Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(88,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.88");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bl (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 88.6 | ||
Root | \(0.874681 - 1.11128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.88 |
Dual form | 273.2.bl.c.121.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92478 | + | 1.11128i | 1.36103 | + | 0.785790i | 0.989761 | − | 0.142736i | \(-0.0455899\pi\) |
0.371268 | + | 0.928526i | \(0.378923\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.46986 | + | 2.54588i | 0.734932 | + | 1.27294i | ||||
\(5\) | 0.701414 | − | 0.404962i | 0.313682 | − | 0.181104i | −0.334891 | − | 0.942257i | \(-0.608699\pi\) |
0.648573 | + | 0.761153i | \(0.275366\pi\) | |||||||
\(6\) | 1.92478 | + | 1.11128i | 0.785790 | + | 0.453676i | ||||
\(7\) | −2.09638 | − | 1.61406i | −0.792357 | − | 0.610058i | ||||
\(8\) | 2.08860i | 0.738430i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.80010 | 0.569240 | ||||||||
\(11\) | 3.07728i | 0.927834i | 0.885879 | + | 0.463917i | \(0.153556\pi\) | ||||
−0.885879 | + | 0.463917i | \(0.846444\pi\) | |||||||
\(12\) | 1.46986 | + | 2.54588i | 0.424313 | + | 0.734932i | ||||
\(13\) | −3.01583 | + | 1.97606i | −0.836439 | + | 0.548059i | ||||
\(14\) | −2.24141 | − | 5.43638i | −0.599042 | − | 1.45293i | ||||
\(15\) | 0.701414 | − | 0.404962i | 0.181104 | − | 0.104561i | ||||
\(16\) | 0.618725 | − | 1.07166i | 0.154681 | − | 0.267916i | ||||
\(17\) | −1.39973 | − | 2.42441i | −0.339485 | − | 0.588006i | 0.644851 | − | 0.764308i | \(-0.276920\pi\) |
−0.984336 | + | 0.176303i | \(0.943586\pi\) | |||||||
\(18\) | 1.92478 | + | 1.11128i | 0.453676 | + | 0.261930i | ||||
\(19\) | − | 4.31115i | − | 0.989045i | −0.869165 | − | 0.494522i | \(-0.835343\pi\) | ||
0.869165 | − | 0.494522i | \(-0.164657\pi\) | |||||||
\(20\) | 2.06197 | + | 1.19048i | 0.461070 | + | 0.266199i | ||||
\(21\) | −2.09638 | − | 1.61406i | −0.457467 | − | 0.352217i | ||||
\(22\) | −3.41970 | + | 5.92310i | −0.729083 | + | 1.26281i | ||||
\(23\) | −2.47614 | + | 4.28881i | −0.516312 | + | 0.894278i | 0.483509 | + | 0.875339i | \(0.339362\pi\) |
−0.999821 | + | 0.0189386i | \(0.993971\pi\) | |||||||
\(24\) | 2.08860i | 0.426333i | ||||||||
\(25\) | −2.17201 | + | 3.76204i | −0.434402 | + | 0.752407i | ||||
\(26\) | −8.00076 | + | 0.452072i | −1.56908 | + | 0.0886587i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.02782 | − | 7.70958i | 0.194239 | − | 1.45697i | ||||
\(29\) | −2.84837 | − | 4.93353i | −0.528930 | − | 0.916133i | −0.999431 | − | 0.0337339i | \(-0.989260\pi\) |
0.470501 | − | 0.882399i | \(-0.344073\pi\) | |||||||
\(30\) | 1.80010 | 0.328651 | ||||||||
\(31\) | −2.93282 | − | 1.69327i | −0.526750 | − | 0.304119i | 0.212942 | − | 0.977065i | \(-0.431696\pi\) |
−0.739692 | + | 0.672945i | \(0.765029\pi\) | |||||||
\(32\) | 5.99938 | − | 3.46374i | 1.06055 | − | 0.612309i | ||||
\(33\) | 3.07728i | 0.535685i | ||||||||
\(34\) | − | 6.22195i | − | 1.06706i | ||||||
\(35\) | −2.12406 | − | 0.283173i | −0.359032 | − | 0.0478650i | ||||
\(36\) | 1.46986 | + | 2.54588i | 0.244977 | + | 0.424313i | ||||
\(37\) | 8.42267 | + | 4.86283i | 1.38468 | + | 0.799445i | 0.992709 | − | 0.120533i | \(-0.0384605\pi\) |
0.391970 | + | 0.919978i | \(0.371794\pi\) | |||||||
\(38\) | 4.79087 | − | 8.29803i | 0.777182 | − | 1.34612i | ||||
\(39\) | −3.01583 | + | 1.97606i | −0.482919 | + | 0.316422i | ||||
\(40\) | 0.845801 | + | 1.46497i | 0.133733 | + | 0.231632i | ||||
\(41\) | 8.48708 | − | 4.90002i | 1.32546 | − | 0.765254i | 0.340865 | − | 0.940112i | \(-0.389280\pi\) |
0.984594 | + | 0.174858i | \(0.0559468\pi\) | |||||||
\(42\) | −2.24141 | − | 5.43638i | −0.345857 | − | 0.838851i | ||||
\(43\) | −2.85083 | + | 4.93777i | −0.434747 | + | 0.753003i | −0.997275 | − | 0.0737747i | \(-0.976495\pi\) |
0.562528 | + | 0.826778i | \(0.309829\pi\) | |||||||
\(44\) | −7.83438 | + | 4.52318i | −1.18108 | + | 0.681895i | ||||
\(45\) | 0.701414 | − | 0.404962i | 0.104561 | − | 0.0603681i | ||||
\(46\) | −9.53209 | + | 5.50335i | −1.40543 | + | 0.811425i | ||||
\(47\) | 5.31465 | − | 3.06841i | 0.775221 | − | 0.447574i | −0.0595130 | − | 0.998228i | \(-0.518955\pi\) |
0.834734 | + | 0.550654i | \(0.185621\pi\) | |||||||
\(48\) | 0.618725 | − | 1.07166i | 0.0893053 | − | 0.154681i | ||||
\(49\) | 1.78961 | + | 6.76737i | 0.255658 | + | 0.966767i | ||||
\(50\) | −8.36131 | + | 4.82741i | −1.18247 | + | 0.682698i | ||||
\(51\) | −1.39973 | − | 2.42441i | −0.196002 | − | 0.339485i | ||||
\(52\) | −9.46366 | − | 4.77339i | −1.31237 | − | 0.661951i | ||||
\(53\) | 2.83659 | − | 4.91312i | 0.389636 | − | 0.674870i | −0.602764 | − | 0.797919i | \(-0.705934\pi\) |
0.992401 | + | 0.123050i | \(0.0392675\pi\) | |||||||
\(54\) | 1.92478 | + | 1.11128i | 0.261930 | + | 0.151225i | ||||
\(55\) | 1.24618 | + | 2.15845i | 0.168035 | + | 0.291045i | ||||
\(56\) | 3.37112 | − | 4.37849i | 0.450485 | − | 0.585100i | ||||
\(57\) | − | 4.31115i | − | 0.571025i | ||||||
\(58\) | − | 12.6613i | − | 1.66251i | ||||||
\(59\) | −4.27457 | + | 2.46792i | −0.556501 | + | 0.321296i | −0.751740 | − | 0.659460i | \(-0.770785\pi\) |
0.195239 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(60\) | 2.06197 | + | 1.19048i | 0.266199 | + | 0.153690i | ||||
\(61\) | −3.03483 | −0.388570 | −0.194285 | − | 0.980945i | \(-0.562239\pi\) | ||||
−0.194285 | + | 0.980945i | \(0.562239\pi\) | |||||||
\(62\) | −3.76337 | − | 6.51834i | −0.477948 | − | 0.827830i | ||||
\(63\) | −2.09638 | − | 1.61406i | −0.264119 | − | 0.203353i | ||||
\(64\) | 12.9218 | 1.61522 | ||||||||
\(65\) | −1.31512 | + | 2.60733i | −0.163120 | + | 0.323399i | ||||
\(66\) | −3.41970 | + | 5.92310i | −0.420936 | + | 0.729083i | ||||
\(67\) | 9.92554i | 1.21260i | 0.795237 | + | 0.606299i | \(0.207346\pi\) | ||||
−0.795237 | + | 0.606299i | \(0.792654\pi\) | |||||||
\(68\) | 4.11484 | − | 7.12711i | 0.498997 | − | 0.864289i | ||||
\(69\) | −2.47614 | + | 4.28881i | −0.298093 | + | 0.516312i | ||||
\(70\) | −3.77368 | − | 2.90547i | −0.451041 | − | 0.347270i | ||||
\(71\) | −7.84155 | − | 4.52732i | −0.930621 | − | 0.537294i | −0.0436133 | − | 0.999048i | \(-0.513887\pi\) |
−0.887008 | + | 0.461754i | \(0.847220\pi\) | |||||||
\(72\) | 2.08860i | 0.246143i | ||||||||
\(73\) | 2.75318 | + | 1.58955i | 0.322235 | + | 0.186043i | 0.652388 | − | 0.757885i | \(-0.273767\pi\) |
−0.330153 | + | 0.943927i | \(0.607100\pi\) | |||||||
\(74\) | 10.8079 | + | 18.7198i | 1.25639 | + | 2.17613i | ||||
\(75\) | −2.17201 | + | 3.76204i | −0.250802 | + | 0.434402i | ||||
\(76\) | 10.9757 | − | 6.33680i | 1.25899 | − | 0.726881i | ||||
\(77\) | 4.96692 | − | 6.45114i | 0.566033 | − | 0.735175i | ||||
\(78\) | −8.00076 | + | 0.452072i | −0.905907 | + | 0.0511871i | ||||
\(79\) | 1.13963 | + | 1.97390i | 0.128219 | + | 0.222082i | 0.922987 | − | 0.384832i | \(-0.125741\pi\) |
−0.794768 | + | 0.606914i | \(0.792407\pi\) | |||||||
\(80\) | − | 1.00224i | − | 0.112054i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 21.7811 | 2.40532 | ||||||||
\(83\) | − | 1.52896i | − | 0.167825i | −0.996473 | − | 0.0839126i | \(-0.973258\pi\) | ||
0.996473 | − | 0.0839126i | \(-0.0267417\pi\) | |||||||
\(84\) | 1.02782 | − | 7.70958i | 0.112144 | − | 0.841184i | ||||
\(85\) | −1.96359 | − | 1.13368i | −0.212981 | − | 0.122965i | ||||
\(86\) | −10.9745 | + | 6.33610i | −1.18341 | + | 0.683239i | ||||
\(87\) | −2.84837 | − | 4.93353i | −0.305378 | − | 0.528930i | ||||
\(88\) | −6.42719 | −0.685140 | ||||||||
\(89\) | 2.87613 | + | 1.66053i | 0.304869 | + | 0.176016i | 0.644628 | − | 0.764496i | \(-0.277012\pi\) |
−0.339759 | + | 0.940512i | \(0.610346\pi\) | |||||||
\(90\) | 1.80010 | 0.189747 | ||||||||
\(91\) | 9.51179 | + | 0.725168i | 0.997106 | + | 0.0760182i | ||||
\(92\) | −14.5584 | −1.51782 | ||||||||
\(93\) | −2.93282 | − | 1.69327i | −0.304119 | − | 0.175583i | ||||
\(94\) | 13.6394 | 1.40680 | ||||||||
\(95\) | −1.74585 | − | 3.02390i | −0.179120 | − | 0.310246i | ||||
\(96\) | 5.99938 | − | 3.46374i | 0.612309 | − | 0.353517i | ||||
\(97\) | 11.0330 | + | 6.36990i | 1.12023 | + | 0.646766i | 0.941460 | − | 0.337125i | \(-0.109454\pi\) |
0.178771 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(98\) | −4.07581 | + | 15.0145i | −0.411718 | + | 1.51669i | ||||
\(99\) | 3.07728i | 0.309278i | ||||||||
\(100\) | −12.7703 | −1.27703 | ||||||||
\(101\) | −15.1754 | −1.51001 | −0.755006 | − | 0.655717i | \(-0.772366\pi\) | ||||
−0.755006 | + | 0.655717i | \(0.772366\pi\) | |||||||
\(102\) | − | 6.22195i | − | 0.616065i | ||||||
\(103\) | −4.00749 | − | 6.94118i | −0.394870 | − | 0.683935i | 0.598214 | − | 0.801336i | \(-0.295877\pi\) |
−0.993085 | + | 0.117401i | \(0.962544\pi\) | |||||||
\(104\) | −4.12718 | − | 6.29884i | −0.404704 | − | 0.617652i | ||||
\(105\) | −2.12406 | − | 0.283173i | −0.207287 | − | 0.0276349i | ||||
\(106\) | 10.9197 | − | 6.30447i | 1.06061 | − | 0.612344i | ||||
\(107\) | 4.89324 | − | 8.47534i | 0.473048 | − | 0.819342i | −0.526477 | − | 0.850190i | \(-0.676487\pi\) |
0.999524 | + | 0.0308472i | \(0.00982052\pi\) | |||||||
\(108\) | 1.46986 | + | 2.54588i | 0.141438 | + | 0.244977i | ||||
\(109\) | −2.60941 | − | 1.50655i | −0.249937 | − | 0.144301i | 0.369799 | − | 0.929112i | \(-0.379427\pi\) |
−0.619735 | + | 0.784811i | \(0.712760\pi\) | |||||||
\(110\) | 5.53939i | 0.528160i | ||||||||
\(111\) | 8.42267 | + | 4.86283i | 0.799445 | + | 0.461560i | ||||
\(112\) | −3.02681 | + | 1.24795i | −0.286007 | + | 0.117920i | ||||
\(113\) | −1.36880 | + | 2.37084i | −0.128766 | + | 0.223030i | −0.923199 | − | 0.384323i | \(-0.874435\pi\) |
0.794433 | + | 0.607352i | \(0.207768\pi\) | |||||||
\(114\) | 4.79087 | − | 8.29803i | 0.448706 | − | 0.777182i | ||||
