Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(69,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.69");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.g (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: | \(1.49320251780\) |
Analytic rank: | \(1\) |
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 | 137.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.137 |
Dual form | 187.2.g.a.86.1 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 1.53884i | −0.353553 | − | 1.08813i | −0.956844 | − | 0.290604i | \(-0.906144\pi\) |
0.603290 | − | 0.797522i | \(-0.293856\pi\) | |||||||
\(3\) | −1.80902 | − | 1.31433i | −1.04444 | − | 0.758827i | −0.0732898 | − | 0.997311i | \(-0.523350\pi\) |
−0.971147 | + | 0.238483i | \(0.923350\pi\) | |||||||
\(4\) | −0.500000 | + | 0.363271i | −0.250000 | + | 0.181636i | ||||
\(5\) | −0.690983 | + | 2.12663i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(6\) | −1.11803 | + | 3.44095i | −0.456435 | + | 1.40476i | ||||
\(7\) | −3.11803 | + | 2.26538i | −1.17851 | + | 0.856235i | −0.992002 | − | 0.126219i | \(-0.959716\pi\) |
−0.186504 | + | 0.982454i | \(0.559716\pi\) | |||||||
\(8\) | −1.80902 | − | 1.31433i | −0.639584 | − | 0.464685i | ||||
\(9\) | 0.618034 | + | 1.90211i | 0.206011 | + | 0.634038i | ||||
\(10\) | 3.61803 | 1.14412 | ||||||||
\(11\) | 1.23607 | + | 3.07768i | 0.372689 | + | 0.927957i | ||||
\(12\) | 1.38197 | 0.398939 | ||||||||
\(13\) | −1.57295 | − | 4.84104i | −0.436258 | − | 1.34266i | −0.891792 | − | 0.452445i | \(-0.850552\pi\) |
0.455535 | − | 0.890218i | \(-0.349448\pi\) | |||||||
\(14\) | 5.04508 | + | 3.66547i | 1.34836 | + | 0.979638i | ||||
\(15\) | 4.04508 | − | 2.93893i | 1.04444 | − | 0.758827i | ||||
\(16\) | −1.50000 | + | 4.61653i | −0.375000 | + | 1.15413i | ||||
\(17\) | −0.309017 | + | 0.951057i | −0.0749476 | + | 0.230665i | ||||
\(18\) | 2.61803 | − | 1.90211i | 0.617077 | − | 0.448332i | ||||
\(19\) | −0.809017 | − | 0.587785i | −0.185601 | − | 0.134847i | 0.491105 | − | 0.871100i | \(-0.336593\pi\) |
−0.676706 | + | 0.736253i | \(0.736593\pi\) | |||||||
\(20\) | −0.427051 | − | 1.31433i | −0.0954915 | − | 0.293893i | ||||
\(21\) | 8.61803 | 1.88061 | ||||||||
\(22\) | 4.11803 | − | 3.44095i | 0.877968 | − | 0.733614i | ||||
\(23\) | −6.23607 | −1.30031 | −0.650155 | − | 0.759802i | \(-0.725296\pi\) | ||||
−0.650155 | + | 0.759802i | \(0.725296\pi\) | |||||||
\(24\) | 1.54508 | + | 4.75528i | 0.315389 | + | 0.970668i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.66312 | + | 4.84104i | −1.30675 | + | 0.949406i | ||||
\(27\) | −0.690983 | + | 2.12663i | −0.132980 | + | 0.409270i | ||||
\(28\) | 0.736068 | − | 2.26538i | 0.139104 | − | 0.428117i | ||||
\(29\) | −3.73607 | + | 2.71441i | −0.693770 | + | 0.504054i | −0.877897 | − | 0.478849i | \(-0.841054\pi\) |
0.184127 | + | 0.982902i | \(0.441054\pi\) | |||||||
\(30\) | −6.54508 | − | 4.75528i | −1.19496 | − | 0.868192i | ||||
\(31\) | −2.85410 | − | 8.78402i | −0.512612 | − | 1.57766i | −0.787586 | − | 0.616205i | \(-0.788669\pi\) |
0.274974 | − | 0.961452i | \(-0.411331\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 1.80902 | − | 7.19218i | 0.314909 | − | 1.25200i | ||||
