Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(64,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.j (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: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.148 |
Dual form | 231.2.j.d.64.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 1.53884i | 0.353553 | + | 1.08813i | 0.956844 | + | 0.290604i | \(0.0938561\pi\) |
−0.603290 | + | 0.797522i | \(0.706144\pi\) | |||||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | −0.500000 | + | 0.363271i | −0.250000 | + | 0.181636i | ||||
\(5\) | −0.809017 | + | 2.48990i | −0.361803 | + | 1.11352i | 0.590155 | + | 0.807290i | \(0.299067\pi\) |
−0.951959 | + | 0.306227i | \(0.900933\pi\) | |||||||
\(6\) | 0.500000 | − | 1.53884i | 0.204124 | − | 0.628230i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | 1.80902 | + | 1.31433i | 0.639584 | + | 0.464685i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −4.23607 | −1.33956 | ||||||||
\(11\) | −0.809017 | + | 3.21644i | −0.243928 | + | 0.969793i | ||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −0.309017 | − | 0.951057i | −0.0857059 | − | 0.263776i | 0.899014 | − | 0.437919i | \(-0.144284\pi\) |
−0.984720 | + | 0.174143i | \(0.944284\pi\) | |||||||
\(14\) | −1.30902 | − | 0.951057i | −0.349850 | − | 0.254181i | ||||
\(15\) | 2.11803 | − | 1.53884i | 0.546874 | − | 0.397327i | ||||
\(16\) | −1.50000 | + | 4.61653i | −0.375000 | + | 1.15413i | ||||
\(17\) | 0.0729490 | − | 0.224514i | 0.0176927 | − | 0.0544526i | −0.941820 | − | 0.336117i | \(-0.890886\pi\) |
0.959513 | + | 0.281664i | \(0.0908864\pi\) | |||||||
\(18\) | −1.30902 | + | 0.951057i | −0.308538 | + | 0.224166i | ||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | −0.500000 | − | 1.53884i | −0.111803 | − | 0.344095i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −5.35410 | + | 0.363271i | −1.14150 | + | 0.0774497i | ||||
\(23\) | 1.23607 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(24\) | −0.690983 | − | 2.12663i | −0.141046 | − | 0.434096i | ||||
\(25\) | −1.50000 | − | 1.08981i | −0.300000 | − | 0.217963i | ||||
\(26\) | 1.30902 | − | 0.951057i | 0.256719 | − | 0.186518i | ||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 0.190983 | − | 0.587785i | 0.0360924 | − | 0.111081i | ||||
\(29\) | 5.42705 | − | 3.94298i | 1.00778 | − | 0.732194i | 0.0440362 | − | 0.999030i | \(-0.485978\pi\) |
0.963742 | + | 0.266836i | \(0.0859783\pi\) | |||||||
\(30\) | 3.42705 | + | 2.48990i | 0.625691 | + | 0.454591i | ||||
\(31\) | −1.78115 | − | 5.48183i | −0.319905 | − | 0.984565i | −0.973688 | − | 0.227884i | \(-0.926819\pi\) |
0.653784 | − | 0.756681i | \(-0.273181\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 2.54508 | − | 2.12663i | 0.443042 | − | 0.370198i | ||||
\(34\) | 0.381966 | 0.0655066 | ||||||||
\(35\) | −0.809017 | − | 2.48990i | −0.136749 | − | 0.420870i | ||||
\(36\) | −0.500000 | − | 0.363271i | −0.0833333 | − | 0.0605452i | ||||
\(37\) | 8.85410 | − | 6.43288i | 1.45561 | − | 1.05756i | 0.471125 | − | 0.882067i | \(-0.343848\pi\) |
0.984481 | − | 0.175493i | \(-0.0561518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.309017 | + | 0.951057i | −0.0494823 | + | 0.152291i | ||||
\(40\) | −4.73607 | + | 3.44095i | −0.748838 | + | 0.544063i | ||||
\(41\) | 4.92705 | + | 3.57971i | 0.769476 | + | 0.559057i | 0.901802 | − | 0.432149i | \(-0.142245\pi\) |
−0.132326 | + | 0.991206i | \(0.542245\pi\) | |||||||
\(42\) | 0.500000 | + | 1.53884i | 0.0771517 | + | 0.237448i | ||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | −0.763932 | − | 1.90211i | −0.115167 | − | 0.286754i | ||||
\(45\) | −2.61803 | −0.390273 | ||||||||
\(46\) | 0.618034 | + | 1.90211i | 0.0911241 | + | 0.280451i | ||||
\(47\) | −6.73607 | − | 4.89404i | −0.982556 | − | 0.713869i | −0.0242780 | − | 0.999705i | \(-0.507729\pi\) |
−0.958279 | + | 0.285836i | \(0.907729\pi\) | |||||||
\(48\) | 3.92705 | − | 2.85317i | 0.566821 | − | 0.411820i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0.927051 | − | 2.85317i | 0.131105 | − | 0.403499i | ||||
\(51\) | −0.190983 | + | 0.138757i | −0.0267430 | + | 0.0194299i | ||||
\(52\) | 0.500000 | + | 0.363271i | 0.0693375 | + | 0.0503767i | ||||
\(53\) | 1.66312 | + | 5.11855i | 0.228447 | + | 0.703087i | 0.997923 | + | 0.0644122i | \(0.0205173\pi\) |
−0.769476 | + | 0.638675i | \(0.779483\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | −7.35410 | − | 4.61653i | −0.991627 | − | 0.622492i | ||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.78115 | + | 6.37988i | 1.15302 | + | 0.837719i | ||||
\(59\) | 8.78115 | − | 6.37988i | 1.14321 | − | 0.830590i | 0.155646 | − | 0.987813i | \(-0.450254\pi\) |
0.987563 | + | 0.157223i | \(0.0502542\pi\) | |||||||
\(60\) | −0.500000 | + | 1.53884i | −0.0645497 | + | 0.198664i | ||||
\(61\) | −3.16312 | + | 9.73508i | −0.404996 | + | 1.24645i | 0.515903 | + | 0.856647i | \(0.327457\pi\) |
−0.920899 | + | 0.389802i | \(0.872543\pi\) | |||||||
\(62\) | 7.54508 | − | 5.48183i | 0.958227 | − | 0.696192i | ||||
\(63\) | −0.809017 | − | 0.587785i | −0.101927 | − | 0.0740540i | ||||
\(64\) | 1.30902 | + | 4.02874i | 0.163627 | + | 0.503593i | ||||
\(65\) | 2.61803 | 0.324727 | ||||||||
\(66\) | 4.54508 | + | 2.85317i | 0.559461 | + | 0.351201i | ||||
\(67\) | −4.76393 | −0.582007 | −0.291003 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291003 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(68\) | 0.0450850 | + | 0.138757i | 0.00546736 | + | 0.0168268i | ||||
\(69\) | −1.00000 | − | 0.726543i | −0.120386 | − | 0.0874654i | ||||
\(70\) | 3.42705 | − | 2.48990i | 0.409611 | − | 0.297600i | ||||
\(71\) | 0.454915 | − | 1.40008i | 0.0539885 | − | 0.166159i | −0.920427 | − | 0.390915i | \(-0.872158\pi\) |
0.974415 | + | 0.224756i | \(0.0721585\pi\) | |||||||
\(72\) | −0.690983 | + | 2.12663i | −0.0814331 | + | 0.250625i | ||||
\(73\) | 6.92705 | − | 5.03280i | 0.810750 | − | 0.589044i | −0.103298 | − | 0.994650i | \(-0.532940\pi\) |
0.914048 | + | 0.405606i | \(0.132940\pi\) | |||||||
\(74\) | 14.3262 | + | 10.4086i | 1.66539 | + | 1.20998i | ||||
\(75\) | 0.572949 | + | 1.76336i | 0.0661585 | + | 0.203615i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.23607 | − | 3.07768i | −0.140863 | − | 0.350735i | ||||
\(78\) | −1.61803 | −0.183206 | ||||||||
\(79\) | 1.28115 | + | 3.94298i | 0.144141 | + | 0.443620i | 0.996900 | − | 0.0786850i | \(-0.0250721\pi\) |
−0.852759 | + | 0.522305i | \(0.825072\pi\) | |||||||
\(80\) | −10.2812 | − | 7.46969i | −1.14947 | − | 0.835137i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −3.04508 | + | 9.37181i | −0.336273 | + | 1.03494i | ||||
\(83\) | −1.85410 | + | 5.70634i | −0.203514 | + | 0.626352i | 0.796257 | + | 0.604959i | \(0.206810\pi\) |
−0.999771 | + | 0.0213936i | \(0.993190\pi\) | |||||||
\(84\) | −0.500000 | + | 0.363271i | −0.0545545 | + | 0.0396361i | ||||
\(85\) | 0.500000 | + | 0.363271i | 0.0542326 | + | 0.0394023i | ||||
\(86\) | −0.500000 | − | 1.53884i | −0.0539164 | − | 0.165938i | ||||
\(87\) | −6.70820 | −0.719195 | ||||||||
\(88\) | −5.69098 | + | 4.75528i | −0.606661 | + | 0.506915i | ||||
\(89\) | −8.61803 | −0.913510 | −0.456755 | − | 0.889593i | \(-0.650988\pi\) | ||||
−0.456755 | + | 0.889593i | \(0.650988\pi\) | |||||||
\(90\) | −1.30902 | − | 4.02874i | −0.137983 | − | 0.424666i | ||||
\(91\) | 0.809017 | + | 0.587785i | 0.0848080 | + | 0.0616166i | ||||
\(92\) | −0.618034 | + | 0.449028i | −0.0644345 | + | 0.0468144i | ||||
\(93\) | −1.78115 | + | 5.48183i | −0.184697 | + | 0.568439i | ||||
\(94\) | 4.16312 | − | 12.8128i | 0.429393 | − | 1.32154i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.73607 | + | 1.98787i | 0.279249 | + | 0.202886i | ||||
\(97\) | −5.25329 | − | 16.1680i | −0.533391 | − | 1.64161i | −0.747101 | − | 0.664711i | \(-0.768555\pi\) |
0.213710 | − | 0.976897i | \(-0.431445\pi\) | |||||||
\(98\) | 1.61803 | 0.163446 | ||||||||
\(99\) | −3.30902 | + | 0.224514i | −0.332569 | + | 0.0225645i | ||||
\(100\) | 1.14590 | 0.114590 | ||||||||
\(101\) | 5.61803 | + | 17.2905i | 0.559015 | + | 1.72047i | 0.685097 | + | 0.728452i | \(0.259760\pi\) |
−0.126081 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(102\) | −0.309017 | − | 0.224514i | −0.0305972 | − | 0.0222302i | ||||
\(103\) | −0.572949 | + | 0.416272i | −0.0564543 | + | 0.0410165i | −0.615655 | − | 0.788016i | \(-0.711108\pi\) |
0.559200 | + | 0.829033i | \(0.311108\pi\) | |||||||
\(104\) | 0.690983 | − | 2.12663i | 0.0677565 | − | 0.208533i | ||||
\(105\) | −0.809017 | + | 2.48990i | −0.0789520 | + | 0.242989i | ||||
\(106\) | −7.04508 | + | 5.11855i | −0.684279 | + | 0.497158i | ||||
\(107\) | −16.3713 | − | 11.8945i | −1.58268 | − | 1.14988i | −0.913546 | − | 0.406735i | \(-0.866667\pi\) |
−0.669129 | − | 0.743146i | \(-0.733333\pi\) | |||||||
\(108\) | 0.190983 | + | 0.587785i | 0.0183773 | + | 0.0565597i | ||||
\(109\) | 12.5623 | 1.20325 | 0.601625 | − | 0.798778i | \(-0.294520\pi\) | ||||
0.601625 | + | 0.798778i | \(0.294520\pi\) | |||||||
\(110\) | 3.42705 | − | 13.6251i | 0.326756 | − | 1.29910i | ||||
\(111\) | −10.9443 | −1.03878 | ||||||||
\(112\) | −1.50000 | − | 4.61653i | −0.141737 | − | 0.436221i | ||||
\(113\) | −15.8992 | − | 11.5514i | −1.49567 | − | 1.08667i | −0.972067 | − | 0.234705i | \(-0.924587\pi\) |
−0.523603 | − | 0.851962i | \(-0.675413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | + | 3.07768i | −0.0932505 | + | 0.286995i | ||||
\(116\) | −1.28115 | + | 3.94298i | −0.118952 | + | 0.366097i | ||||
\(117\) | 0.809017 | − | 0.587785i | 0.0747936 | − | 0.0543408i | ||||
\(118\) | 14.2082 | + | 10.3229i | 1.30797 | + | 0.950297i | ||||
\(119\) | 0.0729490 | + | 0.224514i | 0.00668723 | + | 0.0205812i | ||||
\(120\) | 5.85410 | 0.534404 | ||||||||