\(115\) | 4.01097i | 0.374025i | ||||||||
\(116\) | 8.37345 | − | 14.5032i | 0.777455 | − | 1.34659i | ||||
\(117\) | −3.01583 | + | 1.97606i | −0.278813 | + | 0.182686i | ||||
\(118\) | −10.9702 | −1.00989 | ||||||||
\(119\) | −0.978777 | + | 7.34174i | −0.0897243 | + | 0.673016i | ||||
\(120\) | 0.845801 | + | 1.46497i | 0.0772107 | + | 0.133733i | ||||
\(121\) | 1.53037 | 0.139124 | ||||||||
\(122\) | −5.84139 | − | 3.37253i | −0.528855 | − | 0.305334i | ||||
\(123\) | 8.48708 | − | 4.90002i | 0.765254 | − | 0.441820i | ||||
\(124\) | − | 9.95548i | − | 0.894029i | ||||||
\(125\) | 7.56794i | 0.676898i | ||||||||
\(126\) | −2.24141 | − | 5.43638i | −0.199681 | − | 0.484311i | ||||
\(127\) | 7.39515 | + | 12.8088i | 0.656214 | + | 1.13660i | 0.981588 | + | 0.191010i | \(0.0611763\pi\) |
−0.325374 | + | 0.945585i | \(0.605490\pi\) | |||||||
\(128\) | 12.8729 | + | 7.43217i | 1.13781 | + | 0.656917i | ||||
\(129\) | −2.85083 | + | 4.93777i | −0.251001 | + | 0.434747i | ||||
\(130\) | −5.42877 | + | 3.55709i | −0.476135 | + | 0.311977i | ||||
\(131\) | −1.14893 | − | 1.99001i | −0.100383 | − | 0.173868i | 0.811460 | − | 0.584408i | \(-0.198673\pi\) |
−0.911842 | + | 0.410540i | \(0.865340\pi\) | |||||||
\(132\) | −7.83438 | + | 4.52318i | −0.681895 | + | 0.393692i | ||||
\(133\) | −6.95846 | + | 9.03779i | −0.603375 | + | 0.783676i | ||||
\(134\) | −11.0300 | + | 19.1045i | −0.952847 | + | 1.65038i | ||||
\(135\) | 0.701414 | − | 0.404962i | 0.0603681 | − | 0.0348536i | ||||
\(136\) | 5.06361 | − | 2.92348i | 0.434201 | − | 0.250686i | ||||
\(137\) | 13.5481 | − | 7.82198i | 1.15749 | − | 0.668276i | 0.206788 | − | 0.978386i | \(-0.433699\pi\) |
0.950701 | + | 0.310109i | \(0.100366\pi\) | |||||||
\(138\) | −9.53209 | + | 5.50335i | −0.811425 | + | 0.468477i | ||||
\(139\) | −11.2601 | + | 19.5030i | −0.955068 | + | 1.65423i | −0.220855 | + | 0.975307i | \(0.570885\pi\) |
−0.734213 | + | 0.678919i | \(0.762449\pi\) | |||||||
\(140\) | −2.40116 | − | 5.82384i | −0.202935 | − | 0.492204i | ||||
\(141\) | 5.31465 | − | 3.06841i | 0.447574 | − | 0.258407i | ||||
\(142\) | −10.0622 | − | 17.4282i | −0.844401 | − | 1.46255i | ||||
\(143\) | −6.08087 | − | 9.28053i | −0.508508 | − | 0.776077i | ||||
\(144\) | 0.618725 | − | 1.07166i | 0.0515604 | − | 0.0893053i | ||||
\(145\) | −3.99578 | − | 2.30697i | −0.331832 | − | 0.191583i | ||||
\(146\) | 3.53285 | + | 6.11908i | 0.292381 | + | 0.506419i | ||||
\(147\) | 1.78961 | + | 6.76737i | 0.147604 | + | 0.558163i | ||||
\(148\) | 28.5908i | 2.35015i | ||||||||
\(149\) | 13.5565i | 1.11059i | 0.831654 | + | 0.555294i | \(0.187394\pi\) | ||||
−0.831654 | + | 0.555294i | \(0.812606\pi\) | |||||||
\(150\) | −8.36131 | + | 4.82741i | −0.682698 | + | 0.394156i | ||||
\(151\) | −7.26064 | − | 4.19193i | −0.590863 | − | 0.341135i | 0.174576 | − | 0.984644i | \(-0.444145\pi\) |
−0.765439 | + | 0.643509i | \(0.777478\pi\) | |||||||
\(152\) | 9.00424 | 0.730340 | ||||||||
\(153\) | −1.39973 | − | 2.42441i | −0.113162 | − | 0.196002i | ||||
\(154\) | 16.7292 | − | 6.89744i | 1.34808 | − | 0.555812i | ||||
\(155\) | −2.74283 | −0.220309 | ||||||||
\(156\) | −9.46366 | − | 4.77339i | −0.757699 | − | 0.382177i | ||||
\(157\) | −1.53856 | + | 2.66486i | −0.122790 | + | 0.212679i | −0.920867 | − | 0.389877i | \(-0.872518\pi\) |
0.798077 | + | 0.602556i | \(0.205851\pi\) | |||||||
\(158\) | 5.06579i | 0.403012i | ||||||||
\(159\) | 2.83659 | − | 4.91312i | 0.224957 | − | 0.389636i | ||||
\(160\) | 2.80537 | − | 4.85904i | 0.221784 | − | 0.384141i | ||||
\(161\) | 12.1133 | − | 4.99431i | 0.954665 | − | 0.393607i | ||||
\(162\) | 1.92478 | + | 1.11128i | 0.151225 | + | 0.0873100i | ||||
\(163\) | − | 6.14897i | − | 0.481624i | −0.970572 | − | 0.240812i | \(-0.922586\pi\) | ||
0.970572 | − | 0.240812i | \(-0.0774138\pi\) | |||||||
\(164\) | 24.9497 | + | 14.4047i | 1.94824 | + | 1.12482i | ||||
\(165\) | 1.24618 | + | 2.15845i | 0.0970149 | + | 0.168035i | ||||
\(166\) | 1.69910 | − | 2.94292i | 0.131875 | − | 0.228415i | ||||
\(167\) | −13.6424 | + | 7.87645i | −1.05568 | + | 0.609498i | −0.924235 | − | 0.381825i | \(-0.875296\pi\) |
−0.131447 | + | 0.991323i | \(0.541962\pi\) | |||||||
\(168\) | 3.37112 | − | 4.37849i | 0.260088 | − | 0.337808i | ||||
\(169\) | 5.19040 | − | 11.9189i | 0.399262 | − | 0.916837i | ||||
\(170\) | −2.51965 | − | 4.36417i | −0.193249 | − | 0.334716i | ||||
\(171\) | − | 4.31115i | − | 0.329682i | ||||||
\(172\) | −16.7613 | −1.27804 | ||||||||
\(173\) | 16.3092 | 1.23997 | 0.619983 | − | 0.784615i | \(-0.287139\pi\) | ||||
0.619983 | + | 0.784615i | \(0.287139\pi\) | |||||||
\(174\) | − | 12.6613i | − | 0.959851i | ||||||
\(175\) | 10.6255 | − | 4.38089i | 0.803214 | − | 0.331164i | ||||
\(176\) | 3.29780 | + | 1.90399i | 0.248581 | + | 0.143519i | ||||
\(177\) | −4.27457 | + | 2.46792i | −0.321296 | + | 0.185500i | ||||
\(178\) | 3.69062 | + | 6.39234i | 0.276624 | + | 0.479126i | ||||
\(179\) | −20.3756 | −1.52295 | −0.761473 | − | 0.648196i | \(-0.775524\pi\) | ||||
−0.761473 | + | 0.648196i | \(0.775524\pi\) | |||||||
\(180\) | 2.06197 | + | 1.19048i | 0.153690 | + | 0.0887330i | ||||
\(181\) | −22.1726 | −1.64808 | −0.824039 | − | 0.566533i | \(-0.808285\pi\) | ||||
−0.824039 | + | 0.566533i | \(0.808285\pi\) | |||||||
\(182\) | 17.5023 | + | 11.9660i | 1.29736 | + | 0.886979i | ||||
\(183\) | −3.03483 | −0.224341 | ||||||||
\(184\) | −8.95758 | − | 5.17166i | −0.660362 | − | 0.381260i | ||||
\(185\) | 7.87704 | 0.579132 | ||||||||
\(186\) | −3.76337 | − | 6.51834i | −0.275943 | − | 0.477948i | ||||
\(187\) | 7.46058 | − | 4.30737i | 0.545572 | − | 0.314986i | ||||
\(188\) | 15.6236 | + | 9.02030i | 1.13947 | + | 0.657873i | ||||
\(189\) | −2.09638 | − | 1.61406i | −0.152489 | − | 0.117406i | ||||
\(190\) | − | 7.76047i | − | 0.563004i | ||||||
\(191\) | 21.6850 | 1.56907 | 0.784536 | − | 0.620083i | \(-0.212901\pi\) | ||||
0.784536 | + | 0.620083i | \(0.212901\pi\) | |||||||
\(192\) | 12.9218 | 0.932550 | ||||||||
\(193\) | 0.0505858i | 0.00364124i | 0.999998 | + | 0.00182062i | \(0.000579522\pi\) | ||||
−0.999998 | + | 0.00182062i | \(0.999420\pi\) | |||||||
\(194\) | 14.1574 | + | 24.5214i | 1.01644 | + | 1.76053i | ||||
\(195\) | −1.31512 | + | 2.60733i | −0.0941774 | + | 0.186715i | ||||
\(196\) | −14.5984 | + | 14.5032i | −1.04275 | + | 1.03595i | ||||
\(197\) | 15.4854 | − | 8.94051i | 1.10329 | − | 0.636985i | 0.166207 | − | 0.986091i | \(-0.446848\pi\) |
0.937083 | + | 0.349106i | \(0.113515\pi\) | |||||||
\(198\) | −3.41970 | + | 5.92310i | −0.243028 | + | 0.420936i | ||||
\(199\) | −8.08456 | − | 14.0029i | −0.573099 | − | 0.992637i | −0.996245 | − | 0.0865753i | \(-0.972408\pi\) |
0.423146 | − | 0.906061i | \(-0.360926\pi\) | |||||||
\(200\) | −7.85737 | − | 4.53645i | −0.555600 | − | 0.320776i | ||||
\(201\) | 9.92554i | 0.700094i | ||||||||
\(202\) | −29.2095 | − | 16.8641i | −2.05517 | − | 1.18655i | ||||
\(203\) | −1.99175 | + | 14.9400i | −0.139794 | + | 1.04858i | ||||
\(204\) | 4.11484 | − | 7.12711i | 0.288096 | − | 0.498997i | ||||
\(205\) | 3.96864 | − | 6.87388i | 0.277182 | − | 0.480093i | ||||
\(206\) | − | 17.8137i | − | 1.24114i | ||||||
\(207\) | −2.47614 | + | 4.28881i | −0.172104 | + | 0.298093i | ||||
\(208\) | 0.251700 | + | 4.45458i | 0.0174523 | + | 0.308870i | ||||
\(209\) | 13.2666 | 0.917669 | ||||||||
\(210\) | −3.77368 | − | 2.90547i | −0.260409 | − | 0.200496i | ||||
\(211\) | −2.69037 | − | 4.65986i | −0.185213 | − | 0.320798i | 0.758435 | − | 0.651748i | \(-0.225964\pi\) |
−0.943648 | + | 0.330950i | \(0.892631\pi\) | |||||||
\(212\) | 16.6776 | 1.14542 | ||||||||
\(213\) | −7.84155 | − | 4.52732i | −0.537294 | − | 0.310207i | ||||
\(214\) | 18.8369 | − | 10.8755i | 1.28766 | − | 0.743432i | ||||
\(215\) | 4.61790i | 0.314938i | ||||||||
\(216\) | 2.08860i | 0.142111i | ||||||||
\(217\) | 3.41527 | + | 8.28348i | 0.231843 | + | 0.562319i | ||||
\(218\) | −3.34837 | − | 5.79955i | −0.226781 | − | 0.392795i | ||||
\(219\) | 2.75318 | + | 1.58955i | 0.186043 | + | 0.107412i | ||||
\(220\) | −3.66343 | + | 6.34525i | −0.246988 | + | 0.427796i | ||||
\(221\) | 9.01212 | + | 4.54564i | 0.606221 | + | 0.305773i | ||||
\(222\) | 10.8079 | + | 18.7198i | 0.725378 | + | 1.25639i | ||||
\(223\) | −15.9502 | + | 9.20887i | −1.06811 | + | 0.616671i | −0.927663 | − | 0.373418i | \(-0.878186\pi\) |
−0.140443 | + | 0.990089i | \(0.544853\pi\) | |||||||
\(224\) | −18.1677 | − | 2.42206i | −1.21388 | − | 0.161830i | ||||
\(225\) | −2.17201 | + | 3.76204i | −0.144801 | + | 0.250802i | ||||
\(226\) | −5.26931 | + | 3.04224i | −0.350509 | + | 0.202367i | ||||
\(227\) | 20.0696 | − | 11.5872i | 1.33206 | − | 0.769067i | 0.346448 | − | 0.938069i | \(-0.387388\pi\) |
0.985616 | + | 0.169002i | \(0.0540545\pi\) | |||||||
\(228\) | 10.9757 | − | 6.33680i | 0.726881 | − | 0.419665i | ||||
\(229\) | 23.0419 | − | 13.3032i | 1.52265 | − | 0.879103i | 0.523009 | − | 0.852327i | \(-0.324809\pi\) |
0.999641 | − | 0.0267760i | \(-0.00852410\pi\) | |||||||
\(230\) | −4.45730 | + | 7.72026i | −0.293905 | + | 0.509059i | ||||
\(231\) | 4.96692 | − | 6.45114i | 0.326799 | − | 0.424454i | ||||
\(232\) | 10.3041 | − | 5.94910i | 0.676500 | − | 0.390578i | ||||
\(233\) | −10.9316 | − | 18.9341i | −0.716155 | − | 1.24042i | −0.962512 | − | 0.271238i | \(-0.912567\pi\) |
0.246358 | − | 0.969179i | \(-0.420766\pi\) | |||||||
\(234\) | −8.00076 | + | 0.452072i | −0.523026 | + | 0.0295529i | ||||
\(235\) | 2.48518 | − | 4.30446i | 0.162115 | − | 0.280792i | ||||
\(236\) | −12.5661 | − | 7.25502i | −0.817981 | − | 0.472262i | ||||
\(237\) | 1.13963 | + | 1.97390i | 0.0740272 | + | 0.128219i | ||||
\(238\) | −10.0426 | + | 13.0436i | −0.650967 | + | 0.845489i | ||||
\(239\) | − | 22.4279i | − | 1.45074i | −0.688360 | − | 0.725370i | \(-0.741669\pi\) | ||
