Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), degree \(4\), 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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} - 8420 x^{7} + 13485 x^{6} - 14630 x^{5} + 11615 x^{4} - 5200 x^{3} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.4 | ||
Root | \(-0.619365 + 1.90621i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.k.631.4 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0.619365 | + | 1.90621i | 0.357590 | + | 1.10055i | 0.954492 | + | 0.298236i | \(0.0963981\pi\) |
−0.596902 | + | 0.802314i | \(0.703602\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | −1.62152 | − | 1.17810i | −0.661982 | − | 0.480958i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | −0.822965 | + | 0.597919i | −0.274322 | + | 0.199306i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.948835 | + | 3.17800i | −0.286084 | + | 0.958204i | ||||
\(12\) | 2.00431 | 0.578593 | ||||||||
\(13\) | 3.25978 | − | 2.36837i | 0.904099 | − | 0.656866i | −0.0354166 | − | 0.999373i | \(-0.511276\pi\) |
0.939516 | + | 0.342506i | \(0.111276\pi\) | |||||||
\(14\) | −0.309017 | − | 0.951057i | −0.0825883 | − | 0.254181i | ||||
\(15\) | −0.619365 | + | 1.90621i | −0.159919 | + | 0.492181i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −0.243163 | − | 0.176668i | −0.0589757 | − | 0.0428483i | 0.557907 | − | 0.829904i | \(-0.311605\pi\) |
−0.616883 | + | 0.787055i | \(0.711605\pi\) | |||||||
\(18\) | 0.314345 | − | 0.967454i | 0.0740918 | − | 0.228031i | ||||
\(19\) | 2.39034 | + | 7.35672i | 0.548382 | + | 1.68775i | 0.712810 | + | 0.701358i | \(0.247422\pi\) |
−0.164427 | + | 0.986389i | \(0.552578\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | −2.00431 | −0.437375 | ||||||||
\(22\) | −1.10036 | − | 3.12877i | −0.234598 | − | 0.667056i | ||||
\(23\) | −6.48607 | −1.35244 | −0.676219 | − | 0.736700i | \(-0.736383\pi\) | ||||
−0.676219 | + | 0.736700i | \(0.736383\pi\) | |||||||
\(24\) | −1.62152 | + | 1.17810i | −0.330991 | + | 0.240479i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −1.24512 | + | 3.83210i | −0.244189 | + | 0.751536i | ||||
\(27\) | 3.21508 | + | 2.33589i | 0.618742 | + | 0.449542i | ||||
\(28\) | 0.809017 | + | 0.587785i | 0.152890 | + | 0.111081i | ||||
\(29\) | 0.561399 | − | 1.72781i | 0.104249 | − | 0.320846i | −0.885304 | − | 0.465012i | \(-0.846050\pi\) |
0.989554 | + | 0.144166i | \(0.0460500\pi\) | |||||||
\(30\) | −0.619365 | − | 1.90621i | −0.113080 | − | 0.348024i | ||||
\(31\) | −6.09578 | + | 4.42884i | −1.09483 | + | 0.795443i | −0.980209 | − | 0.197965i | \(-0.936567\pi\) |
−0.114625 | + | 0.993409i | \(0.536567\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.64561 | + | 0.159667i | −1.15685 | + | 0.0277944i | ||||
\(34\) | 0.300566 | 0.0515466 | ||||||||
\(35\) | −0.809017 | + | 0.587785i | −0.136749 | + | 0.0993538i | ||||
\(36\) | 0.314345 | + | 0.967454i | 0.0523908 | + | 0.161242i | ||||
\(37\) | 2.81579 | − | 8.66612i | 0.462914 | − | 1.42470i | −0.398674 | − | 0.917093i | \(-0.630530\pi\) |
0.861588 | − | 0.507609i | \(-0.169470\pi\) | |||||||
\(38\) | −6.25800 | − | 4.54670i | −1.01518 | − | 0.737572i | ||||
\(39\) | 6.53359 | + | 4.74693i | 1.04621 | + | 0.760117i | ||||
\(40\) | −0.309017 | + | 0.951057i | −0.0488599 | + | 0.150375i | ||||
\(41\) | 2.99230 | + | 9.20937i | 0.467319 | + | 1.43826i | 0.856042 | + | 0.516906i | \(0.172917\pi\) |
−0.388722 | + | 0.921355i | \(0.627083\pi\) | |||||||
\(42\) | 1.62152 | − | 1.17810i | 0.250206 | − | 0.181785i | ||||
\(43\) | 3.42569 | 0.522412 | 0.261206 | − | 0.965283i | \(-0.415880\pi\) | ||||
0.261206 | + | 0.965283i | \(0.415880\pi\) | |||||||
\(44\) | 2.72926 | + | 1.88445i | 0.411451 | + | 0.284092i | ||||
\(45\) | −1.01724 | −0.151641 | ||||||||
\(46\) | 5.24734 | − | 3.81242i | 0.773678 | − | 0.562110i | ||||
\(47\) | −1.91962 | − | 5.90798i | −0.280005 | − | 0.861767i | −0.987851 | − | 0.155401i | \(-0.950333\pi\) |
0.707846 | − | 0.706367i | \(-0.249667\pi\) | |||||||
\(48\) | 0.619365 | − | 1.90621i | 0.0893976 | − | 0.275137i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −0.809017 | − | 0.587785i | −0.114412 | − | 0.0831254i | ||||
\(51\) | 0.186160 | − | 0.572941i | 0.0260676 | − | 0.0802278i | ||||
\(52\) | −1.24512 | − | 3.83210i | −0.172668 | − | 0.531416i | ||||
\(53\) | −5.17368 | + | 3.75890i | −0.710659 | + | 0.516324i | −0.883386 | − | 0.468646i | \(-0.844742\pi\) |
0.172727 | + | 0.984970i | \(0.444742\pi\) | |||||||
\(54\) | −3.97405 | −0.540800 | ||||||||
\(55\) | −2.63561 | + | 2.01335i | −0.355385 | + | 0.271480i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −12.5429 | + | 9.11298i | −1.66135 | + | 1.20704i | ||||
\(58\) | 0.561399 | + | 1.72781i | 0.0737153 | + | 0.226872i | ||||
\(59\) | 1.70560 | − | 5.24931i | 0.222051 | − | 0.683402i | −0.776527 | − | 0.630084i | \(-0.783020\pi\) |
0.998578 | − | 0.0533176i | \(-0.0169796\pi\) | |||||||
\(60\) | 1.62152 | + | 1.17810i | 0.209337 | + | 0.152092i | ||||
\(61\) | 2.93547 | + | 2.13274i | 0.375848 | + | 0.273070i | 0.759632 | − | 0.650353i | \(-0.225379\pi\) |
−0.383784 | + | 0.923423i | \(0.625379\pi\) | |||||||
\(62\) | 2.32838 | − | 7.16602i | 0.295705 | − | 0.910085i | ||||
\(63\) | −0.314345 | − | 0.967454i | −0.0396037 | − | 0.121888i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 4.02930 | 0.499774 | ||||||||
\(66\) | 5.28256 | − | 4.03537i | 0.650239 | − | 0.496719i | ||||
\(67\) | 0.505448 | 0.0617503 | 0.0308751 | − | 0.999523i | \(-0.490171\pi\) | ||||
0.0308751 | + | 0.999523i | \(0.490171\pi\) | |||||||
\(68\) | −0.243163 | + | 0.176668i | −0.0294878 | + | 0.0214242i | ||||
\(69\) | −4.01724 | − | 12.3638i | −0.483619 | − | 1.48843i | ||||
\(70\) | 0.309017 | − | 0.951057i | 0.0369346 | − | 0.113673i | ||||
\(71\) | −6.77887 | − | 4.92514i | −0.804504 | − | 0.584507i | 0.107728 | − | 0.994180i | \(-0.465643\pi\) |
−0.912232 | + | 0.409674i | \(0.865643\pi\) | |||||||
\(72\) | −0.822965 | − | 0.597919i | −0.0969874 | − | 0.0704655i | ||||
\(73\) | 0.433471 | − | 1.33409i | 0.0507339 | − | 0.156143i | −0.922480 | − | 0.386046i | \(-0.873841\pi\) |
0.973214 | + | 0.229903i | \(0.0738408\pi\) | |||||||
\(74\) | 2.81579 | + | 8.66612i | 0.327329 | + | 1.00742i | ||||
\(75\) | −1.62152 | + | 1.17810i | −0.187237 | + | 0.136035i | ||||
\(76\) | 7.73531 | 0.887301 | ||||||||
\(77\) | −2.72926 | − | 1.88445i | −0.311028 | − | 0.214753i | ||||
\(78\) | −8.07596 | −0.914422 | ||||||||
\(79\) | −5.01595 | + | 3.64430i | −0.564338 | + | 0.410016i | −0.833044 | − | 0.553207i | \(-0.813404\pi\) |
0.268706 | + | 0.963222i | \(0.413404\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | −3.40442 | + | 10.4777i | −0.378269 | + | 1.16419i | ||||
\(82\) | −7.83396 | − | 5.69170i | −0.865116 | − | 0.628543i | ||||
\(83\) | −11.7929 | − | 8.56803i | −1.29444 | − | 0.940464i | −0.294552 | − | 0.955635i | \(-0.595170\pi\) |
−0.999885 | + | 0.0151718i | \(0.995170\pi\) | |||||||
\(84\) | −0.619365 | + | 1.90621i | −0.0675782 | + | 0.207984i | ||||
\(85\) | −0.0928800 | − | 0.285855i | −0.0100742 | − | 0.0310053i | ||||
\(86\) | −2.77144 | + | 2.01357i | −0.298852 | + | 0.217129i | ||||
\(87\) | 3.64127 | 0.390386 | ||||||||
\(88\) | −3.31567 | + | 0.0796618i | −0.353451 | + | 0.00849198i | ||||
\(89\) | 1.92815 | 0.204384 | 0.102192 | − | 0.994765i | \(-0.467414\pi\) | ||||
0.102192 | + | 0.994765i | \(0.467414\pi\) | |||||||
\(90\) | 0.822965 | − | 0.597919i | 0.0867482 | − | 0.0630262i | ||||
\(91\) | 1.24512 | + | 3.83210i | 0.130524 | + | 0.401713i | ||||
\(92\) | −2.00431 | + | 6.16862i | −0.208963 | + | 0.643123i | ||||
\(93\) | −12.2178 | − | 8.87675i | −1.26693 | − | 0.920476i | ||||
\(94\) | 5.02563 | + | 3.65133i | 0.518354 | + | 0.376606i | ||||
\(95\) | −2.39034 | + | 7.35672i | −0.245244 | + | 0.754783i | ||||
\(96\) | 0.619365 | + | 1.90621i | 0.0632136 | + | 0.194552i | ||||
\(97\) | 13.3442 | − | 9.69514i | 1.35490 | − | 0.984392i | 0.356149 | − | 0.934429i | \(-0.384090\pi\) |
0.998751 | − | 0.0499629i | \(-0.0159103\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.11933 | − | 3.18271i | −0.112497 | − | 0.319875i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.64039 | + | 5.55107i | −0.760247 | + | 0.552352i | −0.898986 | − | 0.437977i | \(-0.855695\pi\) |
0.138739 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(102\) | 0.186160 | + | 0.572941i | 0.0184326 | + | 0.0567296i | ||||
\(103\) | −1.08769 | + | 3.34756i | −0.107173 | + | 0.329845i | −0.990234 | − | 0.139413i | \(-0.955479\pi\) |
0.883061 | + | 0.469258i | \(0.155479\pi\) | |||||||
\(104\) | 3.25978 | + | 2.36837i | 0.319647 | + | 0.232237i | ||||
\(105\) | −1.62152 | − | 1.17810i | −0.158244 | − | 0.114971i | ||||
\(106\) | 1.97617 | − | 6.08202i | 0.191943 | − | 0.590738i | ||||
\(107\) | 3.22154 | + | 9.91487i | 0.311438 | + | 0.958507i | 0.977196 | + | 0.212339i | \(0.0681082\pi\) |
−0.665758 | + | 0.746168i | \(0.731892\pi\) | |||||||
\(108\) | 3.21508 | − | 2.33589i | 0.309371 | − | 0.224771i | ||||
\(109\) | 12.1571 | 1.16444 | 0.582221 | − | 0.813030i | \(-0.302184\pi\) | ||||
0.582221 | + | 0.813030i | \(0.302184\pi\) | |||||||
\(110\) | 0.948835 | − | 3.17800i | 0.0904679 | − | 0.303011i | ||||
\(111\) | 18.2634 | 1.73349 | ||||||||
\(112\) | 0.809017 | − | 0.587785i | 0.0764449 | − | 0.0555405i | ||||
\(113\) | −2.06181 | − | 6.34561i | −0.193959 | − | 0.596944i | −0.999987 | − | 0.00506720i | \(-0.998387\pi\) |
0.806028 | − | 0.591877i | \(-0.201613\pi\) | |||||||
\(114\) | 4.79098 | − | 14.7451i | 0.448716 | − | 1.38101i | ||||
\(115\) | −5.24734 | − | 3.81242i | −0.489317 | − | 0.355510i | ||||
\(116\) | −1.46976 | − | 1.06784i | −0.136464 | − | 0.0991469i | ||||
\(117\) | −1.26659 | + | 3.89817i | −0.117096 | + | 0.360386i | ||||
\(118\) | 1.70560 | + | 5.24931i | 0.157014 | + | 0.483238i | ||||
\(119\) | 0.243163 | − | 0.176668i | 0.0222907 | − | 0.0161951i | ||||