\(121\) | −9.69098 | − | 5.20431i | −0.880998 | − | 0.473119i | ||||
\(122\) | −16.5623 | −1.49948 | ||||||||
\(123\) | −1.88197 | − | 5.79210i | −0.169691 | − | 0.522256i | ||||
\(124\) | 2.88197 | + | 2.09387i | 0.258808 | + | 0.188035i | ||||
\(125\) | −6.66312 | + | 4.84104i | −0.595967 | + | 0.432996i | ||||
\(126\) | 0.500000 | − | 1.53884i | 0.0445435 | − | 0.137091i | ||||
\(127\) | 2.57295 | − | 7.91872i | 0.228312 | − | 0.702673i | −0.769626 | − | 0.638495i | \(-0.779557\pi\) |
0.997938 | − | 0.0641782i | \(-0.0204426\pi\) | |||||||
\(128\) | −11.0172 | + | 8.00448i | −0.973794 | + | 0.707503i | ||||
\(129\) | 0.809017 | + | 0.587785i | 0.0712300 | + | 0.0517516i | ||||
\(130\) | 1.30902 | + | 4.02874i | 0.114808 | + | 0.353344i | ||||
\(131\) | 12.3262 | 1.07695 | 0.538474 | − | 0.842642i | \(-0.319001\pi\) | ||||
0.538474 | + | 0.842642i | \(0.319001\pi\) | |||||||
\(132\) | −0.500000 | + | 1.98787i | −0.0435194 | + | 0.173022i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.38197 | − | 7.33094i | −0.205771 | − | 0.633297i | ||||
\(135\) | 2.11803 | + | 1.53884i | 0.182291 | + | 0.132442i | ||||
\(136\) | 0.427051 | − | 0.310271i | 0.0366193 | − | 0.0266055i | ||||
\(137\) | −6.47214 | + | 19.9192i | −0.552952 | + | 1.70181i | 0.148340 | + | 0.988936i | \(0.452607\pi\) |
−0.701292 | + | 0.712874i | \(0.747393\pi\) | |||||||
\(138\) | 0.618034 | − | 1.90211i | 0.0526105 | − | 0.161919i | ||||
\(139\) | −2.07295 | + | 1.50609i | −0.175825 | + | 0.127745i | −0.672217 | − | 0.740354i | \(-0.734658\pi\) |
0.496392 | + | 0.868099i | \(0.334658\pi\) | |||||||
\(140\) | 1.30902 | + | 0.951057i | 0.110632 | + | 0.0803789i | ||||
\(141\) | 2.57295 | + | 7.91872i | 0.216681 | + | 0.666877i | ||||
\(142\) | 2.38197 | 0.199890 | ||||||||
\(143\) | 3.30902 | − | 0.224514i | 0.276714 | − | 0.0187748i | ||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 5.42705 | + | 16.7027i | 0.450692 | + | 1.38709i | ||||
\(146\) | 11.2082 | + | 8.14324i | 0.927598 | + | 0.673939i | ||||
\(147\) | −0.809017 | + | 0.587785i | −0.0667266 | + | 0.0484797i | ||||
\(148\) | −2.09017 | + | 6.43288i | −0.171811 | + | 0.528780i | ||||
\(149\) | −0.590170 | + | 1.81636i | −0.0483486 | + | 0.148802i | −0.972316 | − | 0.233669i | \(-0.924927\pi\) |
0.923968 | + | 0.382471i | \(0.124927\pi\) | |||||||
\(150\) | −2.42705 | + | 1.76336i | −0.198168 | + | 0.143977i | ||||
\(151\) | 8.01722 | + | 5.82485i | 0.652432 | + | 0.474020i | 0.864099 | − | 0.503322i | \(-0.167889\pi\) |
−0.211667 | + | 0.977342i | \(0.567889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.236068 | 0.0190850 | ||||||||
\(154\) | 4.11803 | − | 3.44095i | 0.331841 | − | 0.277280i | ||||
\(155\) | 15.0902 | 1.21207 | ||||||||
\(156\) | −0.190983 | − | 0.587785i | −0.0152909 | − | 0.0470605i | ||||
\(157\) | 14.0172 | + | 10.1841i | 1.11870 | + | 0.812780i | 0.984011 | − | 0.178108i | \(-0.0569977\pi\) |
0.134685 | + | 0.990888i | \(0.456998\pi\) | |||||||
\(158\) | −5.42705 | + | 3.94298i | −0.431753 | + | 0.313687i | ||||
\(159\) | 1.66312 | − | 5.11855i | 0.131894 | − | 0.405928i | ||||
\(160\) | 2.73607 | − | 8.42075i | 0.216305 | − | 0.665719i | ||||
\(161\) | −1.00000 | + | 0.726543i | −0.0788110 | + | 0.0572596i | ||||
\(162\) | −1.30902 | − | 0.951057i | −0.102846 | − | 0.0747221i | ||||
\(163\) | −7.11803 | − | 21.9071i | −0.557527 | − | 1.71589i | −0.689174 | − | 0.724596i | \(-0.742026\pi\) |
0.131646 | − | 0.991297i | \(-0.457974\pi\) | |||||||
\(164\) | −3.76393 | −0.293914 | ||||||||
\(165\) | 3.23607 | + | 8.05748i | 0.251928 | + | 0.627274i | ||||
\(166\) | −9.70820 | −0.753503 | ||||||||
\(167\) | 3.59017 | + | 11.0494i | 0.277816 | + | 0.855029i | 0.988461 | + | 0.151478i | \(0.0484033\pi\) |
−0.710645 | + | 0.703551i | \(0.751597\pi\) | |||||||
\(168\) | 1.80902 | + | 1.31433i | 0.139569 | + | 0.101403i | ||||
\(169\) | 9.70820 | − | 7.05342i | 0.746785 | − | 0.542571i | ||||
\(170\) | −0.309017 | + | 0.951057i | −0.0237005 | + | 0.0729427i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | − | 0.363271i | 0.0381246 | − | 0.0276992i | ||||
\(173\) | 10.0172 | + | 7.27794i | 0.761595 | + | 0.553331i | 0.899399 | − | 0.437128i | \(-0.144004\pi\) |
−0.137804 | + | 0.990460i | \(0.544004\pi\) | |||||||
\(174\) | −3.35410 | − | 10.3229i | −0.254274 | − | 0.782574i | ||||
\(175\) | 1.85410 | 0.140157 | ||||||||
\(176\) | −13.6353 | − | 8.55951i | −1.02780 | − | 0.645197i | ||||
\(177\) | −10.8541 | −0.815844 | ||||||||
\(178\) | −4.30902 | − | 13.2618i | −0.322974 | − | 0.994013i | ||||
\(179\) | −1.80902 | − | 1.31433i | −0.135212 | − | 0.0982375i | 0.518123 | − | 0.855306i | \(-0.326631\pi\) |
−0.653335 | + | 0.757069i | \(0.726631\pi\) | |||||||
\(180\) | 1.30902 | − | 0.951057i | 0.0975684 | − | 0.0708876i | ||||
\(181\) | 1.30902 | − | 4.02874i | 0.0972985 | − | 0.299454i | −0.890547 | − | 0.454890i | \(-0.849678\pi\) |
0.987846 | + | 0.155437i | \(0.0496784\pi\) | |||||||
\(182\) | −0.500000 | + | 1.53884i | −0.0370625 | + | 0.114067i | ||||
\(183\) | 8.28115 | − | 6.01661i | 0.612160 | − | 0.444761i | ||||
\(184\) | 2.23607 | + | 1.62460i | 0.164845 | + | 0.119767i | ||||
\(185\) | 8.85410 | + | 27.2501i | 0.650967 | + | 2.00347i | ||||
\(186\) | −9.32624 | −0.683833 | ||||||||
\(187\) | 0.663119 | + | 0.416272i | 0.0484921 | + | 0.0304408i | ||||
\(188\) | 5.14590 | 0.375303 | ||||||||
\(189\) | 0.309017 | + | 0.951057i | 0.0224777 | + | 0.0691792i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5172 | + | 8.36775i | −0.833357 | + | 0.605469i | −0.920507 | − | 0.390726i | \(-0.872224\pi\) |
0.0871502 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(192\) | 1.30902 | − | 4.02874i | 0.0944702 | − | 0.290749i | ||||
\(193\) | 7.09017 | − | 21.8213i | 0.510362 | − | 1.57073i | −0.281204 | − | 0.959648i | \(-0.590734\pi\) |
0.791566 | − | 0.611084i | \(-0.209266\pi\) | |||||||
\(194\) | 22.2533 | − | 16.1680i | 1.59769 | − | 1.16079i | ||||
\(195\) | −2.11803 | − | 1.53884i | −0.151676 | − | 0.110199i | ||||
\(196\) | 0.190983 | + | 0.587785i | 0.0136416 | + | 0.0419847i | ||||
\(197\) | −4.76393 | −0.339416 | −0.169708 | − | 0.985494i | \(-0.554282\pi\) | ||||
−0.169708 | + | 0.985494i | \(0.554282\pi\) | |||||||
\(198\) | −2.00000 | − | 4.97980i | −0.142134 | − | 0.353899i | ||||
\(199\) | 12.5623 | 0.890518 | 0.445259 | − | 0.895402i | \(-0.353112\pi\) | ||||
0.445259 | + | 0.895402i | \(0.353112\pi\) | |||||||
\(200\) | −1.28115 | − | 3.94298i | −0.0905912 | − | 0.278811i | ||||
\(201\) | 3.85410 | + | 2.80017i | 0.271847 | + | 0.197509i | ||||
\(202\) | −23.7984 | + | 17.2905i | −1.67445 | + | 1.21656i | ||||
\(203\) | −2.07295 | + | 6.37988i | −0.145492 | + | 0.447780i | ||||
\(204\) | 0.0450850 | − | 0.138757i | 0.00315658 | − | 0.00971495i | ||||
\(205\) | −12.8992 | + | 9.37181i | −0.900918 | + | 0.654555i | ||||
\(206\) | −0.927051 | − | 0.673542i | −0.0645907 | − | 0.0469279i | ||||
\(207\) | 0.381966 | + | 1.17557i | 0.0265485 | + | 0.0817078i | ||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.23607 | −0.292316 | ||||||||
\(211\) | 5.78115 | + | 17.7926i | 0.397991 | + | 1.22489i | 0.926608 | + | 0.376030i | \(0.122711\pi\) |
−0.528617 | + | 0.848861i | \(0.677289\pi\) | |||||||
\(212\) | −2.69098 | − | 1.95511i | −0.184817 | − | 0.134278i | ||||
\(213\) | −1.19098 | + | 0.865300i | −0.0816048 | + | 0.0592894i | ||||
\(214\) | 10.1180 | − | 31.1401i | 0.691655 | − | 2.12869i | ||||
\(215\) | 0.809017 | − | 2.48990i | 0.0551745 | − | 0.169810i | ||||
\(216\) | 1.80902 | − | 1.31433i | 0.123088 | − | 0.0894287i | ||||
\(217\) | 4.66312 | + | 3.38795i | 0.316553 | + | 0.229989i | ||||
\(218\) | 6.28115 | + | 19.3314i | 0.425413 | + | 1.30929i | ||||
\(219\) | −8.56231 | −0.578587 | ||||||||
\(220\) | 5.35410 | − | 0.363271i | 0.360973 | − | 0.0244917i | ||||
\(221\) | −0.236068 | −0.0158797 | ||||||||
\(222\) | −5.47214 | − | 16.8415i | −0.367266 | − | 1.13033i | ||||
\(223\) | −0.572949 | − | 0.416272i | −0.0383675 | − | 0.0278756i | 0.568436 | − | 0.822727i | \(-0.307549\pi\) |
−0.606804 | + | 0.794852i | \(0.707549\pi\) | |||||||
\(224\) | 2.73607 | − | 1.98787i | 0.182811 | − | 0.132820i | ||||
\(225\) | 0.572949 | − | 1.76336i | 0.0381966 | − | 0.117557i | ||||
\(226\) | 9.82624 | − | 30.2421i | 0.653632 | − | 2.01167i | ||||
\(227\) | 22.6353 | − | 16.4455i | 1.50235 | − | 1.09152i | 0.532923 | − | 0.846164i | \(-0.321094\pi\) |
0.969432 | − | 0.245361i | \(-0.0789064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.527864 | + | 1.62460i | 0.0348822 | + | 0.107356i | 0.966982 | − | 0.254846i | \(-0.0820248\pi\) |
−0.932099 | + | 0.362203i | \(0.882025\pi\) | |||||||
\(230\) | −5.23607 | −0.345256 | ||||||||
\(231\) | −0.809017 | + | 3.21644i | −0.0532294 | + | 0.211626i | ||||
\(232\) | 15.0000 | 0.984798 | ||||||||
\(233\) | 0.545085 | + | 1.67760i | 0.0357097 | + | 0.109903i | 0.967323 | − | 0.253549i | \(-0.0815980\pi\) |
−0.931613 | + | 0.363452i | \(0.881598\pi\) | |||||||
\(234\) | 1.30902 | + | 0.951057i | 0.0855731 | + | 0.0621725i | ||||
\(235\) | 17.6353 | − | 12.8128i | 1.15040 | − | 0.835812i | ||||
\(236\) | −2.07295 | + | 6.37988i | −0.134937 | + | 0.415295i | ||||
\(237\) | 1.28115 | − | 3.94298i | 0.0832198 | − | 0.256124i | ||||
\(238\) | −0.309017 | + | 0.224514i | −0.0200306 | + | 0.0145531i | ||||
\(239\) | −20.9164 | − | 15.1967i | −1.35297 | − | 0.982990i | −0.998858 | − | 0.0477873i | \(-0.984783\pi\) |
−0.354112 | − | 0.935203i | \(-0.615217\pi\) | |||||||
\(240\) | 3.92705 | + | 12.0862i | 0.253490 | + | 0.780162i | ||||
\(241\) | −11.2918 | −0.727369 | −0.363684 | − | 0.931522i | \(-0.618481\pi\) | ||||
−0.363684 | + | 0.931522i | \(0.618481\pi\) | |||||||
\(242\) | 3.16312 | − | 17.5150i | 0.203333 | − | 1.12591i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.95492 | − | 6.01661i | −0.125151 | − | 0.385174i | ||||