0.688360 | − | 0.725370i | \(-0.258331\pi\) | |||||||
\(240\) | − | 1.00224i | − | 0.0646943i | ||||||
\(241\) | −1.37512 | + | 0.793924i | −0.0885790 | + | 0.0511411i | −0.543635 | − | 0.839322i | \(-0.682952\pi\) |
0.455056 | + | 0.890463i | \(0.349619\pi\) | |||||||
\(242\) | 2.94563 | + | 1.70066i | 0.189352 | + | 0.109322i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.46079 | − | 7.72631i | −0.285573 | − | 0.494626i | ||||
\(245\) | 3.99578 | + | 4.02201i | 0.255281 | + | 0.256957i | ||||
\(246\) | 21.7811 | 1.38871 | ||||||||
\(247\) | 8.51907 | + | 13.0017i | 0.542055 | + | 0.827276i | ||||
\(248\) | 3.53655 | − | 6.12548i | 0.224571 | − | 0.388968i | ||||
\(249\) | − | 1.52896i | − | 0.0968939i | ||||||
\(250\) | −8.41007 | + | 14.5667i | −0.531899 | + | 0.921277i | ||||
\(251\) | 0.177730 | − | 0.307837i | 0.0112182 | − | 0.0194305i | −0.860362 | − | 0.509684i | \(-0.829762\pi\) |
0.871580 | + | 0.490253i | \(0.163096\pi\) | |||||||
\(252\) | 1.02782 | − | 7.70958i | 0.0647464 | − | 0.485658i | ||||
\(253\) | −13.1978 | − | 7.61978i | −0.829741 | − | 0.479051i | ||||
\(254\) | 32.8722i | 2.06258i | ||||||||
\(255\) | −1.96359 | − | 1.13368i | −0.122965 | − | 0.0709936i | ||||
\(256\) | 3.59659 | + | 6.22948i | 0.224787 | + | 0.389342i | ||||
\(257\) | 2.60424 | − | 4.51067i | 0.162448 | − | 0.281368i | −0.773298 | − | 0.634043i | \(-0.781394\pi\) |
0.935746 | + | 0.352674i | \(0.114728\pi\) | |||||||
\(258\) | −10.9745 | + | 6.33610i | −0.683239 | + | 0.394468i | ||||
\(259\) | −9.80820 | − | 23.7891i | −0.609452 | − | 1.47818i | ||||
\(260\) | −8.57099 | + | 0.484292i | −0.531550 | + | 0.0300345i | ||||
\(261\) | −2.84837 | − | 4.93353i | −0.176310 | − | 0.305378i | ||||
\(262\) | − | 5.10712i | − | 0.315519i | ||||||
\(263\) | −21.2763 | −1.31195 | −0.655975 | − | 0.754782i | \(-0.727742\pi\) | ||||
−0.655975 | + | 0.754782i | \(0.727742\pi\) | |||||||
\(264\) | −6.42719 | −0.395566 | ||||||||
\(265\) | − | 4.59485i | − | 0.282259i | ||||||
\(266\) | −23.4370 | + | 9.66305i | −1.43702 | + | 0.592479i | ||||
\(267\) | 2.87613 | + | 1.66053i | 0.176016 | + | 0.101623i | ||||
\(268\) | −25.2692 | + | 14.5892i | −1.54356 | + | 0.891177i | ||||
\(269\) | −1.90086 | − | 3.29238i | −0.115897 | − | 0.200740i | 0.802241 | − | 0.597001i | \(-0.203641\pi\) |
−0.918138 | + | 0.396261i | \(0.870308\pi\) | |||||||
\(270\) | 1.80010 | 0.109550 | ||||||||
\(271\) | −22.5990 | − | 13.0475i | −1.37279 | − | 0.792581i | −0.381511 | − | 0.924364i | \(-0.624596\pi\) |
−0.991279 | + | 0.131784i | \(0.957930\pi\) | |||||||
\(272\) | −3.46420 | −0.210048 | ||||||||
\(273\) | 9.51179 | + | 0.725168i | 0.575680 | + | 0.0438891i | ||||
\(274\) | 34.7695 | 2.10050 | ||||||||
\(275\) | −11.5768 | − | 6.68388i | −0.698109 | − | 0.403053i | ||||
\(276\) | −14.5584 | −0.876312 | ||||||||
\(277\) | −14.3426 | − | 24.8421i | −0.861762 | − | 1.49262i | −0.870227 | − | 0.492652i | \(-0.836028\pi\) |
0.00846431 | − | 0.999964i | \(-0.497306\pi\) | |||||||
\(278\) | −43.3465 | + | 25.0261i | −2.59975 | + | 1.50097i | ||||
\(279\) | −2.93282 | − | 1.69327i | −0.175583 | − | 0.101373i | ||||
\(280\) | 0.591435 | − | 4.43631i | 0.0353450 | − | 0.265120i | ||||
\(281\) | 0.959007i | 0.0572096i | 0.999591 | + | 0.0286048i | \(0.00910643\pi\) | ||||
−0.999591 | + | 0.0286048i | \(0.990894\pi\) | |||||||
\(282\) | 13.6394 | 0.812215 | ||||||||
\(283\) | −2.25973 | −0.134327 | −0.0671635 | − | 0.997742i | \(-0.521395\pi\) | ||||
−0.0671635 | + | 0.997742i | \(0.521395\pi\) | |||||||
\(284\) | − | 26.6182i | − | 1.57950i | ||||||
\(285\) | −1.74585 | − | 3.02390i | −0.103415 | − | 0.179120i | ||||
\(286\) | −1.39115 | − | 24.6205i | −0.0822605 | − | 1.45584i | ||||
\(287\) | −25.7011 | − | 3.42638i | −1.51709 | − | 0.202253i | ||||
\(288\) | 5.99938 | − | 3.46374i | 0.353517 | − | 0.204103i | ||||
\(289\) | 4.58149 | − | 7.93538i | 0.269500 | − | 0.466787i | ||||
\(290\) | −5.12735 | − | 8.88082i | −0.301088 | − | 0.521500i | ||||
\(291\) | 11.0330 | + | 6.36990i | 0.646766 | + | 0.373410i | ||||
\(292\) | 9.34569i | 0.546915i | ||||||||
\(293\) | 4.64615 | + | 2.68246i | 0.271431 | + | 0.156711i | 0.629538 | − | 0.776970i | \(-0.283244\pi\) |
−0.358107 | + | 0.933681i | \(0.616578\pi\) | |||||||
\(294\) | −4.07581 | + | 15.0145i | −0.237706 | + | 0.875662i | ||||
\(295\) | −1.99883 | + | 3.46207i | −0.116376 | + | 0.201570i | ||||
\(296\) | −10.1565 | + | 17.5916i | −0.590334 | + | 1.02249i | ||||
\(297\) | 3.07728i | 0.178562i | ||||||||
\(298\) | −15.0649 | + | 26.0933i | −0.872689 | + | 1.51154i | ||||
\(299\) | −1.00731 | − | 17.8273i | −0.0582541 | − | 1.03098i | ||||
\(300\) | −12.7703 | −0.737291 | ||||||||
\(301\) | 13.9463 | − | 5.75003i | 0.803850 | − | 0.331426i | ||||
\(302\) | −9.31678 | − | 16.1371i | −0.536121 | − | 0.928588i | ||||
\(303\) | −15.1754 | −0.871806 | ||||||||
\(304\) | −4.62010 | − | 2.66741i | −0.264981 | − | 0.152987i | ||||
\(305\) | −2.12867 | + | 1.22899i | −0.121887 | + | 0.0703717i | ||||
\(306\) | − | 6.22195i | − | 0.355685i | ||||||
\(307\) | − | 1.80266i | − | 0.102883i | −0.998676 | − | 0.0514415i | \(-0.983618\pi\) | ||
0.998676 | − | 0.0514415i | \(-0.0163816\pi\) | |||||||
\(308\) | 23.7245 | + | 3.16288i | 1.35183 | + | 0.180222i | ||||
\(309\) | −4.00749 | − | 6.94118i | −0.227978 | − | 0.394870i | ||||
\(310\) | −5.27936 | − | 3.04804i | −0.299847 | − | 0.173117i | ||||
\(311\) | −9.77057 | + | 16.9231i | −0.554038 | + | 0.959622i | 0.443940 | + | 0.896057i | \(0.353580\pi\) |
−0.997978 | + | 0.0635652i | \(0.979753\pi\) | |||||||
\(312\) | −4.12718 | − | 6.29884i | −0.233656 | − | 0.356602i | ||||
\(313\) | 15.4409 | + | 26.7444i | 0.872770 | + | 1.51168i | 0.859120 | + | 0.511775i | \(0.171012\pi\) |
0.0136500 | + | 0.999907i | \(0.495655\pi\) | |||||||
\(314\) | −5.92279 | + | 3.41952i | −0.334242 | + | 0.192975i | ||||
\(315\) | −2.12406 | − | 0.283173i | −0.119677 | − | 0.0159550i | ||||
\(316\) | −3.35021 | + | 5.80274i | −0.188464 | + | 0.326430i | ||||
\(317\) | 16.1874 | − | 9.34578i | 0.909173 | − | 0.524911i | 0.0290082 | − | 0.999579i | \(-0.490765\pi\) |
0.880165 | + | 0.474668i | \(0.157432\pi\) | |||||||
\(318\) | 10.9197 | − | 6.30447i | 0.612344 | − | 0.353537i | ||||
\(319\) | 15.1818 | − | 8.76524i | 0.850020 | − | 0.490759i | ||||
\(320\) | 9.06353 | − | 5.23283i | 0.506666 | − | 0.292524i | ||||
\(321\) | 4.89324 | − | 8.47534i | 0.273114 | − | 0.473048i | ||||
\(322\) | 28.8656 | + | 3.84827i | 1.60862 | + | 0.214456i | ||||
\(323\) | −10.4520 | + | 6.03445i | −0.581564 | + | 0.335766i | ||||
\(324\) | 1.46986 | + | 2.54588i | 0.0816591 | + | 0.141438i | ||||
\(325\) | −0.883585 | − | 15.6377i | −0.0490125 | − | 0.867421i | ||||
\(326\) | 6.83320 | − | 11.8354i | 0.378456 | − | 0.655505i | ||||
\(327\) | −2.60941 | − | 1.50655i | −0.144301 | − | 0.0833122i | ||||
\(328\) | 10.2342 | + | 17.7261i | 0.565086 | + | 0.978758i | ||||
\(329\) | −16.0941 | − | 2.14562i | −0.887298 | − | 0.118292i | ||||
\(330\) | 5.53939i | 0.304934i | ||||||||
\(331\) | 22.9813i | 1.26316i | 0.775309 | + | 0.631582i | \(0.217594\pi\) | ||||
−0.775309 | + | 0.631582i | \(0.782406\pi\) | |||||||
\(332\) | 3.89255 | − | 2.24737i | 0.213631 | − | 0.123340i | ||||
\(333\) | 8.42267 | + | 4.86283i | 0.461560 | + | 0.266482i | ||||
\(334\) | −35.0116 | −1.91575 | ||||||||
\(335\) | 4.01946 | + | 6.96192i | 0.219607 | + | 0.380370i | ||||
\(336\) | −3.02681 | + | 1.24795i | −0.165126 | + | 0.0680813i | ||||
\(337\) | 30.3389 | 1.65267 | 0.826333 | − | 0.563182i | \(-0.190423\pi\) | ||||
0.826333 | + | 0.563182i | \(0.190423\pi\) | |||||||
\(338\) | 23.2356 | − | 17.1733i | 1.26385 | − | 0.934105i | ||||
\(339\) | −1.36880 | + | 2.37084i | −0.0743433 | + | 0.128766i | ||||
\(340\) | − | 6.66541i | − | 0.361482i | ||||||
\(341\) | 5.21065 | − | 9.02510i | 0.282172 | − | 0.488737i | ||||
\(342\) | 4.79087 | − | 8.29803i | 0.259061 | − | 0.448706i | ||||
\(343\) | 7.17127 | − | 17.0755i | 0.387212 | − | 0.921991i | ||||
\(344\) | −10.3130 | − | 5.95422i | −0.556040 | − | 0.321030i | ||||
\(345\) | 4.01097i | 0.215944i | ||||||||
\(346\) | 31.3917 | + | 18.1240i | 1.68763 | + | 0.974353i | ||||
\(347\) | 0.359991 | + | 0.623522i | 0.0193253 | + | 0.0334724i | 0.875526 | − | 0.483170i | \(-0.160515\pi\) |
−0.856201 | + | 0.516643i | \(0.827182\pi\) | |||||||
\(348\) | 8.37345 | − | 14.5032i | 0.448864 | − | 0.777455i | ||||
\(349\) | 15.4556 | − | 8.92327i | 0.827317 | − | 0.477652i | −0.0256163 | − | 0.999672i | \(-0.508155\pi\) |
0.852933 | + | 0.522020i | \(0.174821\pi\) | |||||||
\(350\) | 25.3202 | + | 3.37561i | 1.35342 | + | 0.180434i | ||||
\(351\) | −3.01583 | + | 1.97606i | −0.160973 | + | 0.105474i | ||||
\(352\) | 10.6589 | + | 18.4618i | 0.568121 | + | 0.984015i | ||||
\(353\) | − | 0.252183i | − | 0.0134223i | −0.999977 | − | 0.00671117i | \(-0.997864\pi\) | ||
0.999977 | − | 0.00671117i | \(-0.00213625\pi\) | |||||||
\(354\) | −10.9702 | −0.583057 | ||||||||
\(355\) | −7.33357 | −0.389226 | ||||||||
\(356\) | 9.76304i | 0.517440i | ||||||||
\(357\) | −0.978777 | + | 7.34174i | −0.0518024 | + | 0.388566i | ||||
\(358\) | −39.2187 | − | 22.6429i | −2.07277 | − | 1.19672i | ||||
\(359\) | 10.2385 | − | 5.91120i | 0.540368 | − | 0.311981i | −0.204860 | − | 0.978791i | \(-0.565674\pi\) |
0.745228 | + | 0.666810i | \(0.232341\pi\) | |||||||
\(360\) | 0.845801 | + | 1.46497i | 0.0445776 | + | 0.0772107i | ||||
\(361\) | 0.414022 | 0.0217906 | ||||||||
\(362\) | −42.6775 | − | 24.6399i | −2.24308 | − | 1.29504i | ||||
\(363\) | 1.53037 | 0.0803234 | ||||||||
\(364\) | 12.1349 | + | 25.2818i | 0.636039 | + | 1.32513i | ||||
\(365\) | 2.57483 | 0.134773 | ||||||||
\(366\) | −5.84139 | − | 3.37253i | −0.305334 | − | 0.176285i | ||||
\(367\) | −14.1834 | −0.740367 | −0.370183 | − | 0.928959i | \(-0.620705\pi\) | ||||