\(120\) | −2.00431 | −0.182967 | ||||||||
\(121\) | −9.19942 | − | 6.03080i | −0.836311 | − | 0.548255i | ||||
\(122\) | −3.62844 | −0.328503 | ||||||||
\(123\) | −15.7016 | + | 11.4079i | −1.41577 | + | 1.02862i | ||||
\(124\) | 2.32838 | + | 7.16602i | 0.209095 | + | 0.643527i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 0.822965 | + | 0.597919i | 0.0733156 | + | 0.0532669i | ||||
\(127\) | 10.4297 | + | 7.57765i | 0.925490 | + | 0.672408i | 0.944884 | − | 0.327404i | \(-0.106174\pi\) |
−0.0193944 | + | 0.999812i | \(0.506174\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 2.12175 | + | 6.53007i | 0.186810 | + | 0.574941i | ||||
\(130\) | −3.25978 | + | 2.36837i | −0.285901 | + | 0.207719i | ||||
\(131\) | 20.3862 | 1.78115 | 0.890577 | − | 0.454833i | \(-0.150301\pi\) | ||||
0.890577 | + | 0.454833i | \(0.150301\pi\) | |||||||
\(132\) | −1.90176 | + | 6.36969i | −0.165527 | + | 0.554411i | ||||
\(133\) | −7.73531 | −0.670737 | ||||||||
\(134\) | −0.408916 | + | 0.297095i | −0.0353249 | + | 0.0256651i | ||||
\(135\) | 1.22805 | + | 3.77955i | 0.105694 | + | 0.325292i | ||||
\(136\) | 0.0928800 | − | 0.285855i | 0.00796439 | − | 0.0245119i | ||||
\(137\) | 14.3159 | + | 10.4011i | 1.22309 | + | 0.888627i | 0.996353 | − | 0.0853292i | \(-0.0271942\pi\) |
0.226737 | + | 0.973956i | \(0.427194\pi\) | |||||||
\(138\) | 10.5173 | + | 7.64125i | 0.895290 | + | 0.650466i | ||||
\(139\) | 4.16475 | − | 12.8178i | 0.353250 | − | 1.08719i | −0.603768 | − | 0.797160i | \(-0.706335\pi\) |
0.957017 | − | 0.290030i | \(-0.0936654\pi\) | |||||||
\(140\) | 0.309017 | + | 0.951057i | 0.0261167 | + | 0.0803789i | ||||
\(141\) | 10.0729 | − | 7.31839i | 0.848291 | − | 0.616319i | ||||
\(142\) | 8.37915 | 0.703163 | ||||||||
\(143\) | 4.43369 | + | 12.6068i | 0.370764 | + | 1.05423i | ||||
\(144\) | 1.01724 | 0.0847701 | ||||||||
\(145\) | 1.46976 | − | 1.06784i | 0.122057 | − | 0.0886797i | ||||
\(146\) | 0.433471 | + | 1.33409i | 0.0358743 | + | 0.110410i | ||||
\(147\) | 0.619365 | − | 1.90621i | 0.0510843 | − | 0.157221i | ||||
\(148\) | −7.37184 | − | 5.35596i | −0.605962 | − | 0.440257i | ||||
\(149\) | 1.39488 | + | 1.01344i | 0.114273 | + | 0.0830242i | 0.643454 | − | 0.765485i | \(-0.277501\pi\) |
−0.529181 | + | 0.848509i | \(0.677501\pi\) | |||||||
\(150\) | 0.619365 | − | 1.90621i | 0.0505709 | − | 0.155641i | ||||
\(151\) | −2.82718 | − | 8.70117i | −0.230073 | − | 0.708091i | −0.997737 | − | 0.0672389i | \(-0.978581\pi\) |
0.767664 | − | 0.640852i | \(-0.221419\pi\) | |||||||
\(152\) | −6.25800 | + | 4.54670i | −0.507591 | + | 0.368786i | ||||
\(153\) | 0.305748 | 0.0247183 | ||||||||
\(154\) | 3.31567 | − | 0.0796618i | 0.267184 | − | 0.00641933i | ||||
\(155\) | −7.53480 | −0.605209 | ||||||||
\(156\) | 6.53359 | − | 4.74693i | 0.523106 | − | 0.380058i | ||||
\(157\) | −0.270707 | − | 0.833150i | −0.0216047 | − | 0.0664926i | 0.939673 | − | 0.342074i | \(-0.111129\pi\) |
−0.961278 | + | 0.275582i | \(0.911129\pi\) | |||||||
\(158\) | 1.91592 | − | 5.89660i | 0.152423 | − | 0.469108i | ||||
\(159\) | −10.3696 | − | 7.53398i | −0.822365 | − | 0.597483i | ||||
\(160\) | 0.809017 | + | 0.587785i | 0.0639584 | + | 0.0464685i | ||||
\(161\) | 2.00431 | − | 6.16862i | 0.157961 | − | 0.486155i | ||||
\(162\) | −3.40442 | − | 10.4777i | −0.267477 | − | 0.823209i | ||||
\(163\) | 5.25270 | − | 3.81631i | 0.411423 | − | 0.298916i | −0.362755 | − | 0.931885i | \(-0.618164\pi\) |
0.774178 | + | 0.632968i | \(0.218164\pi\) | |||||||
\(164\) | 9.68330 | 0.756139 | ||||||||
\(165\) | −5.47026 | − | 3.77702i | −0.425859 | − | 0.294041i | ||||
\(166\) | 14.5768 | 1.13138 | ||||||||
\(167\) | 16.2064 | − | 11.7746i | 1.25409 | − | 0.911150i | 0.255638 | − | 0.966773i | \(-0.417714\pi\) |
0.998452 | + | 0.0556230i | \(0.0177145\pi\) | |||||||
\(168\) | −0.619365 | − | 1.90621i | −0.0477850 | − | 0.147067i | ||||
\(169\) | 0.999759 | − | 3.07694i | 0.0769045 | − | 0.236688i | ||||
\(170\) | 0.243163 | + | 0.176668i | 0.0186497 | + | 0.0135498i | ||||
\(171\) | −6.36589 | − | 4.62509i | −0.486812 | − | 0.353690i | ||||
\(172\) | 1.05860 | − | 3.25802i | 0.0807171 | − | 0.248422i | ||||
\(173\) | 0.469977 | + | 1.44644i | 0.0357317 | + | 0.109971i | 0.967332 | − | 0.253515i | \(-0.0815866\pi\) |
−0.931600 | + | 0.363486i | \(0.881587\pi\) | |||||||
\(174\) | −2.94585 | + | 2.14029i | −0.223324 | + | 0.162255i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.63561 | − | 2.01335i | 0.198666 | − | 0.151762i | ||||
\(177\) | 11.0627 | 0.831521 | ||||||||
\(178\) | −1.55991 | + | 1.13334i | −0.116920 | + | 0.0849473i | ||||
\(179\) | 7.46313 | + | 22.9692i | 0.557821 | + | 1.71680i | 0.688375 | + | 0.725355i | \(0.258324\pi\) |
−0.130554 | + | 0.991441i | \(0.541676\pi\) | |||||||
\(180\) | −0.314345 | + | 0.967454i | −0.0234299 | + | 0.0721098i | ||||
\(181\) | −13.4801 | − | 9.79384i | −1.00197 | − | 0.727971i | −0.0394568 | − | 0.999221i | \(-0.512563\pi\) |
−0.962509 | + | 0.271251i | \(0.912563\pi\) | |||||||
\(182\) | −3.25978 | − | 2.36837i | −0.241631 | − | 0.175555i | ||||
\(183\) | −2.24733 | + | 6.91656i | −0.166127 | + | 0.511286i | ||||
\(184\) | −2.00431 | − | 6.16862i | −0.147759 | − | 0.454757i | ||||
\(185\) | 7.37184 | − | 5.35596i | 0.541989 | − | 0.393778i | ||||
\(186\) | 15.1020 | 1.10733 | ||||||||
\(187\) | 0.792174 | − | 0.605144i | 0.0579295 | − | 0.0442525i | ||||
\(188\) | −6.21202 | −0.453058 | ||||||||
\(189\) | −3.21508 | + | 2.33589i | −0.233862 | + | 0.169911i | ||||
\(190\) | −2.39034 | − | 7.35672i | −0.173414 | − | 0.533712i | ||||
\(191\) | −0.919475 | + | 2.82985i | −0.0665308 | + | 0.204761i | −0.978795 | − | 0.204841i | \(-0.934332\pi\) |
0.912264 | + | 0.409602i | \(0.134332\pi\) | |||||||
\(192\) | −1.62152 | − | 1.17810i | −0.117023 | − | 0.0850221i | ||||
\(193\) | 9.30418 | + | 6.75988i | 0.669730 | + | 0.486587i | 0.869935 | − | 0.493167i | \(-0.164161\pi\) |
−0.200205 | + | 0.979754i | \(0.564161\pi\) | |||||||
\(194\) | −5.09704 | + | 15.6871i | −0.365946 | + | 1.12627i | ||||
\(195\) | 2.49561 | + | 7.68069i | 0.178714 | + | 0.550026i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | 16.0597 | 1.14420 | 0.572101 | − | 0.820183i | \(-0.306128\pi\) | ||||
0.572101 | + | 0.820183i | \(0.306128\pi\) | |||||||
\(198\) | 2.77631 | + | 1.91694i | 0.197304 | + | 0.136231i | ||||
\(199\) | 11.0899 | 0.786140 | 0.393070 | − | 0.919509i | \(-0.371413\pi\) | ||||
0.393070 | + | 0.919509i | \(0.371413\pi\) | |||||||
\(200\) | −0.809017 | + | 0.587785i | −0.0572061 | + | 0.0415627i | ||||
\(201\) | 0.313056 | + | 0.963488i | 0.0220813 | + | 0.0679592i | ||||
\(202\) | 2.91837 | − | 8.98182i | 0.205336 | − | 0.631958i | ||||
\(203\) | 1.46976 | + | 1.06784i | 0.103157 | + | 0.0749480i | ||||
\(204\) | −0.487373 | − | 0.354097i | −0.0341229 | − | 0.0247918i | ||||
\(205\) | −2.99230 | + | 9.20937i | −0.208992 | + | 0.643210i | ||||
\(206\) | −1.08769 | − | 3.34756i | −0.0757829 | − | 0.233236i | ||||
\(207\) | 5.33781 | − | 3.87815i | 0.371004 | − | 0.269550i | ||||
\(208\) | −4.02930 | −0.279382 | ||||||||
\(209\) | −25.6477 | + | 0.616209i | −1.77409 | + | 0.0426241i | ||||
\(210\) | 2.00431 | 0.138310 | ||||||||
\(211\) | 20.6418 | − | 14.9971i | 1.42104 | − | 1.03244i | 0.429438 | − | 0.903096i | \(-0.358712\pi\) |
0.991599 | − | 0.129348i | \(-0.0412884\pi\) | |||||||
\(212\) | 1.97617 | + | 6.08202i | 0.135724 | + | 0.417715i | ||||
\(213\) | 5.18975 | − | 15.9724i | 0.355596 | − | 1.09441i | ||||
\(214\) | −8.43409 | − | 6.12773i | −0.576543 | − | 0.418883i | ||||
\(215\) | 2.77144 | + | 2.01357i | 0.189011 | + | 0.137324i | ||||
\(216\) | −1.22805 | + | 3.77955i | −0.0835582 | + | 0.257166i | ||||
\(217\) | −2.32838 | − | 7.16602i | −0.158061 | − | 0.486461i | ||||
\(218\) | −9.83533 | + | 7.14579i | −0.666133 | + | 0.483974i | ||||
\(219\) | 2.81152 | 0.189985 | ||||||||
\(220\) | 1.10036 | + | 3.12877i | 0.0741863 | + | 0.210942i | ||||
\(221\) | −1.21107 | −0.0814655 | ||||||||
\(222\) | −14.7754 | + | 10.7350i | −0.991662 | + | 0.720484i | ||||
\(223\) | −7.16435 | − | 22.0496i | −0.479760 | − | 1.47655i | −0.839429 | − | 0.543470i | \(-0.817110\pi\) |
0.359669 | − | 0.933080i | \(-0.382890\pi\) | |||||||
\(224\) | −0.309017 | + | 0.951057i | −0.0206471 | + | 0.0635451i | ||||
\(225\) | −0.822965 | − | 0.597919i | −0.0548644 | − | 0.0398613i | ||||
\(226\) | 5.39789 | + | 3.92180i | 0.359063 | + | 0.260874i | ||||
\(227\) | −1.53693 | + | 4.73019i | −0.102010 | + | 0.313954i | −0.989017 | − | 0.147802i | \(-0.952780\pi\) |
0.887007 | + | 0.461755i | \(0.152780\pi\) | |||||||
\(228\) | 4.79098 | + | 14.7451i | 0.317290 | + | 0.976519i | ||||
\(229\) | 20.7616 | − | 15.0842i | 1.37196 | − | 0.996790i | 0.374384 | − | 0.927274i | \(-0.377854\pi\) |
0.997581 | − | 0.0695165i | \(-0.0221456\pi\) | |||||||
\(230\) | 6.48607 | 0.427679 | ||||||||
\(231\) | 1.90176 | − | 6.36969i | 0.125126 | − | 0.419095i | ||||
\(232\) | 1.81673 | 0.119274 | ||||||||
\(233\) | −3.08589 | + | 2.24203i | −0.202164 | + | 0.146880i | −0.684261 | − | 0.729237i | \(-0.739875\pi\) |
0.482097 | + | 0.876118i | \(0.339875\pi\) | |||||||
\(234\) | −1.26659 | − | 3.89817i | −0.0827996 | − | 0.254831i | ||||
\(235\) | 1.91962 | − | 5.90798i | 0.125222 | − | 0.385394i | ||||
\(236\) | −4.46533 | − | 3.24425i | −0.290668 | − | 0.211183i | ||||
\(237\) | −10.0535 | − | 7.30429i | −0.653045 | − | 0.474465i | ||||
\(238\) | −0.0928800 | + | 0.285855i | −0.00602051 | + | 0.0185292i | ||||
\(239\) | 2.03364 | + | 6.25890i | 0.131545 | + | 0.404855i | 0.995037 | − | 0.0995089i | \(-0.0317272\pi\) |
−0.863491 | + | 0.504363i | \(0.831727\pi\) | |||||||
\(240\) | 1.62152 | − | 1.17810i | 0.104668 | − | 0.0760461i | ||||
\(241\) | 23.9679 | 1.54391 | 0.771955 | − | 0.635677i | \(-0.219279\pi\) | ||||
0.771955 | + | 0.635677i | \(0.219279\pi\) | |||||||
\(242\) | 10.9873 | − | 0.528264i | 0.706291 | − | 0.0339581i | ||||
\(243\) | −10.1592 | −0.651710 | ||||||||