\(34\) | 1.61803 | 0.277491 | ||||||||
\(35\) | −2.66312 | − | 8.19624i | −0.450149 | − | 1.38542i | ||||
\(36\) | −1.00000 | − | 0.726543i | −0.166667 | − | 0.121090i | ||||
\(37\) | 4.61803 | − | 3.35520i | 0.759200 | − | 0.551591i | −0.139465 | − | 0.990227i | \(-0.544538\pi\) |
0.898665 | + | 0.438636i | \(0.144538\pi\) | |||||||
\(38\) | −0.500000 | + | 1.53884i | −0.0811107 | + | 0.249633i | ||||
\(39\) | −3.51722 | + | 10.8249i | −0.563206 | + | 1.73337i | ||||
\(40\) | 4.04508 | − | 2.93893i | 0.639584 | − | 0.464685i | ||||
\(41\) | −4.23607 | − | 3.07768i | −0.661563 | − | 0.480653i | 0.205628 | − | 0.978630i | \(-0.434076\pi\) |
−0.867190 | + | 0.497977i | \(0.834076\pi\) | |||||||
\(42\) | −4.30902 | − | 13.2618i | −0.664896 | − | 2.04634i | ||||
\(43\) | −9.00000 | −1.37249 | −0.686244 | − | 0.727372i | \(-0.740742\pi\) | ||||
−0.686244 | + | 0.727372i | \(0.740742\pi\) | |||||||
\(44\) | −1.73607 | − | 1.08981i | −0.261722 | − | 0.164296i | ||||
\(45\) | −4.47214 | −0.666667 | ||||||||
\(46\) | 3.11803 | + | 9.59632i | 0.459729 | + | 1.41490i | ||||
\(47\) | 1.80902 | + | 1.31433i | 0.263872 | + | 0.191714i | 0.711852 | − | 0.702329i | \(-0.247856\pi\) |
−0.447980 | + | 0.894043i | \(0.647856\pi\) | |||||||
\(48\) | 8.78115 | − | 6.37988i | 1.26745 | − | 0.920857i | ||||
\(49\) | 2.42705 | − | 7.46969i | 0.346722 | − | 1.06710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80902 | − | 1.31433i | 0.253313 | − | 0.184043i | ||||
\(52\) | 2.54508 | + | 1.84911i | 0.352940 | + | 0.256426i | ||||
\(53\) | 3.11803 | + | 9.59632i | 0.428295 | + | 1.31816i | 0.899804 | + | 0.436295i | \(0.143710\pi\) |
−0.471509 | + | 0.881861i | \(0.656290\pi\) | |||||||
\(54\) | 3.61803 | 0.492352 | ||||||||
\(55\) | −7.39919 | + | 0.502029i | −0.997706 | + | 0.0676935i | ||||
\(56\) | 8.61803 | 1.15163 | ||||||||
\(57\) | 0.690983 | + | 2.12663i | 0.0915229 | + | 0.281679i | ||||
\(58\) | 6.04508 | + | 4.39201i | 0.793759 | + | 0.576699i | ||||
\(59\) | −3.50000 | + | 2.54290i | −0.455661 | + | 0.331057i | −0.791827 | − | 0.610746i | \(-0.790870\pi\) |
0.336166 | + | 0.941803i | \(0.390870\pi\) | |||||||
\(60\) | −0.954915 | + | 2.93893i | −0.123279 | + | 0.379414i | ||||
\(61\) | 2.33688 | − | 7.19218i | 0.299207 | − | 0.920864i | −0.682569 | − | 0.730821i | \(-0.739137\pi\) |
0.981776 | − | 0.190043i | \(-0.0608627\pi\) | |||||||
\(62\) | −12.0902 | + | 8.78402i | −1.53545 | + | 1.11557i | ||||
\(63\) | −6.23607 | − | 4.53077i | −0.785671 | − | 0.570823i | ||||
\(64\) | 1.30902 | + | 4.02874i | 0.163627 | + | 0.503593i | ||||
\(65\) | 11.3820 | 1.41176 | ||||||||
\(66\) | −11.9721 | + | 0.812299i | −1.47367 | + | 0.0999871i | ||||
\(67\) | −7.14590 | −0.873010 | −0.436505 | − | 0.899702i | \(-0.643784\pi\) | ||||
−0.436505 | + | 0.899702i | \(0.643784\pi\) | |||||||
\(68\) | −0.190983 | − | 0.587785i | −0.0231601 | − | 0.0712794i | ||||
\(69\) | 11.2812 | + | 8.19624i | 1.35809 | + | 0.986711i | ||||
\(70\) | −11.2812 | + | 8.19624i | −1.34836 | + | 0.979638i | ||||
\(71\) | 0.354102 | − | 1.08981i | 0.0420242 | − | 0.129337i | −0.927843 | − | 0.372970i | \(-0.878339\pi\) |