−0.370183 | + | 0.928959i | \(0.620705\pi\) | |||||||
\(368\) | 3.06410 | + | 5.30718i | 0.159727 | + | 0.276656i | ||||
\(369\) | 8.48708 | − | 4.90002i | 0.441820 | − | 0.255085i | ||||
\(370\) | 15.1616 | + | 8.75356i | 0.788215 | + | 0.455076i | ||||
\(371\) | −13.8767 | + | 5.72133i | −0.720440 | + | 0.297037i | ||||
\(372\) | − | 9.95548i | − | 0.516168i | ||||||
\(373\) | −9.94037 | −0.514693 | −0.257346 | − | 0.966319i | \(-0.582848\pi\) | ||||
−0.257346 | + | 0.966319i | \(0.582848\pi\) | |||||||
\(374\) | 19.1467 | 0.990051 | ||||||||
\(375\) | 7.56794i | 0.390807i | ||||||||
\(376\) | 6.40867 | + | 11.1001i | 0.330502 | + | 0.572446i | ||||
\(377\) | 18.3391 | + | 9.25011i | 0.944513 | + | 0.476405i | ||||
\(378\) | −2.24141 | − | 5.43638i | −0.115286 | − | 0.279617i | ||||
\(379\) | 7.91690 | − | 4.57083i | 0.406664 | − | 0.234788i | −0.282691 | − | 0.959211i | \(-0.591227\pi\) |
0.689355 | + | 0.724423i | \(0.257894\pi\) | |||||||
\(380\) | 5.13232 | − | 8.88945i | 0.263283 | − | 0.456019i | ||||
\(381\) | 7.39515 | + | 12.8088i | 0.378865 | + | 0.656214i | ||||
\(382\) | 41.7390 | + | 24.0980i | 2.13555 | + | 1.23296i | ||||
\(383\) | 23.7089i | 1.21147i | 0.795668 | + | 0.605734i | \(0.207120\pi\) | ||||
−0.795668 | + | 0.605734i | \(0.792880\pi\) | |||||||
\(384\) | 12.8729 | + | 7.43217i | 0.656917 | + | 0.379271i | ||||
\(385\) | 0.871403 | − | 6.53633i | 0.0444108 | − | 0.333122i | ||||
\(386\) | −0.0562147 | + | 0.0973667i | −0.00286125 | + | 0.00495584i | ||||
\(387\) | −2.85083 | + | 4.93777i | −0.144916 | + | 0.251001i | ||||
\(388\) | 37.4516i | 1.90132i | ||||||||
\(389\) | −10.2666 | + | 17.7823i | −0.520537 | + | 0.901596i | 0.479178 | + | 0.877718i | \(0.340935\pi\) |
−0.999715 | + | 0.0238784i | \(0.992399\pi\) | |||||||
\(390\) | −5.42877 | + | 3.55709i | −0.274897 | + | 0.180120i | ||||
\(391\) | 13.8638 | 0.701121 | ||||||||
\(392\) | −14.1343 | + | 3.73776i | −0.713890 | + | 0.188786i | ||||
\(393\) | −1.14893 | − | 1.99001i | −0.0579560 | − | 0.100383i | ||||
\(394\) | 39.7415 | 2.00215 | ||||||||
\(395\) | 1.59871 | + | 0.923016i | 0.0804399 | + | 0.0464420i | ||||
\(396\) | −7.83438 | + | 4.52318i | −0.393692 | + | 0.227298i | ||||
\(397\) | − | 26.5917i | − | 1.33460i | −0.744788 | − | 0.667301i | \(-0.767450\pi\) | ||
0.744788 | − | 0.667301i | \(-0.232550\pi\) | |||||||
\(398\) | − | 35.9367i | − | 1.80134i | ||||||
\(399\) | −6.95846 | + | 9.03779i | −0.348359 | + | 0.452456i | ||||
\(400\) | 2.68776 | + | 4.65533i | 0.134388 | + | 0.232767i | ||||
\(401\) | −21.3708 | − | 12.3385i | −1.06721 | − | 0.616153i | −0.139791 | − | 0.990181i | \(-0.544643\pi\) |
−0.927417 | + | 0.374028i | \(0.877976\pi\) | |||||||
\(402\) | −11.0300 | + | 19.1045i | −0.550127 | + | 0.952847i | ||||
\(403\) | 12.1909 | − | 0.688829i | 0.607270 | − | 0.0343130i | ||||
\(404\) | −22.3058 | − | 38.6349i | −1.10976 | − | 1.92216i | ||||
\(405\) | 0.701414 | − | 0.404962i | 0.0348536 | − | 0.0201227i | ||||
\(406\) | −20.4361 | + | 26.5429i | −1.01423 | + | 1.31730i | ||||
\(407\) | −14.9643 | + | 25.9189i | −0.741752 | + | 1.28475i | ||||
\(408\) | 5.06361 | − | 2.92348i | 0.250686 | − | 0.144734i | ||||
\(409\) | −31.3018 | + | 18.0721i | −1.54777 | + | 0.893607i | −0.549460 | + | 0.835520i | \(0.685167\pi\) |
−0.998312 | + | 0.0580869i | \(0.981500\pi\) | |||||||
\(410\) | 15.2775 | − | 8.82050i | 0.754504 | − | 0.435613i | ||||
\(411\) | 13.5481 | − | 7.82198i | 0.668276 | − | 0.385830i | ||||
\(412\) | 11.7809 | − | 20.4052i | 0.580406 | − | 1.00529i | ||||
\(413\) | 12.9445 | + | 1.72572i | 0.636957 | + | 0.0849170i | ||||
\(414\) | −9.53209 | + | 5.50335i | −0.468477 | + | 0.270475i | ||||
\(415\) | −0.619171 | − | 1.07243i | −0.0303939 | − | 0.0526438i | ||||
\(416\) | −11.2485 | + | 22.3012i | −0.551504 | + | 1.09340i | ||||
\(417\) | −11.2601 | + | 19.5030i | −0.551409 | + | 0.955068i | ||||
\(418\) | 25.5353 | + | 14.7428i | 1.24897 | + | 0.721095i | ||||
\(419\) | 1.32411 | + | 2.29343i | 0.0646872 | + | 0.112042i | 0.896555 | − | 0.442932i | \(-0.146062\pi\) |
−0.831868 | + | 0.554974i | \(0.812728\pi\) | |||||||
\(420\) | −2.40116 | − | 5.82384i | −0.117165 | − | 0.284174i | ||||
\(421\) | 4.51819i | 0.220203i | 0.993920 | + | 0.110102i | \(0.0351176\pi\) | ||||
−0.993920 | + | 0.110102i | \(0.964882\pi\) | |||||||
\(422\) | − | 11.9590i | − | 0.582153i | ||||||
\(423\) | 5.31465 | − | 3.06841i | 0.258407 | − | 0.149191i | ||||
\(424\) | 10.2615 | + | 5.92450i | 0.498344 | + | 0.287719i | ||||
\(425\) | 12.1609 | 0.589893 | ||||||||
\(426\) | −10.0622 | − | 17.4282i | −0.487515 | − | 0.844401i | ||||
\(427\) | 6.36215 | + | 4.89840i | 0.307886 | + | 0.237050i | ||||
\(428\) | 28.7696 | 1.39063 | ||||||||
\(429\) | −6.08087 | − | 9.28053i | −0.293587 | − | 0.448068i | ||||
\(430\) | −5.13176 | + | 8.88846i | −0.247475 | + | 0.428640i | ||||
\(431\) | − | 13.6978i | − | 0.659800i | −0.944016 | − | 0.329900i | \(-0.892985\pi\) | ||
0.944016 | − | 0.329900i | \(-0.107015\pi\) | |||||||
\(432\) | 0.618725 | − | 1.07166i | 0.0297684 | − | 0.0515604i | ||||
\(433\) | −11.1388 | + | 19.2929i | −0.535296 | + | 0.927159i | 0.463853 | + | 0.885912i | \(0.346466\pi\) |
−0.999149 | + | 0.0412471i | \(0.986867\pi\) | |||||||
\(434\) | −2.63157 | + | 19.7392i | −0.126319 | + | 0.947513i | ||||
\(435\) | −3.99578 | − | 2.30697i | −0.191583 | − | 0.110611i | ||||
\(436\) | − | 8.85768i | − | 0.424206i | ||||||
\(437\) | 18.4897 | + | 10.6750i | 0.884481 | + | 0.510655i | ||||
\(438\) | 3.53285 | + | 6.11908i | 0.168806 | + | 0.292381i | ||||
\(439\) | −10.7294 | + | 18.5838i | −0.512086 | + | 0.886958i | 0.487816 | + | 0.872946i | \(0.337794\pi\) |
−0.999902 | + | 0.0140120i | \(0.995540\pi\) | |||||||
\(440\) | −4.50812 | + | 2.60276i | −0.214916 | + | 0.124082i | ||||
\(441\) | 1.78961 | + | 6.76737i | 0.0852193 | + | 0.322256i | ||||
\(442\) | 12.2949 | + | 18.7643i | 0.584810 | + | 0.892528i | ||||
\(443\) | 3.43706 | + | 5.95317i | 0.163300 | + | 0.282844i | 0.936050 | − | 0.351866i | \(-0.114453\pi\) |
−0.772750 | + | 0.634710i | \(0.781120\pi\) | |||||||
\(444\) | 28.5908i | 1.35686i | ||||||||
\(445\) | 2.68981 | 0.127509 | ||||||||
\(446\) | −40.9343 | −1.93830 | ||||||||
\(447\) | 13.5565i | 0.641198i | ||||||||
\(448\) | −27.0890 | − | 20.8566i | −1.27983 | − | 0.985380i | ||||
\(449\) | −25.5631 | − | 14.7589i | −1.20640 | − | 0.696515i | −0.244428 | − | 0.969667i | \(-0.578600\pi\) |
−0.961971 | + | 0.273152i | \(0.911934\pi\) | |||||||
\(450\) | −8.36131 | + | 4.82741i | −0.394156 | + | 0.227566i | ||||
\(451\) | 15.0787 | + | 26.1171i | 0.710029 | + | 1.22981i | ||||
\(452\) | −8.04783 | −0.378538 | ||||||||
\(453\) | −7.26064 | − | 4.19193i | −0.341135 | − | 0.196954i | ||||
\(454\) | 51.5061 | 2.41730 | ||||||||
\(455\) | 6.96537 | − | 3.34327i | 0.326542 | − | 0.156735i | ||||
\(456\) | 9.00424 | 0.421662 | ||||||||
\(457\) | 12.9001 | + | 7.44788i | 0.603441 | + | 0.348397i | 0.770394 | − | 0.637568i | \(-0.220059\pi\) |
−0.166953 | + | 0.985965i | \(0.553393\pi\) | |||||||
\(458\) | 59.1342 | 2.76316 | ||||||||
\(459\) | −1.39973 | − | 2.42441i | −0.0653340 | − | 0.113162i | ||||
\(460\) | −10.2115 | + | 5.89559i | −0.476112 | + | 0.274883i | ||||
\(461\) | 21.6772 | + | 12.5154i | 1.00961 | + | 0.582898i | 0.911077 | − | 0.412236i | \(-0.135252\pi\) |
0.0985319 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(462\) | 16.7292 | − | 6.89744i | 0.778314 | − | 0.320898i | ||||
\(463\) | − | 34.2885i | − | 1.59352i | −0.604295 | − | 0.796761i | \(-0.706545\pi\) | ||
0.604295 | − | 0.796761i | \(-0.293455\pi\) | |||||||
\(464\) | −7.04944 | −0.327262 | ||||||||
\(465\) | −2.74283 | −0.127196 | ||||||||
\(466\) | − | 48.5922i | − | 2.25099i | ||||||
\(467\) | 1.46293 | + | 2.53387i | 0.0676964 | + | 0.117254i | 0.897887 | − | 0.440226i | \(-0.145102\pi\) |
−0.830190 | + | 0.557480i | \(0.811768\pi\) | |||||||
\(468\) | −9.46366 | − | 4.77339i | −0.437458 | − | 0.220650i | ||||
\(469\) | 16.0204 | − | 20.8077i | 0.739755 | − | 0.960810i | ||||
\(470\) | 9.56687 | − | 5.52344i | 0.441287 | − | 0.254777i | ||||
\(471\) | −1.53856 | + | 2.66486i | −0.0708930 | + | 0.122790i | ||||
\(472\) | −5.15449 | − | 8.92784i | −0.237255 | − | 0.410937i | ||||
\(473\) | −15.1949 | − | 8.77278i | −0.698662 | − | 0.403373i | ||||
\(474\) | 5.06579i | 0.232679i | ||||||||
\(475\) | 16.2187 | + | 9.36386i | 0.744164 | + | 0.429643i | ||||
\(476\) | −20.1298 | + | 8.29951i | −0.922650 | + | 0.380407i | ||||
\(477\) | 2.83659 | − | 4.91312i | 0.129879 | − | 0.224957i | ||||
\(478\) | 24.9236 | − | 43.1689i | 1.13998 | − | 1.97450i | ||||
\(479\) | − | 33.3149i | − | 1.52220i | −0.648636 | − | 0.761099i | \(-0.724660\pi\) | ||
0.648636 | − | 0.761099i | \(-0.275340\pi\) | |||||||
\(480\) | 2.80537 | − | 4.85904i | 0.128047 | − | 0.221784i | ||||
\(481\) | −35.0105 | + | 1.97822i | −1.59634 | + | 0.0901993i | ||||
\(482\) | −3.52907 | −0.160745 | ||||||||
\(483\) | 12.1133 | − | 4.99431i | 0.551176 | − | 0.227249i | ||||
\(484\) | 2.24943 | + | 3.89613i | 0.102247 | + | 0.177097i | ||||
\(485\) | 10.3183 | 0.468528 | ||||||||
\(486\) | 1.92478 | + | 1.11128i | 0.0873100 | + | 0.0504085i | ||||
\(487\) | −12.9847 | + | 7.49670i | −0.588391 | + | 0.339708i | −0.764461 | − | 0.644670i | \(-0.776995\pi\) |
0.176070 | + | 0.984378i | \(0.443662\pi\) | |||||||
\(488\) | − | 6.33853i | − | 0.286932i | ||||||
\(489\) | − | 6.14897i | − | 0.278066i | ||||||
\(490\) | 3.22146 | + | 12.1819i | 0.145531 | + | 0.550323i | ||||
\(491\) | 20.3637 | + | 35.2709i | 0.918999 | + | 1.59175i | 0.800939 | + | 0.598746i | \(0.204334\pi\) |
0.118060 | + | 0.993006i | \(0.462333\pi\) | |||||||
\(492\) | 24.9497 | + | 14.4047i | 1.12482 | + | 0.649415i | ||||