\(244\) | 2.93547 | − | 2.13274i | 0.187924 | − | 0.136535i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | 5.99749 | − | 18.4584i | 0.382386 | − | 1.17686i | ||||
\(247\) | 25.2154 | + | 18.3200i | 1.60442 | + | 1.16568i | ||||
\(248\) | −6.09578 | − | 4.42884i | −0.387082 | − | 0.281232i | ||||
\(249\) | 9.02836 | − | 27.7864i | 0.572149 | − | 1.76089i | ||||
\(250\) | −0.309017 | − | 0.951057i | −0.0195440 | − | 0.0601501i | ||||
\(251\) | −4.11462 | + | 2.98945i | −0.259712 | + | 0.188692i | −0.710020 | − | 0.704181i | \(-0.751314\pi\) |
0.450308 | + | 0.892873i | \(0.351314\pi\) | |||||||
\(252\) | −1.01724 | −0.0640802 | ||||||||
\(253\) | 6.15421 | − | 20.6128i | 0.386912 | − | 1.29591i | ||||
\(254\) | −12.8919 | −0.808908 | ||||||||
\(255\) | 0.487373 | − | 0.354097i | 0.0305205 | − | 0.0221744i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 3.42909 | − | 10.5537i | 0.213901 | − | 0.658319i | −0.785329 | − | 0.619079i | \(-0.787506\pi\) |
0.999230 | − | 0.0392405i | \(-0.0124938\pi\) | |||||||
\(258\) | −5.55481 | − | 4.03581i | −0.345827 | − | 0.251258i | ||||
\(259\) | 7.37184 | + | 5.35596i | 0.458064 | + | 0.332803i | ||||
\(260\) | 1.24512 | − | 3.83210i | 0.0772193 | − | 0.237656i | ||||
\(261\) | 0.571078 | + | 1.75760i | 0.0353489 | + | 0.108793i | ||||
\(262\) | −16.4928 | + | 11.9827i | −1.01893 | + | 0.740295i | ||||
\(263\) | −2.64779 | −0.163270 | −0.0816348 | − | 0.996662i | \(-0.526014\pi\) | ||||
−0.0816348 | + | 0.996662i | \(0.526014\pi\) | |||||||
\(264\) | −2.20546 | − | 6.27101i | −0.135737 | − | 0.385954i | ||||
\(265\) | −6.39502 | −0.392843 | ||||||||
\(266\) | 6.25800 | − | 4.54670i | 0.383702 | − | 0.278776i | ||||
\(267\) | 1.19423 | + | 3.67546i | 0.0730856 | + | 0.224934i | ||||
\(268\) | 0.156192 | − | 0.480709i | 0.00954094 | − | 0.0293640i | ||||
\(269\) | 2.76845 | + | 2.01139i | 0.168795 | + | 0.122637i | 0.668976 | − | 0.743284i | \(-0.266733\pi\) |
−0.500181 | + | 0.865921i | \(0.666733\pi\) | |||||||
\(270\) | −3.21508 | − | 2.33589i | −0.195663 | − | 0.142158i | ||||
\(271\) | −6.54460 | + | 20.1422i | −0.397556 | + | 1.22355i | 0.529397 | + | 0.848374i | \(0.322418\pi\) |
−0.926953 | + | 0.375177i | \(0.877582\pi\) | |||||||
\(272\) | 0.0928800 | + | 0.285855i | 0.00563168 | + | 0.0173325i | ||||
\(273\) | −6.53359 | + | 4.74693i | −0.395431 | + | 0.287297i | ||||
\(274\) | −17.6954 | −1.06902 | ||||||||
\(275\) | −3.31567 | + | 0.0796618i | −0.199942 | + | 0.00480379i | ||||
\(276\) | −13.0001 | −0.782512 | ||||||||
\(277\) | −22.1602 | + | 16.1003i | −1.33148 | + | 0.967376i | −0.331767 | + | 0.943361i | \(0.607645\pi\) |
−0.999712 | + | 0.0240142i | \(0.992355\pi\) | |||||||
\(278\) | 4.16475 | + | 12.8178i | 0.249785 | + | 0.768760i | ||||
\(279\) | 2.36852 | − | 7.28957i | 0.141800 | − | 0.436415i | ||||
\(280\) | −0.809017 | − | 0.587785i | −0.0483480 | − | 0.0351269i | ||||
\(281\) | −9.11112 | − | 6.61962i | −0.543524 | − | 0.394893i | 0.281868 | − | 0.959453i | \(-0.409046\pi\) |
−0.825392 | + | 0.564560i | \(0.809046\pi\) | |||||||
\(282\) | −3.84750 | + | 11.8414i | −0.229115 | + | 0.705145i | ||||
\(283\) | −6.27083 | − | 19.2996i | −0.372762 | − | 1.14724i | −0.944976 | − | 0.327139i | \(-0.893915\pi\) |
0.572214 | − | 0.820104i | \(-0.306085\pi\) | |||||||
\(284\) | −6.77887 | + | 4.92514i | −0.402252 | + | 0.292253i | ||||
\(285\) | −15.5039 | −0.918373 | ||||||||
\(286\) | −10.9970 | − | 7.59303i | −0.650266 | − | 0.448985i | ||||
\(287\) | −9.68330 | −0.571587 | ||||||||
\(288\) | −0.822965 | + | 0.597919i | −0.0484937 | + | 0.0352327i | ||||
\(289\) | −5.22537 | − | 16.0820i | −0.307375 | − | 0.946002i | ||||
\(290\) | −0.561399 | + | 1.72781i | −0.0329665 | + | 0.101460i | ||||
\(291\) | 26.7459 | + | 19.4320i | 1.56787 | + | 1.13913i | ||||
\(292\) | −1.13484 | − | 0.824510i | −0.0664116 | − | 0.0482508i | ||||
\(293\) | −3.69423 | + | 11.3697i | −0.215819 | + | 0.664222i | 0.783275 | + | 0.621675i | \(0.213547\pi\) |
−0.999094 | + | 0.0425477i | \(0.986453\pi\) | |||||||
\(294\) | 0.619365 | + | 1.90621i | 0.0361221 | + | 0.111172i | ||||
\(295\) | 4.46533 | − | 3.24425i | 0.259981 | − | 0.188888i | ||||
\(296\) | 9.11210 | 0.529630 | ||||||||
\(297\) | −10.4740 | + | 8.00116i | −0.607766 | + | 0.464274i | ||||
\(298\) | −1.72417 | −0.0998783 | ||||||||
\(299\) | −21.1431 | + | 15.3614i | −1.22274 | + | 0.888372i | ||||
\(300\) | 0.619365 | + | 1.90621i | 0.0357590 | + | 0.110055i | ||||
\(301\) | −1.05860 | + | 3.25802i | −0.0610164 | + | 0.187789i | ||||
\(302\) | 7.40166 | + | 5.37762i | 0.425918 | + | 0.309447i | ||||
\(303\) | −15.3137 | − | 11.1260i | −0.879748 | − | 0.639174i | ||||
\(304\) | 2.39034 | − | 7.35672i | 0.137096 | − | 0.421937i | ||||
\(305\) | 1.12125 | + | 3.45085i | 0.0642025 | + | 0.197595i | ||||
\(306\) | −0.247355 | + | 0.179714i | −0.0141404 | + | 0.0102736i | ||||
\(307\) | −19.6625 | −1.12220 | −0.561100 | − | 0.827748i | \(-0.689622\pi\) | ||||
−0.561100 | + | 0.827748i | \(0.689622\pi\) | |||||||
\(308\) | −2.63561 | + | 2.01335i | −0.150178 | + | 0.114721i | ||||
\(309\) | −7.05482 | −0.401335 | ||||||||
\(310\) | 6.09578 | − | 4.42884i | 0.346217 | − | 0.251541i | ||||
\(311\) | −3.33815 | − | 10.2738i | −0.189289 | − | 0.582571i | 0.810707 | − | 0.585452i | \(-0.199083\pi\) |
−0.999996 | + | 0.00288089i | \(0.999083\pi\) | |||||||
\(312\) | −2.49561 | + | 7.68069i | −0.141286 | + | 0.434833i | ||||
\(313\) | 11.9289 | + | 8.66683i | 0.674260 | + | 0.489878i | 0.871448 | − | 0.490487i | \(-0.163181\pi\) |
−0.197189 | + | 0.980366i | \(0.563181\pi\) | |||||||
\(314\) | 0.708719 | + | 0.514915i | 0.0399954 | + | 0.0290583i | ||||
\(315\) | 0.314345 | − | 0.967454i | 0.0177113 | − | 0.0545099i | ||||
\(316\) | 1.91592 | + | 5.89660i | 0.107779 | + | 0.331710i | ||||
\(317\) | −14.1310 | + | 10.2667i | −0.793674 | + | 0.576638i | −0.909052 | − | 0.416684i | \(-0.863192\pi\) |
0.115377 | + | 0.993322i | \(0.463192\pi\) | |||||||
\(318\) | 12.8176 | 0.718774 | ||||||||
\(319\) | 4.95831 | + | 3.42353i | 0.277612 | + | 0.191681i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −16.9045 | + | 12.2818i | −0.943517 | + | 0.685505i | ||||
\(322\) | 2.00431 | + | 6.16862i | 0.111696 | + | 0.343764i | ||||
\(323\) | 0.718455 | − | 2.21118i | 0.0399759 | − | 0.123033i | ||||
\(324\) | 8.91289 | + | 6.47560i | 0.495161 | + | 0.359755i | ||||
\(325\) | 3.25978 | + | 2.36837i | 0.180820 | + | 0.131373i | ||||
\(326\) | −2.00635 | + | 6.17492i | −0.111122 | + | 0.341997i | ||||
\(327\) | 7.52970 | + | 23.1740i | 0.416393 | + | 1.28153i | ||||
\(328\) | −7.83396 | + | 5.69170i | −0.432558 | + | 0.314272i | ||||
\(329\) | 6.21202 | 0.342480 | ||||||||
\(330\) | 6.64561 | − | 0.159667i | 0.365829 | − | 0.00878936i | ||||
\(331\) | 22.3375 | 1.22778 | 0.613890 | − | 0.789391i | \(-0.289604\pi\) | ||||
0.613890 | + | 0.789391i | \(0.289604\pi\) | |||||||
\(332\) | −11.7929 | + | 8.56803i | −0.647219 | + | 0.470232i | ||||
\(333\) | 2.86434 | + | 8.81553i | 0.156965 | + | 0.483088i | ||||
\(334\) | −6.19030 | + | 19.0518i | −0.338718 | + | 1.04247i | ||||
\(335\) | 0.408916 | + | 0.297095i | 0.0223415 | + | 0.0162320i | ||||
\(336\) | 1.62152 | + | 1.17810i | 0.0884610 | + | 0.0642707i | ||||
\(337\) | 4.39996 | − | 13.5417i | 0.239681 | − | 0.737662i | −0.756785 | − | 0.653664i | \(-0.773231\pi\) |
0.996466 | − | 0.0839982i | \(-0.0267690\pi\) | |||||||
\(338\) | 0.999759 | + | 3.07694i | 0.0543797 | + | 0.167364i | ||||
\(339\) | 10.8190 | − | 7.86049i | 0.587609 | − | 0.426923i | ||||
\(340\) | −0.300566 | −0.0163005 | ||||||||
\(341\) | −8.29099 | − | 23.5746i | −0.448982 | − | 1.27664i | ||||
\(342\) | 7.86868 | 0.425489 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | 1.05860 | + | 3.25802i | 0.0570756 | + | 0.175661i | ||||
\(345\) | 4.01724 | − | 12.3638i | 0.216281 | − | 0.665644i | ||||
\(346\) | −1.23042 | − | 0.893950i | −0.0661476 | − | 0.0480591i | ||||
\(347\) | −16.6901 | − | 12.1260i | −0.895969 | − | 0.650960i | 0.0414585 | − | 0.999140i | \(-0.486800\pi\) |
−0.937427 | + | 0.348181i | \(0.886800\pi\) | |||||||
\(348\) | 1.12522 | − | 3.46306i | 0.0603179 | − | 0.185639i | ||||
\(349\) | −4.94572 | − | 15.2214i | −0.264738 | − | 0.814780i | −0.991754 | − | 0.128159i | \(-0.959093\pi\) |
0.727015 | − | 0.686621i | \(-0.240907\pi\) | |||||||
\(350\) | 0.809017 | − | 0.587785i | 0.0432438 | − | 0.0314184i | ||||
\(351\) | 16.0127 | 0.854693 | ||||||||
\(352\) | −0.948835 | + | 3.17800i | −0.0505731 | + | 0.169388i | ||||
\(353\) | −1.46881 | −0.0781767 | −0.0390883 | − | 0.999236i | \(-0.512445\pi\) | ||||
−0.0390883 | + | 0.999236i | \(0.512445\pi\) | |||||||
\(354\) | −8.94988 | + | 6.50247i | −0.475681 | + | 0.345602i | ||||
\(355\) | −2.58930 | − | 7.96904i | −0.137426 | − | 0.422953i | ||||
\(356\) | 0.595831 | − | 1.83378i | 0.0315790 | − | 0.0971901i | ||||
\(357\) | 0.487373 | + | 0.354097i | 0.0257945 | + | 0.0187408i | ||||
\(358\) | −19.5387 | − | 14.1957i | −1.03265 | − | 0.750267i | ||||
\(359\) | −2.60561 | + | 8.01924i | −0.137519 | + | 0.423239i | −0.995973 | − | 0.0896504i | \(-0.971425\pi\) |
0.858454 | + | 0.512890i | \(0.171425\pi\) | |||||||
\(360\) | −0.314345 | − | 0.967454i | −0.0165674 | − | 0.0509893i | ||||
\(361\) | −33.0362 | + | 24.0022i | −1.73875 | + | 1.26328i | ||||
\(362\) | 16.6623 | 0.875750 | ||||||||
\(363\) | 5.79817 | − | 21.2713i | 0.304325 | − | 1.11645i | ||||
\(364\) | 4.02930 | 0.211193 | ||||||||
\(365\) | 1.13484 | − | 0.824510i | 0.0594003 | − | 0.0431568i | ||||
\(366\) | −2.24733 | − | 6.91656i | −0.117470 | − | 0.361534i | ||||
\(367\) | 8.42350 | − | 25.9249i | 0.439703 | − | 1.35327i | −0.448486 | − | 0.893790i | \(-0.648037\pi\) |
0.888190 | − | 0.459477i | \(-0.151963\pi\) | |||||||
\(368\) | 5.24734 | + | 3.81242i | 0.273537 | + | 0.198736i | ||||
\(369\) | −7.96902 | − | 5.78983i | −0.414851 | − | 0.301407i | ||||
