 0.391488 | − | 1.20488i | ||||
\(439\) | −27.7250 | −1.32324 | −0.661621 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661621 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.30278 | 0.109656 | ||||||||
\(442\) | −12.6783 | + | 39.0197i | −0.603044 | + | 1.85598i | ||||
\(443\) | −21.7917 | + | 15.8326i | −1.03536 | + | 0.752231i | −0.969374 | − | 0.245590i | \(-0.921018\pi\) |
−0.0659834 | + | 0.997821i | \(0.521018\pi\) | |||||||
\(444\) | −32.0640 | − | 23.2959i | −1.52169 | − | 1.10557i | ||||
\(445\) | −16.4062 | − | 50.4932i | −0.777730 | − | 2.39361i | ||||
\(446\) | −9.89712 | − | 30.4602i | −0.468642 | − | 1.44233i | ||||
\(447\) | 9.14414 | + | 6.64360i | 0.432503 | + | 0.314232i | ||||
\(448\) | 10.3689 | − | 7.53344i | 0.489884 | − | 0.355922i | ||||
\(449\) | 12.4628 | − | 38.3566i | 0.588157 | − | 1.81016i | 0.00195147 | − | 0.999998i | \(-0.499379\pi\) |
0.586205 | − | 0.810162i | \(-0.300621\pi\) | |||||||
\(450\) | −42.4222 | −1.99980 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −35.3305 | −1.66181 | ||||||||
\(453\) | −0.150220 | + | 0.462329i | −0.00705795 | + | 0.0217221i | ||||
\(454\) | −12.1353 | + | 8.81678i | −0.569536 | + | 0.413792i | ||||
\(455\) | 19.2681 | + | 13.9991i | 0.903301 | + | 0.656287i | ||||
\(456\) | 6.40437 | + | 19.7106i | 0.299912 | + | 0.923035i | ||||
\(457\) | −6.52626 | − | 20.0858i | −0.305286 | − | 0.939573i | −0.979570 | − | 0.201101i | \(-0.935548\pi\) |
0.674285 | − | 0.738471i | \(-0.264452\pi\) | |||||||
\(458\) | −4.85410 | − | 3.52671i | −0.226817 | − | 0.164792i | ||||
\(459\) | 3.50347 | − | 2.54542i | 0.163528 | − | 0.118810i | ||||
\(460\) | −9.92545 | + | 30.5474i | −0.462776 | + | 1.42428i | ||||
\(461\) | −8.09167 | −0.376867 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8167 | −1.43217 | −0.716086 | − | 0.698012i | \(-0.754068\pi\) | ||||
−0.716086 | + | 0.698012i | \(0.754068\pi\) | |||||||
\(464\) | −0.439486 | + | 1.35260i | −0.0204026 | + | 0.0627928i | ||||
\(465\) | 6.71709 | − | 4.88025i | 0.311497 | − | 0.226316i | ||||
\(466\) | −33.5337 | − | 24.3637i | −1.55342 | − | 1.12863i | ||||
\(467\) | −4.18460 | − | 12.8789i | −0.193640 | − | 0.595963i | −0.999990 | − | 0.00452363i | \(-0.998560\pi\) |
0.806350 | − | 0.591439i | \(-0.201440\pi\) | |||||||
\(468\) | −15.5247 | − | 47.7800i | −0.717628 | − | 2.20863i | ||||
\(469\) | −6.88787 | − | 5.00433i | −0.318052 | − | 0.231079i | ||||
\(470\) | −12.8184 | + | 9.31311i | −0.591269 | + | 0.429582i | ||||
\(471\) | −5.13140 | + | 15.7928i | −0.236442 | + | 0.727695i | ||||
\(472\) | −20.0917 | −0.924794 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 44.0278 | 2.02226 | ||||||||
\(475\) | 7.41641 | − | 22.8254i | 0.340288 | − | 1.04730i | ||||
\(476\) | 7.20699 | − | 5.23618i | 0.330332 | − | 0.240000i | ||||
\(477\) | 24.0480 | + | 17.4719i | 1.10108 | + | 0.799984i | ||||
\(478\) | 18.7367 | + | 57.6657i | 0.856998 | + | 2.63757i | ||||
\(479\) | 8.84818 | + | 27.2319i | 0.404284 | + | 1.24426i | 0.921492 | + | 0.388397i | \(0.126971\pi\) |
−0.517208 | + | 0.855860i | \(0.673029\pi\) | |||||||
\(480\) | 35.6192 | + | 25.8789i | 1.62579 | + | 1.18120i | ||||
\(481\) | −27.8481 | + | 20.2329i | −1.26977 | + | 0.922539i | ||||
\(482\) | 0.345923 | − | 1.06464i | 0.0157563 | − | 0.0484931i | ||||
\(483\) | 6.21110 | 0.282615 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | −13.9512 | + | 42.9375i | −0.632841 | + | 1.94769i | ||||
\(487\) | 2.27872 | − | 1.65559i | 0.103259 | − | 0.0750218i | −0.534958 | − | 0.844879i | \(-0.679672\pi\) |
0.638216 | + | 0.769857i | \(0.279672\pi\) | |||||||
\(488\) | 10.4431 | + | 7.58732i | 0.472735 | + | 0.343462i | ||||
\(489\) | −2.00432 | − | 6.16867i | −0.0906386 | − | 0.278957i | ||||
\(490\) | −2.56570 | − | 7.89641i | −0.115906 | − | 0.356723i | ||||
\(491\) | −10.2723 | − | 7.46324i | −0.463581 | − | 0.336811i | 0.331353 | − | 0.943507i | \(-0.392495\pi\) |
−0.794934 | + | 0.606695i | \(0.792495\pi\) | |||||||
\(492\) | −43.0711 | + | 31.2930i | −1.94180 | + | 1.41080i | ||||
\(493\) | 3.91508 | − | 12.0494i | 0.176326 | − | 0.542677i | ||||
\(494\) | 45.6333 | 2.05314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.302776 | 0.0135950 | ||||||||
\(497\) | −1.32963 | + | 4.09218i | −0.0596421 | + | 0.183559i | ||||
\(498\) | 12.8701 | − | 9.35068i | 0.576723 | − | 0.419014i | ||||
\(499\) | −2.35289 | − | 1.70947i | −0.105330 | − | 0.0765265i | 0.533874 | − | 0.845564i | \(-0.320736\pi\) |
−0.639203 | + | 0.769038i | \(0.720736\pi\) | |||||||
\(500\) | 11.0396 | + | 33.9765i | 0.493707 | + | 1.51947i | ||||
\(501\) | −3.70820 | − | 11.4127i | −0.165670 | − | 0.509881i | ||||
\(502\) | 8.18679 | + | 5.94805i | 0.365394 | + | 0.265475i | ||||
\(503\) | 4.51253 | − | 3.27855i | 0.201204 | − | 0.146183i | −0.482621 | − | 0.875829i | \(-0.660315\pi\) |
0.683825 | + | 0.729646i | \(0.260315\pi\) | |||||||
\(504\) | −2.13479 | + | 6.57021i | −0.0950911 | + | 0.292660i | ||||
\(505\) | 19.1194 | 0.850803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −70.5416 | −3.13286 | ||||||||
\(508\) | −2.04123 | + | 6.28225i | −0.0905648 | + | 0.278730i | ||||
\(509\) | −18.0433 | + | 13.1092i | −0.799756 | + | 0.581057i | −0.910843 | − | 0.412754i | \(-0.864567\pi\) |
0.111086 | + | 0.993811i | \(0.464567\pi\) | |||||||