\(493\) | −7.97393 | + | 13.8112i | −0.359128 | + | 0.622027i | ||||
\(494\) | 1.94895 | + | 34.4924i | 0.0876874 | + | 1.55189i | ||||
\(495\) | 1.24618 | + | 2.15845i | 0.0560116 | + | 0.0970149i | ||||
\(496\) | −3.62922 | + | 2.09533i | −0.162957 | + | 0.0940831i | ||||
\(497\) | 9.13148 | + | 22.1477i | 0.409603 | + | 0.993462i | ||||
\(498\) | 1.69910 | − | 2.94292i | 0.0761383 | − | 0.131875i | ||||
\(499\) | −0.946024 | + | 0.546187i | −0.0423498 | + | 0.0244507i | −0.521025 | − | 0.853541i | \(-0.674450\pi\) |
0.478676 | + | 0.877992i | \(0.341117\pi\) | |||||||
\(500\) | −19.2671 | + | 11.1239i | −0.861650 | + | 0.497474i | ||||
\(501\) | −13.6424 | + | 7.87645i | −0.609498 | + | 0.351894i | ||||
\(502\) | 0.684183 | − | 0.395013i | 0.0305366 | − | 0.0176303i | ||||
\(503\) | 18.2104 | − | 31.5413i | 0.811961 | − | 1.40636i | −0.0995283 | − | 0.995035i | \(-0.531733\pi\) |
0.911489 | − | 0.411323i | \(-0.134933\pi\) | |||||||
\(504\) | 3.37112 | − | 4.37849i | 0.150162 | − | 0.195033i | ||||
\(505\) | −10.6443 | + | 6.14547i | −0.473664 | + | 0.273470i | ||||
\(506\) | −16.9353 | − | 29.3329i | −0.752868 | − | 1.30401i | ||||
\(507\) | 5.19040 | − | 11.9189i | 0.230514 | − | 0.529336i | ||||
\(508\) | −21.7397 | + | 37.6543i | −0.964545 | + | 1.67064i | ||||
\(509\) | −6.91042 | − | 3.98973i | −0.306299 | − | 0.176842i | 0.338970 | − | 0.940797i | \(-0.389921\pi\) |
−0.645269 | + | 0.763955i | \(0.723255\pi\) | |||||||
\(510\) | −2.51965 | − | 4.36417i | −0.111572 | − | 0.193249i | ||||
\(511\) | −3.20608 | − | 7.77610i | −0.141828 | − | 0.343994i | ||||
\(512\) | − | 13.7415i | − | 0.607294i | ||||||
\(513\) | − | 4.31115i | − | 0.190342i | ||||||
\(514\) | 10.0252 | − | 5.78805i | 0.442193 | − | 0.255300i | ||||
\(515\) | −5.62183 | − | 3.24576i | −0.247727 | − | 0.143025i | ||||
\(516\) | −16.7613 | −0.737875 | ||||||||
\(517\) | 9.44236 | + | 16.3546i | 0.415274 | + | 0.719276i | ||||
\(518\) | 7.55752 | − | 56.6884i | 0.332058 | − | 2.49075i | ||||
\(519\) | 16.3092 | 0.715895 | ||||||||
\(520\) | −5.44565 | − | 2.74674i | −0.238808 | − | 0.120453i | ||||
\(521\) | −3.02902 | + | 5.24643i | −0.132704 | + | 0.229850i | −0.924718 | − | 0.380653i | \(-0.875699\pi\) |
0.792014 | + | 0.610503i | \(0.209033\pi\) | |||||||
\(522\) | − | 12.6613i | − | 0.554171i | ||||||
\(523\) | −5.73446 | + | 9.93238i | −0.250750 | + | 0.434313i | −0.963733 | − | 0.266870i | \(-0.914011\pi\) |
0.712982 | + | 0.701182i | \(0.247344\pi\) | |||||||
\(524\) | 3.37755 | − | 5.85009i | 0.147549 | − | 0.255562i | ||||
\(525\) | 10.6255 | − | 4.38089i | 0.463736 | − | 0.191198i | ||||
\(526\) | −40.9522 | − | 23.6438i | −1.78560 | − | 1.03092i | ||||
\(527\) | 9.48048i | 0.412976i | ||||||||
\(528\) | 3.29780 | + | 1.90399i | 0.143519 | + | 0.0828605i | ||||
\(529\) | −0.762574 | − | 1.32082i | −0.0331554 | − | 0.0574268i | ||||
\(530\) | 5.10614 | − | 8.84409i | 0.221797 | − | 0.384163i | ||||
\(531\) | −4.27457 | + | 2.46792i | −0.185500 | + | 0.107099i | ||||
\(532\) | −33.2371 | − | 4.43107i | −1.44101 | − | 0.192111i | ||||
\(533\) | −15.9128 | + | 31.5485i | −0.689261 | + | 1.36652i | ||||
\(534\) | 3.69062 | + | 6.39234i | 0.159709 | + | 0.276624i | ||||
\(535\) | − | 7.92630i | − | 0.342684i | ||||||
\(536\) | −20.7304 | −0.895419 | ||||||||
\(537\) | −20.3756 | −0.879274 | ||||||||
\(538\) | − | 8.44950i | − | 0.364284i | ||||||
\(539\) | −20.8251 | + | 5.50711i | −0.897000 | + | 0.237208i | ||||
\(540\) | 2.06197 | + | 1.19048i | 0.0887330 | + | 0.0512300i | ||||
\(541\) | −21.2518 | + | 12.2697i | −0.913687 | + | 0.527517i | −0.881616 | − | 0.471968i | \(-0.843544\pi\) |
−0.0320714 | + | 0.999486i | \(0.510210\pi\) | |||||||
\(542\) | −28.9988 | − | 50.2274i | −1.24560 | − | 2.15745i | ||||
\(543\) | −22.1726 | −0.951519 | ||||||||
\(544\) | −16.7951 | − | 9.69663i | −0.720082 | − | 0.415740i | ||||
\(545\) | −2.44037 | −0.104534 | ||||||||
\(546\) | 17.5023 | + | 11.9660i | 0.749029 | + | 0.512098i | ||||
\(547\) | −20.6787 | −0.884155 | −0.442078 | − | 0.896977i | \(-0.645758\pi\) | ||||
−0.442078 | + | 0.896977i | \(0.645758\pi\) | |||||||
\(548\) | 39.8276 | + | 22.9945i | 1.70135 | + | 0.982276i | ||||
\(549\) | −3.03483 | −0.129523 | ||||||||
\(550\) | −14.8553 | − | 25.7301i | −0.633431 | − | 1.09713i | ||||
\(551\) | −21.2692 | + | 12.2798i | −0.906097 | + | 0.523135i | ||||
\(552\) | −8.95758 | − | 5.17166i | −0.381260 | − | 0.220121i | ||||
\(553\) | 0.796900 | − | 5.97749i | 0.0338876 | − | 0.254189i | ||||
\(554\) | − | 63.7542i | − | 2.70866i | ||||||
\(555\) | 7.87704 | 0.334362 | ||||||||
\(556\) | −66.2032 | −2.80764 | ||||||||
\(557\) | 19.2157i | 0.814196i | 0.913384 | + | 0.407098i | \(0.133459\pi\) | ||||
−0.913384 | + | 0.407098i | \(0.866541\pi\) | |||||||
\(558\) | −3.76337 | − | 6.51834i | −0.159316 | − | 0.275943i | ||||
\(559\) | −1.15973 | − | 20.5249i | −0.0490513 | − | 0.868109i | ||||
\(560\) | −1.61768 | + | 2.10107i | −0.0683594 | + | 0.0887866i | ||||
\(561\) | 7.46058 | − | 4.30737i | 0.314986 | − | 0.181857i | ||||
\(562\) | −1.06572 | + | 1.84588i | −0.0449547 | + | 0.0778639i | ||||
\(563\) | 2.96132 | + | 5.12915i | 0.124805 | + | 0.216168i | 0.921657 | − | 0.388007i | \(-0.126836\pi\) |
−0.796852 | + | 0.604175i | \(0.793503\pi\) | |||||||
\(564\) | 15.6236 | + | 9.02030i | 0.657873 | + | 0.379823i | ||||
\(565\) | 2.21725i | 0.0932806i | ||||||||
\(566\) | −4.34949 | − | 2.51118i | −0.182823 | − | 0.105553i | ||||
\(567\) | −2.09638 | − | 1.61406i | −0.0880396 | − | 0.0677842i | ||||
\(568\) | 9.45575 | − | 16.3778i | 0.396754 | − | 0.687199i | ||||
\(569\) | −17.8849 | + | 30.9775i | −0.749773 | + | 1.29865i | 0.198158 | + | 0.980170i | \(0.436504\pi\) |
−0.947931 | + | 0.318475i | \(0.896829\pi\) | |||||||
\(570\) | − | 7.76047i | − | 0.325051i | ||||||
\(571\) | 1.69895 | − | 2.94266i | 0.0710987 | − | 0.123147i | −0.828284 | − | 0.560308i | \(-0.810683\pi\) |
0.899383 | + | 0.437161i | \(0.144016\pi\) | |||||||
\(572\) | 14.6891 | − | 29.1223i | 0.614180 | − | 1.21766i | ||||
\(573\) | 21.6850 | 0.905904 | ||||||||
\(574\) | −45.6613 | − | 35.1560i | −1.90587 | − | 1.46738i | ||||
\(575\) | −10.7564 | − | 18.6307i | −0.448574 | − | 0.776953i | ||||
\(576\) | 12.9218 | 0.538408 | ||||||||
\(577\) | 7.14796 | + | 4.12687i | 0.297573 | + | 0.171804i | 0.641352 | − | 0.767247i | \(-0.278374\pi\) |
−0.343779 | + | 0.939051i | \(0.611707\pi\) | |||||||
\(578\) | 17.6368 | − | 10.1826i | 0.733593 | − | 0.423540i | ||||
\(579\) | 0.0505858i | 0.00210227i | ||||||||
\(580\) | − | 13.5637i | − | 0.563202i | ||||||
\(581\) | −2.46784 | + | 3.20528i | −0.102383 | + | 0.132977i | ||||
\(582\) | 14.1574 | + | 24.5214i | 0.586844 | + | 1.01644i | ||||
\(583\) | 15.1190 | + | 8.72898i | 0.626167 | + | 0.361518i | ||||
\(584\) | −3.31992 | + | 5.75028i | −0.137379 | + | 0.237948i | ||||
\(585\) | −1.31512 | + | 2.60733i | −0.0543733 | + | 0.107800i | ||||
\(586\) | 5.96189 | + | 10.3263i | 0.246283 | + | 0.426576i | ||||
\(587\) | −20.9087 | + | 12.0716i | −0.862994 | + | 0.498250i | −0.865014 | − | 0.501748i | \(-0.832690\pi\) |
0.00201975 | + | 0.999998i | \(0.499357\pi\) | |||||||
\(588\) | −14.5984 | + | 14.5032i | −0.602029 | + | 0.598104i | ||||
\(589\) | −7.29991 | + | 12.6438i | −0.300788 | + | 0.520980i | ||||
\(590\) | −7.69463 | + | 4.44249i | −0.316783 | + | 0.182895i | ||||
\(591\) | 15.4854 | − | 8.94051i | 0.636985 | − | 0.367764i | ||||
\(592\) | 10.4226 | − | 6.01751i | 0.428368 | − | 0.247318i | ||||
\(593\) | 7.24219 | − | 4.18128i | 0.297401 | − | 0.171705i | −0.343874 | − | 0.939016i | \(-0.611739\pi\) |
0.641275 | + | 0.767311i | \(0.278406\pi\) | |||||||
\(594\) | −3.41970 | + | 5.92310i | −0.140312 | + | 0.243028i | ||||
\(595\) | 2.28659 | + | 5.54597i | 0.0937412 | + | 0.227362i | ||||
\(596\) | −34.5131 | + | 19.9262i | −1.41371 | + | 0.816207i | ||||
\(597\) | −8.08456 | − | 14.0029i | −0.330879 | − | 0.573099i | ||||
\(598\) | 17.8722 | − | 35.4331i | 0.730847 | − | 1.44897i | ||||
\(599\) | −4.25916 | + | 7.37709i | −0.174025 | + | 0.301420i | −0.939823 | − | 0.341661i | \(-0.889011\pi\) |
0.765799 | + | 0.643080i | \(0.222344\pi\) | |||||||
\(600\) | −7.85737 | − | 4.53645i | −0.320776 | − | 0.185200i | ||||
\(601\) | 0.714622 | + | 1.23776i | 0.0291500 | + | 0.0504894i | 0.880232 | − | 0.474543i | \(-0.157387\pi\) |
−0.851082 | + | 0.525032i | \(0.824053\pi\) | |||||||
\(602\) | 33.2335 | + | 4.43058i | 1.35449 | + | 0.180577i | ||||
\(603\) | 9.92554i | 0.404199i | ||||||||
\(604\) | − | 24.6463i | − | 1.00284i | ||||||
\(605\) | 1.07342 | − | 0.619740i | 0.0436408 | − | 0.0251960i | ||||
\(606\) | −29.2095 | − | 16.8641i | −1.18655 | − | 0.685057i | ||||
\(607\) | 15.0311 | 0.610094 | 0.305047 | − | 0.952337i | \(-0.401328\pi\) | ||||
0.305047 | + | 0.952337i | \(0.401328\pi\) | |||||||
\(608\) | −14.9327 | − | 25.8642i | −0.605601 | − | 1.04893i | ||||
\(609\) | −1.99175 | + | 14.9400i | −0.0807099 | + | 0.605399i | ||||
\(610\) | −5.46298 | −0.221190 | ||||||||
\(611\) | −9.96469 | + | 19.7558i | −0.403128 | + | 0.799236i | ||||
\(612\) | 4.11484 | − | 7.12711i | 0.166332 | − | 0.288096i | ||||
\(613\) | 17.9059i | 0.723213i | 0.932331 | + | 0.361606i | \(0.117772\pi\) | ||||
−0.932331 | + | 0.361606i | \(0.882228\pi\) | |||||||
\(614\) | 2.00325 | − | 3.46973i | 0.0808445 | − | 0.140027i | ||||
\(615\) | 3.96864 | − | 6.87388i | 0.160031 | − | 0.277182i | ||||
\(616\) | 13.4738 | + | 10.3739i | 0.542876 | + | 0.417976i | ||||
\(617\) | 34.2385 | + | 19.7676i | 1.37839 | + | 0.795813i | 0.991966 | − | 0.126509i | \(-0.0403771\pi\) |
0.386423 | + | 0.922322i | \(0.373710\pi\) | |||||||
\(618\) | − | 17.8137i | − | 0.716573i | ||||||
\(619\) | 23.1290 | + | 13.3535i | 0.929634 | + | 0.536724i | 0.886696 | − | 0.462354i | \(-0.152995\pi\) |
0.0429379 | + | 0.999078i | \(0.486328\pi\) | |||||||