\(370\) | −2.81579 | + | 8.66612i | −0.146386 | + | 0.450530i | ||||
\(371\) | −1.97617 | − | 6.08202i | −0.102598 | − | 0.315763i | ||||
\(372\) | −12.2178 | + | 8.87675i | −0.633463 | + | 0.460238i | ||||
\(373\) | 14.7417 | 0.763299 | 0.381649 | − | 0.924307i | \(-0.375356\pi\) | ||||
0.381649 | + | 0.924307i | \(0.375356\pi\) | |||||||
\(374\) | −0.285187 | + | 0.955200i | −0.0147467 | + | 0.0493922i | ||||
\(375\) | −2.00431 | −0.103502 | ||||||||
\(376\) | 5.02563 | − | 3.65133i | 0.259177 | − | 0.188303i | ||||
\(377\) | −2.26205 | − | 6.96187i | −0.116501 | − | 0.358554i | ||||
\(378\) | 1.22805 | − | 3.77955i | 0.0631641 | − | 0.194399i | ||||
\(379\) | 21.2022 | + | 15.4043i | 1.08908 | + | 0.791266i | 0.979244 | − | 0.202683i | \(-0.0649663\pi\) |
0.109840 | + | 0.993949i | \(0.464966\pi\) | |||||||
\(380\) | 6.25800 | + | 4.54670i | 0.321029 | + | 0.233241i | ||||
\(381\) | −7.98477 | + | 24.5746i | −0.409072 | + | 1.25899i | ||||
\(382\) | −0.919475 | − | 2.82985i | −0.0470444 | − | 0.144788i | ||||
\(383\) | 14.6056 | − | 10.6116i | 0.746312 | − | 0.542227i | −0.148370 | − | 0.988932i | \(-0.547403\pi\) |
0.894681 | + | 0.446705i | \(0.147403\pi\) | |||||||
\(384\) | 2.00431 | 0.102282 | ||||||||
\(385\) | −1.10036 | − | 3.12877i | −0.0560796 | − | 0.159457i | ||||
\(386\) | −11.5006 | −0.585365 | ||||||||
\(387\) | −2.81922 | + | 2.04828i | −0.143309 | + | 0.104120i | ||||
\(388\) | −5.09704 | − | 15.6871i | −0.258763 | − | 0.796390i | ||||
\(389\) | −6.61462 | + | 20.3577i | −0.335375 | + | 1.03218i | 0.631162 | + | 0.775651i | \(0.282578\pi\) |
−0.966537 | + | 0.256527i | \(0.917422\pi\) | |||||||
\(390\) | −6.53359 | − | 4.74693i | −0.330841 | − | 0.240370i | ||||
\(391\) | 1.57717 | + | 1.14588i | 0.0797610 | + | 0.0579498i | ||||
\(392\) | 0.309017 | − | 0.951057i | 0.0156077 | − | 0.0480356i | ||||
\(393\) | 12.6265 | + | 38.8604i | 0.636923 | + | 1.96025i | ||||
\(394\) | −12.9925 | + | 9.43963i | −0.654554 | + | 0.475561i | ||||
\(395\) | −6.20005 | −0.311959 | ||||||||
\(396\) | −3.37283 | + | 0.0810353i | −0.169491 | + | 0.00407218i | ||||
\(397\) | 4.87615 | 0.244727 | 0.122364 | − | 0.992485i | \(-0.460953\pi\) | ||||
0.122364 | + | 0.992485i | \(0.460953\pi\) | |||||||
\(398\) | −8.97189 | + | 6.51846i | −0.449720 | + | 0.326741i | ||||
\(399\) | −4.79098 | − | 14.7451i | −0.239849 | − | 0.738179i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −12.6757 | − | 9.20942i | −0.632994 | − | 0.459897i | 0.224442 | − | 0.974487i | \(-0.427944\pi\) |
−0.857436 | + | 0.514591i | \(0.827944\pi\) | |||||||
\(402\) | −0.819592 | − | 0.595469i | −0.0408775 | − | 0.0296993i | ||||
\(403\) | −9.38175 | + | 28.8741i | −0.467338 | + | 1.43832i | ||||
\(404\) | 2.91837 | + | 8.98182i | 0.145194 | + | 0.446862i | ||||
\(405\) | −8.91289 | + | 6.47560i | −0.442885 | + | 0.321775i | ||||
\(406\) | −1.81673 | −0.0901626 | ||||||||
\(407\) | 24.8692 | + | 17.1713i | 1.23272 | + | 0.851151i | ||||
\(408\) | 0.602426 | 0.0298245 | ||||||||
\(409\) | −30.0809 | + | 21.8551i | −1.48741 | + | 1.08066i | −0.512331 | + | 0.858788i | \(0.671218\pi\) |
−0.975075 | + | 0.221876i | \(0.928782\pi\) | |||||||
\(410\) | −2.99230 | − | 9.20937i | −0.147779 | − | 0.454818i | ||||
\(411\) | −10.9599 | + | 33.7312i | −0.540613 | + | 1.66384i | ||||
\(412\) | 2.84761 | + | 2.06891i | 0.140291 | + | 0.101928i | ||||
\(413\) | 4.46533 | + | 3.24425i | 0.219724 | + | 0.159639i | ||||
\(414\) | −2.03886 | + | 6.27497i | −0.100205 | + | 0.308398i | ||||
\(415\) | −4.50448 | − | 13.8634i | −0.221116 | − | 0.680526i | ||||
\(416\) | 3.25978 | − | 2.36837i | 0.159824 | − | 0.116119i | ||||
\(417\) | 27.0129 | 1.32283 | ||||||||
\(418\) | 20.3872 | − | 15.5739i | 0.997173 | − | 0.761743i | ||||
\(419\) | −27.2599 | −1.33173 | −0.665865 | − | 0.746072i | \(-0.731938\pi\) | ||||
−0.665865 | + | 0.746072i | \(0.731938\pi\) | |||||||
\(420\) | −1.62152 | + | 1.17810i | −0.0791219 | + | 0.0574855i | ||||
\(421\) | −4.07894 | − | 12.5537i | −0.198795 | − | 0.611829i | −0.999911 | − | 0.0133199i | \(-0.995760\pi\) |
0.801116 | − | 0.598509i | \(-0.204240\pi\) | |||||||
\(422\) | −7.88445 | + | 24.2658i | −0.383809 | + | 1.18124i | ||||
\(423\) | 5.11228 | + | 3.71429i | 0.248567 | + | 0.180595i | ||||
\(424\) | −5.17368 | − | 3.75890i | −0.251256 | − | 0.182548i | ||||
\(425\) | 0.0928800 | − | 0.285855i | 0.00450534 | − | 0.0138660i | ||||
\(426\) | 5.18975 | + | 15.9724i | 0.251444 | + | 0.773865i | ||||
\(427\) | −2.93547 | + | 2.13274i | −0.142057 | + | 0.103211i | ||||
\(428\) | 10.4251 | 0.503917 | ||||||||
\(429\) | −21.2851 | + | 16.2597i | −1.02765 | + | 0.785026i | ||||
\(430\) | −3.42569 | −0.165201 | ||||||||
\(431\) | 14.1201 | − | 10.2588i | 0.680140 | − | 0.494151i | −0.193264 | − | 0.981147i | \(-0.561907\pi\) |
0.873404 | + | 0.486996i | \(0.161907\pi\) | |||||||
\(432\) | −1.22805 | − | 3.77955i | −0.0590846 | − | 0.181844i | ||||
\(433\) | −8.73900 | + | 26.8959i | −0.419970 | + | 1.29253i | 0.487760 | + | 0.872978i | \(0.337814\pi\) |
−0.907729 | + | 0.419556i | \(0.862186\pi\) | |||||||
\(434\) | 6.09578 | + | 4.42884i | 0.292607 | + | 0.212591i | ||||
\(435\) | 2.94585 | + | 2.14029i | 0.141243 | + | 0.102619i | ||||
\(436\) | 3.75676 | − | 11.5621i | 0.179916 | − | 0.553725i | ||||
\(437\) | −15.5039 | − | 47.7162i | −0.741653 | − | 2.28257i | ||||
\(438\) | −2.27457 | + | 1.65257i | −0.108683 | + | 0.0789629i | ||||
\(439\) | 35.7484 | 1.70618 | 0.853090 | − | 0.521764i | \(-0.174726\pi\) | ||||
0.853090 | + | 0.521764i | \(0.174726\pi\) | |||||||
\(440\) | −2.72926 | − | 1.88445i | −0.130112 | − | 0.0898378i | ||||
\(441\) | 1.01724 | 0.0484401 | ||||||||
\(442\) | 0.979777 | − | 0.711850i | 0.0466032 | − | 0.0338592i | ||||
\(443\) | 4.61798 | + | 14.2127i | 0.219407 | + | 0.675266i | 0.998811 | + | 0.0487441i | \(0.0155219\pi\) |
−0.779404 | + | 0.626521i | \(0.784478\pi\) | |||||||
\(444\) | 5.64371 | − | 17.3696i | 0.267839 | − | 0.824323i | ||||
\(445\) | 1.55991 | + | 1.13334i | 0.0739467 | + | 0.0537254i | ||||
\(446\) | 18.7565 | + | 13.6274i | 0.888146 | + | 0.645276i | ||||
\(447\) | −1.06789 | + | 3.28662i | −0.0505094 | + | 0.155452i | ||||
\(448\) | −0.309017 | − | 0.951057i | −0.0145997 | − | 0.0449332i | ||||
\(449\) | −11.3139 | + | 8.22003i | −0.533936 | + | 0.387927i | −0.821828 | − | 0.569736i | \(-0.807046\pi\) |
0.287892 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(450\) | 1.01724 | 0.0479532 | ||||||||
\(451\) | −32.1066 | + | 0.771389i | −1.51184 | + | 0.0363233i | ||||
\(452\) | −6.67216 | −0.313832 | ||||||||
\(453\) | 14.8352 | − | 10.7784i | 0.697018 | − | 0.506413i | ||||
\(454\) | −1.53693 | − | 4.73019i | −0.0721318 | − | 0.221999i | ||||
\(455\) | −1.24512 | + | 3.83210i | −0.0583723 | + | 0.179651i | ||||
\(456\) | −12.5429 | − | 9.11298i | −0.587377 | − | 0.426754i | ||||
\(457\) | −8.30976 | − | 6.03739i | −0.388714 | − | 0.282417i | 0.376214 | − | 0.926533i | \(-0.377226\pi\) |
−0.764928 | + | 0.644115i | \(0.777226\pi\) | |||||||
\(458\) | −7.93022 | + | 24.4067i | −0.370555 | + | 1.14045i | ||||
\(459\) | −0.369110 | − | 1.13600i | −0.0172286 | − | 0.0530241i | ||||
\(460\) | −5.24734 | + | 3.81242i | −0.244659 | + | 0.177755i | ||||
\(461\) | −17.4058 | −0.810671 | −0.405335 | − | 0.914168i | \(-0.632845\pi\) | ||||
−0.405335 | + | 0.914168i | \(0.632845\pi\) | |||||||
\(462\) | 2.20546 | + | 6.27101i | 0.102607 | + | 0.291754i | ||||
\(463\) | −30.3943 | −1.41254 | −0.706271 | − | 0.707942i | \(-0.749624\pi\) | ||||
−0.706271 | + | 0.707942i | \(0.749624\pi\) | |||||||
\(464\) | −1.46976 | + | 1.06784i | −0.0682320 | + | 0.0495734i | ||||
\(465\) | −4.66678 | − | 14.3629i | −0.216417 | − | 0.666063i | ||||
\(466\) | 1.17871 | − | 3.62769i | 0.0546025 | − | 0.168049i | ||||
\(467\) | −19.2588 | − | 13.9924i | −0.891193 | − | 0.647490i | 0.0449959 | − | 0.998987i | \(-0.485673\pi\) |
−0.936189 | + | 0.351498i | \(0.885673\pi\) | |||||||
\(468\) | 3.31598 | + | 2.40920i | 0.153281 | + | 0.111365i | ||||
\(469\) | −0.156192 | + | 0.480709i | −0.00721227 | + | 0.0221971i | ||||
\(470\) | 1.91962 | + | 5.90798i | 0.0885454 | + | 0.272515i | ||||
\(471\) | 1.42049 | − | 1.03205i | 0.0654527 | − | 0.0475542i | ||||
\(472\) | 5.51945 | 0.254053 | ||||||||
\(473\) | −3.25041 | + | 10.8868i | −0.149454 | + | 0.500578i | ||||
\(474\) | 12.4268 | 0.570782 | ||||||||
\(475\) | −6.25800 | + | 4.54670i | −0.287137 | + | 0.208617i | ||||
\(476\) | −0.0928800 | − | 0.285855i | −0.00425715 | − | 0.0131021i | ||||
\(477\) | 2.01024 | − | 6.18688i | 0.0920426 | − | 0.283278i | ||||
\(478\) | −5.32414 | − | 3.86821i | −0.243520 | − | 0.176928i | ||||
\(479\) | −6.31030 | − | 4.58470i | −0.288325 | − | 0.209480i | 0.434215 | − | 0.900809i | \(-0.357026\pi\) |
−0.722540 | + | 0.691329i | \(0.757026\pi\) | |||||||
\(480\) | −0.619365 | + | 1.90621i | −0.0282700 | + | 0.0870061i | ||||
\(481\) | −11.3457 | − | 34.9184i | −0.517319 | − | 1.59214i | ||||
\(482\) | −19.3905 | + | 14.0880i | −0.883211 | + | 0.641690i | ||||
\(483\) | 13.0001 | 0.591523 | ||||||||
\(484\) | −8.57841 | + | 6.88555i | −0.389928 | + | 0.312980i | ||||
\(485\) | 16.4944 | 0.748970 | ||||||||
\(486\) | 8.21893 | − | 5.97140i | 0.372818 | − | 0.270868i | ||||
\(487\) | −5.96739 | − | 18.3657i | −0.270408 | − | 0.832232i | −0.990398 | − | 0.138246i | \(-0.955853\pi\) |
0.719989 | − | 0.693985i | \(-0.244147\pi\) | |||||||
\(488\) | −1.12125 | + | 3.45085i | −0.0507565 | + | 0.156213i | ||||
\(489\) | 10.5280 | + | 7.64905i | 0.476093 | + | 0.345902i | ||||
\(490\) | 0.809017 | + | 0.587785i | 0.0365477 | + | 0.0265534i | ||||
\(491\) | 5.10436 | − | 15.7096i | 0.230356 | − | 0.708964i | −0.767347 | − | 0.641232i | \(-0.778424\pi\) |
0.997704 | − | 0.0677321i | \(-0.0215763\pi\) | |||||||
\(492\) | 5.99749 | + | 18.4584i | 0.270388 | + | 0.832168i | ||||
\(493\) | −0.441760 | + | 0.320958i | −0.0198959 | + | 0.0144552i | ||||
\(494\) | −31.1679 | −1.40231 | ||||||||