\(245\) | 2.11803 | + | 1.53884i | 0.135316 | + | 0.0983130i | ||||
\(246\) | 7.97214 | − | 5.79210i | 0.508285 | − | 0.369291i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.98278 | − | 12.2577i | 0.252907 | − | 0.778367i | ||||
\(249\) | 4.85410 | − | 3.52671i | 0.307616 | − | 0.223496i | ||||
\(250\) | −10.7812 | − | 7.83297i | −0.681860 | − | 0.495400i | ||||
\(251\) | −6.98278 | − | 21.4908i | −0.440749 | − | 1.35649i | −0.887079 | − | 0.461618i | \(-0.847269\pi\) |
0.446330 | − | 0.894869i | \(-0.352731\pi\) | |||||||
\(252\) | 0.618034 | 0.0389325 | ||||||||
\(253\) | −1.00000 | + | 3.97574i | −0.0628695 | + | 0.249953i | ||||
\(254\) | 13.4721 | 0.845317 | ||||||||
\(255\) | −0.190983 | − | 0.587785i | −0.0119598 | − | 0.0368085i | ||||
\(256\) | −10.9721 | − | 7.97172i | −0.685758 | − | 0.498233i | ||||
\(257\) | −7.32624 | + | 5.32282i | −0.456998 | + | 0.332029i | −0.792353 | − | 0.610063i | \(-0.791144\pi\) |
0.335354 | + | 0.942092i | \(0.391144\pi\) | |||||||
\(258\) | −0.500000 | + | 1.53884i | −0.0311286 | + | 0.0958041i | ||||
\(259\) | −3.38197 | + | 10.4086i | −0.210145 | + | 0.646760i | ||||
\(260\) | −1.30902 | + | 0.951057i | −0.0811818 | + | 0.0589820i | ||||
\(261\) | 5.42705 | + | 3.94298i | 0.335926 | + | 0.244065i | ||||
\(262\) | 6.16312 | + | 18.9681i | 0.380759 | + | 1.17185i | ||||
\(263\) | −12.7082 | −0.783621 | −0.391811 | − | 0.920046i | \(-0.628151\pi\) | ||||
−0.391811 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(264\) | 7.39919 | − | 0.502029i | 0.455388 | − | 0.0308977i | ||||
\(265\) | −14.0902 | −0.865552 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.97214 | + | 5.06555i | 0.426688 | + | 0.310007i | ||||
\(268\) | 2.38197 | − | 1.73060i | 0.145502 | − | 0.105713i | ||||
\(269\) | 1.87132 | − | 5.75934i | 0.114097 | − | 0.351153i | −0.877661 | − | 0.479282i | \(-0.840897\pi\) |
0.991758 | + | 0.128129i | \(0.0408971\pi\) | |||||||
\(270\) | −1.30902 | + | 4.02874i | −0.0796642 | + | 0.245181i | ||||
\(271\) | −16.5172 | + | 12.0005i | −1.00335 | + | 0.728976i | −0.962804 | − | 0.270201i | \(-0.912910\pi\) |
−0.0405459 | + | 0.999178i | \(0.512910\pi\) | |||||||
\(272\) | 0.927051 | + | 0.673542i | 0.0562107 | + | 0.0408395i | ||||
\(273\) | −0.309017 | − | 0.951057i | −0.0187026 | − | 0.0575606i | ||||
\(274\) | −33.8885 | −2.04728 | ||||||||
\(275\) | 4.71885 | − | 3.94298i | 0.284557 | − | 0.237771i | ||||
\(276\) | 0.763932 | 0.0459833 | ||||||||
\(277\) | 0.437694 | + | 1.34708i | 0.0262985 | + | 0.0809384i | 0.963344 | − | 0.268268i | \(-0.0864512\pi\) |
−0.937046 | + | 0.349206i | \(0.886451\pi\) | |||||||
\(278\) | −3.35410 | − | 2.43690i | −0.201166 | − | 0.146155i | ||||
\(279\) | 4.66312 | − | 3.38795i | 0.279174 | − | 0.202832i | ||||
\(280\) | 1.80902 | − | 5.56758i | 0.108109 | − | 0.332727i | ||||
\(281\) | 4.13525 | − | 12.7270i | 0.246689 | − | 0.759230i | −0.748666 | − | 0.662948i | \(-0.769305\pi\) |
0.995354 | − | 0.0962816i | \(-0.0306949\pi\) | |||||||
\(282\) | −10.8992 | + | 7.91872i | −0.649037 | + | 0.471553i | ||||
\(283\) | −16.7533 | − | 12.1720i | −0.995880 | − | 0.723549i | −0.0346788 | − | 0.999399i | \(-0.511041\pi\) |
−0.961201 | + | 0.275850i | \(0.911041\pi\) | |||||||
\(284\) | 0.281153 | + | 0.865300i | 0.0166834 | + | 0.0513461i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | + | 4.97980i | 0.118262 | + | 0.294462i | ||||
\(287\) | −6.09017 | −0.359491 | ||||||||
\(288\) | −1.04508 | − | 3.21644i | −0.0615822 | − | 0.189531i | ||||
\(289\) | 13.7082 | + | 9.95959i | 0.806365 | + | 0.585858i | ||||
\(290\) | −22.9894 | + | 16.7027i | −1.34998 | + | 0.980819i | ||||
\(291\) | −5.25329 | + | 16.1680i | −0.307953 | + | 0.947783i | ||||
\(292\) | −1.63525 | + | 5.03280i | −0.0956961 | + | 0.294522i | ||||
\(293\) | 7.09017 | − | 5.15131i | 0.414212 | − | 0.300943i | −0.361093 | − | 0.932530i | \(-0.617596\pi\) |
0.775305 | + | 0.631587i | \(0.217596\pi\) | |||||||
\(294\) | −1.30902 | − | 0.951057i | −0.0763434 | − | 0.0554667i | ||||
\(295\) | 8.78115 | + | 27.0256i | 0.511258 | + | 1.57349i | ||||
\(296\) | 24.4721 | 1.42241 | ||||||||
\(297\) | 2.80902 | + | 1.76336i | 0.162996 | + | 0.102320i | ||||
\(298\) | −3.09017 | −0.179009 | ||||||||
\(299\) | −0.381966 | − | 1.17557i | −0.0220897 | − | 0.0679850i | ||||
\(300\) | −0.927051 | − | 0.673542i | −0.0535233 | − | 0.0388870i | ||||
\(301\) | 0.809017 | − | 0.587785i | 0.0466310 | − | 0.0338794i | ||||
\(302\) | −4.95492 | + | 15.2497i | −0.285123 | + | 0.877519i | ||||
\(303\) | 5.61803 | − | 17.2905i | 0.322748 | − | 0.993315i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.6803 | − | 15.7517i | −1.24141 | − | 0.901939i | ||||
\(306\) | 0.118034 | + | 0.363271i | 0.00674755 | + | 0.0207668i | ||||
\(307\) | −3.18034 | −0.181512 | −0.0907558 | − | 0.995873i | \(-0.528928\pi\) | ||||
−0.0907558 | + | 0.995873i | \(0.528928\pi\) | |||||||
\(308\) | 1.73607 | + | 1.08981i | 0.0989217 | + | 0.0620979i | ||||
\(309\) | 0.708204 | 0.0402883 | ||||||||
\(310\) | 7.54508 | + | 23.2214i | 0.428532 | + | 1.31889i | ||||
\(311\) | 6.30902 | + | 4.58377i | 0.357752 | + | 0.259922i | 0.752114 | − | 0.659033i | \(-0.229034\pi\) |
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(312\) | −1.80902 | + | 1.31433i | −0.102415 | + | 0.0744092i | ||||
\(313\) | 2.71885 | − | 8.36775i | 0.153678 | − | 0.472973i | −0.844346 | − | 0.535798i | \(-0.820011\pi\) |
0.998025 | + | 0.0628247i | \(0.0200109\pi\) | |||||||
\(314\) | −8.66312 | + | 26.6623i | −0.488888 | + | 1.50464i | ||||
\(315\) | 2.11803 | − | 1.53884i | 0.119338 | − | 0.0867039i | ||||
\(316\) | −2.07295 | − | 1.50609i | −0.116612 | − | 0.0847239i | ||||
\(317\) | −5.98278 | − | 18.4131i | −0.336026 | − | 1.03418i | −0.966214 | − | 0.257740i | \(-0.917022\pi\) |
0.630188 | − | 0.776443i | \(-0.282978\pi\) | |||||||
\(318\) | 8.70820 | 0.488332 | ||||||||
\(319\) | 8.29180 | + | 20.6457i | 0.464251 | + | 1.15594i | ||||
\(320\) | −11.0902 | −0.619959 | ||||||||
\(321\) | 6.25329 | + | 19.2456i | 0.349025 | + | 1.07419i | ||||
\(322\) | −1.61803 | − | 1.17557i | −0.0901695 | − | 0.0655120i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.190983 | − | 0.587785i | 0.0106102 | − | 0.0326547i | ||||
\(325\) | −0.572949 | + | 1.76336i | −0.0317815 | + | 0.0978134i | ||||
\(326\) | 30.1525 | − | 21.9071i | 1.66999 | − | 1.21332i | ||||
\(327\) | −10.1631 | − | 7.38394i | −0.562022 | − | 0.408333i | ||||
\(328\) | 4.20820 | + | 12.9515i | 0.232359 | + | 0.715128i | ||||
\(329\) | 8.32624 | 0.459040 | ||||||||
\(330\) | −10.7812 | + | 9.00854i | −0.593483 | + | 0.495904i | ||||
\(331\) | −1.29180 | −0.0710035 | −0.0355018 | − | 0.999370i | \(-0.511303\pi\) | ||||
−0.0355018 | + | 0.999370i | \(0.511303\pi\) | |||||||
\(332\) | −1.14590 | − | 3.52671i | −0.0628893 | − | 0.193553i | ||||
\(333\) | 8.85410 | + | 6.43288i | 0.485202 | + | 0.352520i | ||||
\(334\) | −15.2082 | + | 11.0494i | −0.832156 | + | 0.604597i | ||||
\(335\) | 3.85410 | − | 11.8617i | 0.210572 | − | 0.648074i | ||||
\(336\) | −1.50000 | + | 4.61653i | −0.0818317 | + | 0.251852i | ||||
\(337\) | −11.8992 | + | 8.64527i | −0.648190 | + | 0.470938i | −0.862654 | − | 0.505794i | \(-0.831199\pi\) |
0.214464 | + | 0.976732i | \(0.431199\pi\) | |||||||
\(338\) | 15.7082 | + | 11.4127i | 0.854414 | + | 0.620768i | ||||
\(339\) | 6.07295 | + | 18.6906i | 0.329837 | + | 1.01513i | ||||
\(340\) | −0.381966 | −0.0207150 | ||||||||
\(341\) | 19.0729 | − | 1.29408i | 1.03286 | − | 0.0700785i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | −1.80902 | − | 1.31433i | −0.0975357 | − | 0.0708638i | ||||
\(345\) | 2.61803 | − | 1.90211i | 0.140950 | − | 0.102406i | ||||
\(346\) | −6.19098 | + | 19.0539i | −0.332829 | + | 1.02434i | ||||
\(347\) | 0.437694 | − | 1.34708i | 0.0234967 | − | 0.0723153i | −0.938621 | − | 0.344951i | \(-0.887895\pi\) |
0.962117 | + | 0.272636i | \(0.0878955\pi\) | |||||||
\(348\) | 3.35410 | − | 2.43690i | 0.179799 | − | 0.130631i | ||||
\(349\) | 24.2082 | + | 17.5883i | 1.29584 | + | 0.941480i | 0.999906 | − | 0.0137302i | \(-0.00437058\pi\) |
0.295930 | + | 0.955210i | \(0.404371\pi\) | |||||||
\(350\) | 0.927051 | + | 2.85317i | 0.0495530 | + | 0.152508i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.73607 | − | 10.8779i | 0.145833 | − | 0.579794i | ||||
\(353\) | −16.5279 | −0.879689 | −0.439845 | − | 0.898074i | \(-0.644967\pi\) | ||||
−0.439845 | + | 0.898074i | \(0.644967\pi\) | |||||||
\(354\) | −5.42705 | − | 16.7027i | −0.288445 | − | 0.887741i | ||||
\(355\) | 3.11803 | + | 2.26538i | 0.165488 | + | 0.120234i | ||||
\(356\) | 4.30902 | − | 3.13068i | 0.228377 | − | 0.165926i | ||||
\(357\) | 0.0729490 | − | 0.224514i | 0.00386087 | − | 0.0118825i | ||||
\(358\) | 1.11803 | − | 3.44095i | 0.0590899 | − | 0.181860i | ||||
\(359\) | −14.7361 | + | 10.7064i | −0.777740 | + | 0.565061i | −0.904300 | − | 0.426898i | \(-0.859606\pi\) |
0.126560 | + | 0.991959i | \(0.459606\pi\) | |||||||
\(360\) | −4.73607 | − | 3.44095i | −0.249613 | − | 0.181354i | ||||
\(361\) | −5.87132 | − | 18.0701i | −0.309017 | − | 0.951057i | ||||
\(362\) | 6.85410 | 0.360244 | ||||||||
\(363\) | 4.78115 | + | 9.90659i | 0.250945 | + | 0.519961i | ||||
\(364\) | −0.618034 | −0.0323938 | ||||||||
\(365\) | 6.92705 | + | 21.3193i | 0.362578 | + | 1.11590i | ||||
\(366\) | 13.3992 | + | 9.73508i | 0.700387 | + | 0.508861i | ||||
\(367\) | −19.9894 | + | 14.5231i | −1.04344 | + | 0.758101i | −0.970953 | − | 0.239269i | \(-0.923092\pi\) |
−0.0724826 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(368\) | −1.85410 | + | 5.70634i | −0.0966517 | + | 0.297463i | ||||
\(369\) | −1.88197 | + | 5.79210i | −0.0979712 | + | 0.301524i | ||||