\(620\) | −4.03159 | − | 6.98292i | −0.161913 | − | 0.280441i | ||||
\(621\) | −2.47614 | + | 4.28881i | −0.0993642 | + | 0.172104i | ||||
\(622\) | −37.6125 | + | 21.7156i | −1.50812 | + | 0.870715i | ||||
\(623\) | −3.34925 | − | 8.12335i | −0.134185 | − | 0.325455i | ||||
\(624\) | 0.251700 | + | 4.45458i | 0.0100761 | + | 0.178326i | ||||
\(625\) | −7.79533 | − | 13.5019i | −0.311813 | − | 0.540076i | ||||
\(626\) | 68.6362i | 2.74326i | ||||||||
\(627\) | 13.2666 | 0.529817 | ||||||||
\(628\) | −9.04589 | −0.360970 | ||||||||
\(629\) | − | 27.2267i | − | 1.08560i | ||||||
\(630\) | −3.77368 | − | 2.90547i | −0.150347 | − | 0.115757i | ||||
\(631\) | 15.8415 | + | 9.14610i | 0.630640 | + | 0.364100i | 0.781000 | − | 0.624531i | \(-0.214710\pi\) |
−0.150360 | + | 0.988631i | \(0.548043\pi\) | |||||||
\(632\) | −4.12269 | + | 2.38023i | −0.163992 | + | 0.0946806i | ||||
\(633\) | −2.69037 | − | 4.65986i | −0.106933 | − | 0.185213i | ||||
\(634\) | 41.5429 | 1.64988 | ||||||||
\(635\) | 10.3741 | + | 5.98951i | 0.411685 | + | 0.237686i | ||||
\(636\) | 16.6776 | 0.661311 | ||||||||
\(637\) | −18.7698 | − | 16.8728i | −0.743688 | − | 0.668527i | ||||
\(638\) | 38.9624 | 1.54253 | ||||||||
\(639\) | −7.84155 | − | 4.52732i | −0.310207 | − | 0.179098i | ||||
\(640\) | 12.0390 | 0.475883 | ||||||||
\(641\) | −19.2412 | − | 33.3267i | −0.759981 | − | 1.31633i | −0.942860 | − | 0.333190i | \(-0.891875\pi\) |
0.182879 | − | 0.983135i | \(-0.441458\pi\) | |||||||
\(642\) | 18.8369 | − | 10.8755i | 0.743432 | − | 0.429221i | ||||
\(643\) | 9.32291 | + | 5.38258i | 0.367660 | + | 0.212268i | 0.672436 | − | 0.740156i | \(-0.265248\pi\) |
−0.304776 | + | 0.952424i | \(0.598582\pi\) | |||||||
\(644\) | 30.5199 | + | 23.4981i | 1.20265 | + | 0.925956i | ||||
\(645\) | 4.61790i | 0.181830i | ||||||||
\(646\) | −26.8238 | −1.05537 | ||||||||
\(647\) | −6.12507 | −0.240801 | −0.120401 | − | 0.992725i | \(-0.538418\pi\) | ||||
−0.120401 | + | 0.992725i | \(0.538418\pi\) | |||||||
\(648\) | 2.08860i | 0.0820478i | ||||||||
\(649\) | −7.59448 | − | 13.1540i | −0.298109 | − | 0.516341i | ||||
\(650\) | 15.6770 | − | 31.0810i | 0.614904 | − | 1.21910i | ||||
\(651\) | 3.41527 | + | 8.28348i | 0.133855 | + | 0.324655i | ||||
\(652\) | 15.6545 | − | 9.03815i | 0.613079 | − | 0.353961i | ||||
\(653\) | −11.7103 | + | 20.2828i | −0.458258 | + | 0.793726i | −0.998869 | − | 0.0475467i | \(-0.984860\pi\) |
0.540611 | + | 0.841273i | \(0.318193\pi\) | |||||||
\(654\) | −3.34837 | − | 5.79955i | −0.130932 | − | 0.226781i | ||||
\(655\) | −1.61176 | − | 0.930547i | −0.0629765 | − | 0.0363595i | ||||
\(656\) | − | 12.1270i | − | 0.473482i | ||||||
\(657\) | 2.75318 | + | 1.58955i | 0.107412 | + | 0.0620142i | ||||
\(658\) | −28.5933 | − | 22.0148i | −1.11468 | − | 0.858228i | ||||
\(659\) | −8.15148 | + | 14.1188i | −0.317537 | + | 0.549989i | −0.979973 | − | 0.199128i | \(-0.936189\pi\) |
0.662437 | + | 0.749118i | \(0.269522\pi\) | |||||||
\(660\) | −3.66343 | + | 6.34525i | −0.142599 | + | 0.246988i | ||||
\(661\) | 48.0978i | 1.87079i | 0.353608 | + | 0.935394i | \(0.384955\pi\) | ||||
−0.353608 | + | 0.935394i | \(0.615045\pi\) | |||||||
\(662\) | −25.5385 | + | 44.2340i | −0.992582 | + | 1.71920i | ||||
\(663\) | 9.01212 | + | 4.54564i | 0.350002 | + | 0.176538i | ||||
\(664\) | 3.19338 | 0.123927 | ||||||||
\(665\) | −1.22080 | + | 9.15715i | −0.0473407 | + | 0.355099i | ||||
\(666\) | 10.8079 | + | 18.7198i | 0.418797 | + | 0.725378i | ||||
\(667\) | 28.2119 | 1.09237 | ||||||||
\(668\) | −40.1050 | − | 23.1546i | −1.55171 | − | 0.895880i | ||||
\(669\) | −15.9502 | + | 9.20887i | −0.616671 | + | 0.356035i | ||||
\(670\) | 17.8669i | 0.690259i | ||||||||
\(671\) | − | 9.33901i | − | 0.360528i | ||||||
\(672\) | −18.1677 | − | 2.42206i | −0.700833 | − | 0.0934328i | ||||
\(673\) | −22.0349 | − | 38.1655i | −0.849382 | − | 1.47117i | −0.881760 | − | 0.471698i | \(-0.843641\pi\) |
0.0323778 | − | 0.999476i | \(-0.489692\pi\) | |||||||
\(674\) | 58.3959 | + | 33.7149i | 2.24932 | + | 1.29865i | ||||
\(675\) | −2.17201 | + | 3.76204i | −0.0836008 | + | 0.144801i | ||||
\(676\) | 37.9732 | − | 4.30500i | 1.46051 | − | 0.165577i | ||||
\(677\) | −3.08805 | − | 5.34866i | −0.118684 | − | 0.205566i | 0.800563 | − | 0.599249i | \(-0.204534\pi\) |
−0.919246 | + | 0.393683i | \(0.871201\pi\) | |||||||
\(678\) | −5.26931 | + | 3.04224i | −0.202367 | + | 0.116836i | ||||
\(679\) | −12.8479 | − | 31.1617i | −0.493058 | − | 1.19588i | ||||
\(680\) | 2.36779 | − | 4.10114i | 0.0908007 | − | 0.157271i | ||||
\(681\) | 20.0696 | − | 11.5872i | 0.769067 | − | 0.444021i | ||||
\(682\) | 20.0587 | − | 11.5809i | 0.768089 | − | 0.443456i | ||||
\(683\) | −12.2977 | + | 7.10008i | −0.470558 | + | 0.271677i | −0.716473 | − | 0.697614i | \(-0.754245\pi\) |
0.245915 | + | 0.969291i | \(0.420912\pi\) | |||||||
\(684\) | 10.9757 | − | 6.33680i | 0.419665 | − | 0.242294i | ||||
\(685\) | 6.33520 | − | 10.9729i | 0.242056 | − | 0.419253i | ||||
\(686\) | 32.7787 | − | 24.8974i | 1.25150 | − | 0.950588i | ||||
\(687\) | 23.0419 | − | 13.3032i | 0.879103 | − | 0.507550i | ||||
\(688\) | 3.52775 | + | 6.11025i | 0.134494 | + | 0.232951i | ||||
\(689\) | 1.15394 | + | 20.4224i | 0.0439616 | + | 0.778031i | ||||
\(690\) | −4.45730 | + | 7.72026i | −0.169686 | + | 0.293905i | ||||
\(691\) | −0.336981 | − | 0.194556i | −0.0128193 | − | 0.00740126i | 0.493577 | − | 0.869702i | \(-0.335689\pi\) |
−0.506396 | + | 0.862301i | \(0.669023\pi\) | |||||||
\(692\) | 23.9723 | + | 41.5213i | 0.911291 | + | 1.57840i | ||||
\(693\) | 4.96692 | − | 6.45114i | 0.188678 | − | 0.245058i | ||||
\(694\) | 1.60020i | 0.0607426i | ||||||||
\(695\) | 18.2396i | 0.691868i | ||||||||
\(696\) | 10.3041 | − | 5.94910i | 0.390578 | − | 0.225500i | ||||
\(697\) | −23.7593 | − | 13.7174i | −0.899947 | − | 0.519585i | ||||
\(698\) | 39.6648 | 1.50134 | ||||||||
\(699\) | −10.9316 | − | 18.9341i | −0.413472 | − | 0.716155i | ||||
\(700\) | 26.7713 | + | 20.6120i | 1.01186 | + | 0.779060i | ||||
\(701\) | −3.60438 | −0.136135 | −0.0680677 | − | 0.997681i | \(-0.521683\pi\) | ||||
−0.0680677 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(702\) | −8.00076 | + | 0.452072i | −0.301969 | + | 0.0170624i | ||||
\(703\) | 20.9644 | − | 36.3114i | 0.790687 | − | 1.36951i | ||||
\(704\) | 39.7639i | 1.49866i | ||||||||
\(705\) | 2.48518 | − | 4.30446i | 0.0935973 | − | 0.162115i | ||||
\(706\) | 0.280244 | − | 0.485397i | 0.0105471 | − | 0.0182682i | ||||
\(707\) | 31.8135 | + | 24.4941i | 1.19647 | + | 0.921196i | ||||
\(708\) | −12.5661 | − | 7.25502i | −0.472262 | − | 0.272660i | ||||
\(709\) | 41.5509i | 1.56048i | 0.625483 | + | 0.780238i | \(0.284902\pi\) | ||||
−0.625483 | + | 0.780238i | \(0.715098\pi\) | |||||||
\(710\) | −14.1155 | − | 8.14962i | −0.529747 | − | 0.305850i | ||||
\(711\) | 1.13963 | + | 1.97390i | 0.0427396 | + | 0.0740272i | ||||
\(712\) | −3.46818 | + | 6.00707i | −0.129976 | + | 0.225124i | ||||
\(713\) | 14.5242 | − | 8.38554i | 0.543935 | − | 0.314041i | ||||
\(714\) | −10.0426 | + | 13.0436i | −0.375836 | + | 0.488143i | ||||
\(715\) | −8.02347 | − | 4.04698i | −0.300061 | − | 0.151348i | ||||
\(716\) | −29.9494 | − | 51.8739i | −1.11926 | − | 1.93862i | ||||
\(717\) | − | 22.4279i | − | 0.837585i | ||||||
\(718\) | 26.2759 | 0.980607 | ||||||||
\(719\) | 40.2967 | 1.50281 | 0.751407 | − | 0.659839i | \(-0.229376\pi\) | ||||
0.751407 | + | 0.659839i | \(0.229376\pi\) | |||||||
\(720\) | − | 1.00224i | − | 0.0373513i | ||||||
\(721\) | −2.80228 | + | 21.0197i | −0.104362 | + | 0.782814i | ||||
\(722\) | 0.796903 | + | 0.460092i | 0.0296577 | + | 0.0171229i | ||||
\(723\) | −1.37512 | + | 0.793924i | −0.0511411 | + | 0.0295263i | ||||
\(724\) | −32.5908 | − | 56.4489i | −1.21123 | − | 2.09791i | ||||
\(725\) | 24.7468 | 0.919074 | ||||||||
\(726\) | 2.94563 | + | 1.70066i | 0.109322 | + | 0.0631173i | ||||
\(727\) | −31.8052 | −1.17959 | −0.589796 | − | 0.807553i | \(-0.700792\pi\) | ||||
−0.589796 | + | 0.807553i | \(0.700792\pi\) | |||||||
\(728\) | −1.51458 | + | 19.8663i | −0.0561341 | + | 0.736293i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.95599 | + | 2.86134i | 0.183429 | + | 0.105903i | ||||
\(731\) | 15.9616 | 0.590360 | ||||||||
\(732\) | −4.46079 | − | 7.72631i | −0.164875 | − | 0.285573i | ||||
\(733\) | −13.1128 | + | 7.57067i | −0.484332 | + | 0.279629i | −0.722220 | − | 0.691664i | \(-0.756878\pi\) |
0.237888 | + | 0.971293i | \(0.423545\pi\) | |||||||
\(734\) | −27.3000 | − | 15.7616i | −1.00766 | − | 0.581773i | ||||
\(735\) | 3.99578 | + | 4.02201i | 0.147387 | + | 0.148354i | ||||
\(736\) | 34.3069i | 1.26457i | ||||||||
\(737\) | −30.5436 | −1.12509 | ||||||||
\(738\) | 21.7811 | 0.801772 | ||||||||
\(739\) | 23.6795i | 0.871066i | 0.900173 | + | 0.435533i | \(0.143440\pi\) | ||||
−0.900173 | + | 0.435533i | \(0.856560\pi\) | |||||||
\(740\) | 11.5782 | + | 20.0540i | 0.425623 | + | 0.737200i | ||||
\(741\) | 8.51907 | + | 13.0017i | 0.312956 | + | 0.477628i | ||||
\(742\) | −33.0676 | − | 4.40846i | −1.21395 | − | 0.161840i | ||||
\(743\) | 37.9709 | − | 21.9225i | 1.39302 | − | 0.804260i | 0.399370 | − | 0.916790i | \(-0.369229\pi\) |
0.993648 | + | 0.112530i | \(0.0358954\pi\) | |||||||
\(744\) | 3.53655 | − | 6.12548i | 0.129656 | − | 0.224571i | ||||
\(745\) | 5.48984 | + | 9.50869i | 0.201132 | + | 0.348371i | ||||
\(746\) | −19.1331 | − | 11.0465i | −0.700512 | − | 0.404441i | ||||
\(747\) | − | 1.52896i | − | 0.0559417i | ||||||
\(748\) | 21.9321 | + | 12.6625i | 0.801916 | + | 0.462987i | ||||
\(749\) | −23.9378 | + | 9.86953i | −0.874669 | + | 0.360625i | ||||
\(750\) | −8.41007 | + | 14.5667i | −0.307092 | + | 0.531899i | ||||
\(751\) | −7.54542 | + | 13.0690i | −0.275336 | + | 0.476896i | −0.970220 | − | 0.242226i | \(-0.922123\pi\) |