\(510\) | 41.7205 | + | 30.3117i | 1.84742 | + | 1.34223i | ||||
\(511\) | 1.54508 | + | 4.75528i | 0.0683505 | + | 0.210361i | ||||
\(512\) | 1.05752 | + | 3.25471i | 0.0467362 | + | 0.143839i | ||||
\(513\) | −3.89675 | − | 2.83116i | −0.172046 | − | 0.124999i | ||||
\(514\) | 12.0835 | − | 8.77921i | 0.532982 | − | 0.387234i | ||||
\(515\) | −15.9358 | + | 49.0454i | −0.702216 | + | 2.16120i | ||||
\(516\) | 12.9083 | 0.568257 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.0000 | 0.527250 | ||||||||
\(519\) | −0.927051 | + | 2.85317i | −0.0406930 | + | 0.125240i | ||||
\(520\) | −57.8042 | + | 41.9972i | −2.53488 | + | 1.84170i | ||||
\(521\) | −6.00469 | − | 4.36266i | −0.263070 | − | 0.191132i | 0.448429 | − | 0.893818i | \(-0.351984\pi\) |
−0.711499 | + | 0.702687i | \(0.751984\pi\) | |||||||
\(522\) | 7.69710 | + | 23.6892i | 0.336893 | + | 1.03685i | ||||
\(523\) | 13.7641 | + | 42.3616i | 0.601863 | + | 1.85234i | 0.517066 | + | 0.855946i | \(0.327024\pi\) |
0.0847974 | + | 0.996398i | \(0.472976\pi\) | |||||||
\(524\) | −16.0320 | − | 11.6479i | −0.700362 | − | 0.508842i | ||||
\(525\) | 14.9039 | − | 10.8283i | 0.650459 | − | 0.472586i | ||||
\(526\) | 14.4019 | − | 44.3245i | 0.627953 | − | 1.93264i | ||||
\(527\) | −2.69722 | −0.117493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7250 | −0.683695 | ||||||||
\(530\) | 33.1189 | − | 101.929i | 1.43859 | − | 4.42753i | ||||
\(531\) | −12.4768 | + | 9.06494i | −0.541448 | + | 0.393385i | ||||
\(532\) | −8.01600 | − | 5.82397i | −0.347538 | − | 0.252501i | ||||
\(533\) | 14.2886 | + | 43.9758i | 0.618908 | + | 1.90480i | ||||
\(534\) | −24.1291 | − | 74.2616i | −1.04417 | − | 3.21361i | ||||
\(535\) | 36.1540 | + | 26.2674i | 1.56307 | + | 1.13564i | ||||
\(536\) | 20.6636 | − | 15.0130i | 0.892532 | − | 0.648463i | ||||
\(537\) | 4.55027 | − | 14.0043i | 0.196359 | − | 0.604330i | ||||
\(538\) | −37.1194 | −1.60033 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.1194 | 0.822769 | ||||||||
\(541\) | 10.0104 | − | 30.8090i | 0.430382 | − | 1.32458i | −0.467363 | − | 0.884065i | \(-0.654796\pi\) |
0.897745 | − | 0.440515i | \(-0.145204\pi\) | |||||||
\(542\) | 53.1209 | − | 38.5946i | 2.28174 | − | 1.65778i | ||||
\(543\) | −46.9679 | − | 34.1242i | −2.01559 | − | 1.46441i | ||||
\(544\) | −4.41980 | − | 13.6027i | −0.189497 | − | 0.583213i | ||||
\(545\) | 8.91341 | + | 27.4327i | 0.381809 | + | 1.17509i | ||||
\(546\) | 28.3381 | + | 20.5888i | 1.21276 | + | 0.881119i | ||||
\(547\) | −24.2188 | + | 17.5960i | −1.03552 | + | 0.752350i | −0.969406 | − | 0.245462i | \(-0.921060\pi\) |
−0.0661149 | + | 0.997812i | \(0.521060\pi\) | |||||||
\(548\) | −10.3280 | + | 31.7864i | −0.441192 | + | 1.35785i | ||||
\(549\) | 9.90833 | 0.422877 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0917 | −0.600325 | ||||||||
\(552\) | −5.75801 | + | 17.7213i | −0.245077 | + | 0.754270i | ||||
\(553\) | −6.71709 | + | 4.88025i | −0.285640 | + | 0.207529i | ||||
\(554\) | −55.7705 | − | 40.5196i | −2.36946 | − | 1.72151i | ||||
\(555\) | 13.3701 | + | 41.1490i | 0.567530 | + | 1.74668i | ||||
\(556\) | −22.0509 | − | 67.8658i | −0.935167 | − | 2.87815i | ||||
\(557\) | 5.85636 | + | 4.25489i | 0.248142 | + | 0.180286i | 0.704903 | − | 0.709304i | \(-0.250991\pi\) |
−0.456761 | + | 0.889589i | \(0.650991\pi\) | |||||||
\(558\) | 4.29004 | − | 3.11689i | 0.181612 | − | 0.131949i | ||||
\(559\) | 3.46442 | − | 10.6624i | 0.146529 | − | 0.450971i | ||||
\(560\) | 1.09167 | 0.0461316 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7250 | 0.621136 | ||||||||
\(563\) | 0.0935628 | − | 0.287957i | 0.00394320 | − | 0.0121359i | −0.949066 | − | 0.315079i | \(-0.897969\pi\) |
0.953009 | + | 0.302943i | \(0.0979691\pi\) | |||||||
\(564\) | −11.7420 | + | 8.53104i | −0.494426 | + | 0.359222i | ||||
\(565\) | 31.2033 | + | 22.6705i | 1.31273 | + | 0.953756i | ||||
\(566\) | 3.12708 | + | 9.62415i | 0.131441 | + | 0.404533i | ||||
\(567\) | −3.27730 | − | 10.0865i | −0.137633 | − | 0.423592i | ||||
\(568\) | −10.4431 | − | 7.58732i | −0.438181 | − | 0.318357i | ||||
\(569\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(570\) | 17.7247 | − | 54.5510i | 0.742405 | − | 2.28489i | ||||
\(571\) | −25.8444 | −1.08155 | −0.540777 | − | 0.841166i | \(-0.681870\pi\) | ||||
−0.540777 | + | 0.841166i | \(0.681870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 61.7527 | 2.57976 | ||||||||
\(574\) | 4.98118 | − | 15.3305i | 0.207910 | − | 0.639882i | ||||
\(575\) | 17.4568 | − | 12.6831i | 0.727999 | − | 0.528922i | ||||
\(576\) | 23.8772 | + | 17.3478i | 0.994885 | + | 0.722826i | ||||
\(577\) | 0.683268 | + | 2.10288i | 0.0284448 | + | 0.0875442i | 0.964271 | − | 0.264917i | \(-0.0853447\pi\) |
−0.935826 | + | 0.352462i | \(0.885345\pi\) | |||||||
\(578\) | 6.92027 | + | 21.2984i | 0.287845 | + | 0.885896i | ||||
\(579\) | 3.94846 | + | 2.86873i | 0.164093 | + | 0.119220i | ||||
\(580\) | 45.2532 | − | 32.8784i | 1.87904 | − | 1.36520i | ||||
\(581\) | −0.927051 | + | 2.85317i | −0.0384606 | + | 0.118369i | ||||
\(582\) | −19.1194 | −0.792526 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.0000 | −0.620704 | ||||||||
\(585\) | −16.9479 | + | 52.1601i | −0.700708 | + | 2.15656i | ||||
\(586\) | −8.97335 | + | 6.51952i | −0.370686 | + | 0.269319i | ||||