\(370\) | −37.5066 | + | 27.2501i | −1.94987 | + | 1.41667i | ||||
\(371\) | −4.35410 | − | 3.16344i | −0.226054 | − | 0.164238i | ||||
\(372\) | −1.10081 | − | 3.38795i | −0.0570745 | − | 0.175657i | ||||
\(373\) | 7.81966 | 0.404887 | 0.202443 | − | 0.979294i | \(-0.435112\pi\) | ||||
0.202443 | + | 0.979294i | \(0.435112\pi\) | |||||||
\(374\) | −0.309017 | + | 1.22857i | −0.0159789 | + | 0.0635279i | ||||
\(375\) | 8.23607 | 0.425309 | ||||||||
\(376\) | −5.75329 | − | 17.7068i | −0.296703 | − | 0.913159i | ||||
\(377\) | −5.42705 | − | 3.94298i | −0.279507 | − | 0.203074i | ||||
\(378\) | −1.30902 | + | 0.951057i | −0.0673286 | + | 0.0489171i | ||||
\(379\) | −1.28115 | + | 3.94298i | −0.0658084 | + | 0.202537i | −0.978554 | − | 0.205991i | \(-0.933958\pi\) |
0.912745 | + | 0.408529i | \(0.133958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.73607 | + | 4.89404i | −0.345099 | + | 0.250729i | ||||
\(382\) | −18.6353 | − | 13.5393i | −0.953463 | − | 0.692731i | ||||
\(383\) | −5.89919 | − | 18.1558i | −0.301434 | − | 0.927720i | −0.980984 | − | 0.194090i | \(-0.937825\pi\) |
0.679549 | − | 0.733630i | \(-0.262175\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 8.66312 | − | 0.587785i | 0.441513 | − | 0.0299563i | ||||
\(386\) | 37.1246 | 1.88959 | ||||||||
\(387\) | −0.309017 | − | 0.951057i | −0.0157082 | − | 0.0483449i | ||||
\(388\) | 8.50000 | + | 6.17561i | 0.431522 | + | 0.313519i | ||||
\(389\) | 8.61803 | − | 6.26137i | 0.436952 | − | 0.317464i | −0.347471 | − | 0.937691i | \(-0.612959\pi\) |
0.784423 | + | 0.620227i | \(0.212959\pi\) | |||||||
\(390\) | 1.30902 | − | 4.02874i | 0.0662847 | − | 0.204003i | ||||
\(391\) | 0.0901699 | − | 0.277515i | 0.00456009 | − | 0.0140345i | ||||
\(392\) | 1.80902 | − | 1.31433i | 0.0913692 | − | 0.0663836i | ||||
\(393\) | −9.97214 | − | 7.24518i | −0.503028 | − | 0.365471i | ||||
\(394\) | −2.38197 | − | 7.33094i | −0.120002 | − | 0.369327i | ||||
\(395\) | −10.8541 | −0.546129 | ||||||||
\(396\) | 1.57295 | − | 1.31433i | 0.0790437 | − | 0.0660475i | ||||
\(397\) | −34.6869 | −1.74089 | −0.870443 | − | 0.492269i | \(-0.836168\pi\) | ||||
−0.870443 | + | 0.492269i | \(0.836168\pi\) | |||||||
\(398\) | 6.28115 | + | 19.3314i | 0.314846 | + | 0.968996i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.28115 | − | 5.29007i | 0.364058 | − | 0.264503i | ||||
\(401\) | 8.44427 | − | 25.9888i | 0.421687 | − | 1.29782i | −0.484444 | − | 0.874822i | \(-0.660978\pi\) |
0.906131 | − | 0.422997i | \(-0.139022\pi\) | |||||||
\(402\) | −2.38197 | + | 7.33094i | −0.118802 | + | 0.365634i | ||||
\(403\) | −4.66312 | + | 3.38795i | −0.232287 | + | 0.168766i | ||||
\(404\) | −9.09017 | − | 6.60440i | −0.452253 | − | 0.328581i | ||||
\(405\) | −0.809017 | − | 2.48990i | −0.0402004 | − | 0.123724i | ||||
\(406\) | −10.8541 | −0.538680 | ||||||||
\(407\) | 13.5279 | + | 33.6830i | 0.670551 | + | 1.66960i | ||||
\(408\) | −0.527864 | −0.0261332 | ||||||||
\(409\) | −8.84346 | − | 27.2174i | −0.437281 | − | 1.34581i | −0.890731 | − | 0.454531i | \(-0.849807\pi\) |
0.453450 | − | 0.891282i | \(-0.350193\pi\) | |||||||
\(410\) | −20.8713 | − | 15.1639i | −1.03076 | − | 0.748892i | ||||
\(411\) | 16.9443 | − | 12.3107i | 0.835799 | − | 0.607244i | ||||
\(412\) | 0.135255 | − | 0.416272i | 0.00666353 | − | 0.0205082i | ||||
\(413\) | −3.35410 | + | 10.3229i | −0.165045 | + | 0.507955i | ||||
\(414\) | −1.61803 | + | 1.17557i | −0.0795220 | + | 0.0577761i | ||||
\(415\) | −12.7082 | − | 9.23305i | −0.623821 | − | 0.453233i | ||||
\(416\) | 1.04508 | + | 3.21644i | 0.0512395 | + | 0.157699i | ||||
\(417\) | 2.56231 | 0.125477 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.326238 | 0.0159378 | 0.00796888 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00796888 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(420\) | −0.500000 | − | 1.53884i | −0.0243975 | − | 0.0750878i | ||||
\(421\) | −29.3435 | − | 21.3193i | −1.43011 | − | 1.03904i | −0.989996 | − | 0.141097i | \(-0.954937\pi\) |
−0.440117 | − | 0.897940i | \(-0.645063\pi\) | |||||||
\(422\) | −24.4894 | + | 17.7926i | −1.19212 | + | 0.866128i | ||||
\(423\) | 2.57295 | − | 7.91872i | 0.125101 | − | 0.385021i | ||||
\(424\) | −3.71885 | + | 11.4454i | −0.180603 | + | 0.555839i | ||||
\(425\) | −0.354102 | + | 0.257270i | −0.0171765 | + | 0.0124794i | ||||
\(426\) | −1.92705 | − | 1.40008i | −0.0933659 | − | 0.0678343i | ||||
\(427\) | −3.16312 | − | 9.73508i | −0.153074 | − | 0.471114i | ||||
\(428\) | 12.5066 | 0.604528 | ||||||||
\(429\) | −2.80902 | − | 1.76336i | −0.135621 | − | 0.0851356i | ||||
\(430\) | 4.23607 | 0.204281 | ||||||||
\(431\) | −4.07953 | − | 12.5555i | −0.196504 | − | 0.604777i | −0.999956 | − | 0.00940707i | \(-0.997006\pi\) |
0.803452 | − | 0.595370i | \(-0.202994\pi\) | |||||||
\(432\) | 3.92705 | + | 2.85317i | 0.188940 | + | 0.137273i | ||||
\(433\) | 23.7984 | − | 17.2905i | 1.14368 | − | 0.830930i | 0.156050 | − | 0.987749i | \(-0.450124\pi\) |
0.987627 | + | 0.156819i | \(0.0501240\pi\) | |||||||
\(434\) | −2.88197 | + | 8.86978i | −0.138339 | + | 0.425763i | ||||
\(435\) | 5.42705 | − | 16.7027i | 0.260207 | − | 0.800835i | ||||
\(436\) | −6.28115 | + | 4.56352i | −0.300813 | + | 0.218553i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −4.28115 | − | 13.1760i | −0.204561 | − | 0.629575i | ||||
\(439\) | 9.47214 | 0.452080 | 0.226040 | − | 0.974118i | \(-0.427422\pi\) | ||||
0.226040 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(440\) | −7.23607 | − | 18.0171i | −0.344966 | − | 0.858930i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.118034 | − | 0.363271i | −0.00561430 | − | 0.0172791i | ||||
\(443\) | 4.32624 | + | 3.14320i | 0.205546 | + | 0.149338i | 0.685796 | − | 0.727794i | \(-0.259454\pi\) |
−0.480250 | + | 0.877131i | \(0.659454\pi\) | |||||||
\(444\) | 5.47214 | − | 3.97574i | 0.259696 | − | 0.188680i | ||||
\(445\) | 6.97214 | − | 21.4580i | 0.330511 | − | 1.01721i | ||||
\(446\) | 0.354102 | − | 1.08981i | 0.0167672 | − | 0.0516042i | ||||
\(447\) | 1.54508 | − | 1.12257i | 0.0730800 | − | 0.0530957i | ||||
\(448\) | −3.42705 | − | 2.48990i | −0.161913 | − | 0.117637i | ||||
\(449\) | −4.83688 | − | 14.8864i | −0.228267 | − | 0.702532i | −0.997944 | − | 0.0640987i | \(-0.979583\pi\) |
0.769677 | − | 0.638433i | \(-0.220417\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | −15.5000 | + | 12.9515i | −0.729866 | + | 0.609863i | ||||
\(452\) | 12.1459 | 0.571295 | ||||||||
\(453\) | −3.06231 | − | 9.42481i | −0.143880 | − | 0.442816i | ||||
\(454\) | 36.6246 | + | 26.6093i | 1.71888 | + | 1.24884i | ||||
\(455\) | −2.11803 | + | 1.53884i | −0.0992950 | + | 0.0721420i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.57295 | + | 20.2295i | −0.307470 | + | 0.946294i | 0.671275 | + | 0.741209i | \(0.265747\pi\) |
−0.978744 | + | 0.205085i | \(0.934253\pi\) | |||||||
\(458\) | −2.23607 | + | 1.62460i | −0.104485 | + | 0.0759125i | ||||
\(459\) | −0.190983 | − | 0.138757i | −0.00891432 | − | 0.00647663i | ||||
\(460\) | −0.618034 | − | 1.90211i | −0.0288160 | − | 0.0886865i | ||||
\(461\) | 0.819660 | 0.0381754 | 0.0190877 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190877 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(462\) | −5.35410 | + | 0.363271i | −0.249095 | + | 0.0169009i | ||||
\(463\) | 28.9230 | 1.34417 | 0.672083 | − | 0.740476i | \(-0.265400\pi\) | ||||
0.672083 | + | 0.740476i | \(0.265400\pi\) | |||||||
\(464\) | 10.0623 | + | 30.9686i | 0.467131 | + | 1.43768i | ||||
\(465\) | −12.2082 | − | 8.86978i | −0.566142 | − | 0.411326i | ||||
\(466\) | −2.30902 | + | 1.67760i | −0.106963 | + | 0.0777133i | ||||
\(467\) | 4.34346 | − | 13.3678i | 0.200991 | − | 0.618588i | −0.798863 | − | 0.601513i | \(-0.794565\pi\) |
0.999854 | − | 0.0170745i | \(-0.00543525\pi\) | |||||||
\(468\) | −0.190983 | + | 0.587785i | −0.00882819 | + | 0.0271704i | ||||
\(469\) | 3.85410 | − | 2.80017i | 0.177966 | − | 0.129300i | ||||
\(470\) | 28.5344 | + | 20.7315i | 1.31620 | + | 0.956272i | ||||
\(471\) | −5.35410 | − | 16.4782i | −0.246704 | − | 0.759277i | ||||
\(472\) | 24.2705 | 1.11714 | ||||||||
\(473\) | 0.809017 | − | 3.21644i | 0.0371986 | − | 0.147892i | ||||
\(474\) | 6.70820 | 0.308118 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.118034 | − | 0.0857567i | −0.00541008 | − | 0.00393065i | ||||
\(477\) | −4.35410 | + | 3.16344i | −0.199361 | + | 0.144844i | ||||
\(478\) | 12.9271 | − | 39.7854i | 0.591270 | − | 1.81974i | ||||
\(479\) | −5.10081 | + | 15.6987i | −0.233062 | + | 0.717291i | 0.764310 | + | 0.644848i | \(0.223080\pi\) |
−0.997373 | + | 0.0724429i | \(0.976920\pi\) | |||||||
\(480\) | −7.16312 | + | 5.20431i | −0.326950 | + | 0.237543i | ||||
\(481\) | −8.85410 | − | 6.43288i | −0.403712 | − | 0.293314i | ||||
\(482\) | −5.64590 | − | 17.3763i | −0.257164 | − | 0.791468i | ||||
\(483\) | 1.23607 | 0.0562430 | ||||||||
\(484\) | 6.73607 | − | 0.918300i | 0.306185 | − | 0.0417409i | ||||
\(485\) | 44.5066 | 2.02094 | ||||||||
\(486\) | 0.500000 | + | 1.53884i | 0.0226805 | + | 0.0698033i | ||||
\(487\) | −11.6353 | − | 8.45351i | −0.527244 | − | 0.383065i | 0.292082 | − | 0.956393i | \(-0.405652\pi\) |
−0.819326 | + | 0.573328i | \(0.805652\pi\) | |||||||
\(488\) | −18.5172 | + | 13.4535i | −0.838235 | + | 0.609014i | ||||
\(489\) | −7.11803 | + | 21.9071i | −0.321889 | + | 0.990671i | ||||
\(490\) | −1.30902 | + | 4.02874i | −0.0591354 | + | 0.182000i | ||||
\(491\) | 7.85410 | − | 5.70634i | 0.354451 | − | 0.257523i | −0.396283 | − | 0.918128i | \(-0.629700\pi\) |
0.750734 | + | 0.660605i | \(0.229700\pi\) | |||||||
\(492\) | 3.04508 | + | 2.21238i | 0.137283 | + | 0.0997420i | ||||
\(493\) | −0.489357 | − | 1.50609i | −0.0220395 | − | 0.0678307i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.11803 | − | 8.42075i | 0.0951985 | − | 0.378485i | ||||