0.694884 | + | 0.719122i | \(0.255456\pi\) | |||||||
\(752\) | − | 7.59401i | − | 0.276925i | ||||||
\(753\) | 0.177730 | − | 0.307837i | 0.00647683 | − | 0.0112182i | ||||
\(754\) | 25.0195 | + | 38.1843i | 0.911155 | + | 1.39059i | ||||
\(755\) | −6.79029 | −0.247124 | ||||||||
\(756\) | 1.02782 | − | 7.70958i | 0.0373813 | − | 0.280395i | ||||
\(757\) | −8.25531 | − | 14.2986i | −0.300044 | − | 0.519692i | 0.676101 | − | 0.736809i | \(-0.263668\pi\) |
−0.976146 | + | 0.217117i | \(0.930335\pi\) | |||||||
\(758\) | 20.3178 | 0.737975 | ||||||||
\(759\) | −13.1978 | − | 7.61978i | −0.479051 | − | 0.276580i | ||||
\(760\) | 6.31570 | − | 3.64637i | 0.229095 | − | 0.132268i | ||||
\(761\) | − | 20.3189i | − | 0.736560i | −0.929715 | − | 0.368280i | \(-0.879947\pi\) | ||
0.929715 | − | 0.368280i | \(-0.120053\pi\) | |||||||
\(762\) | 32.8722i | 1.19083i | ||||||||
\(763\) | 3.03866 | + | 7.37005i | 0.110007 | + | 0.266814i | ||||
\(764\) | 31.8740 | + | 55.2074i | 1.15316 | + | 1.99733i | ||||
\(765\) | −1.96359 | − | 1.13368i | −0.0709936 | − | 0.0409882i | ||||
\(766\) | −26.3471 | + | 45.6345i | −0.951959 | + | 1.64884i | ||||
\(767\) | 8.01459 | − | 15.8896i | 0.289390 | − | 0.573740i | ||||
\(768\) | 3.59659 | + | 6.22948i | 0.129781 | + | 0.224787i | ||||
\(769\) | −29.3351 | + | 16.9366i | −1.05785 | + | 0.610750i | −0.924837 | − | 0.380364i | \(-0.875799\pi\) |
−0.133013 | + | 0.991114i | \(0.542465\pi\) | |||||||
\(770\) | 8.94093 | − | 11.6127i | 0.322209 | − | 0.418491i | ||||
\(771\) | 2.60424 | − | 4.51067i | 0.0937894 | − | 0.162448i | ||||
\(772\) | −0.128785 | + | 0.0743542i | −0.00463508 | + | 0.00267607i | ||||
\(773\) | 11.7224 | − | 6.76796i | 0.421627 | − | 0.243426i | −0.274146 | − | 0.961688i | \(-0.588395\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(774\) | −10.9745 | + | 6.33610i | −0.394468 | + | 0.227746i | ||||
\(775\) | 12.7402 | − | 7.35558i | 0.457643 | − | 0.264220i | ||||
\(776\) | −13.3042 | + | 23.0435i | −0.477591 | + | 0.827212i | ||||
\(777\) | −9.80820 | − | 23.7891i | −0.351867 | − | 0.853428i | ||||
\(778\) | −39.5220 | + | 22.8180i | −1.41693 | + | 0.818065i | ||||
\(779\) | −21.1247 | − | 36.5890i | −0.756870 | − | 1.31094i | ||||
\(780\) | −8.57099 | + | 0.484292i | −0.306891 | + | 0.0173404i | ||||
\(781\) | 13.9318 | − | 24.1306i | 0.498520 | − | 0.863462i | ||||
\(782\) | 26.6848 | + | 15.4065i | 0.954245 | + | 0.550934i | ||||
\(783\) | −2.84837 | − | 4.93353i | −0.101793 | − | 0.176310i | ||||
\(784\) | 8.35962 | + | 2.26929i | 0.298558 | + | 0.0810460i | ||||
\(785\) | 2.49223i | 0.0889515i | ||||||||
\(786\) | − | 5.10712i | − | 0.182165i | ||||||
\(787\) | 39.6850 | − | 22.9121i | 1.41462 | − | 0.816729i | 0.418797 | − | 0.908080i | \(-0.362452\pi\) |
0.995819 | + | 0.0913511i | \(0.0291186\pi\) | |||||||
\(788\) | 45.5230 | + | 26.2827i | 1.62169 | + | 0.936282i | ||||
\(789\) | −21.2763 | −0.757455 | ||||||||
\(790\) | 2.05145 | + | 3.55322i | 0.0729873 | + | 0.126418i | ||||
\(791\) | 6.69622 | − | 2.76084i | 0.238090 | − | 0.0981642i | ||||
\(792\) | −6.42719 | −0.228380 | ||||||||
\(793\) | 9.15251 | − | 5.99699i | 0.325015 | − | 0.212959i | ||||
\(794\) | 29.5507 | − | 51.1834i | 1.04872 | − | 1.81643i | ||||
\(795\) | − | 4.59485i | − | 0.162962i | ||||||
\(796\) | 23.7664 | − | 41.1646i | 0.842378 | − | 1.45904i | ||||
\(797\) | −4.79076 | + | 8.29783i | −0.169697 | + | 0.293924i | −0.938313 | − | 0.345786i | \(-0.887612\pi\) |
0.768616 | + | 0.639710i | \(0.220946\pi\) | |||||||
\(798\) | −23.4370 | + | 9.66305i | −0.829661 | + | 0.342068i | ||||
\(799\) | −14.8782 | − | 8.58992i | −0.526352 | − | 0.303889i | ||||
\(800\) | 30.0932i | 1.06395i | ||||||||
\(801\) | 2.87613 | + | 1.66053i | 0.101623 | + | 0.0586720i | ||||
\(802\) | −27.4228 | − | 47.4977i | −0.968334 | − | 1.67720i | ||||
\(803\) | −4.89148 | + | 8.47230i | −0.172617 | + | 0.298981i | ||||
\(804\) | −25.2692 | + | 14.5892i | −0.891177 | + | 0.514521i | ||||
\(805\) | 6.47396 | − | 8.40852i | 0.228177 | − | 0.296361i | ||||
\(806\) | 24.2303 | + | 12.2216i | 0.853475 | + | 0.430486i | ||||
\(807\) | −1.90086 | − | 3.29238i | −0.0669133 | − | 0.115897i | ||||
\(808\) | − | 31.6954i | − | 1.11504i | ||||||
\(809\) | 49.9290 | 1.75541 | 0.877705 | − | 0.479202i | \(-0.159074\pi\) | ||||
0.877705 | + | 0.479202i | \(0.159074\pi\) | |||||||
\(810\) | 1.80010 | 0.0632489 | ||||||||
\(811\) | − | 12.4298i | − | 0.436470i | −0.975896 | − | 0.218235i | \(-0.929970\pi\) | ||
0.975896 | − | 0.218235i | \(-0.0700299\pi\) | |||||||
\(812\) | −40.9631 | + | 16.8890i | −1.43752 | + | 0.592688i | ||||
\(813\) | −22.5990 | − | 13.0475i | −0.792581 | − | 0.457597i | ||||
\(814\) | −57.6061 | + | 33.2589i | −2.01909 | + | 1.16572i | ||||
\(815\) | −2.49010 | − | 4.31297i | −0.0872243 | − | 0.151077i | ||||
\(816\) | −3.46420 | −0.121271 | ||||||||
\(817\) | 21.2875 | + | 12.2903i | 0.744754 | + | 0.429984i | ||||
\(818\) | −80.3322 | −2.80875 | ||||||||
\(819\) | 9.51179 | + | 0.725168i | 0.332369 | + | 0.0253394i | ||||
\(820\) | 23.3334 | 0.814839 | ||||||||
\(821\) | −21.3546 | − | 12.3291i | −0.745280 | − | 0.430288i | 0.0787058 | − | 0.996898i | \(-0.474921\pi\) |
−0.823986 | + | 0.566610i | \(0.808255\pi\) | |||||||
\(822\) | 34.7695 | 1.21272 | ||||||||
\(823\) | −1.24407 | − | 2.15479i | −0.0433655 | − | 0.0751113i | 0.843528 | − | 0.537085i | \(-0.180475\pi\) |
−0.886893 | + | 0.461974i | \(0.847141\pi\) | |||||||
\(824\) | 14.4973 | − | 8.37003i | 0.505038 | − | 0.291584i | ||||
\(825\) | −11.5768 | − | 6.68388i | −0.403053 | − | 0.232703i | ||||
\(826\) | 22.9976 | + | 17.7065i | 0.800189 | + | 0.616089i | ||||
\(827\) | 5.29835i | 0.184242i | 0.995748 | + | 0.0921208i | \(0.0293646\pi\) | ||||
−0.995748 | + | 0.0921208i | \(0.970635\pi\) | |||||||
\(828\) | −14.5584 | −0.505939 | ||||||||
\(829\) | −15.1316 | −0.525542 | −0.262771 | − | 0.964858i | \(-0.584636\pi\) | ||||
−0.262771 | + | 0.964858i | \(0.584636\pi\) | |||||||
\(830\) | − | 2.75228i | − | 0.0955329i | ||||||
\(831\) | −14.3426 | − | 24.8421i | −0.497539 | − | 0.861762i | ||||
\(832\) | −38.9698 | + | 25.5342i | −1.35104 | + | 0.885238i | ||||
\(833\) | 13.9019 | − | 13.8112i | 0.481672 | − | 0.478531i | ||||
\(834\) | −43.3465 | + | 25.0261i | −1.50097 | + | 0.866583i | ||||
\(835\) | −6.37933 | + | 11.0493i | −0.220766 | + | 0.382377i | ||||
\(836\) | 19.5001 | + | 33.7751i | 0.674425 | + | 1.16814i | ||||
\(837\) | −2.93282 | − | 1.69327i | −0.101373 | − | 0.0585278i | ||||
\(838\) | 5.88582i | 0.203322i | ||||||||
\(839\) | −31.1992 | − | 18.0129i | −1.07712 | − | 0.621874i | −0.147000 | − | 0.989136i | \(-0.546962\pi\) |
−0.930117 | + | 0.367262i | \(0.880295\pi\) | |||||||
\(840\) | 0.591435 | − | 4.43631i | 0.0204064 | − | 0.153067i | ||||
\(841\) | −1.72648 | + | 2.99034i | −0.0595336 | + | 0.103115i | ||||
\(842\) | −5.02096 | + | 8.69655i | −0.173034 | + | 0.299703i | ||||
\(843\) | 0.959007i | 0.0330300i | ||||||||
\(844\) | 7.90896 | − | 13.6987i | 0.272238 | − | 0.471529i | ||||
\(845\) | −1.18607 | − | 10.4620i | −0.0408020 | − | 0.359903i | ||||
\(846\) | 13.6394 | 0.468932 | ||||||||
\(847\) | −3.20823 | − | 2.47011i | −0.110236 | − | 0.0848739i | ||||
\(848\) | −3.51014 | − | 6.07975i | −0.120539 | − | 0.208779i | ||||
\(849\) | −2.25973 | −0.0775537 | ||||||||
\(850\) | 23.4072 | + | 13.5142i | 0.802861 | + | 0.463532i | ||||
\(851\) | −41.7115 | + | 24.0821i | −1.42985 | + | 0.825525i | ||||
\(852\) | − | 26.6182i | − | 0.911925i | ||||||
\(853\) | 32.0255i | 1.09653i | 0.836304 | + | 0.548266i | \(0.184712\pi\) | ||||
−0.836304 | + | 0.548266i | \(0.815288\pi\) | |||||||
\(854\) | 6.80229 | + | 16.4985i | 0.232770 | + | 0.564566i | ||||
\(855\) | −1.74585 | − | 3.02390i | −0.0597068 | − | 0.103415i | ||||
\(856\) | 17.7016 | + | 10.2200i | 0.605027 | + | 0.349313i | ||||
\(857\) | 4.19647 | − | 7.26850i | 0.143349 | − | 0.248287i | −0.785407 | − | 0.618980i | \(-0.787546\pi\) |
0.928756 | + | 0.370693i | \(0.120880\pi\) | |||||||
\(858\) | −1.39115 | − | 24.6205i | −0.0474931 | − | 0.840532i | ||||
\(859\) | 8.88475 | + | 15.3888i | 0.303144 | + | 0.525060i | 0.976846 | − | 0.213942i | \(-0.0686304\pi\) |
−0.673703 | + | 0.739003i | \(0.735297\pi\) | |||||||
\(860\) | −11.7566 | + | 6.78769i | −0.400897 | + | 0.231458i | ||||
\(861\) | −25.7011 | − | 3.42638i | −0.875890 | − | 0.116771i | ||||
\(862\) | 15.2220 | − | 26.3653i | 0.518464 | − | 0.898007i | ||||
\(863\) | −1.15148 | + | 0.664805i | −0.0391967 | + | 0.0226302i | −0.519470 | − | 0.854489i | \(-0.673871\pi\) |
0.480274 | + | 0.877119i | \(0.340537\pi\) | |||||||
\(864\) | 5.99938 | − | 3.46374i | 0.204103 | − | 0.117839i | ||||
\(865\) | 11.4395 | − | 6.60461i | 0.388955 | − | 0.224563i | ||||
\(866\) | −42.8795 | + | 24.7565i | −1.45710 | + | 0.841260i | ||||
\(867\) | 4.58149 | − | 7.93538i | 0.155596 | − | 0.269500i | ||||
\(868\) | −16.0688 | + | 20.8705i | −0.545410 | + | 0.708390i | ||||
\(869\) | −6.07425 | + | 3.50697i | −0.206055 | + | 0.118966i | ||||
\(870\) | −5.12735 | − | 8.88082i | −0.173833 | − | 0.301088i | ||||
\(871\) | −19.6134 | − | 29.9337i | −0.664576 | − | 1.01426i | ||||
\(872\) | 3.14657 | − | 5.45001i | 0.106556 | − | 0.184561i | ||||
\(873\) | 11.0330 | + | 6.36990i | 0.373410 | + | 0.215589i | ||||
\(874\) | 23.7258 | + | 41.0942i | 0.802536 | + | 1.39003i | ||||
\(875\) | 12.2151 | − | 15.8653i | 0.412947 | − | 0.536344i | ||||
\(876\) | 9.34569i | 0.315762i | ||||||||
\(877\) | − | 52.9883i | − | 1.78929i | −0.446778 | − | 0.894645i | \(-0.647429\pi\) | ||
0.446778 | − | 0.894645i | \(-0.352571\pi\) | |||||||
\(878\) | −41.3035 | + | 23.8466i | −1.39393 | + | 0.804784i | ||||
\(879\) | 4.64615 | + | 2.68246i | 0.156711 | + | 0.0904770i | ||||
\(880\) | 3.08417 | 0.103967 | ||||||||