\(587\) | 11.0071 | + | 7.99714i | 0.454313 | + | 0.330077i | 0.791296 | − | 0.611433i | \(-0.209407\pi\) |
−0.336984 | + | 0.941511i | \(0.609407\pi\) | |||||||
\(588\) | −2.35024 | − | 7.23331i | −0.0969225 | − | 0.298297i | ||||
\(589\) | 0.927051 | + | 2.85317i | 0.0381985 | + | 0.117563i | ||||
\(590\) | 44.9858 | + | 32.6841i | 1.85204 | + | 1.34558i | ||||
\(591\) | 19.7580 | − | 14.3550i | 0.812735 | − | 0.590486i | ||||
\(592\) | −0.487565 | + | 1.50057i | −0.0200388 | + | 0.0616731i | ||||
\(593\) | −22.6056 | −0.928299 | −0.464149 | − | 0.885757i | \(-0.653640\pi\) | ||||
−0.464149 | + | 0.885757i | \(0.653640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.72498 | −0.398685 | ||||||||
\(596\) | 5.00951 | − | 15.4177i | 0.205197 | − | 0.631533i | ||||
\(597\) | 36.1833 | − | 26.2887i | 1.48088 | − | 1.07592i | ||||
\(598\) | 33.1922 | + | 24.1155i | 1.35733 | + | 0.986157i | ||||
\(599\) | −4.57002 | − | 14.0651i | −0.186726 | − | 0.574683i | 0.813248 | − | 0.581917i | \(-0.197697\pi\) |
−0.999974 | + | 0.00723398i | \(0.997697\pi\) | |||||||
\(600\) | 17.0783 | + | 52.5617i | 0.697220 | + | 2.14582i | ||||
\(601\) | −4.70577 | − | 3.41894i | −0.191952 | − | 0.139462i | 0.487658 | − | 0.873035i | \(-0.337851\pi\) |
−0.679611 | + | 0.733573i | \(0.737851\pi\) | |||||||
\(602\) | −3.16190 | + | 2.29726i | −0.128870 | + | 0.0936292i | ||||
\(603\) | 6.05845 | − | 18.6460i | 0.246719 | − | 0.759323i | ||||
\(604\) | 0.697224 | 0.0283697 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 28.1194 | 1.14227 | ||||||||
\(607\) | 6.34771 | − | 19.5363i | 0.257646 | − | 0.792952i | −0.735651 | − | 0.677361i | \(-0.763124\pi\) |
0.993297 | − | 0.115591i | \(-0.0368763\pi\) | |||||||
\(608\) | −12.8701 | + | 9.35068i | −0.521952 | + | 0.379220i | ||||
\(609\) | −8.75086 | − | 6.35787i | −0.354603 | − | 0.257634i | ||||
\(610\) | −11.0396 | − | 33.9765i | −0.446981 | − | 1.37567i | ||||
\(611\) | 3.89533 | + | 11.9886i | 0.157588 | + | 0.485007i | ||||
\(612\) | 16.5961 | + | 12.0578i | 0.670857 | + | 0.487406i | ||||
\(613\) | −26.7425 | + | 19.4295i | −1.08012 | + | 0.784752i | −0.977704 | − | 0.209990i | \(-0.932657\pi\) |
−0.102415 | + | 0.994742i | \(0.532657\pi\) | |||||||
\(614\) | −11.8362 | + | 36.4281i | −0.477671 | + | 1.47012i | ||||
\(615\) | 58.1194 | 2.34360 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6333 | 0.870924 | 0.435462 | − | 0.900207i | \(-0.356585\pi\) | ||||
0.435462 | + | 0.900207i | \(0.356585\pi\) | |||||||
\(618\) | −23.4372 | + | 72.1323i | −0.942783 | + | 2.90159i | ||||
\(619\) | −32.2123 | + | 23.4036i | −1.29472 | + | 0.940672i | −0.999889 | − | 0.0148766i | \(-0.995264\pi\) |
−0.294834 | + | 0.955548i | \(0.595264\pi\) | |||||||
\(620\) | −9.63404 | − | 6.99954i | −0.386912 | − | 0.281108i | ||||
\(621\) | −1.33821 | − | 4.11858i | −0.0537004 | − | 0.165273i | ||||
\(622\) | −4.55027 | − | 14.0043i | −0.182449 | − | 0.561521i | ||||
\(623\) | 11.9128 | + | 8.65513i | 0.477275 | + | 0.346760i | ||||
\(624\) | −3.72597 | + | 2.70708i | −0.149158 | + | 0.108370i | ||||
\(625\) | −0.309017 | + | 0.951057i | −0.0123607 | + | 0.0380423i | ||||
\(626\) | −35.2389 | −1.40843 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.8167 | 0.950388 | ||||||||
\(629\) | 4.34339 | − | 13.3676i | 0.173182 | − | 0.533001i | ||||
\(630\) | 15.4679 | − | 11.2381i | 0.616258 | − | 0.447737i | ||||
\(631\) | 25.1244 | + | 18.2540i | 1.00019 | + | 0.726679i | 0.962129 | − | 0.272596i | \(-0.0878823\pi\) |
0.0380596 | + | 0.999275i | \(0.487882\pi\) | |||||||
\(632\) | −7.69710 | − | 23.6892i | −0.306174 | − | 0.942307i | ||||
\(633\) | 11.0396 | + | 33.9765i | 0.438786 | + | 1.35044i | ||||
\(634\) | 32.2348 | + | 23.4200i | 1.28021 | + | 0.930125i | ||||
\(635\) | 5.83390 | − | 4.23858i | 0.231511 | − | 0.168203i | ||||
\(636\) | 30.3377 | − | 93.3699i | 1.20297 | − | 3.70236i | ||||
\(637\) | −6.60555 | −0.261721 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.90833 | −0.391967 | ||||||||
\(640\) | 21.0672 | − | 64.8382i | 0.832755 | − | 2.56296i | ||||
\(641\) | 23.3132 | − | 16.9380i | 0.920815 | − | 0.669011i | −0.0229121 | − | 0.999737i | \(-0.507294\pi\) |
0.943727 | + | 0.330727i | \(0.107294\pi\) | |||||||
\(642\) | 53.1726 | + | 38.6322i | 2.09856 | + | 1.52469i | ||||
\(643\) | −0.382828 | − | 1.17822i | −0.0150973 | − | 0.0464647i | 0.943224 | − | 0.332157i | \(-0.107776\pi\) |
−0.958321 | + | 0.285692i | \(0.907776\pi\) | |||||||
\(644\) | −2.75282 | − | 8.47232i | −0.108476 | − | 0.333856i | ||||
\(645\) | −11.4004 | − | 8.28288i | −0.448890 | − | 0.326138i | ||||
\(646\) | −15.0747 | + | 10.9524i | −0.593105 | + | 0.430916i | ||||
\(647\) | 3.27730 | − | 10.0865i | 0.128844 | − | 0.396540i | −0.865738 | − | 0.500497i | \(-0.833150\pi\) |
0.994582 | + | 0.103957i | \(0.0331505\pi\) | |||||||
\(648\) | 31.8167 | 1.24988 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 121.689 | 4.77303 | ||||||||
\(651\) | −0.711597 | + | 2.19007i | −0.0278897 | + | 0.0858356i | ||||
\(652\) | −7.52610 | + | 5.46803i | −0.294745 | + | 0.214145i | ||||
\(653\) | 5.51479 | + | 4.00673i | 0.215810 | + | 0.156795i | 0.690439 | − | 0.723391i | \(-0.257418\pi\) |
−0.474628 | + | 0.880186i | \(0.657418\pi\) | |||||||
\(654\) | 13.1092 | + | 40.3459i | 0.512610 | + | 1.57765i | ||||