\(496\) | 27.9787 | 1.25628 | ||||||||
\(497\) | 0.454915 | + | 1.40008i | 0.0204057 | + | 0.0628024i | ||||
\(498\) | 7.85410 | + | 5.70634i | 0.351951 | + | 0.255707i | ||||
\(499\) | 4.04508 | − | 2.93893i | 0.181083 | − | 0.131564i | −0.493551 | − | 0.869717i | \(-0.664301\pi\) |
0.674634 | + | 0.738152i | \(0.264301\pi\) | |||||||
\(500\) | 1.57295 | − | 4.84104i | 0.0703444 | − | 0.216498i | ||||
\(501\) | 3.59017 | − | 11.0494i | 0.160397 | − | 0.493651i | ||||
\(502\) | 29.5795 | − | 21.4908i | 1.32020 | − | 0.959181i | ||||
\(503\) | −24.5172 | − | 17.8128i | −1.09317 | − | 0.794234i | −0.113237 | − | 0.993568i | \(-0.536122\pi\) |
−0.979932 | + | 0.199334i | \(0.936122\pi\) | |||||||
\(504\) | −0.690983 | − | 2.12663i | −0.0307788 | − | 0.0947275i | ||||
\(505\) | −47.5967 | −2.11803 | ||||||||
\(506\) | −6.61803 | + | 0.449028i | −0.294207 | + | 0.0199617i | ||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | 1.59017 | + | 4.89404i | 0.0705524 | + | 0.217138i | ||||
\(509\) | 9.57295 | + | 6.95515i | 0.424314 | + | 0.308282i | 0.779371 | − | 0.626563i | \(-0.215539\pi\) |
−0.355058 | + | 0.934844i | \(0.615539\pi\) | |||||||
\(510\) | 0.809017 | − | 0.587785i | 0.0358239 | − | 0.0260276i | ||||
\(511\) | −2.64590 | + | 8.14324i | −0.117048 | + | 0.360236i | ||||
\(512\) | −1.63525 | + | 5.03280i | −0.0722687 | + | 0.222420i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.8541 | − | 8.61251i | −0.522862 | − | 0.379881i | ||||
\(515\) | −0.572949 | − | 1.76336i | −0.0252472 | − | 0.0777027i | ||||
\(516\) | −0.618034 | −0.0272074 | ||||||||
\(517\) | 21.1910 | − | 17.7068i | 0.931978 | − | 0.778744i | ||||
\(518\) | −17.7082 | −0.778054 | ||||||||
\(519\) | −3.82624 | − | 11.7759i | −0.167953 | − | 0.516907i | ||||
\(520\) | 4.73607 | + | 3.44095i | 0.207690 | + | 0.150896i | ||||
\(521\) | −2.57295 | + | 1.86936i | −0.112723 | + | 0.0818980i | −0.642719 | − | 0.766102i | \(-0.722194\pi\) |
0.529996 | + | 0.848000i | \(0.322194\pi\) | |||||||
\(522\) | −3.35410 | + | 10.3229i | −0.146805 | + | 0.451820i | ||||
\(523\) | −13.0729 | + | 40.2344i | −0.571640 | + | 1.75933i | 0.0757048 | + | 0.997130i | \(0.475879\pi\) |
−0.647345 | + | 0.762197i | \(0.724121\pi\) | |||||||
\(524\) | −6.16312 | + | 4.47777i | −0.269237 | + | 0.195612i | ||||
\(525\) | −1.50000 | − | 1.08981i | −0.0654654 | − | 0.0475634i | ||||
\(526\) | −6.35410 | − | 19.5559i | −0.277052 | − | 0.852678i | ||||
\(527\) | −1.36068 | −0.0592721 | ||||||||
\(528\) | 6.00000 | + | 14.9394i | 0.261116 | + | 0.650153i | ||||
\(529\) | −21.4721 | −0.933571 | ||||||||
\(530\) | −7.04508 | − | 21.6825i | −0.306019 | − | 0.941829i | ||||
\(531\) | 8.78115 | + | 6.37988i | 0.381070 | + | 0.276863i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88197 | − | 5.79210i | 0.0815170 | − | 0.250884i | ||||
\(534\) | −4.30902 | + | 13.2618i | −0.186469 | + | 0.573894i | ||||
\(535\) | 42.8607 | − | 31.1401i | 1.85303 | − | 1.34630i | ||||
\(536\) | −8.61803 | − | 6.26137i | −0.372242 | − | 0.270450i | ||||
\(537\) | 0.690983 | + | 2.12663i | 0.0298181 | + | 0.0917707i | ||||
\(538\) | 9.79837 | 0.422438 | ||||||||
\(539\) | 2.80902 | + | 1.76336i | 0.120993 | + | 0.0759531i | ||||
\(540\) | −1.61803 | −0.0696291 | ||||||||
\(541\) | 2.75329 | + | 8.47375i | 0.118373 | + | 0.364315i | 0.992636 | − | 0.121138i | \(-0.0386545\pi\) |
−0.874262 | + | 0.485454i | \(0.838655\pi\) | |||||||
\(542\) | −26.7254 | − | 19.4172i | −1.14796 | − | 0.834038i | ||||
\(543\) | −3.42705 | + | 2.48990i | −0.147069 | + | 0.106852i | ||||
\(544\) | −0.246711 | + | 0.759299i | −0.0105777 | + | 0.0325547i | ||||
\(545\) | −10.1631 | + | 31.2789i | −0.435340 | + | 1.33984i | ||||
\(546\) | 1.30902 | − | 0.951057i | 0.0560208 | − | 0.0407015i | ||||
\(547\) | 21.5172 | + | 15.6332i | 0.920010 | + | 0.668426i | 0.943526 | − | 0.331297i | \(-0.107486\pi\) |
−0.0235166 | + | 0.999723i | \(0.507486\pi\) | |||||||
\(548\) | −4.00000 | − | 12.3107i | −0.170872 | − | 0.525888i | ||||
\(549\) | −10.2361 | −0.436865 | ||||||||
\(550\) | 8.42705 | + | 5.29007i | 0.359331 | + | 0.225569i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.854102 | − | 2.62866i | −0.0363530 | − | 0.111883i | ||||
\(553\) | −3.35410 | − | 2.43690i | −0.142631 | − | 0.103627i | ||||
\(554\) | −1.85410 | + | 1.34708i | −0.0787732 | + | 0.0572321i | ||||
\(555\) | 8.85410 | − | 27.2501i | 0.375836 | − | 1.15670i | ||||
\(556\) | 0.489357 | − | 1.50609i | 0.0207534 | − | 0.0638723i | ||||
\(557\) | −4.23607 | + | 3.07768i | −0.179488 | + | 0.130406i | −0.673902 | − | 0.738821i | \(-0.735383\pi\) |
0.494414 | + | 0.869227i | \(0.335383\pi\) | |||||||
\(558\) | 7.54508 | + | 5.48183i | 0.319409 | + | 0.232064i | ||||
\(559\) | 0.309017 | + | 0.951057i | 0.0130700 | + | 0.0402254i | ||||
\(560\) | 12.7082 | 0.537020 | ||||||||
\(561\) | −0.291796 | − | 0.726543i | −0.0123196 | − | 0.0306746i | ||||
\(562\) | 21.6525 | 0.913355 | ||||||||
\(563\) | 4.03851 | + | 12.4292i | 0.170203 | + | 0.523830i | 0.999382 | − | 0.0351526i | \(-0.0111917\pi\) |
−0.829179 | + | 0.558983i | \(0.811192\pi\) | |||||||
\(564\) | −4.16312 | − | 3.02468i | −0.175299 | − | 0.127362i | ||||
\(565\) | 41.6246 | − | 30.2421i | 1.75116 | − | 1.27229i | ||||
\(566\) | 10.3541 | − | 31.8666i | 0.435215 | − | 1.33946i | ||||
\(567\) | 0.309017 | − | 0.951057i | 0.0129775 | − | 0.0399406i | ||||
\(568\) | 2.66312 | − | 1.93487i | 0.111742 | − | 0.0811853i | ||||
\(569\) | 15.4271 | + | 11.2084i | 0.646736 | + | 0.469881i | 0.862158 | − | 0.506640i | \(-0.169113\pi\) |
−0.215422 | + | 0.976521i | \(0.569113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | −1.57295 | + | 1.31433i | −0.0657683 | + | 0.0549548i | ||||
\(573\) | 14.2361 | 0.594720 | ||||||||
\(574\) | −3.04508 | − | 9.37181i | −0.127099 | − | 0.391172i | ||||
\(575\) | −1.85410 | − | 1.34708i | −0.0773214 | − | 0.0561773i | ||||
\(576\) | −3.42705 | + | 2.48990i | −0.142794 | + | 0.103746i | ||||
\(577\) | −9.13525 | + | 28.1154i | −0.380306 | + | 1.17046i | 0.559523 | + | 0.828815i | \(0.310984\pi\) |
−0.939829 | + | 0.341646i | \(0.889016\pi\) | |||||||
\(578\) | −8.47214 | + | 26.0746i | −0.352394 | + | 1.08456i | ||||
\(579\) | −18.5623 | + | 13.4863i | −0.771423 | + | 0.560472i | ||||
\(580\) | −8.78115 | − | 6.37988i | −0.364618 | − | 0.264910i | ||||
\(581\) | −1.85410 | − | 5.70634i | −0.0769211 | − | 0.236739i | ||||
\(582\) | −27.5066 | −1.14018 | ||||||||
\(583\) | −17.8090 | + | 1.20833i | −0.737574 | + | 0.0500438i | ||||
\(584\) | 19.1459 | 0.792263 | ||||||||
\(585\) | 0.809017 | + | 2.48990i | 0.0334487 | + | 0.102945i | ||||
\(586\) | 11.4721 | + | 8.33499i | 0.473910 | + | 0.344315i | ||||
\(587\) | −0.0901699 | + | 0.0655123i | −0.00372171 | + | 0.00270398i | −0.589645 | − | 0.807663i | \(-0.700732\pi\) |
0.585923 | + | 0.810367i | \(0.300732\pi\) | |||||||
\(588\) | 0.190983 | − | 0.587785i | 0.00787601 | − | 0.0242399i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −37.1976 | + | 27.0256i | −1.53140 | + | 1.11263i | ||||
\(591\) | 3.85410 | + | 2.80017i | 0.158537 | + | 0.115184i | ||||
\(592\) | 16.4164 | + | 50.5245i | 0.674710 | + | 2.07654i | ||||
\(593\) | 11.8885 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(594\) | −1.30902 | + | 5.20431i | −0.0537096 | + | 0.213535i | ||||
\(595\) | −0.618034 | −0.0253369 | ||||||||
\(596\) | −0.364745 | − | 1.12257i | −0.0149405 | − | 0.0459823i | ||||
\(597\) | −10.1631 | − | 7.38394i | −0.415949 | − | 0.302204i | ||||
\(598\) | 1.61803 | − | 1.17557i | 0.0661663 | − | 0.0480727i | ||||
\(599\) | −2.01064 | + | 6.18812i | −0.0821527 | + | 0.252840i | −0.983693 | − | 0.179855i | \(-0.942437\pi\) |
0.901541 | + | 0.432695i | \(0.142437\pi\) | |||||||
\(600\) | −1.28115 | + | 3.94298i | −0.0523029 | + | 0.160972i | ||||
\(601\) | −31.4164 | + | 22.8254i | −1.28150 | + | 0.931066i | −0.999597 | − | 0.0283767i | \(-0.990966\pi\) |
−0.281905 | + | 0.959442i | \(0.590966\pi\) | |||||||
\(602\) | 1.30902 | + | 0.951057i | 0.0533515 | + | 0.0387622i | ||||
\(603\) | −1.47214 | − | 4.53077i | −0.0599500 | − | 0.184507i | ||||
\(604\) | −6.12461 | −0.249207 | ||||||||
\(605\) | 20.7984 | − | 19.9192i | 0.845574 | − | 0.809830i | ||||
\(606\) | 29.4164 | 1.19496 | ||||||||
\(607\) | −7.06231 | − | 21.7355i | −0.286650 | − | 0.882218i | −0.985899 | − | 0.167340i | \(-0.946482\pi\) |
0.699249 | − | 0.714878i | \(-0.253518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.42705 | − | 3.94298i | 0.219915 | − | 0.159778i | ||||
\(610\) | 13.3992 | − | 41.2385i | 0.542517 | − | 1.66970i | ||||
\(611\) | −2.57295 | + | 7.91872i | −0.104090 | + | 0.320357i | ||||
\(612\) | −0.118034 | + | 0.0857567i | −0.00477124 | + | 0.00346651i | ||||
\(613\) | 17.3541 | + | 12.6085i | 0.700926 | + | 0.509252i | 0.880234 | − | 0.474541i | \(-0.157386\pi\) |
−0.179308 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(614\) | −1.59017 | − | 4.89404i | −0.0641740 | − | 0.197507i | ||||
\(615\) | 15.9443 | 0.642935 | ||||||||
\(616\) | 1.80902 | − | 7.19218i | 0.0728874 | − | 0.289781i | ||||
\(617\) | 1.09017 | 0.0438886 | 0.0219443 | − | 0.999759i | \(-0.493014\pi\) | ||||
0.0219443 | + | 0.999759i | \(0.493014\pi\) | |||||||
\(618\) | 0.354102 | + | 1.08981i | 0.0142441 | + | 0.0438387i | ||||
\(619\) | 4.14590 | + | 3.01217i | 0.166638 | + | 0.121069i | 0.667979 | − | 0.744180i | \(-0.267160\pi\) |
−0.501341 | + | 0.865250i | \(0.667160\pi\) | |||||||
\(620\) | −7.54508 | + | 5.48183i | −0.303018 | + | 0.220155i | ||||
\(621\) | 0.381966 | − | 1.17557i | 0.0153278 | − | 0.0471740i | ||||
\(622\) | −3.89919 | + | 12.0005i | −0.156343 | + | 0.481175i | ||||
\(623\) | 6.97214 | − | 5.06555i | 0.279333 | − | 0.202947i | ||||