\(881\) | −18.3266 | − | 31.7426i | −0.617439 | − | 1.06944i | −0.989951 | − | 0.141408i | \(-0.954837\pi\) |
0.372512 | − | 0.928027i | \(-0.378496\pi\) | |||||||
\(882\) | −4.07581 | + | 15.0145i | −0.137239 | + | 0.505564i | ||||
\(883\) | 45.3649 | 1.52665 | 0.763324 | − | 0.646015i | \(-0.223566\pi\) | ||||
0.763324 | + | 0.646015i | \(0.223566\pi\) | |||||||
\(884\) | 1.67394 | + | 29.6253i | 0.0563006 | + | 0.996405i | ||||
\(885\) | −1.99883 | + | 3.46207i | −0.0671899 | + | 0.116376i | ||||
\(886\) | 15.2781i | 0.513278i | ||||||||
\(887\) | −14.9103 | + | 25.8254i | −0.500639 | + | 0.867132i | 0.499361 | + | 0.866394i | \(0.333568\pi\) |
−1.00000 | 0.000738181i | \(0.999765\pi\) | ||||||||
\(888\) | −10.1565 | + | 17.5916i | −0.340830 | + | 0.590334i | ||||
\(889\) | 5.17113 | − | 38.7883i | 0.173434 | − | 1.30092i | ||||
\(890\) | 5.17730 | + | 2.98912i | 0.173544 | + | 0.100195i | ||||
\(891\) | 3.07728i | 0.103093i | ||||||||
\(892\) | −46.8893 | − | 27.0716i | −1.56997 | − | 0.906423i | ||||
\(893\) | −13.2284 | − | 22.9122i | −0.442671 | − | 0.766728i | ||||
\(894\) | −15.0649 | + | 26.0933i | −0.503847 | + | 0.872689i | ||||
\(895\) | −14.2918 | + | 8.25136i | −0.477721 | + | 0.275812i | ||||
\(896\) | −14.9905 | − | 36.3583i | −0.500797 | − | 1.21465i | ||||
\(897\) | −1.00731 | − | 17.8273i | −0.0336330 | − | 0.595236i | ||||
\(898\) | −32.8024 | − | 56.8154i | −1.09463 | − | 1.89595i | ||||
\(899\) | 19.2922i | 0.643431i | ||||||||
\(900\) | −12.7703 | −0.425675 | ||||||||
\(901\) | −15.8819 | −0.529103 | ||||||||
\(902\) | 67.0264i | 2.23173i | ||||||||
\(903\) | 13.9463 | − | 5.75003i | 0.464103 | − | 0.191349i | ||||
\(904\) | −4.95173 | − | 2.85888i | −0.164692 | − | 0.0950849i | ||||
\(905\) | −15.5522 | + | 8.97907i | −0.516973 | + | 0.298474i | ||||
\(906\) | −9.31678 | − | 16.1371i | −0.309529 | − | 0.536121i | ||||
\(907\) | 49.4066 | 1.64052 | 0.820259 | − | 0.571993i | \(-0.193829\pi\) | ||||
0.820259 | + | 0.571993i | \(0.193829\pi\) | |||||||
\(908\) | 58.9991 | + | 34.0631i | 1.95795 | + | 1.13042i | ||||
\(909\) | −15.1754 | −0.503338 | ||||||||
\(910\) | 17.1221 | + | 1.30537i | 0.567593 | + | 0.0432726i | ||||
\(911\) | −22.3495 | −0.740471 | −0.370235 | − | 0.928938i | \(-0.620723\pi\) | ||||
−0.370235 | + | 0.928938i | \(0.620723\pi\) | |||||||
\(912\) | −4.62010 | − | 2.66741i | −0.152987 | − | 0.0883269i | ||||
\(913\) | 4.70504 | 0.155714 | ||||||||
\(914\) | 16.5533 | + | 28.6711i | 0.547534 | + | 0.948357i | ||||
\(915\) | −2.12867 | + | 1.22899i | −0.0703717 | + | 0.0406291i | ||||
\(916\) | 67.7369 | + | 39.1079i | 2.23809 | + | 1.29216i | ||||
\(917\) | −0.803402 | + | 6.02626i | −0.0265307 | + | 0.199005i | ||||
\(918\) | − | 6.22195i | − | 0.205355i | ||||||
\(919\) | 35.0529 | 1.15629 | 0.578144 | − | 0.815935i | \(-0.303777\pi\) | ||||
0.578144 | + | 0.815935i | \(0.303777\pi\) | |||||||
\(920\) | −8.37730 | −0.276191 | ||||||||
\(921\) | − | 1.80266i | − | 0.0593996i | ||||||
\(922\) | 27.8160 | + | 48.1787i | 0.916071 | + | 1.58668i | ||||
\(923\) | 32.5950 | − | 1.84174i | 1.07288 | − | 0.0606215i | ||||
\(924\) | 23.7245 | + | 3.16288i | 0.780479 | + | 0.104051i | ||||
\(925\) | −36.5883 | + | 21.1243i | −1.20302 | + | 0.694561i | ||||
\(926\) | 38.1039 | − | 65.9980i | 1.25217 | − | 2.16883i | ||||
\(927\) | −4.00749 | − | 6.94118i | −0.131623 | − | 0.227978i | ||||
\(928\) | −34.1770 | − | 19.7321i | −1.12191 | − | 0.647737i | ||||
\(929\) | − | 54.5442i | − | 1.78954i | −0.446530 | − | 0.894768i | \(-0.647341\pi\) | ||
0.446530 | − | 0.894768i | \(-0.352659\pi\) | |||||||
\(930\) | −5.27936 | − | 3.04804i | −0.173117 | − | 0.0999491i | ||||
\(931\) | 29.1751 | − | 7.71525i | 0.956176 | − | 0.252857i | ||||
\(932\) | 32.1360 | − | 55.6612i | 1.05265 | − | 1.82324i | ||||
\(933\) | −9.77057 | + | 16.9231i | −0.319874 | + | 0.554038i | ||||
\(934\) | 6.50288i | 0.212781i | ||||||||
\(935\) | 3.48864 | − | 6.04250i | 0.114091 | − | 0.197611i | ||||
\(936\) | −4.12718 | − | 6.29884i | −0.134901 | − | 0.205884i | ||||
\(937\) | −4.92743 | −0.160972 | −0.0804861 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804861 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(938\) | 53.9590 | − | 22.2472i | 1.76182 | − | 0.726397i | ||||
\(939\) | 15.4409 | + | 26.7444i | 0.503894 | + | 0.872770i | ||||
\(940\) | 14.6115 | 0.476575 | ||||||||
\(941\) | 21.0883 | + | 12.1753i | 0.687459 | + | 0.396905i | 0.802659 | − | 0.596438i | \(-0.203418\pi\) |
−0.115201 | + | 0.993342i | \(0.536751\pi\) | |||||||
\(942\) | −5.92279 | + | 3.41952i | −0.192975 | + | 0.111414i | ||||
\(943\) | 48.5326i | 1.58044i | ||||||||
\(944\) | 6.10786i | 0.198794i | ||||||||
\(945\) | −2.12406 | − | 0.283173i | −0.0690958 | − | 0.00921163i | ||||
\(946\) | −19.4979 | − | 33.7714i | −0.633933 | − | 1.09800i | ||||
\(947\) | 21.3651 | + | 12.3351i | 0.694271 | + | 0.400838i | 0.805210 | − | 0.592990i | \(-0.202053\pi\) |
−0.110939 | + | 0.993827i | \(0.535386\pi\) | |||||||
\(948\) | −3.35021 | + | 5.80274i | −0.108810 | + | 0.188464i | ||||
\(949\) | −11.4441 | + | 0.646636i | −0.371493 | + | 0.0209907i | ||||
\(950\) | 20.8116 | + | 36.0468i | 0.675219 | + | 1.16951i | ||||
\(951\) | 16.1874 | − | 9.34578i | 0.524911 | − | 0.303058i | ||||
\(952\) | −15.3339 | − | 2.04427i | −0.496975 | − | 0.0662551i | ||||
\(953\) | 3.31494 | − | 5.74164i | 0.107381 | − | 0.185990i | −0.807327 | − | 0.590104i | \(-0.799087\pi\) |
0.914709 | + | 0.404114i | \(0.132420\pi\) | |||||||
\(954\) | 10.9197 | − | 6.30447i | 0.353537 | − | 0.204115i | ||||
\(955\) | 15.2102 | − | 8.78160i | 0.492190 | − | 0.284166i | ||||
\(956\) | 57.0987 | − | 32.9660i | 1.84670 | − | 1.06620i | ||||
\(957\) | 15.1818 | − | 8.76524i | 0.490759 | − | 0.283340i | ||||
\(958\) | 37.0220 | − | 64.1241i | 1.19613 | − | 2.07175i | ||||
\(959\) | −41.0270 | − | 5.46959i | −1.32483 | − | 0.176622i | ||||
\(960\) | 9.06353 | − | 5.23283i | 0.292524 | − | 0.168889i | ||||
\(961\) | −9.76571 | − | 16.9147i | −0.315023 | − | 0.545635i | ||||
\(962\) | −69.5861 | − | 35.0987i | −2.24355 | − | 1.13163i | ||||
\(963\) | 4.89324 | − | 8.47534i | 0.157683 | − | 0.273114i | ||||
\(964\) | −4.04247 | − | 2.33392i | −0.130199 | − | 0.0751705i | ||||
\(965\) | 0.0204853 | + | 0.0354816i | 0.000659445 | + | 0.00114219i | ||||
\(966\) | 28.8656 | + | 3.84827i | 0.928736 | + | 0.123816i | ||||
\(967\) | 47.9993i | 1.54355i | 0.635893 | + | 0.771777i | \(0.280632\pi\) | ||||
−0.635893 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(968\) | 3.19632i | 0.102733i | ||||||||
\(969\) | −10.4520 | + | 6.03445i | −0.335766 | + | 0.193855i | ||||
\(970\) | 19.8604 | + | 11.4664i | 0.637681 | + | 0.368165i | ||||
\(971\) | 37.8183 | 1.21365 | 0.606824 | − | 0.794836i | \(-0.292443\pi\) | ||||
0.606824 | + | 0.794836i | \(0.292443\pi\) | |||||||
\(972\) | 1.46986 | + | 2.54588i | 0.0471459 | + | 0.0816591i | ||||
\(973\) | 55.0845 | − | 22.7113i | 1.76593 | − | 0.728090i | ||||
\(974\) | −33.3236 | −1.06776 | ||||||||
\(975\) | −0.883585 | − | 15.6377i | −0.0282974 | − | 0.500806i | ||||
\(976\) | −1.87772 | + | 3.25231i | −0.0601045 | + | 0.104104i | ||||
\(977\) | − | 28.5939i | − | 0.914801i | −0.889261 | − | 0.457400i | \(-0.848781\pi\) | ||
0.889261 | − | 0.457400i | \(-0.151219\pi\) | |||||||
\(978\) | 6.83320 | − | 11.8354i | 0.218502 | − | 0.378456i | ||||
\(979\) | −5.10992 | + | 8.85064i | −0.163314 | + | 0.282868i | ||||
\(980\) | −4.36630 | + | 16.0846i | −0.139476 | + | 0.513803i | ||||
\(981\) | −2.60941 | − | 1.50655i | −0.0833122 | − | 0.0481003i | ||||
\(982\) | 90.5185i | 2.88856i | ||||||||
\(983\) | −2.49292 | − | 1.43929i | −0.0795118 | − | 0.0459061i | 0.459717 | − | 0.888065i | \(-0.347951\pi\) |
−0.539229 | + | 0.842159i | \(0.681284\pi\) | |||||||
\(984\) | 10.2342 | + | 17.7261i | 0.326253 | + | 0.565086i | ||||
\(985\) | 7.24113 | − | 12.5420i | 0.230722 | − | 0.399622i | ||||
\(986\) | −30.6962 | + | 17.7225i | −0.977566 | + | 0.564398i | ||||
\(987\) | −16.0941 | − | 2.14562i | −0.512281 | − | 0.0682957i | ||||
\(988\) | −20.5788 | + | 40.7992i | −0.654699 | + | 1.29800i | ||||
\(989\) | −14.1181 | − | 24.4533i | −0.448930 | − | 0.777569i | ||||
\(990\) | 5.53939i | 0.176053i | ||||||||
\(991\) | 20.7810 | 0.660130 | 0.330065 | − | 0.943958i | \(-0.392929\pi\) | ||||
0.330065 | + | 0.943958i | \(0.392929\pi\) | |||||||
\(992\) | −23.4601 | −0.744860 | ||||||||
\(993\) | 22.9813i | 0.729289i | ||||||||
\(994\) | −7.03609 | + | 52.7772i | −0.223171 | + | 1.67399i | ||||
\(995\) | −11.3412 | − | 6.54787i | −0.359542 | − | 0.207582i | ||||
\(996\) | 3.89255 | − | 2.24737i | 0.123340 | − | 0.0712105i | ||||
\(997\) | 20.5619 | + | 35.6143i | 0.651202 | + | 1.12792i | 0.982831 | + | 0.184506i | \(0.0590685\pi\) |
−0.331629 | + | 0.943410i | \(0.607598\pi\) | |||||||
\(998\) | −2.42786 | −0.0768525 | ||||||||
\(999\) | 8.42267 | + | 4.86283i | 0.266482 | + | 0.153853i |
(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 | 273.2.bl.c.88.6 | yes | 12 | |
3.2 | odd | 2 | 819.2.do.f.361.1 | 12 | |||
7.2 | even | 3 | 273.2.t.c.205.1 | yes | 12 | ||
13.4 | even | 6 | 273.2.t.c.4.6 | ✓ | 12 | ||
21.2 | odd | 6 | 819.2.bm.e.478.6 | 12 | |||
39.17 | odd | 6 | 819.2.bm.e.550.1 | 12 | |||
91.30 | even | 6 | inner | 273.2.bl.c.121.6 | yes | 12 | |
273.212 | odd | 6 | 819.2.do.f.667.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.c.4.6 | ✓ | 12 | 13.4 | even | 6 | ||
273.2.t.c.205.1 | yes | 12 | 7.2 | even | 3 | ||
273.2.bl.c.88.6 | yes | 12 | 1.1 | even | 1 | trivial | |
273.2.bl.c.121.6 | yes | 12 | 91.30 | even | 6 | inner | |
819.2.bm.e.478.6 | 12 | 21.2 | odd | 6 | |||
819.2.bm.e.550.1 | 12 | 39.17 | odd | 6 | |||
819.2.do.f.361.1 | 12 | 3.2 | odd | 2 | |||
819.2.do.f.667.1 | 12 | 273.212 | odd | 6 |