\(655\) | 6.68506 | + | 20.5745i | 0.261207 | + | 0.803912i | ||||
\(656\) | 1.71465 | + | 1.24577i | 0.0669460 | + | 0.0486391i | ||||
\(657\) | −9.31492 | + | 6.76769i | −0.363410 | + | 0.264033i | ||||
\(658\) | 1.35796 | − | 4.17937i | 0.0529388 | − | 0.162929i | ||||
\(659\) | −4.63331 | −0.180488 | −0.0902440 | − | 0.995920i | \(-0.528765\pi\) | ||||
−0.0902440 | + | 0.995920i | \(0.528765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.3028 | −0.711895 | −0.355948 | − | 0.934506i | \(-0.615842\pi\) | ||||
−0.355948 | + | 0.934506i | \(0.615842\pi\) | |||||||
\(662\) | −16.9479 | + | 52.1601i | −0.658697 | + | 2.02726i | ||||
\(663\) | 33.1922 | − | 24.1155i | 1.28908 | − | 0.936569i | ||||
\(664\) | −7.28115 | − | 5.29007i | −0.282564 | − | 0.205294i | ||||
\(665\) | 3.34253 | + | 10.2872i | 0.129618 | + | 0.398922i | ||||
\(666\) | 8.53916 | + | 26.2808i | 0.330886 | + | 1.01836i | ||||
\(667\) | −10.2498 | − | 7.44693i | −0.396874 | − | 0.288346i | ||||
\(668\) | −13.9241 | + | 10.1164i | −0.538739 | + | 0.391417i | ||||
\(669\) | −9.89712 | + | 30.4602i | −0.382645 | + | 1.17766i | ||||
\(670\) | −70.6888 | −2.73095 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12.2111 | −0.471054 | ||||||||
\(673\) | 2.60260 | − | 8.00999i | 0.100323 | − | 0.308763i | −0.888281 | − | 0.459300i | \(-0.848100\pi\) |
0.988604 | + | 0.150537i | \(0.0481004\pi\) | |||||||
\(674\) | −21.9625 | + | 15.9567i | −0.845965 | + | 0.614630i | ||||
\(675\) | −10.3913 | − | 7.54975i | −0.399963 | − | 0.290590i | ||||
\(676\) | 31.2648 | + | 96.2231i | 1.20249 | + | 3.70089i | ||||
\(677\) | −3.18373 | − | 9.79852i | −0.122361 | − | 0.376588i | 0.871050 | − | 0.491194i | \(-0.163439\pi\) |
−0.993411 | + | 0.114606i | \(0.963439\pi\) | |||||||
\(678\) | 45.8915 | + | 33.3421i | 1.76245 | + | 1.28050i | ||||
\(679\) | 2.91695 | − | 2.11929i | 0.111942 | − | 0.0813309i | ||||
\(680\) | 9.01555 | − | 27.7470i | 0.345731 | − | 1.06405i | ||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6972 | 0.600638 | 0.300319 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300319 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(684\) | 7.05073 | − | 21.6999i | 0.269592 | − | 0.829717i | ||||
\(685\) | 29.5179 | − | 21.4460i | 1.12782 | − | 0.819410i | ||||
\(686\) | 1.86298 | + | 1.35354i | 0.0711291 | + | 0.0516783i | ||||
\(687\) | 1.85410 | + | 5.70634i | 0.0707384 | + | 0.217710i | ||||
\(688\) | −0.158797 | − | 0.488727i | −0.00605408 | − | 0.0186325i | ||||
\(689\) | −68.9821 | − | 50.1185i | −2.62801 | − | 1.90936i | ||||
\(690\) | 41.7205 | − | 30.3117i | 1.58827 | − | 1.15395i | ||||
\(691\) | −5.26187 | + | 16.1944i | −0.200171 | + | 0.616062i | 0.799706 | + | 0.600391i | \(0.204988\pi\) |
−0.999877 | + | 0.0156711i | \(0.995012\pi\) | |||||||
\(692\) | 4.30278 | 0.163567 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.1194 | 0.839642 | ||||||||
\(695\) | −24.0724 | + | 74.0872i | −0.913118 | + | 2.81029i | ||||
\(696\) | 26.2526 | − | 19.0736i | 0.995101 | − | 0.722983i | ||||
\(697\) | −15.2747 | − | 11.0977i | −0.578571 | − | 0.420356i | ||||
\(698\) | −3.34253 | − | 10.2872i | −0.126517 | − | 0.389378i | ||||
\(699\) | 12.8087 | + | 39.4213i | 0.484471 | + | 1.49105i | ||||
\(700\) | −21.3760 | − | 15.5306i | −0.807937 | − | 0.587001i | ||||
\(701\) | −25.1761 | + | 18.2915i | −0.950890 | + | 0.690862i | −0.951017 | − | 0.309138i | \(-0.899960\pi\) |
0.000127232 | 1.00000i | \(0.499960\pi\) | ||||||||
\(702\) | 7.54688 | − | 23.2269i | 0.284838 | − | 0.876643i | ||||
\(703\) | −15.6333 | −0.589621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.8444 | 0.596735 | ||||||||
\(706\) | −3.62322 | + | 11.1511i | −0.136362 | + | 0.419678i | ||||
\(707\) | −4.29004 | + | 3.11689i | −0.161343 | + | 0.117223i | ||||
\(708\) | 41.2082 | + | 29.9395i | 1.54870 | + | 1.12519i | ||||
\(709\) | 7.82756 | + | 24.0908i | 0.293970 | + | 0.904748i | 0.983565 | + | 0.180553i | \(0.0577886\pi\) |
−0.689595 | + | 0.724195i | \(0.742211\pi\) | |||||||
\(710\) | 11.0396 | + | 33.9765i | 0.414310 | + | 1.27511i | ||||
\(711\) | −15.4679 | − | 11.2381i | −0.580093 | − | 0.421462i | ||||
\(712\) | −35.7383 | + | 25.9654i | −1.33935 | + | 0.973094i | ||||
\(713\) | −0.833488 | + | 2.56521i | −0.0312144 | + | 0.0960680i | ||||
\(714\) | −14.3028 | −0.535268 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.1194 | −0.789270 | ||||||||
\(717\) | 18.7367 | − | 57.6657i | 0.699736 | − | 2.15357i | ||||
\(718\) | 63.2224 | − | 45.9338i | 2.35944 | − | 1.71423i | ||||
\(719\) | −17.1826 | − | 12.4839i | −0.640803 | − | 0.465570i | 0.219323 | − | 0.975652i | \(-0.429615\pi\) |
−0.860126 | + | 0.510082i | \(0.829615\pi\) | |||||||
\(720\) | 0.776831 | + | 2.39084i | 0.0289508 | + | 0.0891014i | ||||
\(721\) | −4.41980 | − | 13.6027i | −0.164602 | − | 0.506593i | ||||
\(722\) | −18.6298 | − | 13.5354i | −0.693331 | − | 0.503735i | ||||
\(723\) | −0.905637 | + | 0.657984i | −0.0336810 | + | 0.0244707i | ||||
\(724\) | −25.7308 | + | 79.1913i | −0.956278 | + | 2.94312i | ||||
\(725\) | −37.5778 | −1.39560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1194 | 0.894540 | 0.447270 | − | 0.894399i | \(-0.352396\pi\) | ||||
0.447270 | + | 0.894399i | \(0.352396\pi\) | |||||||
\(728\) | 6.12368 | − | 18.8468i | 0.226959 | − | 0.698507i | ||||