\(624\) | −3.92705 | − | 2.85317i | −0.157208 | − | 0.114218i | ||||
\(625\) | −9.52786 | − | 29.3238i | −0.381115 | − | 1.17295i | ||||
\(626\) | 14.2361 | 0.568988 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.7082 | −0.427304 | ||||||||
\(629\) | −0.798374 | − | 2.45714i | −0.0318333 | − | 0.0979727i | ||||
\(630\) | 3.42705 | + | 2.48990i | 0.136537 | + | 0.0991999i | ||||
\(631\) | −10.6631 | + | 7.74721i | −0.424492 | + | 0.308412i | −0.779443 | − | 0.626473i | \(-0.784498\pi\) |
0.354951 | + | 0.934885i | \(0.384498\pi\) | |||||||
\(632\) | −2.86475 | + | 8.81678i | −0.113953 | + | 0.350713i | ||||
\(633\) | 5.78115 | − | 17.7926i | 0.229780 | − | 0.707191i | ||||
\(634\) | 25.3435 | − | 18.4131i | 1.00652 | − | 0.731278i | ||||
\(635\) | 17.6353 | + | 12.8128i | 0.699834 | + | 0.508459i | ||||
\(636\) | 1.02786 | + | 3.16344i | 0.0407575 | + | 0.125439i | ||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −27.6246 | + | 23.0826i | −1.09367 | + | 0.913850i | ||||
\(639\) | 1.47214 | 0.0582368 | ||||||||
\(640\) | −11.0172 | − | 33.9075i | −0.435494 | − | 1.34031i | ||||
\(641\) | 15.3541 | + | 11.1554i | 0.606451 | + | 0.440612i | 0.848163 | − | 0.529736i | \(-0.177709\pi\) |
−0.241712 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(642\) | −26.4894 | + | 19.2456i | −1.04545 | + | 0.759565i | ||||
\(643\) | −4.94427 | + | 15.2169i | −0.194983 | + | 0.600096i | 0.804994 | + | 0.593283i | \(0.202169\pi\) |
−0.999977 | + | 0.00681282i | \(0.997831\pi\) | |||||||
\(644\) | 0.236068 | − | 0.726543i | 0.00930238 | − | 0.0286298i | ||||
\(645\) | −2.11803 | + | 1.53884i | −0.0833975 | + | 0.0605918i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.3992 | + | 32.0054i | 0.408834 | + | 1.25826i | 0.917651 | + | 0.397387i | \(0.130083\pi\) |
−0.508817 | + | 0.860875i | \(0.669917\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | 13.4164 | + | 33.4055i | 0.526640 | + | 1.31128i | ||||
\(650\) | −3.00000 | −0.117670 | ||||||||
\(651\) | −1.78115 | − | 5.48183i | −0.0698089 | − | 0.214850i | ||||
\(652\) | 11.5172 | + | 8.36775i | 0.451049 | + | 0.327706i | ||||
\(653\) | 10.2812 | − | 7.46969i | 0.402333 | − | 0.292312i | −0.368158 | − | 0.929763i | \(-0.620011\pi\) |
0.770490 | + | 0.637452i | \(0.220011\pi\) | |||||||
\(654\) | 6.28115 | − | 19.3314i | 0.245613 | − | 0.755918i | ||||
\(655\) | −9.97214 | + | 30.6911i | −0.389644 | + | 1.19920i | ||||
\(656\) | −23.9164 | + | 17.3763i | −0.933779 | + | 0.678430i | ||||
\(657\) | 6.92705 | + | 5.03280i | 0.270250 | + | 0.196348i | ||||
\(658\) | 4.16312 | + | 12.8128i | 0.162295 | + | 0.499493i | ||||
\(659\) | −11.8328 | −0.460941 | −0.230471 | − | 0.973079i | \(-0.574027\pi\) | ||||
−0.230471 | + | 0.973079i | \(0.574027\pi\) | |||||||
\(660\) | −4.54508 | − | 2.85317i | −0.176917 | − | 0.111059i | ||||
\(661\) | −3.00000 | −0.116686 | −0.0583432 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583432 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(662\) | −0.645898 | − | 1.98787i | −0.0251035 | − | 0.0772608i | ||||
\(663\) | 0.190983 | + | 0.138757i | 0.00741717 | + | 0.00538889i | ||||
\(664\) | −10.8541 | + | 7.88597i | −0.421221 | + | 0.306035i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.47214 | + | 16.8415i | −0.212041 | + | 0.652595i | ||||
\(667\) | 6.70820 | − | 4.87380i | 0.259743 | − | 0.188714i | ||||
\(668\) | −5.80902 | − | 4.22050i | −0.224758 | − | 0.163296i | ||||
\(669\) | 0.218847 | + | 0.673542i | 0.00846112 | + | 0.0260406i | ||||
\(670\) | 20.1803 | 0.779635 | ||||||||
\(671\) | −28.7533 | − | 18.0498i | −1.11001 | − | 0.696806i | ||||
\(672\) | −3.38197 | −0.130462 | ||||||||
\(673\) | −10.6353 | − | 32.7319i | −0.409959 | − | 1.26172i | −0.916683 | − | 0.399616i | \(-0.869144\pi\) |
0.506724 | − | 0.862108i | \(-0.330856\pi\) | |||||||
\(674\) | −19.2533 | − | 13.9883i | −0.741609 | − | 0.538810i | ||||
\(675\) | −1.50000 | + | 1.08981i | −0.0577350 | + | 0.0419470i | ||||
\(676\) | −2.29180 | + | 7.05342i | −0.0881460 | + | 0.271286i | ||||
\(677\) | −10.0279 | + | 30.8626i | −0.385402 | + | 1.18615i | 0.550786 | + | 0.834646i | \(0.314328\pi\) |
−0.936188 | + | 0.351499i | \(0.885672\pi\) | |||||||
\(678\) | −25.7254 | + | 18.6906i | −0.987979 | + | 0.717809i | ||||
\(679\) | 13.7533 | + | 9.99235i | 0.527803 | + | 0.383471i | ||||
\(680\) | 0.427051 | + | 1.31433i | 0.0163767 | + | 0.0504022i | ||||
\(681\) | −27.9787 | −1.07215 | ||||||||
\(682\) | 11.5279 | + | 28.7032i | 0.441425 | + | 1.09910i | ||||
\(683\) | 30.3050 | 1.15959 | 0.579793 | − | 0.814764i | \(-0.303133\pi\) | ||||
0.579793 | + | 0.814764i | \(0.303133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.3607 | − | 32.2299i | −1.69493 | − | 1.23144i | ||||
\(686\) | −1.30902 | + | 0.951057i | −0.0499785 | + | 0.0363115i | ||||
\(687\) | 0.527864 | − | 1.62460i | 0.0201393 | − | 0.0619823i | ||||
\(688\) | 1.50000 | − | 4.61653i | 0.0571870 | − | 0.176003i | ||||
\(689\) | 4.35410 | − | 3.16344i | 0.165878 | − | 0.120517i | ||||
\(690\) | 4.23607 | + | 3.07768i | 0.161264 | + | 0.117165i | ||||
\(691\) | −1.71885 | − | 5.29007i | −0.0653880 | − | 0.201244i | 0.913025 | − | 0.407904i | \(-0.133740\pi\) |
−0.978413 | + | 0.206661i | \(0.933740\pi\) | |||||||
\(692\) | −7.65248 | −0.290903 | ||||||||
\(693\) | 2.54508 | − | 2.12663i | 0.0966798 | − | 0.0807839i | ||||
\(694\) | 2.29180 | 0.0869954 | ||||||||
\(695\) | −2.07295 | − | 6.37988i | −0.0786314 | − | 0.242003i | ||||
\(696\) | −12.1353 | − | 8.81678i | −0.459986 | − | 0.334199i | ||||
\(697\) | 1.16312 | − | 0.845055i | 0.0440563 | − | 0.0320088i | ||||
\(698\) | −14.9615 | + | 46.0467i | −0.566301 | + | 1.74289i | ||||
\(699\) | 0.545085 | − | 1.67760i | 0.0206170 | − | 0.0634526i | ||||
\(700\) | −0.927051 | + | 0.673542i | −0.0350392 | + | 0.0254575i | ||||
\(701\) | −21.8435 | − | 15.8702i | −0.825016 | − | 0.599409i | 0.0931288 | − | 0.995654i | \(-0.470313\pi\) |
−0.918145 | + | 0.396245i | \(0.870313\pi\) | |||||||
\(702\) | −0.500000 | − | 1.53884i | −0.0188713 | − | 0.0580798i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −14.0172 | + | 0.951057i | −0.528294 | + | 0.0358443i | ||||
\(705\) | −21.7984 | −0.820974 | ||||||||
\(706\) | −8.26393 | − | 25.4338i | −0.311017 | − | 0.957212i | ||||
\(707\) | −14.7082 | − | 10.6861i | −0.553159 | − | 0.401893i | ||||
\(708\) | 5.42705 | − | 3.94298i | 0.203961 | − | 0.148186i | ||||
\(709\) | −5.97871 | + | 18.4006i | −0.224535 | + | 0.691049i | 0.773803 | + | 0.633426i | \(0.218352\pi\) |
−0.998338 | + | 0.0576225i | \(0.981648\pi\) | |||||||
\(710\) | −1.92705 | + | 5.93085i | −0.0723209 | + | 0.222581i | ||||
\(711\) | −3.35410 | + | 2.43690i | −0.125789 | + | 0.0913908i | ||||
\(712\) | −15.5902 | − | 11.3269i | −0.584266 | − | 0.424494i | ||||
\(713\) | −2.20163 | − | 6.77591i | −0.0824515 | − | 0.253760i | ||||
\(714\) | 0.381966 | 0.0142947 | ||||||||
\(715\) | −2.11803 | + | 8.42075i | −0.0792100 | + | 0.314918i | ||||
\(716\) | 1.38197 | 0.0516465 | ||||||||
\(717\) | 7.98936 | + | 24.5887i | 0.298368 | + | 0.918282i | ||||
\(718\) | −23.8435 | − | 17.3233i | −0.889830 | − | 0.646499i | ||||
\(719\) | 5.16312 | − | 3.75123i | 0.192552 | − | 0.139897i | −0.487332 | − | 0.873217i | \(-0.662030\pi\) |
0.679884 | + | 0.733319i | \(0.262030\pi\) | |||||||
\(720\) | 3.92705 | − | 12.0862i | 0.146353 | − | 0.450427i | ||||
\(721\) | 0.218847 | − | 0.673542i | 0.00815029 | − | 0.0250840i | ||||
\(722\) | 24.8713 | − | 18.0701i | 0.925615 | − | 0.672499i | ||||
\(723\) | 9.13525 | + | 6.63715i | 0.339744 | + | 0.246838i | ||||
\(724\) | 0.809017 | + | 2.48990i | 0.0300669 | + | 0.0925363i | ||||
\(725\) | −12.4377 | −0.461924 | ||||||||
\(726\) | −12.8541 | + | 12.3107i | −0.477060 | + | 0.456894i | ||||
\(727\) | 28.8541 | 1.07014 | 0.535070 | − | 0.844808i | \(-0.320285\pi\) | ||||
0.535070 | + | 0.844808i | \(0.320285\pi\) | |||||||
\(728\) | 0.690983 | + | 2.12663i | 0.0256095 | + | 0.0788180i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −29.3435 | + | 21.3193i | −1.08605 | + | 0.789062i | ||||
\(731\) | −0.0729490 | + | 0.224514i | −0.00269812 | + | 0.00830395i | ||||
\(732\) | −1.95492 | + | 6.01661i | −0.0722557 | + | 0.222380i | ||||
\(733\) | 29.2254 | − | 21.2335i | 1.07947 | − | 0.784278i | 0.101876 | − | 0.994797i | \(-0.467516\pi\) |
0.977590 | + | 0.210519i | \(0.0675155\pi\) | |||||||
\(734\) | −32.3435 | − | 23.4989i | −1.19382 | − | 0.867360i | ||||
\(735\) | −0.809017 | − | 2.48990i | −0.0298410 | − | 0.0918413i | ||||
\(736\) | −4.18034 | −0.154089 | ||||||||
\(737\) | 3.85410 | − | 15.3229i | 0.141968 | − | 0.564426i | ||||
\(738\) | −9.85410 | −0.362735 | ||||||||
\(739\) | −5.46556 | − | 16.8213i | −0.201054 | − | 0.618780i | −0.999852 | − | 0.0171814i | \(-0.994531\pi\) |
0.798799 | − | 0.601599i | \(-0.205469\pi\) | |||||||
\(740\) | −14.3262 | − | 10.4086i | −0.526643 | − | 0.382629i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.69098 | − | 8.28199i | 0.0987891 | − | 0.304042i | ||||
\(743\) | 11.4615 | − | 35.2748i | 0.420481 | − | 1.29411i | −0.486774 | − | 0.873528i | \(-0.661826\pi\) |
0.907255 | − | 0.420581i | \(-0.138174\pi\) | |||||||
\(744\) | −10.4271 | + | 7.57570i | −0.382274 | + | 0.277738i | ||||
\(745\) | −4.04508 | − | 2.93893i | −0.148200 | − | 0.107674i | ||||
\(746\) | 3.90983 | + | 12.0332i | 0.143149 | + | 0.440567i | ||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | −0.482779 | + | 0.0327561i | −0.0176522 | + | 0.00119768i | ||||
\(749\) | 20.2361 | 0.739410 | ||||||||
\(750\) | 4.11803 | + | 12.6740i | 0.150369 | + | 0.462789i | ||||
\(751\) | 17.9164 | + | 13.0170i | 0.653779 | + | 0.474998i | 0.864556 | − | 0.502536i | \(-0.167600\pi\) |
−0.210777 | + | 0.977534i | \(0.567600\pi\) | |||||||