\(495\) | 0.965194 | − | 3.23280i | 0.0433822 | − | 0.145303i | ||||
\(496\) | 7.53480 | 0.338322 | ||||||||
\(497\) | 6.77887 | − | 4.92514i | 0.304074 | − | 0.220923i | ||||
\(498\) | 9.02836 | + | 27.7864i | 0.404570 | + | 1.24514i | ||||
\(499\) | 3.66780 | − | 11.2883i | 0.164193 | − | 0.505335i | −0.834783 | − | 0.550580i | \(-0.814407\pi\) |
0.998976 | + | 0.0452447i | \(0.0144068\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | 32.4826 | + | 23.6000i | 1.45122 | + | 1.05437i | ||||
\(502\) | 1.57164 | − | 4.83702i | 0.0701459 | − | 0.215887i | ||||
\(503\) | −2.08942 | − | 6.43058i | −0.0931628 | − | 0.286726i | 0.893608 | − | 0.448849i | \(-0.148166\pi\) |
−0.986771 | + | 0.162123i | \(0.948166\pi\) | |||||||
\(504\) | 0.822965 | − | 0.597919i | 0.0366578 | − | 0.0266334i | ||||
\(505\) | −9.44404 | −0.420254 | ||||||||
\(506\) | 7.13702 | + | 20.2934i | 0.317279 | + | 0.902153i | ||||
\(507\) | 6.48451 | 0.287987 | ||||||||
\(508\) | 10.4297 | − | 7.57765i | 0.462745 | − | 0.336204i | ||||
\(509\) | −11.5367 | − | 35.5064i | −0.511357 | − | 1.57379i | −0.789814 | − | 0.613346i | \(-0.789823\pi\) |
0.278457 | − | 0.960449i | \(-0.410177\pi\) | |||||||
\(510\) | −0.186160 | + | 0.572941i | −0.00824330 | + | 0.0253703i | ||||
\(511\) | 1.13484 | + | 0.824510i | 0.0502024 | + | 0.0364742i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −9.49935 | + | 29.2360i | −0.419407 | + | 1.29080i | ||||
\(514\) | 3.42909 | + | 10.5537i | 0.151251 | + | 0.465502i | ||||
\(515\) | −2.84761 | + | 2.06891i | −0.125480 | + | 0.0911669i | ||||
\(516\) | 6.86612 | 0.302264 | ||||||||
\(517\) | 20.5970 | − | 0.494861i | 0.905854 | − | 0.0217639i | ||||
\(518\) | −9.11210 | −0.400363 | ||||||||
\(519\) | −2.46613 | + | 1.79175i | −0.108251 | + | 0.0786491i | ||||
\(520\) | 1.24512 | + | 3.83210i | 0.0546023 | + | 0.168049i | ||||
\(521\) | −4.21188 | + | 12.9628i | −0.184526 | + | 0.567911i | −0.999940 | − | 0.0109664i | \(-0.996509\pi\) |
0.815414 | + | 0.578878i | \(0.196509\pi\) | |||||||
\(522\) | −1.49510 | − | 1.08626i | −0.0654389 | − | 0.0475441i | ||||
\(523\) | 5.68747 | + | 4.13219i | 0.248696 | + | 0.180688i | 0.705149 | − | 0.709060i | \(-0.250880\pi\) |
−0.456453 | + | 0.889748i | \(0.650880\pi\) | |||||||
\(524\) | 6.29969 | − | 19.3885i | 0.275203 | − | 0.846989i | ||||
\(525\) | −0.619365 | − | 1.90621i | −0.0270313 | − | 0.0831937i | ||||
\(526\) | 2.14210 | − | 1.55633i | 0.0934002 | − | 0.0678592i | ||||
\(527\) | 2.26470 | 0.0986520 | ||||||||
\(528\) | 5.47026 | + | 3.77702i | 0.238063 | + | 0.164374i | ||||
\(529\) | 19.0691 | 0.829091 | ||||||||
\(530\) | 5.17368 | − | 3.75890i | 0.224730 | − | 0.163276i | ||||
\(531\) | 1.73501 | + | 5.33981i | 0.0752930 | + | 0.231728i | ||||
\(532\) | −2.39034 | + | 7.35672i | −0.103634 | + | 0.318954i | ||||
\(533\) | 31.5654 | + | 22.9336i | 1.36725 | + | 0.993364i | ||||
\(534\) | −3.12653 | − | 2.27156i | −0.135298 | − | 0.0982999i | ||||
\(535\) | −3.22154 | + | 9.91487i | −0.139279 | + | 0.428657i | ||||
\(536\) | 0.156192 | + | 0.480709i | 0.00674646 | + | 0.0207635i | ||||
\(537\) | −39.1616 | + | 28.4526i | −1.68995 | + | 1.22782i | ||||
\(538\) | −3.42199 | −0.147532 | ||||||||
\(539\) | 2.63561 | − | 2.01335i | 0.113524 | − | 0.0867211i | ||||
\(540\) | 3.97405 | 0.171016 | ||||||||
\(541\) | −12.4101 | + | 9.01647i | −0.533552 | + | 0.387648i | −0.821685 | − | 0.569942i | \(-0.806966\pi\) |
0.288133 | + | 0.957590i | \(0.406966\pi\) | |||||||
\(542\) | −6.54460 | − | 20.1422i | −0.281114 | − | 0.865181i | ||||
\(543\) | 10.3200 | − | 31.7618i | 0.442875 | − | 1.36303i | ||||
\(544\) | −0.243163 | − | 0.176668i | −0.0104255 | − | 0.00757459i | ||||
\(545\) | 9.83533 | + | 7.14579i | 0.421299 | + | 0.306092i | ||||
\(546\) | 2.49561 | − | 7.68069i | 0.106802 | − | 0.328703i | ||||
\(547\) | 5.45498 | + | 16.7887i | 0.233238 | + | 0.717834i | 0.997350 | + | 0.0727500i | \(0.0231775\pi\) |
−0.764112 | + | 0.645084i | \(0.776822\pi\) | |||||||
\(548\) | 14.3159 | − | 10.4011i | 0.611545 | − | 0.444313i | ||||
\(549\) | −3.69100 | −0.157528 | ||||||||
\(550\) | 2.63561 | − | 2.01335i | 0.112383 | − | 0.0858495i | ||||
\(551\) | 14.0529 | 0.598675 | ||||||||
\(552\) | 10.5173 | − | 7.64125i | 0.447645 | − | 0.325233i | ||||
\(553\) | −1.91592 | − | 5.89660i | −0.0814733 | − | 0.250749i | ||||
\(554\) | 8.46445 | − | 26.0509i | 0.359620 | − | 1.10680i | ||||
\(555\) | 14.7754 | + | 10.7350i | 0.627182 | + | 0.455674i | ||||
\(556\) | −10.9035 | − | 7.92183i | −0.462410 | − | 0.335960i | ||||
\(557\) | 8.52089 | − | 26.2246i | 0.361042 | − | 1.11117i | −0.591381 | − | 0.806392i | \(-0.701417\pi\) |
0.952423 | − | 0.304780i | \(-0.0985828\pi\) | |||||||
\(558\) | 2.36852 | + | 7.28957i | 0.100268 | + | 0.308592i | ||||
\(559\) | 11.1670 | − | 8.11328i | 0.472312 | − | 0.343155i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 1.64417 | + | 1.13524i | 0.0694171 | + | 0.0479300i | ||||
\(562\) | 11.2620 | 0.475057 | ||||||||
\(563\) | 11.5918 | − | 8.42196i | 0.488538 | − | 0.354943i | −0.316084 | − | 0.948731i | \(-0.602368\pi\) |
0.804622 | + | 0.593788i | \(0.202368\pi\) | |||||||
\(564\) | −3.84750 | − | 11.8414i | −0.162009 | − | 0.498613i | ||||
\(565\) | 2.06181 | − | 6.34561i | 0.0867411 | − | 0.266962i | ||||
\(566\) | 16.4172 | + | 11.9278i | 0.690068 | + | 0.501364i | ||||
\(567\) | −8.91289 | − | 6.47560i | −0.374306 | − | 0.271950i | ||||
\(568\) | 2.58930 | − | 7.96904i | 0.108645 | − | 0.334374i | ||||
\(569\) | −9.03211 | − | 27.7980i | −0.378646 | − | 1.16535i | −0.940986 | − | 0.338446i | \(-0.890099\pi\) |
0.562340 | − | 0.826906i | \(-0.309901\pi\) | |||||||
\(570\) | 12.5429 | − | 9.11298i | 0.525366 | − | 0.381701i | ||||
\(571\) | −42.5911 | −1.78238 | −0.891190 | − | 0.453630i | \(-0.850129\pi\) | ||||
−0.891190 | + | 0.453630i | \(0.850129\pi\) | |||||||
\(572\) | 13.3598 | − | 0.320982i | 0.558603 | − | 0.0134209i | ||||
\(573\) | −5.96378 | −0.249140 | ||||||||
\(574\) | 7.83396 | − | 5.69170i | 0.326983 | − | 0.237567i | ||||
\(575\) | −2.00431 | − | 6.16862i | −0.0835853 | − | 0.257249i | ||||
\(576\) | 0.314345 | − | 0.967454i | 0.0130977 | − | 0.0403106i | ||||
\(577\) | −20.5602 | − | 14.9378i | −0.855931 | − | 0.621870i | 0.0708441 | − | 0.997487i | \(-0.477431\pi\) |
−0.926775 | + | 0.375617i | \(0.877431\pi\) | |||||||
\(578\) | 13.6802 | + | 9.93925i | 0.569021 | + | 0.413418i | ||||
\(579\) | −7.12306 | + | 21.9225i | −0.296024 | + | 0.911069i | ||||
\(580\) | −0.561399 | − | 1.72781i | −0.0233108 | − | 0.0717434i | ||||
\(581\) | 11.7929 | − | 8.56803i | 0.489251 | − | 0.355462i | ||||
\(582\) | −33.0597 | −1.37037 | ||||||||
\(583\) | −7.03683 | − | 20.0085i | −0.291436 | − | 0.828669i | ||||
\(584\) | 1.40274 | 0.0580458 | ||||||||
\(585\) | −3.31598 | + | 2.40920i | −0.137099 | + | 0.0996081i | ||||
\(586\) | −3.69423 | − | 11.3697i | −0.152607 | − | 0.469676i | ||||
\(587\) | 14.8328 | − | 45.6507i | 0.612216 | − | 1.88421i | 0.175915 | − | 0.984405i | \(-0.443711\pi\) |
0.436300 | − | 0.899801i | \(-0.356289\pi\) | |||||||
\(588\) | −1.62152 | − | 1.17810i | −0.0668702 | − | 0.0485841i | ||||
\(589\) | −47.1527 | − | 34.2585i | −1.94289 | − | 1.41160i | ||||
\(590\) | −1.70560 | + | 5.24931i | −0.0702186 | + | 0.216111i | ||||
\(591\) | 9.94678 | + | 30.6130i | 0.409156 | + | 1.25925i | ||||
\(592\) | −7.37184 | + | 5.35596i | −0.302981 | + | 0.220128i | ||||
\(593\) | 3.34128 | 0.137210 | 0.0686050 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686050 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(594\) | 3.77072 | − | 12.6296i | 0.154715 | − | 0.518197i | ||||
\(595\) | 0.300566 | 0.0123220 | ||||||||
\(596\) | 1.39488 | − | 1.01344i | 0.0571365 | − | 0.0415121i | ||||
\(597\) | 6.86867 | + | 21.1396i | 0.281116 | + | 0.865186i | ||||
\(598\) | 8.07596 | − | 24.8552i | 0.330250 | − | 1.01641i | ||||
\(599\) | 34.8735 | + | 25.3371i | 1.42489 | + | 1.03525i | 0.990939 | + | 0.134310i | \(0.0428818\pi\) |
0.433954 | + | 0.900935i | \(0.357118\pi\) | |||||||
\(600\) | −1.62152 | − | 1.17810i | −0.0661982 | − | 0.0480958i | ||||
\(601\) | −5.51386 | + | 16.9699i | −0.224915 | + | 0.692217i | 0.773385 | + | 0.633936i | \(0.218562\pi\) |
−0.998300 | + | 0.0582807i | \(0.981438\pi\) | |||||||
\(602\) | −1.05860 | − | 3.25802i | −0.0431451 | − | 0.132787i | ||||
\(603\) | −0.415966 | + | 0.302217i | −0.0169394 | + | 0.0123072i | ||||
\(604\) | −9.14895 | −0.372266 | ||||||||
\(605\) | −3.89767 | − | 10.2863i | −0.158463 | − | 0.418198i | ||||
\(606\) | 18.9287 | 0.768928 | ||||||||
\(607\) | 9.16115 | − | 6.65596i | 0.371839 | − | 0.270157i | −0.386134 | − | 0.922443i | \(-0.626190\pi\) |
0.757973 | + | 0.652286i | \(0.226190\pi\) | |||||||
\(608\) | 2.39034 | + | 7.35672i | 0.0969412 | + | 0.298354i | ||||
\(609\) | −1.12522 | + | 3.46306i | −0.0455960 | + | 0.140330i | ||||
\(610\) | −2.93547 | − | 2.13274i | −0.118854 | − | 0.0863522i | ||||
\(611\) | −20.2498 | − | 14.7123i | −0.819218 | − | 0.595197i | ||||
\(612\) | 0.0944813 | − | 0.290784i | 0.00381918 | − | 0.0117542i | ||||
\(613\) | −11.2013 | − | 34.4742i | −0.452418 | − | 1.39240i | −0.874140 | − | 0.485674i | \(-0.838574\pi\) |
0.421723 | − | 0.906725i | \(-0.361426\pi\) | |||||||
\(614\) | 15.9073 | − | 11.5574i | 0.641968 | − | 0.466417i | ||||
\(615\) | −19.4083 | −0.782618 | ||||||||
\(616\) | 0.948835 | − | 3.17800i | 0.0382296 | − | 0.128045i | ||||
\(617\) | 40.1661 | 1.61702 | 0.808512 | − | 0.588479i | \(-0.200273\pi\) | ||||
0.808512 | + | 0.588479i | \(0.200273\pi\) | |||||||
\(618\) | 5.70747 | − | 4.14672i | 0.229588 | − | 0.166806i | ||||
\(619\) | 2.73811 | + | 8.42702i | 0.110054 | + | 0.338711i | 0.990883 | − | 0.134723i | \(-0.0430144\pi\) |
−0.880830 | + | 0.473433i | \(0.843014\pi\) | |||||||
\(620\) | −2.32838 | + | 7.16602i | −0.0935100 | + | 0.287794i | ||||
\(621\) | −20.8532 | − | 15.1507i | −0.836811 | − | 0.607979i | ||||