\(729\) | 10.7846 | − | 7.83549i | 0.399431 | − | 0.290203i | ||||
\(730\) | 33.5854 | + | 24.4012i | 1.24305 | + | 0.903131i | ||||
\(731\) | 1.41462 | + | 4.35374i | 0.0523215 | + | 0.161029i | ||||
\(732\) | −10.1126 | − | 31.1233i | −0.373772 | − | 1.15035i | ||||
\(733\) | −5.49233 | − | 3.99041i | −0.202864 | − | 0.147389i | 0.481715 | − | 0.876328i | \(-0.340014\pi\) |
−0.684579 | + | 0.728939i | \(0.740014\pi\) | |||||||
\(734\) | −32.8506 | + | 23.8673i | −1.21254 | + | 0.880960i | ||||
\(735\) | −2.56570 | + | 7.89641i | −0.0946372 | + | 0.291263i | ||||
\(736\) | −14.3028 | −0.527207 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 37.1194 | 1.36639 | ||||||||
\(739\) | 13.3246 | − | 41.0090i | 0.490155 | − | 1.50854i | −0.334219 | − | 0.942495i | \(-0.608473\pi\) |
0.824374 | − | 0.566046i | \(-0.191527\pi\) | |||||||
\(740\) | 50.2040 | − | 36.4753i | 1.84553 | − | 1.34086i | ||||
\(741\) | −36.9181 | − | 26.8226i | −1.35622 | − | 0.985352i | ||||
\(742\) | 9.18552 | + | 28.2701i | 0.337211 | + | 1.03783i | ||||
\(743\) | −13.8860 | − | 42.7368i | −0.509428 | − | 1.56786i | −0.793196 | − | 0.608966i | \(-0.791584\pi\) |
0.283768 | − | 0.958893i | \(-0.408416\pi\) | |||||||
\(744\) | −5.58895 | − | 4.06061i | −0.204901 | − | 0.148869i | ||||
\(745\) | −14.3174 | + | 10.4022i | −0.524547 | + | 0.381106i | ||||
\(746\) | −14.3169 | + | 44.0630i | −0.524180 | + | 1.61326i | ||||
\(747\) | −6.90833 | −0.252762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3944 | −0.452883 | ||||||||
\(750\) | 17.7247 | − | 54.5510i | 0.647214 | − | 1.99192i | ||||
\(751\) | −6.17548 | + | 4.48675i | −0.225346 | + | 0.163724i | −0.694730 | − | 0.719271i | \(-0.744476\pi\) |
0.469384 | + | 0.882994i | \(0.344476\pi\) | |||||||
\(752\) | 0.467446 | + | 0.339619i | 0.0170460 | + | 0.0123846i | ||||
\(753\) | −3.12708 | − | 9.62415i | −0.113957 | − | 0.350723i | ||||
\(754\) | −22.0793 | − | 67.9530i | −0.804079 | − | 2.47470i | ||||
\(755\) | −0.615776 | − | 0.447387i | −0.0224104 | − | 0.0162821i | ||||
\(756\) | −4.29004 | + | 3.11689i | −0.156027 | + | 0.113360i | ||||
\(757\) | −7.35975 | + | 22.6510i | −0.267495 | + | 0.823264i | 0.723613 | + | 0.690205i | \(0.242480\pi\) |
−0.991108 | + | 0.133059i | \(0.957520\pi\) | |||||||
\(758\) | 36.4222 | 1.32291 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.4500 | −1.17708 | ||||||||
\(761\) | −12.9787 | + | 39.9444i | −0.470478 | + | 1.44798i | 0.381482 | + | 0.924376i | \(0.375414\pi\) |
−0.851960 | + | 0.523606i | \(0.824586\pi\) | |||||||
\(762\) | 8.58007 | − | 6.23379i | 0.310823 | − | 0.225826i | ||||
\(763\) | −6.47214 | − | 4.70228i | −0.234307 | − | 0.170234i | ||||
\(764\) | −27.3694 | − | 84.2345i | −0.990192 | − | 3.04750i | ||||
\(765\) | −6.92027 | − | 21.2984i | −0.250203 | − | 0.770045i | ||||
\(766\) | 71.9733 | + | 52.2916i | 2.60050 | + | 1.88937i | ||||
\(767\) | 35.7900 | − | 26.0029i | 1.29230 | − | 0.938912i | ||||
\(768\) | 12.7435 | − | 39.2205i | 0.459842 | − | 1.41525i | ||||
\(769\) | 39.3305 | 1.41830 | 0.709148 | − | 0.705060i | \(-0.249080\pi\) | ||||
0.709148 | + | 0.705060i | \(0.249080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9361 | −0.537910 | ||||||||
\(772\) | 2.16312 | − | 6.65740i | 0.0778524 | − | 0.239605i | ||||
\(773\) | −24.7829 | + | 18.0058i | −0.891378 | + | 0.647624i | −0.936237 | − | 0.351369i | \(-0.885716\pi\) |
0.0448591 | + | 0.998993i | \(0.485716\pi\) | |||||||
\(774\) | −7.28115 | − | 5.29007i | −0.261716 | − | 0.190148i | ||||
\(775\) | 2.47214 | + | 7.60845i | 0.0888017 | + | 0.273304i | ||||
\(776\) | 3.34253 | + | 10.2872i | 0.119990 | + | 0.369291i | ||||
\(777\) | −9.70820 | − | 7.05342i | −0.348280 | − | 0.253040i | ||||
\(778\) | −14.5623 | + | 10.5801i | −0.522084 | + | 0.379316i | ||||
\(779\) | −6.48936 | + | 19.9722i | −0.232505 | + | 0.715578i | ||||
\(780\) | 181.139 | 6.48581 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16.7527 | −0.599077 | ||||||||
\(783\) | −2.33049 | + | 7.17252i | −0.0832850 | + | 0.256325i | ||||
\(784\) | −0.244951 | + | 0.177967i | −0.00874824 | + | 0.00635597i | ||||
\(785\) | −21.0344 | − | 15.2824i | −0.750751 | − | 0.545453i | ||||
\(786\) | 9.83189 | + | 30.2594i | 0.350692 | + | 1.07932i | ||||
\(787\) | 6.94859 | + | 21.3856i | 0.247691 | + | 0.762313i | 0.995182 | + | 0.0980421i | \(0.0312580\pi\) |
−0.747492 | + | 0.664271i | \(0.768742\pi\) | |||||||
\(788\) | −28.3381 | − | 20.5888i | −1.00950 | − | 0.733446i | ||||
\(789\) | −37.7047 | + | 27.3941i | −1.34232 | + | 0.975254i | ||||
\(790\) | −21.3024 | + | 65.5621i | −0.757906 | + | 2.33260i | ||||
\(791\) | −10.6972 | −0.380350 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.4222 | −1.00930 | ||||||||
\(794\) | −21.4981 | + | 66.1644i | −0.762940 | + | 2.34809i | ||||
\(795\) | −86.7063 | + | 62.9959i | −3.07516 | + | 2.23423i | ||||
\(796\) | −51.8962 | − | 37.7048i | −1.83941 | − | 1.33641i | ||||
\(797\) | −8.84818 | − | 27.2319i | −0.313419 | − | 0.964603i | −0.976400 | − | 0.215968i | \(-0.930709\pi\) |
0.662982 | − | 0.748635i | \(-0.269291\pi\) | |||||||
\(798\) | 4.91594 | + | 15.1297i | 0.174023 | + | 0.535586i | ||||
\(799\) | −4.16416 | − | 3.02544i | −0.147317 | − | 0.107032i | ||||
\(800\) | −34.3203 | + | 24.9351i | −1.21341 | + | 0.881591i | ||||