\(752\) | 32.6976 | − | 23.7562i | 1.19236 | − | 0.866298i | ||||
\(753\) | −6.98278 | + | 21.4908i | −0.254467 | + | 0.783168i | ||||
\(754\) | 3.35410 | − | 10.3229i | 0.122149 | − | 0.375937i | ||||
\(755\) | −20.9894 | + | 15.2497i | −0.763881 | + | 0.554992i | ||||
\(756\) | −0.500000 | − | 0.363271i | −0.0181848 | − | 0.0132120i | ||||
\(757\) | 12.5967 | + | 38.7688i | 0.457837 | + | 1.40908i | 0.867772 | + | 0.496962i | \(0.165551\pi\) |
−0.409936 | + | 0.912114i | \(0.634449\pi\) | |||||||
\(758\) | −6.70820 | −0.243653 | ||||||||
\(759\) | 3.14590 | − | 2.62866i | 0.114189 | − | 0.0954142i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.42705 | − | 10.5474i | −0.124231 | − | 0.382342i | 0.869530 | − | 0.493881i | \(-0.164422\pi\) |
−0.993760 | + | 0.111539i | \(0.964422\pi\) | |||||||
\(762\) | −10.8992 | − | 7.91872i | −0.394836 | − | 0.286865i | ||||
\(763\) | −10.1631 | + | 7.38394i | −0.367930 | + | 0.267317i | ||||
\(764\) | 2.71885 | − | 8.36775i | 0.0983644 | − | 0.302735i | ||||
\(765\) | −0.190983 | + | 0.587785i | −0.00690501 | + | 0.0212514i | ||||
\(766\) | 24.9894 | − | 18.1558i | 0.902902 | − | 0.655997i | ||||
\(767\) | −8.78115 | − | 6.37988i | −0.317069 | − | 0.230364i | ||||
\(768\) | 4.19098 | + | 12.8985i | 0.151229 | + | 0.465435i | ||||
\(769\) | 35.5279 | 1.28117 | 0.640584 | − | 0.767888i | \(-0.278692\pi\) | ||||
0.640584 | + | 0.767888i | \(0.278692\pi\) | |||||||
\(770\) | 5.23607 | + | 13.0373i | 0.188695 | + | 0.469831i | ||||
\(771\) | 9.05573 | 0.326134 | ||||||||
\(772\) | 4.38197 | + | 13.4863i | 0.157710 | + | 0.485383i | ||||
\(773\) | −30.2705 | − | 21.9928i | −1.08875 | − | 0.791026i | −0.109566 | − | 0.993980i | \(-0.534946\pi\) |
−0.979188 | + | 0.202953i | \(0.934946\pi\) | |||||||
\(774\) | 1.30902 | − | 0.951057i | 0.0470516 | − | 0.0341850i | ||||
\(775\) | −3.30244 | + | 10.1639i | −0.118627 | + | 0.365097i | ||||
\(776\) | 11.7467 | − | 36.1527i | 0.421682 | − | 1.29780i | ||||
\(777\) | 8.85410 | − | 6.43288i | 0.317639 | − | 0.230778i | ||||
\(778\) | 13.9443 | + | 10.1311i | 0.499926 | + | 0.363218i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.61803 | 0.0579349 | ||||||||
\(781\) | 4.13525 | + | 2.59590i | 0.147971 | + | 0.0928886i | ||||
\(782\) | 0.472136 | 0.0168835 | ||||||||
\(783\) | −2.07295 | − | 6.37988i | −0.0740812 | − | 0.227998i | ||||
\(784\) | 3.92705 | + | 2.85317i | 0.140252 | + | 0.101899i | ||||
\(785\) | −36.6976 | + | 26.6623i | −1.30979 | + | 0.951620i | ||||
\(786\) | 6.16312 | − | 18.9681i | 0.219831 | − | 0.676571i | ||||
\(787\) | −8.07953 | + | 24.8662i | −0.288004 | + | 0.886385i | 0.697478 | + | 0.716606i | \(0.254305\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(788\) | 2.38197 | − | 1.73060i | 0.0848540 | − | 0.0616501i | ||||
\(789\) | 10.2812 | + | 7.46969i | 0.366019 | + | 0.265928i | ||||
\(790\) | −5.42705 | − | 16.7027i | −0.193086 | − | 0.594257i | ||||
\(791\) | 19.6525 | 0.698762 | ||||||||
\(792\) | −6.28115 | − | 3.94298i | −0.223191 | − | 0.140108i | ||||
\(793\) | 10.2361 | 0.363493 | ||||||||
\(794\) | −17.3435 | − | 53.3777i | −0.615496 | − | 1.89430i | ||||
\(795\) | 11.3992 | + | 8.28199i | 0.404287 | + | 0.293732i | ||||
\(796\) | −6.28115 | + | 4.56352i | −0.222630 | + | 0.161750i | ||||
\(797\) | 7.24671 | − | 22.3031i | 0.256692 | − | 0.790016i | −0.736800 | − | 0.676111i | \(-0.763664\pi\) |
0.993492 | − | 0.113905i | \(-0.0363359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.59017 | + | 1.15533i | −0.0562562 | + | 0.0408725i | ||||
\(800\) | 5.07295 | + | 3.68571i | 0.179356 | + | 0.130310i | ||||
\(801\) | −2.66312 | − | 8.19624i | −0.0940967 | − | 0.289600i | ||||
\(802\) | 44.2148 | 1.56128 | ||||||||
\(803\) | 10.5836 | + | 26.3521i | 0.373487 | + | 0.929944i | ||||
\(804\) | −2.94427 | −0.103836 | ||||||||
\(805\) | −1.00000 | − | 3.07768i | −0.0352454 | − | 0.108474i | ||||
\(806\) | −7.54508 | − | 5.48183i | −0.265764 | − | 0.193089i | ||||
\(807\) | −4.89919 | + | 3.55947i | −0.172460 | + | 0.125299i | ||||
\(808\) | −12.5623 | + | 38.6628i | −0.441940 | + | 1.36015i | ||||
\(809\) | −4.93769 | + | 15.1967i | −0.173600 | + | 0.534286i | −0.999567 | − | 0.0294328i | \(-0.990630\pi\) |
0.825967 | + | 0.563719i | \(0.190630\pi\) | |||||||
\(810\) | 3.42705 | − | 2.48990i | 0.120414 | − | 0.0874861i | ||||
\(811\) | −13.8541 | − | 10.0656i | −0.486483 | − | 0.353451i | 0.317347 | − | 0.948309i | \(-0.397208\pi\) |
−0.803830 | + | 0.594859i | \(0.797208\pi\) | |||||||
\(812\) | −1.28115 | − | 3.94298i | −0.0449597 | − | 0.138372i | ||||
\(813\) | 20.4164 | 0.716035 | ||||||||
\(814\) | −45.0689 | + | 37.6587i | −1.57966 | + | 1.31994i | ||||
\(815\) | 60.3050 | 2.11239 | ||||||||
\(816\) | −0.354102 | − | 1.08981i | −0.0123960 | − | 0.0381511i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 37.4615 | − | 27.2174i | 1.30981 | − | 0.951633i | ||||
\(819\) | −0.309017 | + | 0.951057i | −0.0107979 | + | 0.0332326i | ||||
\(820\) | 3.04508 | − | 9.37181i | 0.106339 | − | 0.327278i | ||||
\(821\) | −22.7984 | + | 16.5640i | −0.795669 | + | 0.578087i | −0.909640 | − | 0.415397i | \(-0.863643\pi\) |
0.113972 | + | 0.993484i | \(0.463643\pi\) | |||||||
\(822\) | 27.4164 | + | 19.9192i | 0.956257 | + | 0.694761i | ||||
\(823\) | 16.7639 | + | 51.5941i | 0.584354 | + | 1.79846i | 0.601849 | + | 0.798610i | \(0.294431\pi\) |
−0.0174955 | + | 0.999847i | \(0.505569\pi\) | |||||||
\(824\) | −1.58359 | −0.0551670 | ||||||||
\(825\) | −6.13525 | + | 0.416272i | −0.213602 | + | 0.0144927i | ||||
\(826\) | −17.5623 | −0.611071 | ||||||||
\(827\) | 12.6353 | + | 38.8873i | 0.439371 | + | 1.35224i | 0.888541 | + | 0.458798i | \(0.151720\pi\) |
−0.449170 | + | 0.893446i | \(0.648280\pi\) | |||||||
\(828\) | −0.618034 | − | 0.449028i | −0.0214782 | − | 0.0156048i | ||||
\(829\) | 18.3541 | − | 13.3350i | 0.637464 | − | 0.463145i | −0.221514 | − | 0.975157i | \(-0.571100\pi\) |
0.858978 | + | 0.512012i | \(0.171100\pi\) | |||||||
\(830\) | 7.85410 | − | 24.1724i | 0.272620 | − | 0.839038i | ||||
\(831\) | 0.437694 | − | 1.34708i | 0.0151834 | − | 0.0467298i | ||||
\(832\) | 3.42705 | − | 2.48990i | 0.118812 | − | 0.0863217i | ||||
\(833\) | −0.190983 | − | 0.138757i | −0.00661717 | − | 0.00480765i | ||||
\(834\) | 1.28115 | + | 3.94298i | 0.0443627 | + | 0.136534i | ||||
\(835\) | −30.4164 | −1.05260 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.76393 | −0.199231 | ||||||||
\(838\) | 0.163119 | + | 0.502029i | 0.00563485 | + | 0.0173423i | ||||
\(839\) | 23.5172 | + | 17.0863i | 0.811905 | + | 0.589883i | 0.914382 | − | 0.404852i | \(-0.132677\pi\) |
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(840\) | −4.73607 | + | 3.44095i | −0.163410 | + | 0.118724i | ||||
\(841\) | 4.94427 | − | 15.2169i | 0.170492 | − | 0.524721i | ||||
\(842\) | 18.1353 | − | 55.8146i | 0.624982 | − | 1.92350i | ||||
\(843\) | −10.8262 | + | 7.86572i | −0.372875 | + | 0.270910i | ||||
\(844\) | −9.35410 | − | 6.79615i | −0.321981 | − | 0.233933i | ||||
\(845\) | 9.70820 | + | 29.8788i | 0.333972 | + | 1.02786i | ||||
\(846\) | 13.4721 | 0.463182 | ||||||||
\(847\) | 10.8992 | − | 1.48584i | 0.374500 | − | 0.0510541i | ||||
\(848\) | −26.1246 | −0.897123 | ||||||||
\(849\) | 6.39919 | + | 19.6947i | 0.219620 | + | 0.675919i | ||||
\(850\) | −0.572949 | − | 0.416272i | −0.0196520 | − | 0.0142780i | ||||
\(851\) | 10.9443 | − | 7.95148i | 0.375165 | − | 0.272573i | ||||
\(852\) | 0.281153 | − | 0.865300i | 0.00963214 | − | 0.0296447i | ||||
\(853\) | 10.4443 | − | 32.1442i | 0.357605 | − | 1.10060i | −0.596878 | − | 0.802332i | \(-0.703593\pi\) |
0.954484 | − | 0.298264i | \(-0.0964074\pi\) | |||||||
\(854\) | 13.3992 | − | 9.73508i | 0.458511 | − | 0.333128i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.9828 | − | 43.0346i | −0.477922 | − | 1.47089i | ||||
\(857\) | −49.7639 | −1.69990 | −0.849952 | − | 0.526861i | \(-0.823369\pi\) | ||||
−0.849952 | + | 0.526861i | \(0.823369\pi\) | |||||||
\(858\) | 1.30902 | − | 5.20431i | 0.0446891 | − | 0.177672i | ||||
\(859\) | 11.8328 | 0.403730 | 0.201865 | − | 0.979413i | \(-0.435300\pi\) | ||||
0.201865 | + | 0.979413i | \(0.435300\pi\) | |||||||
\(860\) | 0.500000 | + | 1.53884i | 0.0170499 | + | 0.0524741i | ||||
\(861\) | 4.92705 | + | 3.57971i | 0.167913 | + | 0.121996i | ||||
\(862\) | 17.2812 | − | 12.5555i | 0.588598 | − | 0.427642i | ||||
\(863\) | −4.12868 | + | 12.7068i | −0.140542 | + | 0.432543i | −0.996411 | − | 0.0846495i | \(-0.973023\pi\) |
0.855869 | + | 0.517193i | \(0.173023\pi\) | |||||||
\(864\) | −1.04508 | + | 3.21644i | −0.0355545 | + | 0.109426i | ||||
\(865\) | −26.2254 | + | 19.0539i | −0.891691 | + | 0.647852i | ||||
\(866\) | 38.5066 | + | 27.9767i | 1.30851 | + | 0.950686i | ||||
\(867\) | −5.23607 | − | 16.1150i | −0.177826 | − | 0.547293i | ||||
\(868\) | −3.56231 | −0.120913 | ||||||||
\(869\) | −13.7188 | + | 0.930812i | −0.465380 | + | 0.0315756i | ||||
\(870\) | 28.4164 | 0.963406 | ||||||||
\(871\) | 1.47214 | + | 4.53077i | 0.0498814 | + | 0.153519i | ||||
\(872\) | 22.7254 | + | 16.5110i | 0.769580 | + | 0.559133i | ||||
\(873\) | 13.7533 | − | 9.99235i | 0.465478 | − | 0.338190i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.54508 | − | 7.83297i | 0.0860396 | − | 0.264803i | ||||
\(876\) | 4.28115 | − | 3.11044i | 0.144647 | − | 0.105092i | ||||
\(877\) | 0.600813 | + | 0.436516i | 0.0202880 | + | 0.0147401i | 0.597883 | − | 0.801583i | \(-0.296009\pi\) |
−0.577595 | + | 0.816323i | \(0.696009\pi\) | |||||||
\(878\) | 4.73607 | + | 14.5761i | 0.159835 | + | 0.491920i | ||||
\(879\) | −8.76393 | −0.295600 | ||||||||
\(880\) | 32.3435 | − | 27.0256i | 1.09030 | − | 0.911033i | ||||
\(881\) | 5.94427 | 0.200268 | 0.100134 | − | 0.994974i | \(-0.468073\pi\) | ||||
0.100134 | + | 0.994974i | \(0.468073\pi\) | |||||||