\(622\) | 8.73938 | + | 6.34953i | 0.350417 | + | 0.254593i | ||||
\(623\) | −0.595831 | + | 1.83378i | −0.0238715 | + | 0.0734688i | ||||
\(624\) | −2.49561 | − | 7.68069i | −0.0999043 | − | 0.307474i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −14.7449 | −0.589325 | ||||||||
\(627\) | −17.0599 | − | 48.5082i | −0.681307 | − | 1.93723i | ||||
\(628\) | −0.876025 | −0.0349572 | ||||||||
\(629\) | −2.21572 | + | 1.60982i | −0.0883467 | + | 0.0641876i | ||||
\(630\) | 0.314345 | + | 0.967454i | 0.0125238 | + | 0.0385443i | ||||
\(631\) | −0.738828 | + | 2.27388i | −0.0294123 | + | 0.0905217i | −0.964685 | − | 0.263406i | \(-0.915154\pi\) |
0.935273 | + | 0.353928i | \(0.115154\pi\) | |||||||
\(632\) | −5.01595 | − | 3.64430i | −0.199524 | − | 0.144962i | ||||
\(633\) | 41.3724 | + | 30.0588i | 1.64441 | + | 1.19473i | ||||
\(634\) | 5.39755 | − | 16.6119i | 0.214364 | − | 0.659745i | ||||
\(635\) | 3.98381 | + | 12.2609i | 0.158093 | + | 0.486559i | ||||
\(636\) | −10.3696 | + | 7.53398i | −0.411183 | + | 0.298742i | ||||
\(637\) | −4.02930 | −0.159647 | ||||||||
\(638\) | −6.02366 | + | 0.144724i | −0.238479 | + | 0.00572967i | ||||
\(639\) | 8.52362 | 0.337189 | ||||||||
\(640\) | 0.809017 | − | 0.587785i | 0.0319792 | − | 0.0232343i | ||||
\(641\) | −2.24826 | − | 6.91942i | −0.0888008 | − | 0.273301i | 0.896788 | − | 0.442461i | \(-0.145894\pi\) |
−0.985589 | + | 0.169160i | \(0.945894\pi\) | |||||||
\(642\) | 6.45695 | − | 19.8724i | 0.254835 | − | 0.784302i | ||||
\(643\) | 7.31762 | + | 5.31656i | 0.288579 | + | 0.209665i | 0.722651 | − | 0.691213i | \(-0.242924\pi\) |
−0.434072 | + | 0.900878i | \(0.642924\pi\) | |||||||
\(644\) | −5.24734 | − | 3.81242i | −0.206774 | − | 0.150230i | ||||
\(645\) | −2.12175 | + | 6.53007i | −0.0835438 | + | 0.257121i | ||||
\(646\) | 0.718455 | + | 2.21118i | 0.0282673 | + | 0.0869977i | ||||
\(647\) | 25.1052 | − | 18.2400i | 0.986989 | − | 0.717089i | 0.0277291 | − | 0.999615i | \(-0.491172\pi\) |
0.959260 | + | 0.282526i | \(0.0911724\pi\) | |||||||
\(648\) | −11.0169 | −0.432786 | ||||||||
\(649\) | 15.0640 | + | 10.4011i | 0.591313 | + | 0.408281i | ||||
\(650\) | −4.02930 | −0.158042 | ||||||||
\(651\) | 12.2178 | − | 8.87675i | 0.478853 | − | 0.347907i | ||||
\(652\) | −2.00635 | − | 6.17492i | −0.0785748 | − | 0.241828i | ||||
\(653\) | 13.0937 | − | 40.2981i | 0.512394 | − | 1.57699i | −0.275579 | − | 0.961278i | \(-0.588870\pi\) |
0.787973 | − | 0.615709i | \(-0.211130\pi\) | |||||||
\(654\) | −19.7130 | − | 14.3223i | −0.770840 | − | 0.560048i | ||||
\(655\) | 16.4928 | + | 11.9827i | 0.644427 | + | 0.468204i | ||||
\(656\) | 2.99230 | − | 9.20937i | 0.116830 | − | 0.359565i | ||||
\(657\) | 0.440944 | + | 1.35709i | 0.0172029 | + | 0.0529450i | ||||
\(658\) | −5.02563 | + | 3.65133i | −0.195919 | + | 0.142344i | ||||
\(659\) | 25.5490 | 0.995247 | 0.497624 | − | 0.867393i | \(-0.334206\pi\) | ||||
0.497624 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(660\) | −5.28256 | + | 4.03537i | −0.205624 | + | 0.157076i | ||||
\(661\) | 1.55717 | 0.0605669 | 0.0302834 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302834 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(662\) | −18.0714 | + | 13.1297i | −0.702366 | + | 0.510299i | ||||
\(663\) | −0.750095 | − | 2.30855i | −0.0291313 | − | 0.0896568i | ||||
\(664\) | 4.50448 | − | 13.8634i | 0.174808 | − | 0.538003i | ||||
\(665\) | −6.25800 | − | 4.54670i | −0.242675 | − | 0.176314i | ||||
\(666\) | −7.49894 | − | 5.44830i | −0.290578 | − | 0.211117i | ||||
\(667\) | −3.64127 | + | 11.2067i | −0.140991 | + | 0.433925i | ||||
\(668\) | −6.19030 | − | 19.0518i | −0.239510 | − | 0.737136i | ||||
\(669\) | 37.5938 | − | 27.3135i | 1.45346 | − | 1.05600i | ||||
\(670\) | −0.505448 | −0.0195271 | ||||||||
\(671\) | −9.56314 | + | 7.30531i | −0.369181 | + | 0.282018i | ||||
\(672\) | −2.00431 | −0.0773178 | ||||||||
\(673\) | −20.2452 | + | 14.7090i | −0.780394 | + | 0.566990i | −0.905097 | − | 0.425204i | \(-0.860202\pi\) |
0.124703 | + | 0.992194i | \(0.460202\pi\) | |||||||
\(674\) | 4.39996 | + | 13.5417i | 0.169480 | + | 0.521606i | ||||
\(675\) | −1.22805 | + | 3.77955i | −0.0472677 | + | 0.145475i | ||||
\(676\) | −2.61740 | − | 1.90165i | −0.100669 | − | 0.0731406i | ||||
\(677\) | −18.9740 | − | 13.7854i | −0.729231 | − | 0.529818i | 0.160089 | − | 0.987103i | \(-0.448822\pi\) |
−0.889320 | + | 0.457285i | \(0.848822\pi\) | |||||||
\(678\) | −4.13250 | + | 12.7185i | −0.158708 | + | 0.488452i | ||||
\(679\) | 5.09704 | + | 15.6871i | 0.195606 | + | 0.602014i | ||||
\(680\) | 0.243163 | − | 0.176668i | 0.00932487 | − | 0.00677492i | ||||
\(681\) | −9.96865 | −0.381999 | ||||||||
\(682\) | 20.5644 | + | 14.1990i | 0.787451 | + | 0.543707i | ||||
\(683\) | −36.6815 | −1.40358 | −0.701790 | − | 0.712384i | \(-0.747616\pi\) | ||||
−0.701790 | + | 0.712384i | \(0.747616\pi\) | |||||||
\(684\) | −6.36589 | + | 4.62509i | −0.243406 | + | 0.176845i | ||||
\(685\) | 5.46819 | + | 16.8294i | 0.208929 | + | 0.643016i | ||||
\(686\) | −0.309017 | + | 0.951057i | −0.0117983 | + | 0.0363115i | ||||
\(687\) | 41.6126 | + | 30.2333i | 1.58762 | + | 1.15347i | ||||
\(688\) | −2.77144 | − | 2.01357i | −0.105660 | − | 0.0767666i | ||||
\(689\) | −7.96259 | + | 24.5063i | −0.303350 | + | 0.933616i | ||||
\(690\) | 4.01724 | + | 12.3638i | 0.152934 | + | 0.470682i | ||||
\(691\) | −22.3427 | + | 16.2330i | −0.849958 | + | 0.617531i | −0.925135 | − | 0.379639i | \(-0.876048\pi\) |
0.0751763 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(692\) | 1.52088 | 0.0578151 | ||||||||
\(693\) | 3.37283 | − | 0.0810353i | 0.128123 | − | 0.00307828i | ||||
\(694\) | 20.6300 | 0.783106 | ||||||||
\(695\) | 10.9035 | − | 7.92183i | 0.413592 | − | 0.300492i | ||||
\(696\) | 1.12522 | + | 3.46306i | 0.0426512 | + | 0.131267i | ||||
\(697\) | 0.899385 | − | 2.76802i | 0.0340666 | − | 0.104846i | ||||
\(698\) | 12.9481 | + | 9.40731i | 0.490091 | + | 0.356072i | ||||
\(699\) | −6.18507 | − | 4.49372i | −0.233941 | − | 0.169968i | ||||
\(700\) | −0.309017 | + | 0.951057i | −0.0116797 | + | 0.0359466i | ||||
\(701\) | 9.26683 | + | 28.5204i | 0.350003 | + | 1.07720i | 0.958850 | + | 0.283912i | \(0.0916322\pi\) |
−0.608847 | + | 0.793287i | \(0.708368\pi\) | |||||||
\(702\) | −12.9545 | + | 9.41201i | −0.488937 | + | 0.355234i | ||||
\(703\) | 70.4849 | 2.65839 | ||||||||
\(704\) | −1.10036 | − | 3.12877i | −0.0414714 | − | 0.117920i | ||||
\(705\) | 12.4508 | 0.468924 | ||||||||
\(706\) | 1.18829 | − | 0.863343i | 0.0447219 | − | 0.0324923i | ||||
\(707\) | −2.91837 | − | 8.98182i | −0.109757 | − | 0.337796i | ||||
\(708\) | 3.41855 | − | 10.5212i | 0.128477 | − | 0.395412i | ||||
\(709\) | 4.19485 | + | 3.04774i | 0.157541 | + | 0.114460i | 0.663763 | − | 0.747943i | \(-0.268958\pi\) |
−0.506222 | + | 0.862403i | \(0.668958\pi\) | |||||||
\(710\) | 6.77887 | + | 4.92514i | 0.254407 | + | 0.184837i | ||||
\(711\) | 1.94895 | − | 5.99827i | 0.0730915 | − | 0.224953i | ||||
\(712\) | 0.595831 | + | 1.83378i | 0.0223297 | + | 0.0687238i | ||||
\(713\) | 39.5376 | − | 28.7258i | 1.48070 | − | 1.07579i | ||||
\(714\) | −0.602426 | −0.0225452 | ||||||||
\(715\) | −3.82314 | + | 12.8051i | −0.142977 | + | 0.478885i | ||||
\(716\) | 24.1512 | 0.902573 | ||||||||
\(717\) | −10.6712 | + | 7.75308i | −0.398523 | + | 0.289544i | ||||
\(718\) | −2.60561 | − | 8.01924i | −0.0972405 | − | 0.299275i | ||||
\(719\) | −5.18617 | + | 15.9614i | −0.193411 | + | 0.595259i | 0.806580 | + | 0.591125i | \(0.201316\pi\) |
−0.999991 | + | 0.00413409i | \(0.998684\pi\) | |||||||
\(720\) | 0.822965 | + | 0.597919i | 0.0306701 | + | 0.0222831i | ||||
\(721\) | −2.84761 | − | 2.06891i | −0.106050 | − | 0.0770501i | ||||
\(722\) | 12.6187 | − | 38.8364i | 0.469620 | − | 1.44534i | ||||
\(723\) | 14.8449 | + | 45.6878i | 0.552087 | + | 1.69915i | ||||
\(724\) | −13.4801 | + | 9.79384i | −0.500983 | + | 0.363985i | ||||
\(725\) | 1.81673 | 0.0674715 | ||||||||
\(726\) | 7.81213 | + | 20.6169i | 0.289935 | + | 0.765165i | ||||
\(727\) | 9.72794 | 0.360789 | 0.180395 | − | 0.983594i | \(-0.442263\pi\) | ||||
0.180395 | + | 0.983594i | \(0.442263\pi\) | |||||||
\(728\) | −3.25978 | + | 2.36837i | −0.120815 | + | 0.0877775i | ||||
\(729\) | 3.92105 | + | 12.0677i | 0.145224 | + | 0.446953i | ||||
\(730\) | −0.433471 | + | 1.33409i | −0.0160435 | + | 0.0493767i | ||||
\(731\) | −0.833000 | − | 0.605210i | −0.0308096 | − | 0.0223845i | ||||
\(732\) | 5.88357 | + | 4.27467i | 0.217463 | + | 0.157996i | ||||
\(733\) | 3.27165 | − | 10.0691i | 0.120841 | − | 0.371911i | −0.872279 | − | 0.489008i | \(-0.837359\pi\) |
0.993120 | + | 0.117097i | \(0.0373589\pi\) | |||||||
\(734\) | 8.42350 | + | 25.9249i | 0.310917 | + | 0.956904i | ||||
\(735\) | 1.62152 | − | 1.17810i | 0.0598106 | − | 0.0434549i | ||||
\(736\) | −6.48607 | −0.239080 | ||||||||
\(737\) | −0.479586 | + | 1.60632i | −0.0176658 | + | 0.0591694i | ||||
\(738\) | 9.85025 | 0.362593 | ||||||||
\(739\) | 9.45815 | − | 6.87175i | 0.347924 | − | 0.252781i | −0.400074 | − | 0.916483i | \(-0.631015\pi\) |
0.747998 | + | 0.663702i | \(0.231015\pi\) | |||||||
\(740\) | −2.81579 | − | 8.66612i | −0.103511 | − | 0.318573i | ||||
\(741\) | −19.3043 | + | 59.4125i | −0.709161 | + | 2.18257i | ||||
\(742\) | 5.17368 | + | 3.75890i | 0.189932 | + | 0.137993i | ||||
\(743\) | −1.88042 | − | 1.36621i | −0.0689859 | − | 0.0501212i | 0.552758 | − | 0.833342i | \(-0.313575\pi\) |
−0.621744 | + | 0.783221i | \(0.713575\pi\) | |||||||
\(744\) | 4.66678 | − | 14.3629i | 0.171093 | − | 0.526569i | ||||
\(745\) | 0.532797 | + | 1.63978i | 0.0195202 | + | 0.0600769i | ||||
\(746\) | −11.9263 | + | 8.66498i | −0.436654 | + | 0.317247i | ||||
\(747\) | 14.8281 | 0.542533 | ||||||||
\(748\) | −0.330731 | − | 0.940402i | −0.0120927 | − | 0.0343845i | ||||
\(749\) | −10.4251 | −0.380925 | ||||||||