\(801\) | −10.4782 | + | 32.2487i | −0.370231 | + | 1.13945i | ||||
\(802\) | 48.8444 | 1.72476 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −64.7527 | −2.28365 | ||||||||
\(805\) | −3.00518 | + | 9.24901i | −0.105919 | + | 0.325985i | ||||
\(806\) | −12.3060 | + | 8.94086i | −0.433462 | + | 0.314928i | ||||
\(807\) | 30.0302 | + | 21.8183i | 1.05711 | + | 0.768039i | ||||
\(808\) | −4.91594 | − | 15.1297i | −0.172942 | − | 0.532262i | ||||
\(809\) | −2.50046 | − | 7.69564i | −0.0879117 | − | 0.270564i | 0.897430 | − | 0.441157i | \(-0.145432\pi\) |
−0.985342 | + | 0.170593i | \(0.945432\pi\) | |||||||
\(810\) | −71.2384 | − | 51.7577i | −2.50306 | − | 1.81858i | ||||
\(811\) | −33.0438 | + | 24.0077i | −1.16033 | + | 0.843026i | −0.989819 | − | 0.142331i | \(-0.954540\pi\) |
−0.170506 | + | 0.985357i | \(0.554540\pi\) | |||||||
\(812\) | −4.79405 | + | 14.7546i | −0.168238 | + | 0.517784i | ||||
\(813\) | −65.6611 | −2.30283 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1556 | 0.355735 | ||||||||
\(816\) | 0.581128 | − | 1.78853i | 0.0203436 | − | 0.0626110i | ||||
\(817\) | 4.11925 | − | 2.99281i | 0.144114 | − | 0.104705i | ||||
\(818\) | −38.3878 | − | 27.8904i | −1.34220 | − | 0.975165i | ||||
\(819\) | −4.70049 | − | 14.4666i | −0.164248 | − | 0.505505i | ||||
\(820\) | −25.7591 | − | 79.2784i | −0.899548 | − | 2.76852i | ||||
\(821\) | −22.1850 | − | 16.1184i | −0.774263 | − | 0.562535i | 0.128989 | − | 0.991646i | \(-0.458827\pi\) |
−0.903252 | + | 0.429111i | \(0.858827\pi\) | |||||||
\(822\) | 43.4127 | − | 31.5412i | 1.51419 | − | 1.10013i | ||||
\(823\) | 10.8808 | − | 33.4877i | 0.379282 | − | 1.16731i | −0.561262 | − | 0.827638i | \(-0.689684\pi\) |
0.940544 | − | 0.339672i | \(-0.110316\pi\) | |||||||
\(824\) | 42.9083 | 1.49478 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.4222 | −0.536607 | ||||||||
\(827\) | 4.38290 | − | 13.4892i | 0.152408 | − | 0.469064i | −0.845481 | − | 0.534006i | \(-0.820686\pi\) |
0.997889 | + | 0.0649415i | \(0.0206861\pi\) | |||||||
\(828\) | 16.5961 | − | 12.0578i | 0.576754 | − | 0.419036i | ||||
\(829\) | −10.7397 | − | 7.80286i | −0.373006 | − | 0.271005i | 0.385450 | − | 0.922729i | \(-0.374046\pi\) |
−0.758456 | + | 0.651724i | \(0.774046\pi\) | |||||||
\(830\) | 7.69710 | + | 23.6892i | 0.267170 | + | 0.822265i | ||||
\(831\) | 21.3024 | + | 65.5621i | 0.738973 | + | 2.27432i | ||||
\(832\) | −68.4922 | − | 49.7625i | −2.37454 | − | 1.72521i | ||||
\(833\) | 2.18210 | − | 1.58539i | 0.0756053 | − | 0.0549305i | ||||
\(834\) | −35.4039 | + | 108.962i | −1.22594 | + | 3.77304i | ||||
\(835\) | 18.7889 | 0.650217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.60555 | 0.0554960 | ||||||||
\(838\) | 27.3411 | − | 84.1473i | 0.944483 | − | 2.90682i | ||||
\(839\) | −34.1495 | + | 24.8111i | −1.17897 | + | 0.856573i | −0.992055 | − | 0.125803i | \(-0.959849\pi\) |
−0.186916 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(840\) | −20.1513 | − | 14.6407i | −0.695285 | − | 0.505154i | ||||
\(841\) | −2.14337 | − | 6.59661i | −0.0739092 | − | 0.227469i | ||||
\(842\) | 15.5247 | + | 47.7800i | 0.535015 | + | 1.64661i | ||||
\(843\) | −11.9128 | − | 8.65513i | −0.410297 | − | 0.298098i | ||||
\(844\) | 41.4531 | − | 30.1174i | 1.42687 | − | 1.03669i | ||||
\(845\) | 34.1309 | − | 105.044i | 1.17414 | − | 3.61363i | ||||
\(846\) | 10.1194 | 0.347913 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.90833 | −0.134212 | ||||||||
\(849\) | 3.12708 | − | 9.62415i | 0.107321 | − | 0.330300i | ||||
\(850\) | −40.1991 | + | 29.2064i | −1.37882 | + | 1.00177i | ||||
\(851\) | −11.3711 | − | 8.26162i | −0.389798 | − | 0.283205i | ||||
\(852\) | 10.1126 | + | 31.1233i | 0.346451 | + | 1.06627i | ||||
\(853\) | 14.1298 | + | 43.4870i | 0.483795 | + | 1.48897i | 0.833719 | + | 0.552190i | \(0.186208\pi\) |
−0.349924 | + | 0.936778i | \(0.613792\pi\) | |||||||
\(854\) | 8.01600 | + | 5.82397i | 0.274302 | + | 0.199292i | ||||
\(855\) | −20.1513 | + | 14.6407i | −0.689159 | + | 0.500703i | ||||
\(856\) | 11.4903 | − | 35.3635i | 0.392730 | − | 1.20870i | ||||
\(857\) | −35.3583 | −1.20782 | −0.603908 | − | 0.797054i | \(-0.706391\pi\) | ||||
−0.603908 | + | 0.797054i | \(0.706391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.3028 | −0.863320 | −0.431660 | − | 0.902036i | \(-0.642072\pi\) | ||||
−0.431660 | + | 0.902036i | \(0.642072\pi\) | |||||||
\(860\) | −6.24557 | + | 19.2219i | −0.212972 | + | 0.655461i | ||||
\(861\) | −13.0409 | + | 9.47476i | −0.444432 | + | 0.322899i | ||||
\(862\) | 5.81145 | + | 4.22226i | 0.197939 | + | 0.143811i | ||||
\(863\) | 9.71000 | + | 29.8843i | 0.330532 | + | 1.01727i | 0.968881 | + | 0.247526i | \(0.0796176\pi\) |
−0.638349 | + | 0.769747i | \(0.720382\pi\) | |||||||
\(864\) | 2.63093 | + | 8.09718i | 0.0895062 | + | 0.275472i | ||||
\(865\) | −3.80013 | − | 2.76096i | −0.129208 | − | 0.0938754i | ||||
\(866\) | 54.3008 | − | 39.4518i | 1.84521 | − | 1.34063i | ||||
\(867\) | 6.92027 | − | 21.2984i | 0.235025 | − | 0.723331i | ||||
\(868\) | 3.30278 | 0.112104 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −89.8082 | −3.04478 | ||||||||
\(871\) | −17.3788 | + | 53.4863i | −0.588857 | + | 1.81232i | ||||
\(872\) | 19.4164 | − | 14.1068i | 0.657523 | − | 0.477718i | ||||
\(873\) | 6.71709 | + | 4.88025i | 0.227339 | + | 0.165171i | ||||