\(882\) | 0.500000 | + | 1.53884i | 0.0168359 | + | 0.0518155i | ||||
\(883\) | 3.20820 | + | 2.33090i | 0.107965 | + | 0.0784409i | 0.640458 | − | 0.767994i | \(-0.278745\pi\) |
−0.532493 | + | 0.846434i | \(0.678745\pi\) | |||||||
\(884\) | 0.118034 | − | 0.0857567i | 0.00396991 | − | 0.00288431i | ||||
\(885\) | 8.78115 | − | 27.0256i | 0.295175 | − | 0.908456i | ||||
\(886\) | −2.67376 | + | 8.22899i | −0.0898268 | + | 0.276458i | ||||
\(887\) | 10.1353 | − | 7.36369i | 0.340309 | − | 0.247249i | −0.404483 | − | 0.914545i | \(-0.632549\pi\) |
0.744792 | + | 0.667297i | \(0.232549\pi\) | |||||||
\(888\) | −19.7984 | − | 14.3844i | −0.664390 | − | 0.482708i | ||||
\(889\) | 2.57295 | + | 7.91872i | 0.0862939 | + | 0.265585i | ||||
\(890\) | 36.5066 | 1.22370 | ||||||||
\(891\) | −1.23607 | − | 3.07768i | −0.0414098 | − | 0.103106i | ||||
\(892\) | 0.437694 | 0.0146551 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 2.50000 | + | 1.81636i | 0.0836125 | + | 0.0607480i | ||||
\(895\) | 4.73607 | − | 3.44095i | 0.158309 | − | 0.115018i | ||||
\(896\) | 4.20820 | − | 12.9515i | 0.140586 | − | 0.432680i | ||||
\(897\) | −0.381966 | + | 1.17557i | −0.0127535 | + | 0.0392512i | ||||
\(898\) | 20.4894 | − | 14.8864i | 0.683739 | − | 0.496765i | ||||
\(899\) | −31.2812 | − | 22.7271i | −1.04328 | − | 0.757991i | ||||
\(900\) | 0.354102 | + | 1.08981i | 0.0118034 | + | 0.0363271i | ||||
\(901\) | 1.27051 | 0.0423268 | ||||||||
\(902\) | −27.6803 | − | 17.3763i | −0.921655 | − | 0.578567i | ||||
\(903\) | −1.00000 | −0.0332779 | ||||||||
\(904\) | −13.5795 | − | 41.7935i | −0.451648 | − | 1.39003i | ||||
\(905\) | 8.97214 | + | 6.51864i | 0.298244 | + | 0.216687i | ||||
\(906\) | 12.9721 | − | 9.42481i | 0.430970 | − | 0.313118i | ||||
\(907\) | −8.64590 | + | 26.6093i | −0.287082 | + | 0.883549i | 0.698684 | + | 0.715430i | \(0.253769\pi\) |
−0.985767 | + | 0.168119i | \(0.946231\pi\) | |||||||
\(908\) | −5.34346 | + | 16.4455i | −0.177329 | + | 0.545762i | ||||
\(909\) | −14.7082 | + | 10.6861i | −0.487840 | + | 0.354437i | ||||
\(910\) | −3.42705 | − | 2.48990i | −0.113606 | − | 0.0825393i | ||||
\(911\) | −14.9336 | − | 45.9610i | −0.494773 | − | 1.52276i | −0.817310 | − | 0.576198i | \(-0.804536\pi\) |
0.322537 | − | 0.946557i | \(-0.395464\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.8541 | − | 10.5801i | −0.557789 | − | 0.350151i | ||||
\(914\) | −34.4164 | −1.13839 | ||||||||
\(915\) | 8.28115 | + | 25.4868i | 0.273766 | + | 0.842567i | ||||
\(916\) | −0.854102 | − | 0.620541i | −0.0282203 | − | 0.0205033i | ||||
\(917\) | −9.97214 | + | 7.24518i | −0.329309 | + | 0.239257i | ||||
\(918\) | 0.118034 | − | 0.363271i | 0.00389570 | − | 0.0119897i | ||||
\(919\) | −13.4164 | + | 41.2915i | −0.442566 | + | 1.36208i | 0.442564 | + | 0.896737i | \(0.354069\pi\) |
−0.885131 | + | 0.465343i | \(0.845931\pi\) | |||||||
\(920\) | −5.85410 | + | 4.25325i | −0.193004 | + | 0.140226i | ||||
\(921\) | 2.57295 | + | 1.86936i | 0.0847816 | + | 0.0615974i | ||||
\(922\) | 0.409830 | + | 1.26133i | 0.0134970 | + | 0.0415396i | ||||
\(923\) | −1.47214 | −0.0484559 | ||||||||
\(924\) | −0.763932 | − | 1.90211i | −0.0251315 | − | 0.0625749i | ||||
\(925\) | −20.2918 | −0.667190 | ||||||||
\(926\) | 14.4615 | + | 44.5079i | 0.475234 | + | 1.46262i | ||||
\(927\) | −0.572949 | − | 0.416272i | −0.0188181 | − | 0.0136722i | ||||
\(928\) | −18.3541 | + | 13.3350i | −0.602503 | + | 0.437744i | ||||
\(929\) | 17.2361 | − | 53.0472i | 0.565497 | − | 1.74042i | −0.100973 | − | 0.994889i | \(-0.532196\pi\) |
0.666470 | − | 0.745532i | \(-0.267804\pi\) | |||||||
\(930\) | 7.54508 | − | 23.2214i | 0.247413 | − | 0.761459i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.881966 | − | 0.640786i | −0.0288898 | − | 0.0209896i | ||||
\(933\) | −2.40983 | − | 7.41669i | −0.0788943 | − | 0.242812i | ||||
\(934\) | 22.7426 | 0.744162 | ||||||||
\(935\) | −1.57295 | + | 1.31433i | −0.0514409 | + | 0.0429831i | ||||
\(936\) | 2.23607 | 0.0730882 | ||||||||
\(937\) | −2.16312 | − | 6.65740i | −0.0706660 | − | 0.217488i | 0.909486 | − | 0.415734i | \(-0.136475\pi\) |
−0.980152 | + | 0.198247i | \(0.936475\pi\) | |||||||
\(938\) | 6.23607 | + | 4.53077i | 0.203615 | + | 0.147935i | ||||
\(939\) | −7.11803 | + | 5.17155i | −0.232288 | + | 0.168767i | ||||
\(940\) | −4.16312 | + | 12.8128i | −0.135786 | + | 0.417906i | ||||
\(941\) | −9.83282 | + | 30.2623i | −0.320541 | + | 0.986523i | 0.652873 | + | 0.757468i | \(0.273564\pi\) |
−0.973413 | + | 0.229055i | \(0.926436\pi\) | |||||||
\(942\) | 22.6803 | − | 16.4782i | 0.738965 | − | 0.536890i | ||||
\(943\) | 6.09017 | + | 4.42477i | 0.198323 | + | 0.144090i | ||||
\(944\) | 16.2812 | + | 50.1082i | 0.529906 | + | 1.63088i | ||||
\(945\) | −2.61803 | −0.0851647 | ||||||||
\(946\) | 5.35410 | − | 0.363271i | 0.174077 | − | 0.0118110i | ||||
\(947\) | 1.61803 | 0.0525790 | 0.0262895 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262895 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(948\) | 0.791796 | + | 2.43690i | 0.0257163 | + | 0.0791468i | ||||
\(949\) | −6.92705 | − | 5.03280i | −0.224862 | − | 0.163372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.98278 | + | 18.4131i | −0.194005 | + | 0.597086i | ||||
\(952\) | −0.163119 | + | 0.502029i | −0.00528672 | + | 0.0162708i | ||||
\(953\) | −35.4336 | + | 25.7440i | −1.14781 | + | 0.833931i | −0.988188 | − | 0.153247i | \(-0.951027\pi\) |
−0.159620 | + | 0.987179i | \(0.551027\pi\) | |||||||
\(954\) | −7.04508 | − | 5.11855i | −0.228093 | − | 0.165719i | ||||
\(955\) | −11.5172 | − | 35.4464i | −0.372689 | − | 1.14702i | ||||
\(956\) | 15.9787 | 0.516789 | ||||||||
\(957\) | 5.42705 | − | 21.5765i | 0.175432 | − | 0.697471i | ||||
\(958\) | −26.7082 | −0.862903 | ||||||||
\(959\) | −6.47214 | − | 19.9192i | −0.208996 | − | 0.643224i | ||||
\(960\) | 8.97214 | + | 6.51864i | 0.289574 | + | 0.210388i | ||||
\(961\) | −1.79837 | + | 1.30660i | −0.0580121 | + | 0.0421482i | ||||
\(962\) | 5.47214 | − | 16.8415i | 0.176429 | − | 0.542992i | ||||
\(963\) | 6.25329 | − | 19.2456i | 0.201509 | − | 0.620182i | ||||
\(964\) | 5.64590 | − | 4.10199i | 0.181842 | − | 0.132116i | ||||
\(965\) | 48.5967 | + | 35.3076i | 1.56438 | + | 1.13659i | ||||
\(966\) | 0.618034 | + | 1.90211i | 0.0198849 | + | 0.0611995i | ||||
\(967\) | 49.7082 | 1.59851 | 0.799254 | − | 0.600993i | \(-0.205228\pi\) | ||||
0.799254 | + | 0.600993i | \(0.205228\pi\) | |||||||
\(968\) | −10.6910 | − | 22.1518i | −0.343621 | − | 0.711986i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.2533 | + | 68.4886i | 0.714510 | + | 2.19904i | ||||
\(971\) | 9.13525 | + | 6.63715i | 0.293164 | + | 0.212996i | 0.724639 | − | 0.689129i | \(-0.242007\pi\) |
−0.431475 | + | 0.902125i | \(0.642007\pi\) | |||||||
\(972\) | −0.500000 | + | 0.363271i | −0.0160375 | + | 0.0116519i | ||||
\(973\) | 0.791796 | − | 2.43690i | 0.0253838 | − | 0.0781234i | ||||
\(974\) | 7.19098 | − | 22.1316i | 0.230414 | − | 0.709141i | ||||
\(975\) | 1.50000 | − | 1.08981i | 0.0480384 | − | 0.0349020i | ||||
\(976\) | −40.1976 | − | 29.2052i | −1.28669 | − | 0.934837i | ||||
\(977\) | 10.1976 | + | 31.3849i | 0.326249 | + | 1.00409i | 0.970874 | + | 0.239592i | \(0.0770136\pi\) |
−0.644625 | + | 0.764499i | \(0.722986\pi\) | |||||||
\(978\) | −37.2705 | −1.19178 | ||||||||
\(979\) | 6.97214 | − | 27.7194i | 0.222830 | − | 0.885916i | ||||
\(980\) | −1.61803 | −0.0516862 | ||||||||
\(981\) | 3.88197 | + | 11.9475i | 0.123942 | + | 0.381453i | ||||
\(982\) | 12.7082 | + | 9.23305i | 0.405535 | + | 0.294638i | ||||
\(983\) | 9.75329 | − | 7.08618i | 0.311082 | − | 0.226014i | −0.421279 | − | 0.906931i | \(-0.638419\pi\) |
0.732360 | + | 0.680917i | \(0.238419\pi\) | |||||||
\(984\) | 4.20820 | − | 12.9515i | 0.134153 | − | 0.412879i | ||||
\(985\) | 3.85410 | − | 11.8617i | 0.122802 | − | 0.377945i | ||||
\(986\) | 2.07295 | − | 1.50609i | 0.0660161 | − | 0.0479635i | ||||
\(987\) | −6.73607 | − | 4.89404i | −0.214411 | − | 0.155779i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.23607 | −0.0393047 | ||||||||
\(990\) | 14.0172 | − | 0.951057i | 0.445497 | − | 0.0302266i | ||||
\(991\) | −44.6312 | −1.41776 | −0.708878 | − | 0.705331i | \(-0.750798\pi\) | ||||
−0.708878 | + | 0.705331i | \(0.750798\pi\) | |||||||
\(992\) | 6.02380 | + | 18.5393i | 0.191256 | + | 0.588625i | ||||
\(993\) | 1.04508 | + | 0.759299i | 0.0331648 | + | 0.0240956i | ||||
\(994\) | −1.92705 | + | 1.40008i | −0.0611223 | + | 0.0444080i | ||||
\(995\) | −10.1631 | + | 31.2789i | −0.322193 | + | 0.991607i | ||||
\(996\) | −1.14590 | + | 3.52671i | −0.0363092 | + | 0.111748i | ||||
\(997\) | 20.5623 | − | 14.9394i | 0.651215 | − | 0.473135i | −0.212470 | − | 0.977168i | \(-0.568151\pi\) |
0.863685 | + | 0.504032i | \(0.168151\pi\) | |||||||
\(998\) | 6.54508 | + | 4.75528i | 0.207181 | + | 0.150526i | ||||
\(999\) | −3.38197 | − | 10.4086i | −0.107001 | − | 0.329314i |
(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 | 231.2.j.d.148.1 | yes | 4 | |
3.2 | odd | 2 | 693.2.m.b.379.1 | 4 | |||
11.3 | even | 5 | 2541.2.a.bb.1.2 | 2 | |||
11.8 | odd | 10 | 2541.2.a.s.1.1 | 2 | |||
11.9 | even | 5 | inner | 231.2.j.d.64.1 | ✓ | 4 | |
33.8 | even | 10 | 7623.2.a.bp.1.2 | 2 | |||
33.14 | odd | 10 | 7623.2.a.ba.1.1 | 2 | |||
33.20 | odd | 10 | 693.2.m.b.64.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.d.64.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
231.2.j.d.148.1 | yes | 4 | 1.1 | even | 1 | trivial | |
693.2.m.b.64.1 | 4 | 33.20 | odd | 10 | |||
693.2.m.b.379.1 | 4 | 3.2 | odd | 2 | |||
2541.2.a.s.1.1 | 2 | 11.8 | odd | 10 | |||
2541.2.a.bb.1.2 | 2 | 11.3 | even | 5 | |||
7623.2.a.ba.1.1 | 2 | 33.14 | odd | 10 | |||
7623.2.a.bp.1.2 | 2 | 33.8 | even | 10 |