\(750\) | 1.62152 | − | 1.17810i | 0.0592094 | − | 0.0430182i | ||||
\(751\) | −4.22108 | − | 12.9912i | −0.154029 | − | 0.474054i | 0.844032 | − | 0.536293i | \(-0.180176\pi\) |
−0.998061 | + | 0.0622392i | \(0.980176\pi\) | |||||||
\(752\) | −1.91962 | + | 5.90798i | −0.0700013 | + | 0.215442i | ||||
\(753\) | −8.24695 | − | 5.99176i | −0.300536 | − | 0.218352i | ||||
\(754\) | 5.92212 | + | 4.30267i | 0.215671 | + | 0.156694i | ||||
\(755\) | 2.82718 | − | 8.70117i | 0.102892 | − | 0.316668i | ||||
\(756\) | 1.22805 | + | 3.77955i | 0.0446638 | + | 0.137461i | ||||
\(757\) | −16.5366 | + | 12.0146i | −0.601034 | + | 0.436677i | −0.846246 | − | 0.532793i | \(-0.821143\pi\) |
0.245212 | + | 0.969470i | \(0.421143\pi\) | |||||||
\(758\) | −26.2074 | −0.951894 | ||||||||
\(759\) | 43.1039 | − | 1.03561i | 1.56457 | − | 0.0375902i | ||||
\(760\) | −7.73531 | −0.280589 | ||||||||
\(761\) | −4.48873 | + | 3.26126i | −0.162716 | + | 0.118220i | −0.666164 | − | 0.745806i | \(-0.732065\pi\) |
0.503447 | + | 0.864026i | \(0.332065\pi\) | |||||||
\(762\) | −7.98477 | − | 24.5746i | −0.289258 | − | 0.890243i | ||||
\(763\) | −3.75676 | + | 11.5621i | −0.136004 | + | 0.418577i | ||||
\(764\) | 2.40722 | + | 1.74894i | 0.0870900 | + | 0.0632746i | ||||
\(765\) | 0.247355 | + | 0.179714i | 0.00894315 | + | 0.00649758i | ||||
\(766\) | −5.57885 | + | 17.1699i | −0.201572 | + | 0.620374i | ||||
\(767\) | −6.87239 | − | 21.1511i | −0.248148 | − | 0.763720i | ||||
\(768\) | −1.62152 | + | 1.17810i | −0.0585115 | + | 0.0425111i | ||||
\(769\) | 8.18880 | 0.295296 | 0.147648 | − | 0.989040i | \(-0.452830\pi\) | ||||
0.147648 | + | 0.989040i | \(0.452830\pi\) | |||||||
\(770\) | 2.72926 | + | 1.88445i | 0.0983556 | + | 0.0679110i | ||||
\(771\) | 22.2413 | 0.801002 | ||||||||
\(772\) | 9.30418 | − | 6.75988i | 0.334865 | − | 0.243293i | ||||
\(773\) | 3.24605 | + | 9.99033i | 0.116752 | + | 0.359327i | 0.992309 | − | 0.123789i | \(-0.0395047\pi\) |
−0.875556 | + | 0.483117i | \(0.839505\pi\) | |||||||
\(774\) | 1.07685 | − | 3.31419i | 0.0387065 | − | 0.119126i | ||||
\(775\) | −6.09578 | − | 4.42884i | −0.218967 | − | 0.159089i | ||||
\(776\) | 13.3442 | + | 9.69514i | 0.479029 | + | 0.348035i | ||||
\(777\) | −5.64371 | + | 17.3696i | −0.202467 | + | 0.623129i | ||||
\(778\) | −6.61462 | − | 20.3577i | −0.237146 | − | 0.729860i | ||||
\(779\) | −60.5981 | + | 44.0271i | −2.17115 | + | 1.57743i | ||||
\(780\) | 8.07596 | 0.289166 | ||||||||
\(781\) | 22.0842 | − | 16.8701i | 0.790233 | − | 0.603661i | ||||
\(782\) | −1.94949 | −0.0697137 | ||||||||
\(783\) | 5.84091 | − | 4.24367i | 0.208737 | − | 0.151656i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | 0.270707 | − | 0.833150i | 0.00966194 | − | 0.0297364i | ||||
\(786\) | −33.0566 | − | 24.0171i | −1.17909 | − | 0.856660i | ||||
\(787\) | −9.58138 | − | 6.96128i | −0.341539 | − | 0.248143i | 0.403772 | − | 0.914860i | \(-0.367699\pi\) |
−0.745311 | + | 0.666717i | \(0.767699\pi\) | |||||||
\(788\) | 4.96270 | − | 15.2736i | 0.176789 | − | 0.544101i | ||||
\(789\) | −1.63994 | − | 5.04723i | −0.0583836 | − | 0.179686i | ||||
\(790\) | 5.01595 | − | 3.64430i | 0.178459 | − | 0.129658i | ||||
\(791\) | 6.67216 | 0.237235 | ||||||||
\(792\) | 2.68105 | − | 2.04806i | 0.0952669 | − | 0.0727747i | ||||
\(793\) | 14.6201 | 0.519174 | ||||||||
\(794\) | −3.94489 | + | 2.86613i | −0.139999 | + | 0.101715i | ||||
\(795\) | −3.96085 | − | 12.1902i | −0.140477 | − | 0.432343i | ||||
\(796\) | 3.42696 | − | 10.5471i | 0.121465 | − | 0.373832i | ||||
\(797\) | 18.0603 | + | 13.1216i | 0.639728 | + | 0.464789i | 0.859757 | − | 0.510704i | \(-0.170615\pi\) |
−0.220029 | + | 0.975493i | \(0.570615\pi\) | |||||||
\(798\) | 12.5429 | + | 9.11298i | 0.444015 | + | 0.322596i | ||||
\(799\) | −0.576972 | + | 1.77574i | −0.0204118 | + | 0.0628211i | ||||
\(800\) | 0.309017 | + | 0.951057i | 0.0109254 | + | 0.0336249i | ||||
\(801\) | −1.58680 | + | 1.15288i | −0.0560669 | + | 0.0407350i | ||||
\(802\) | 15.6680 | 0.553257 | ||||||||
\(803\) | 3.82844 | + | 2.64340i | 0.135103 | + | 0.0932835i | ||||
\(804\) | 1.01307 | 0.0357283 | ||||||||
\(805\) | 5.24734 | − | 3.81242i | 0.184944 | − | 0.134370i | ||||
\(806\) | −9.38175 | − | 28.8741i | −0.330458 | − | 1.01705i | ||||
\(807\) | −2.11946 | + | 6.52302i | −0.0746085 | + | 0.229621i | ||||
\(808\) | −7.64039 | − | 5.55107i | −0.268788 | − | 0.195286i | ||||
\(809\) | 25.9692 | + | 18.8677i | 0.913027 | + | 0.663353i | 0.941779 | − | 0.336234i | \(-0.109153\pi\) |
−0.0287516 | + | 0.999587i | \(0.509153\pi\) | |||||||
\(810\) | 3.40442 | − | 10.4777i | 0.119619 | − | 0.368150i | ||||
\(811\) | 13.1177 | + | 40.3721i | 0.460625 | + | 1.41766i | 0.864403 | + | 0.502800i | \(0.167697\pi\) |
−0.403778 | + | 0.914857i | \(0.632303\pi\) | |||||||
\(812\) | 1.46976 | − | 1.06784i | 0.0515785 | − | 0.0374740i | ||||
\(813\) | −42.4487 | −1.48874 | ||||||||
\(814\) | −30.2127 | + | 0.725886i | −1.05895 | + | 0.0254423i | ||||
\(815\) | 6.49269 | 0.227429 | ||||||||
\(816\) | −0.487373 | + | 0.354097i | −0.0170615 | + | 0.0123959i | ||||
\(817\) | 8.18856 | + | 25.2018i | 0.286482 | + | 0.881700i | ||||
\(818\) | 11.4899 | − | 35.3623i | 0.401735 | − | 1.23641i | ||||
\(819\) | −3.31598 | − | 2.40920i | −0.115870 | − | 0.0841842i | ||||
\(820\) | 7.83396 | + | 5.69170i | 0.273574 | + | 0.198763i | ||||
\(821\) | −5.48048 | + | 16.8672i | −0.191270 | + | 0.588668i | 0.808730 | + | 0.588180i | \(0.200155\pi\) |
−1.00000 | 0.000488150i | \(0.999845\pi\) | ||||||||
\(822\) | −10.9599 | − | 33.7312i | −0.382271 | − | 1.17651i | ||||
\(823\) | −30.6936 | + | 22.3002i | −1.06991 | + | 0.777336i | −0.975896 | − | 0.218235i | \(-0.929970\pi\) |
−0.0940145 | + | 0.995571i | \(0.529970\pi\) | |||||||
\(824\) | −3.51983 | −0.122619 | ||||||||
\(825\) | −2.20546 | − | 6.27101i | −0.0767842 | − | 0.218329i | ||||
\(826\) | −5.51945 | −0.192046 | ||||||||
\(827\) | −33.1095 | + | 24.0555i | −1.15133 | + | 0.836491i | −0.988657 | − | 0.150189i | \(-0.952012\pi\) |
−0.162673 | + | 0.986680i | \(0.552012\pi\) | |||||||
\(828\) | −2.03886 | − | 6.27497i | −0.0708554 | − | 0.218070i | ||||
\(829\) | 0.871400 | − | 2.68189i | 0.0302650 | − | 0.0931460i | −0.934783 | − | 0.355219i | \(-0.884406\pi\) |
0.965048 | + | 0.262073i | \(0.0844062\pi\) | |||||||
\(830\) | 11.7929 | + | 8.56803i | 0.409337 | + | 0.297401i | ||||
\(831\) | −44.4158 | − | 32.2700i | −1.54077 | − | 1.11943i | ||||
\(832\) | −1.24512 | + | 3.83210i | −0.0431669 | + | 0.132854i | ||||
\(833\) | 0.0928800 | + | 0.285855i | 0.00321810 | + | 0.00990429i | ||||
\(834\) | −21.8539 | + | 15.8778i | −0.756738 | + | 0.549802i | ||||
\(835\) | 20.0322 | 0.693244 | ||||||||
\(836\) | −7.33953 | + | 24.5829i | −0.253843 | + | 0.850216i | ||||
\(837\) | −29.9437 | −1.03501 | ||||||||
\(838\) | 22.0537 | − | 16.0229i | 0.761832 | − | 0.553503i | ||||
\(839\) | −17.1176 | − | 52.6827i | −0.590967 | − | 1.81881i | −0.573858 | − | 0.818954i | \(-0.694554\pi\) |
−0.0171081 | − | 0.999854i | \(-0.505446\pi\) | |||||||
\(840\) | 0.619365 | − | 1.90621i | 0.0213701 | − | 0.0657704i | ||||
\(841\) | 20.7913 | + | 15.1058i | 0.716943 | + | 0.520889i | ||||
\(842\) | 10.6788 | + | 7.75860i | 0.368016 | + | 0.267379i | ||||
\(843\) | 6.97526 | − | 21.4676i | 0.240241 | − | 0.739385i | ||||
\(844\) | −7.88445 | − | 24.2658i | −0.271394 | − | 0.835265i | ||||
\(845\) | 2.61740 | − | 1.90165i | 0.0900414 | − | 0.0654189i | ||||
\(846\) | −6.31912 | −0.217256 | ||||||||
\(847\) | 8.57841 | − | 6.88555i | 0.294758 | − | 0.236590i | ||||
\(848\) | 6.39502 | 0.219606 | ||||||||
\(849\) | 32.9052 | − | 23.9070i | 1.12930 | − | 0.820486i | ||||
\(850\) | 0.0928800 | + | 0.285855i | 0.00318576 | + | 0.00980475i | ||||
\(851\) | −18.2634 | + | 56.2091i | −0.626062 | + | 1.92682i | ||||
\(852\) | −13.5869 | − | 9.87149i | −0.465481 | − | 0.338192i | ||||
\(853\) | 40.1908 | + | 29.2003i | 1.37611 | + | 0.999800i | 0.997232 | + | 0.0743526i | \(0.0236890\pi\) |
0.378875 | + | 0.925448i | \(0.376311\pi\) | |||||||
\(854\) | 1.12125 | − | 3.45085i | 0.0383683 | − | 0.118086i | ||||
\(855\) | −2.43155 | − | 7.48356i | −0.0831574 | − | 0.255932i | ||||
\(856\) | −8.43409 | + | 6.12773i | −0.288271 | + | 0.209441i | ||||
\(857\) | −20.7002 | −0.707104 | −0.353552 | − | 0.935415i | \(-0.615026\pi\) | ||||
−0.353552 | + | 0.935415i | \(0.615026\pi\) | |||||||
\(858\) | 7.66275 | − | 25.6654i | 0.261602 | − | 0.876203i | ||||
\(859\) | −15.2630 | −0.520766 | −0.260383 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260383 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(860\) | 2.77144 | − | 2.01357i | 0.0945053 | − | 0.0686621i | ||||
\(861\) | −5.99749 | − | 18.4584i | −0.204394 | − | 0.629060i | ||||
\(862\) | −5.39339 | + | 16.5991i | −0.183700 | + | 0.565369i | ||||
\(863\) | −7.17063 | − | 5.20977i | −0.244091 | − | 0.177343i | 0.459013 | − | 0.888430i | \(-0.348203\pi\) |
−0.703104 | + | 0.711087i | \(0.748203\pi\) | |||||||
\(864\) | 3.21508 | + | 2.33589i | 0.109379 | + | 0.0794686i | ||||
\(865\) | −0.469977 | + | 1.44644i | −0.0159797 | + | 0.0491805i | ||||
\(866\) | −8.73900 | − | 26.8959i | −0.296963 | − | 0.913959i | ||||
\(867\) | 27.4193 | − | 19.9213i | 0.931208 | − | 0.676563i | ||||
\(868\) | −7.53480 | −0.255748 | ||||||||
\(869\) | −6.82229 | − | 19.3985i | −0.231430 | − | 0.658051i | ||||
\(870\) | −3.64127 | −0.123451 | ||||||||
\(871\) | 1.64765 | − | 1.19708i | 0.0558284 | − | 0.0405617i | ||||
\(872\) | 3.75676 | + | 11.5621i | 0.127220 | + | 0.391543i | ||||
\(873\) | −5.18492 | + | 15.9575i | −0.175483 | + | 0.540081i | ||||
\(874\) | 40.5898 | + | 29.4902i | 1.37297 | + | 0.997522i | ||||
\(875\) | −0.809017 | − | 0.587785i | −0.0273498 | − | 0.0198708i | ||||
\(876\) | 0.868808 | − | 2.67392i | 0.0293543 | − | 0.0903432i | ||||
\(877\) | 5.17223 | + | 15.9185i | 0.174654 | + | 0.537530i | 0.999617 | − | 0.0276564i | \(-0.00880442\pi\) |