\(874\) | 5.75801 | + | 17.7213i | 0.194768 | + | 0.599433i | ||||
\(875\) | 3.34253 | + | 10.2872i | 0.112998 | + | 0.347772i | ||||
\(876\) | 30.7651 | + | 22.3522i | 1.03946 | + | 0.755209i | ||||
\(877\) | 38.0687 | − | 27.6585i | 1.28549 | − | 0.933962i | 0.285785 | − | 0.958294i | \(-0.407746\pi\) |
0.999704 | + | 0.0243313i | \(0.00774567\pi\) | |||||||
\(878\) | 19.7290 | − | 60.7196i | 0.665822 | − | 2.04919i | ||||
\(879\) | 11.0917 | 0.374113 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3305 | 1.15663 | 0.578313 | − | 0.815815i | \(-0.303711\pi\) | ||||
0.578313 | + | 0.815815i | \(0.303711\pi\) | |||||||
\(882\) | −1.63865 | + | 5.04324i | −0.0551761 | + | 0.169815i | ||||
\(883\) | 6.24964 | − | 4.54063i | 0.210317 | − | 0.152804i | −0.477640 | − | 0.878556i | \(-0.658508\pi\) |
0.687957 | + | 0.725751i | \(0.258508\pi\) | |||||||
\(884\) | −47.6061 | − | 34.5879i | −1.60117 | − | 1.16332i | ||||
\(885\) | −17.1831 | − | 52.8840i | −0.577602 | − | 1.77768i | ||||
\(886\) | −19.1676 | − | 58.9919i | −0.643949 | − | 1.98187i | ||||
\(887\) | 35.6934 | + | 25.9327i | 1.19847 | + | 0.870737i | 0.994133 | − | 0.108165i | \(-0.0344974\pi\) |
0.204333 | + | 0.978901i | \(0.434497\pi\) | |||||||
\(888\) | 29.1246 | − | 21.1603i | 0.977358 | − | 0.710092i | ||||
\(889\) | −0.618034 | + | 1.90211i | −0.0207282 | + | 0.0637948i | ||||
\(890\) | 122.258 | 4.09810 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.9361 | 1.53805 | ||||||||
\(893\) | −1.76912 | + | 5.44478i | −0.0592012 | + | 0.182203i | ||||
\(894\) | −21.0569 | + | 15.2987i | −0.704248 | + | 0.511666i | ||||
\(895\) | 18.6523 | + | 13.5517i | 0.623478 | + | 0.452983i | ||||
\(896\) | 5.84299 | + | 17.9829i | 0.195201 | + | 0.600766i | ||||
\(897\) | −12.6783 | − | 39.0197i | −0.423315 | − | 1.30283i | ||||
\(898\) | 75.1352 | + | 54.5889i | 2.50729 | + | 1.82165i | ||||
\(899\) | 3.80013 | − | 2.76096i | 0.126742 | − | 0.0920831i | ||||
\(900\) | 18.8020 | − | 57.8665i | 0.626732 | − | 1.92888i | ||||
\(901\) | 34.8167 | 1.15991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.90833 | 0.130061 | ||||||||
\(904\) | 9.91687 | − | 30.5210i | 0.329830 | − | 1.01511i | ||||
\(905\) | 73.5396 | − | 53.4296i | 2.44454 | − | 1.77606i | ||||
\(906\) | −0.905637 | − | 0.657984i | −0.0300878 | − | 0.0218601i | ||||
\(907\) | 0.121891 | + | 0.375143i | 0.00404734 | + | 0.0124564i | 0.953060 | − | 0.302782i | \(-0.0979155\pi\) |
−0.949012 | + | 0.315239i | \(0.897915\pi\) | |||||||
\(908\) | −6.64815 | − | 20.4609i | −0.220627 | − | 0.679019i | ||||
\(909\) | −9.87899 | − | 7.17751i | −0.327665 | − | 0.238063i | ||||
\(910\) | −44.3701 | + | 32.2367i | −1.47085 | + | 1.06864i | ||||
\(911\) | −15.5899 | + | 47.9808i | −0.516516 | + | 1.58967i | 0.263990 | + | 0.964525i | \(0.414961\pi\) |
−0.780506 | + | 0.625148i | \(0.785039\pi\) | |||||||
\(912\) | −2.09167 | −0.0692622 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 48.6333 | 1.60865 | ||||||||
\(915\) | −11.0396 | + | 33.9765i | −0.364959 | + | 1.12323i | ||||
\(916\) | 6.96204 | − | 5.05822i | 0.230032 | − | 0.167128i | ||||
\(917\) | −4.85410 | − | 3.52671i | −0.160297 | − | 0.116462i | ||||
\(918\) | 3.08159 | + | 9.48417i | 0.101708 | + | 0.313024i | ||||
\(919\) | −17.1436 | − | 52.7624i | −0.565514 | − | 1.74047i | −0.666420 | − | 0.745577i | \(-0.732174\pi\) |
0.100906 | − | 0.994896i | \(-0.467826\pi\) | |||||||
\(920\) | −23.6030 | − | 17.1486i | −0.778169 | − | 0.565373i | ||||
\(921\) | 30.9876 | − | 22.5138i | 1.02108 | − | 0.741855i | ||||
\(922\) | 5.75801 | − | 17.7213i | 0.189630 | − | 0.583621i | ||||
\(923\) | 28.4222 | 0.935528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.6888 | −1.37072 | ||||||||
\(926\) | 21.9290 | − | 67.4906i | 0.720633 | − | 2.21788i | ||||
\(927\) | 26.6459 | − | 19.3593i | 0.875165 | − | 0.635844i | ||||
\(928\) | 20.1513 | + | 14.6407i | 0.661498 | + | 0.480606i | ||||
\(929\) | −8.53916 | − | 26.2808i | −0.280161 | − | 0.862246i | −0.987808 | − | 0.155680i | \(-0.950243\pi\) |
0.707647 | − | 0.706566i | \(-0.249757\pi\) | |||||||
\(930\) | 5.90823 | + | 18.1837i | 0.193738 | + | 0.596266i | ||||
\(931\) | −2.42705 | − | 1.76336i | −0.0795434 | − | 0.0577917i | ||||
\(932\) | 48.0960 | − | 34.9438i | 1.57544 | − | 1.14462i | ||||
\(933\) | −4.55027 | + | 14.0043i | −0.148969 | + | 0.458480i | ||||
\(934\) | 31.1833 | 1.02035 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 45.6333 | 1.49157 | ||||||||
\(937\) | −9.76665 | + | 30.0587i | −0.319063 | + | 0.981974i | 0.654987 | + | 0.755640i | \(0.272674\pi\) |
−0.974050 | + | 0.226334i | \(0.927326\pi\) | |||||||
\(938\) | 15.8612 | − | 11.5239i | 0.517887 | − | 0.376267i | ||||
\(939\) | 28.5088 | + | 20.7129i | 0.930351 | + | 0.675939i | ||||
\(940\) | −7.02241 | − | 21.6127i | −0.229046 | − | 0.704930i | ||||
\(941\) | −11.5641 | − | 35.5906i | −0.376979 | − | 1.16022i | −0.942134 | − | 0.335237i | \(-0.891184\pi\) |
0.565155 | − | 0.824985i | \(-0.308816\pi\) | |||||||
\(942\) | −30.9359 | − | 22.4762i | −1.00795 | − | 0.732315i | ||||
\(943\) | −15.2747 | + | 11.0977i | −0.497413 | + | 0.361392i | ||||
\(944\) | 0.626611 | − | 1.92851i | 0.0203945 | − | 0.0627677i | ||||
\(945\) | 5.78890 | 0.188313 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6611 | 1.51628 | 0.758140 | − | 0.652091i | \(-0.226108\pi\) | ||||
0.758140 | + | 0.652091i | \(0.226108\pi\) | |||||||
\(948\) | −19.5136 | + | 60.0565i | −0.633771 | + | 1.95055i | ||||
\(949\) | 26.7200 | − | 19.4132i | 0.867368 | − | 0.630180i | ||||
\(950\) | 44.7116 | + | 32.4849i | 1.45064 | + | 1.05395i | ||||
\(951\) | −12.3126 | − | 37.8943i | −0.399263 | − | 1.22881i | ||||
\(952\) | 2.50046 | + | 7.69564i | 0.0810405 | + | 0.249417i | ||||
\(953\) | −4.87656 | − | 3.54303i | −0.157967 | − | 0.114770i | 0.505994 | − | 0.862537i | \(-0.331126\pi\) |
−0.663961 | + | 0.747767i | \(0.731126\pi\) | |||||||
\(954\) | −55.3772 | + | 40.2339i | −1.79290 | + | 1.30262i | ||||
\(955\) | −29.8785 | + | 91.9565i | −0.966845 | + | 2.97564i | ||||
\(956\) | −86.9638 | −2.81261 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −65.9361 | −2.13030 | ||||||||
\(959\) | −3.12708 | + | 9.62415i | −0.100979 | + | 0.310780i | ||||
\(960\) | −86.0906 | + | 62.5485i | −2.77856 | + | 2.01874i | ||||
\(961\) | 24.2705 | + | 17.6336i | 0.782920 | + | 0.568824i | ||||
\(962\) | −24.4947 | − | 75.3870i | −0.789742 | − | 2.43058i | ||||
\(963\) | −8.81985 | − | 27.1447i | −0.284216 | − | 0.874726i | ||||
\(964\) | 1.29892 | + | 0.943719i | 0.0418353 | + | 0.0303952i | ||||
\(965\) | −6.18227 | + | 4.49169i | −0.199014 | + | 0.144592i | ||||
\(966\) | −4.41980 | + | 13.6027i | −0.142205 | + | 0.437661i | ||||
\(967\) | −40.5139 | −1.30284 | −0.651419 | − | 0.758718i | \(-0.725826\pi\) | ||||
−0.651419 | + | 0.758718i | \(0.725826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.6333 | 0.598588 | ||||||||
\(970\) | 9.25076 | − | 28.4709i | 0.297024 | − | 0.914146i | ||||
\(971\) | 5.15076 | − | 3.74225i | 0.165296 | − | 0.120094i | −0.502062 | − | 0.864832i | \(-0.667425\pi\) |
0.667358 | + | 0.744737i | \(0.267425\pi\) | |||||||
\(972\) | −52.3861 | − | 38.0607i | −1.68028 | − | 1.22080i | ||||
\(973\) | −6.67648 | − | 20.5481i | −0.214038 | − | 0.658742i | ||||
\(974\) | 2.00432 | + | 6.16867i | 0.0642226 | + | 0.197657i | ||||
\(975\) | −98.4483 | − | 71.5269i | −3.15287 | − | 2.29069i | ||||
\(976\) | −1.05397 | + | 0.765752i | −0.0337367 | + | 0.0245111i | ||||
\(977\) | 12.3693 | − | 38.0687i | 0.395728 | − | 1.21792i | −0.532666 | − | 0.846326i | \(-0.678810\pi\) |
0.928393 | − | 0.371599i | \(-0.121190\pi\) | |||||||
\(978\) | 14.9361 | 0.477603 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.9083 | 0.380398 | ||||||||
\(981\) | 5.69277 | − | 17.5206i | 0.181756 | − | 0.559388i | ||||
\(982\) | 23.6547 | − | 17.1862i | 0.754853 | − | 0.548433i | ||||
\(983\) | 7.50365 | + | 5.45172i | 0.239329 | + | 0.173883i | 0.700984 | − | 0.713177i | \(-0.252744\pi\) |
−0.461655 | + | 0.887059i | \(0.652744\pi\) | |||||||
\(984\) | −14.9435 | − | 45.9915i | −0.476382 | − | 1.46615i | ||||
\(985\) | 11.8165 | + | 36.3673i | 0.376504 | + | 1.15876i | ||||
\(986\) | 23.6030 | + | 17.1486i | 0.751673 | + | 0.546123i | ||||
\(987\) | −3.55518 | + | 2.58299i | −0.113163 | + | 0.0822175i | ||||
\(988\) | −20.2252 | + | 62.2466i | −0.643448 | + | 1.98033i | ||||
\(989\) | 4.57779 | 0.145565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7250 | −1.38897 | −0.694485 | − | 0.719507i | \(-0.744368\pi\) | ||||
−0.694485 | + | 0.719507i | \(0.744368\pi\) | |||||||
\(992\) | 1.63865 | − | 5.04324i | 0.0520271 | − | 0.160123i | ||||
\(993\) | 44.3701 | − | 32.2367i | 1.40804 | − | 1.02300i | ||||
\(994\) | −8.01600 | − | 5.82397i | −0.254252 | − | 0.184725i | ||||
\(995\) | 21.6398 | + | 66.6004i | 0.686027 | + | 2.11137i | ||||
\(996\) | 7.05073 | + | 21.6999i | 0.223411 | + | 0.687589i | ||||
\(997\) | 36.9698 | + | 26.8602i | 1.17085 | + | 0.850670i | 0.991110 | − | 0.133045i | \(-0.0424755\pi\) |
0.179736 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(998\) | 5.41817 | − | 3.93653i | 0.171509 | − | 0.124609i | ||||
\(999\) | −2.58545 | + | 7.95720i | −0.0818000 | + | 0.251755i |
(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 | 847.2.f.r.372.1 | 8 | ||
11.2 | odd | 10 | 847.2.f.o.729.1 | 8 | |||
11.3 | even | 5 | inner | 847.2.f.r.323.2 | 8 | ||
11.4 | even | 5 | 847.2.a.e.1.1 | ✓ | 2 | ||
11.5 | even | 5 | inner | 847.2.f.r.148.1 | 8 | ||
11.6 | odd | 10 | 847.2.f.o.148.2 | 8 | |||
11.7 | odd | 10 | 847.2.a.g.1.2 | yes | 2 | ||
11.8 | odd | 10 | 847.2.f.o.323.1 | 8 | |||
11.9 | even | 5 | inner | 847.2.f.r.729.2 | 8 | ||
11.10 | odd | 2 | 847.2.f.o.372.2 | 8 | |||
33.26 | odd | 10 | 7623.2.a.bs.1.2 | 2 | |||
33.29 | even | 10 | 7623.2.a.bc.1.1 | 2 | |||
77.48 | odd | 10 | 5929.2.a.k.1.1 | 2 | |||
77.62 | even | 10 | 5929.2.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.e.1.1 | ✓ | 2 | 11.4 | even | 5 | ||
847.2.a.g.1.2 | yes | 2 | 11.7 | odd | 10 | ||
847.2.f.o.148.2 | 8 | 11.6 | odd | 10 | |||
847.2.f.o.323.1 | 8 | 11.8 | odd | 10 | |||
847.2.f.o.372.2 | 8 | 11.10 | odd | 2 | |||
847.2.f.o.729.1 | 8 | 11.2 | odd | 10 | |||
847.2.f.r.148.1 | 8 | 11.5 | even | 5 | inner | ||
847.2.f.r.323.2 | 8 | 11.3 | even | 5 | inner | ||
847.2.f.r.372.1 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.r.729.2 | 8 | 11.9 | even | 5 | inner | ||
5929.2.a.k.1.1 | 2 | 77.48 | odd | 10 | |||
5929.2.a.p.1.2 | 2 | 77.62 | even | 10 | |||
7623.2.a.bc.1.1 | 2 | 33.29 | even | 10 | |||
7623.2.a.bs.1.2 | 2 | 33.26 | odd | 10 |