−0.824964 | + | 0.565186i | \(0.808804\pi\) | |||||||
\(878\) | −28.9211 | + | 21.0124i | −0.976040 | + | 0.709134i | ||||
\(879\) | −23.9610 | −0.808185 | ||||||||
\(880\) | 3.31567 | − | 0.0796618i | 0.111771 | − | 0.00268540i | ||||
\(881\) | −4.10239 | −0.138213 | −0.0691065 | − | 0.997609i | \(-0.522015\pi\) | ||||
−0.0691065 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(882\) | −0.822965 | + | 0.597919i | −0.0277107 | + | 0.0201330i | ||||
\(883\) | 12.5875 | + | 38.7405i | 0.423604 | + | 1.30372i | 0.904324 | + | 0.426846i | \(0.140375\pi\) |
−0.480720 | + | 0.876874i | \(0.659625\pi\) | |||||||
\(884\) | −0.374242 | + | 1.15180i | −0.0125871 | + | 0.0387391i | ||||
\(885\) | 8.94988 | + | 6.50247i | 0.300847 | + | 0.218578i | ||||
\(886\) | −12.0900 | − | 8.78393i | −0.406173 | − | 0.295102i | ||||
\(887\) | −5.49718 | + | 16.9186i | −0.184577 | + | 0.568071i | −0.999941 | − | 0.0108787i | \(-0.996537\pi\) |
0.815363 | + | 0.578949i | \(0.196537\pi\) | |||||||
\(888\) | 5.64371 | + | 17.3696i | 0.189391 | + | 0.582884i | ||||
\(889\) | −10.4297 | + | 7.57765i | −0.349802 | + | 0.254146i | ||||
\(890\) | −1.92815 | −0.0646318 | ||||||||
\(891\) | −30.0681 | − | 20.7609i | −1.00732 | − | 0.695517i | ||||
\(892\) | −23.1843 | −0.776268 | ||||||||
\(893\) | 38.8748 | − | 28.2442i | 1.30090 | − | 0.945156i | ||||
\(894\) | −1.06789 | − | 3.28662i | −0.0357155 | − | 0.109921i | ||||
\(895\) | −7.46313 | + | 22.9692i | −0.249465 | + | 0.767775i | ||||
\(896\) | 0.809017 | + | 0.587785i | 0.0270274 | + | 0.0196365i | ||||
\(897\) | −42.3773 | − | 30.7889i | −1.41494 | − | 1.02801i | ||||
\(898\) | 4.32152 | − | 13.3003i | 0.144211 | − | 0.443836i | ||||
\(899\) | 4.23003 | + | 13.0187i | 0.141079 | + | 0.434197i | ||||
\(900\) | −0.822965 | + | 0.597919i | −0.0274322 | + | 0.0199306i | ||||
\(901\) | 1.92212 | 0.0640352 | ||||||||
\(902\) | 25.5214 | − | 19.4959i | 0.849769 | − | 0.649141i | ||||
\(903\) | −6.86612 | −0.228490 | ||||||||
\(904\) | 5.39789 | − | 3.92180i | 0.179531 | − | 0.130437i | ||||
\(905\) | −5.14893 | − | 15.8468i | −0.171156 | − | 0.526764i | ||||
\(906\) | −5.66654 | + | 17.4398i | −0.188258 | + | 0.579399i | ||||
\(907\) | 3.05718 | + | 2.22117i | 0.101512 | + | 0.0737528i | 0.637383 | − | 0.770547i | \(-0.280017\pi\) |
−0.535871 | + | 0.844300i | \(0.680017\pi\) | |||||||
\(908\) | 4.02374 | + | 2.92342i | 0.133533 | + | 0.0970170i | ||||
\(909\) | 2.96869 | − | 9.13667i | 0.0984651 | − | 0.303044i | ||||
\(910\) | −1.24512 | − | 3.83210i | −0.0412754 | − | 0.127033i | ||||
\(911\) | −29.8108 | + | 21.6588i | −0.987677 | + | 0.717589i | −0.959411 | − | 0.282011i | \(-0.908998\pi\) |
−0.0282656 | + | 0.999600i | \(0.508998\pi\) | |||||||
\(912\) | 15.5039 | 0.513386 | ||||||||
\(913\) | 38.4187 | − | 29.3482i | 1.27147 | − | 0.971283i | ||||
\(914\) | 10.2714 | 0.339748 | ||||||||
\(915\) | −5.88357 | + | 4.27467i | −0.194505 | + | 0.141316i | ||||
\(916\) | −7.93022 | − | 24.4067i | −0.262022 | − | 0.806420i | ||||
\(917\) | −6.29969 | + | 19.3885i | −0.208034 | + | 0.640263i | ||||
\(918\) | 0.966343 | + | 0.702089i | 0.0318941 | + | 0.0231724i | ||||
\(919\) | 45.9478 | + | 33.3830i | 1.51568 | + | 1.10120i | 0.963578 | + | 0.267426i | \(0.0861731\pi\) |
0.552099 | + | 0.833778i | \(0.313827\pi\) | |||||||
\(920\) | 2.00431 | − | 6.16862i | 0.0660800 | − | 0.203373i | ||||
\(921\) | −12.1783 | − | 37.4809i | −0.401288 | − | 1.23504i | ||||
\(922\) | 14.0816 | − | 10.2309i | 0.463753 | − | 0.336937i | ||||
\(923\) | −33.7621 | −1.11129 | ||||||||
\(924\) | −5.47026 | − | 3.77702i | −0.179958 | − | 0.124255i | ||||
\(925\) | 9.11210 | 0.299604 | ||||||||
\(926\) | 24.5895 | − | 17.8653i | 0.808061 | − | 0.587091i | ||||
\(927\) | −1.10644 | − | 3.40528i | −0.0363403 | − | 0.111844i | ||||
\(928\) | 0.561399 | − | 1.72781i | 0.0184288 | − | 0.0567181i | ||||
\(929\) | 14.5874 | + | 10.5984i | 0.478598 | + | 0.347722i | 0.800783 | − | 0.598955i | \(-0.204417\pi\) |
−0.322185 | + | 0.946677i | \(0.604417\pi\) | |||||||
\(930\) | 12.2178 | + | 8.87675i | 0.400637 | + | 0.291080i | ||||
\(931\) | 2.39034 | − | 7.35672i | 0.0783403 | − | 0.241107i | ||||
\(932\) | 1.17871 | + | 3.62769i | 0.0386098 | + | 0.118829i | ||||
\(933\) | 17.5164 | − | 12.7264i | 0.573461 | − | 0.416644i | ||||
\(934\) | 23.8052 | 0.778931 | ||||||||
\(935\) | 0.996577 | − | 0.0239436i | 0.0325915 | − | 0.000783040i | ||||
\(936\) | −4.09877 | −0.133973 | ||||||||
\(937\) | 16.8154 | − | 12.2171i | 0.549335 | − | 0.399116i | −0.278205 | − | 0.960522i | \(-0.589739\pi\) |
0.827540 | + | 0.561406i | \(0.189739\pi\) | |||||||
\(938\) | −0.156192 | − | 0.480709i | −0.00509985 | − | 0.0156957i | ||||
\(939\) | −9.13247 | + | 28.1068i | −0.298027 | + | 0.917232i | ||||
\(940\) | −5.02563 | − | 3.65133i | −0.163918 | − | 0.119093i | ||||
\(941\) | −3.32988 | − | 2.41930i | −0.108551 | − | 0.0788669i | 0.532186 | − | 0.846628i | \(-0.321371\pi\) |
−0.640736 | + | 0.767761i | \(0.721371\pi\) | |||||||
\(942\) | −0.542579 | + | 1.66989i | −0.0176782 | + | 0.0544078i | ||||
\(943\) | −19.4083 | − | 59.7326i | −0.632021 | − | 1.94516i | ||||
\(944\) | −4.46533 | + | 3.24425i | −0.145334 | + | 0.105591i | ||||
\(945\) | −3.97405 | −0.129276 | ||||||||
\(946\) | −3.76949 | − | 10.7182i | −0.122557 | − | 0.348478i | ||||
\(947\) | −31.0569 | −1.00921 | −0.504607 | − | 0.863349i | \(-0.668363\pi\) | ||||
−0.504607 | + | 0.863349i | \(0.668363\pi\) | |||||||
\(948\) | −10.0535 | + | 7.30429i | −0.326522 | + | 0.237232i | ||||
\(949\) | −1.74659 | − | 5.37544i | −0.0566966 | − | 0.174494i | ||||
\(950\) | 2.39034 | − | 7.35672i | 0.0775530 | − | 0.238683i | ||||
\(951\) | −28.3228 | − | 20.5777i | −0.918429 | − | 0.667278i | ||||
\(952\) | 0.243163 | + | 0.176668i | 0.00788096 | + | 0.00572585i | ||||
\(953\) | 5.52793 | − | 17.0132i | 0.179067 | − | 0.551112i | −0.820729 | − | 0.571318i | \(-0.806432\pi\) |
0.999796 | + | 0.0202059i | \(0.00643218\pi\) | |||||||
\(954\) | 2.01024 | + | 6.18688i | 0.0650839 | + | 0.200308i | ||||
\(955\) | −2.40722 | + | 1.74894i | −0.0778957 | + | 0.0565945i | ||||
\(956\) | 6.58100 | 0.212845 | ||||||||
\(957\) | −3.45497 | + | 11.5720i | −0.111683 | + | 0.374069i | ||||
\(958\) | 7.79996 | 0.252005 | ||||||||
\(959\) | −14.3159 | + | 10.4011i | −0.462285 | + | 0.335869i | ||||
\(960\) | −0.619365 | − | 1.90621i | −0.0199899 | − | 0.0615226i | ||||
\(961\) | 7.96434 | − | 24.5117i | 0.256914 | − | 0.790700i | ||||
\(962\) | 29.7034 | + | 21.5808i | 0.957676 | + | 0.695792i | ||||
\(963\) | −8.57951 | − | 6.23338i | −0.276471 | − | 0.200868i | ||||
\(964\) | 7.40650 | − | 22.7948i | 0.238547 | − | 0.734173i | ||||
\(965\) | 3.55388 | + | 10.9377i | 0.114403 | + | 0.352098i | ||||
\(966\) | −10.5173 | + | 7.64125i | −0.338388 | + | 0.245853i | ||||
\(967\) | −59.5313 | −1.91440 | −0.957199 | − | 0.289431i | \(-0.906534\pi\) | ||||
−0.957199 | + | 0.289431i | \(0.906534\pi\) | |||||||
\(968\) | 2.89286 | − | 10.6128i | 0.0929799 | − | 0.341108i | ||||
\(969\) | 4.65995 | 0.149699 | ||||||||
\(970\) | −13.3442 | + | 9.69514i | −0.428457 | + | 0.311292i | ||||
\(971\) | −13.3350 | − | 41.0408i | −0.427940 | − | 1.31706i | −0.900151 | − | 0.435577i | \(-0.856544\pi\) |
0.472212 | − | 0.881485i | \(-0.343456\pi\) | |||||||
\(972\) | −3.13935 | + | 9.66193i | −0.100695 | + | 0.309907i | ||||
\(973\) | 10.9035 | + | 7.92183i | 0.349549 | + | 0.253962i | ||||
\(974\) | 15.6228 | + | 11.3507i | 0.500588 | + | 0.363699i | ||||
\(975\) | −2.49561 | + | 7.68069i | −0.0799234 | + | 0.245979i | ||||
\(976\) | −1.12125 | − | 3.45085i | −0.0358903 | − | 0.110459i | ||||
\(977\) | 37.2480 | − | 27.0623i | 1.19167 | − | 0.865799i | 0.198231 | − | 0.980155i | \(-0.436480\pi\) |
0.993440 | + | 0.114356i | \(0.0364804\pi\) | |||||||
\(978\) | −13.0133 | −0.416121 | ||||||||
\(979\) | −1.82950 | + | 6.12767i | −0.0584710 | + | 0.195841i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −10.0049 | + | 7.26899i | −0.319432 | + | 0.232081i | ||||
\(982\) | 5.10436 | + | 15.7096i | 0.162887 | + | 0.501313i | ||||
\(983\) | 13.9657 | − | 42.9821i | 0.445438 | − | 1.37092i | −0.436565 | − | 0.899673i | \(-0.643805\pi\) |
0.882003 | − | 0.471245i | \(-0.156195\pi\) | |||||||
\(984\) | −15.7016 | − | 11.4079i | −0.500550 | − | 0.363671i | ||||
\(985\) | 12.9925 | + | 9.43963i | 0.413976 | + | 0.300771i | ||||
\(986\) | 0.168737 | − | 0.519320i | 0.00537369 | − | 0.0165385i | ||||
\(987\) | 3.84750 | + | 11.8414i | 0.122467 | + | 0.376916i | ||||
\(988\) | 25.2154 | − | 18.3200i | 0.802208 | − | 0.582838i | ||||
\(989\) | −22.2192 | −0.706531 | ||||||||
\(990\) | 1.11933 | + | 3.18271i | 0.0355747 | + | 0.101153i | ||||
\(991\) | −32.5442 | −1.03380 | −0.516900 | − | 0.856046i | \(-0.672914\pi\) | ||||
−0.516900 | + | 0.856046i | \(0.672914\pi\) | |||||||
\(992\) | −6.09578 | + | 4.42884i | −0.193541 | + | 0.140616i | ||||
\(993\) | 13.8351 | + | 42.5799i | 0.439042 | + | 1.35123i | ||||
\(994\) | −2.58930 | + | 7.96904i | −0.0821276 | + | 0.252763i | ||||
\(995\) | 8.97189 | + | 6.51846i | 0.284428 | + | 0.206649i | ||||
\(996\) | −23.6365 | − | 17.1730i | −0.748952 | − | 0.544146i | ||||
\(997\) | −13.8467 | + | 42.6157i | −0.438529 | + | 1.34965i | 0.450897 | + | 0.892576i | \(0.351104\pi\) |
−0.889427 | + | 0.457078i | \(0.848896\pi\) | |||||||
\(998\) | 3.66780 | + | 11.2883i | 0.116102 | + | 0.357326i | ||||
\(999\) | 29.2961 | − | 21.2849i | 0.926888 | − | 0.673423i |
(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 | 770.2.n.k.421.4 | ✓ | 16 | |
11.2 | odd | 10 | 8470.2.a.dg.1.7 | 8 | |||
11.4 | even | 5 | inner | 770.2.n.k.631.4 | yes | 16 | |
11.9 | even | 5 | 8470.2.a.dh.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.421.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
770.2.n.k.631.4 | yes | 16 | 11.4 | even | 5 | inner | |
8470.2.a.dg.1.7 | 8 | 11.2 | odd | 10 | |||
8470.2.a.dh.1.7 | 8 | 11.9 | even | 5 |