0.969867 | + | 0.243633i | \(0.0783393\pi\) | |||||||
\(72\) | 1.38197 | − | 4.25325i | 0.162866 | − | 0.501251i | ||||
\(73\) | 10.7812 | − | 7.83297i | 1.26184 | − | 0.916779i | 0.262992 | − | 0.964798i | \(-0.415291\pi\) |
0.998846 | + | 0.0480187i | \(0.0152907\pi\) | |||||||
\(74\) | −7.47214 | − | 5.42882i | −0.868618 | − | 0.631088i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.618034 | 0.0708934 | ||||||||
\(77\) | −10.8262 | − | 6.79615i | −1.23376 | − | 0.774494i | ||||
\(78\) | 18.4164 | 2.08525 | ||||||||
\(79\) | 0.309017 | + | 0.951057i | 0.0347671 | + | 0.107002i | 0.966934 | − | 0.255027i | \(-0.0820842\pi\) |
−0.932167 | + | 0.362029i | \(0.882084\pi\) | |||||||
\(80\) | −8.78115 | − | 6.37988i | −0.981763 | − | 0.713292i | ||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | −2.61803 | + | 8.05748i | −0.289113 | + | 0.889800i | ||||
\(83\) | −0.336881 | + | 1.03681i | −0.0369775 | + | 0.113805i | −0.967841 | − | 0.251561i | \(-0.919056\pi\) |
0.930864 | + | 0.365366i | \(0.119056\pi\) | |||||||
\(84\) | −4.30902 | + | 3.13068i | −0.470152 | + | 0.341586i | ||||
\(85\) | −1.80902 | − | 1.31433i | −0.196215 | − | 0.142559i | ||||
\(86\) | 4.50000 | + | 13.8496i | 0.485247 | + | 1.49344i | ||||
\(87\) | 10.3262 | 1.10709 | ||||||||
\(88\) | 1.80902 | − | 7.19218i | 0.192842 | − | 0.766689i | ||||
\(89\) | 4.09017 | 0.433557 | 0.216779 | − | 0.976221i | \(-0.430445\pi\) | ||||
0.216779 | + | 0.976221i | \(0.430445\pi\) | |||||||
\(90\) | 2.23607 | + | 6.88191i | 0.235702 | + | 0.725417i | ||||
\(91\) | 15.8713 | + | 11.5312i | 1.66377 | + | 1.20880i | ||||
\(92\) | 3.11803 | − | 2.26538i | 0.325078 | − | 0.236183i | ||||
\(93\) | −6.38197 | + | 19.6417i | −0.661779 | + | 2.03675i | ||||
\(94\) | 1.11803 | − | 3.44095i | 0.115316 | − | 0.354907i | ||||
\(95\) | 1.80902 | − | 1.31433i | 0.185601 | − | 0.134847i | ||||
\(96\) | −6.11803 | − | 4.44501i | −0.624419 | − | 0.453667i | ||||
\(97\) | 3.32624 | + | 10.2371i | 0.337728 | + | 1.03942i | 0.965362 | + | 0.260912i | \(0.0840234\pi\) |
−0.627634 | + | 0.778508i | \(0.715977\pi\) | |||||||
\(98\) | −12.7082 | −1.28372 | ||||||||
\(99\) | −5.09017 | + | 4.25325i | −0.511581 | + | 0.427468i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.51722 | − | 10.8249i | −0.349977 | − | 1.07712i | −0.958865 | − | 0.283861i | \(-0.908384\pi\) |
0.608889 | − | 0.793256i | \(-0.291616\pi\) | |||||||
\(102\) | −2.92705 | − | 2.12663i | −0.289821 | − | 0.210567i | ||||
\(103\) | 12.1353 | − | 8.81678i | 1.19572 | − | 0.868743i | 0.201865 | − | 0.979413i | \(-0.435300\pi\) |
0.993857 | + | 0.110670i | \(0.0352998\pi\) | |||||||
\(104\) | −3.51722 | + | 10.8249i | −0.344892 | + | 1.06147i | ||||
\(105\) | −5.95492 | + | 18.3273i | −0.581140 | + | 1.78857i | ||||
\(106\) | 13.2082 | − | 9.59632i | 1.28289 | − | 0.932077i | ||||
\(107\) | 2.42705 | + | 1.76336i | 0.234632 | + | 0.170470i | 0.698888 | − | 0.715231i | \(-0.253678\pi\) |
−0.464256 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(108\) | −0.427051 | − | 1.31433i | −0.0410930 | − | 0.126471i | ||||
\(109\) | −11.5623 | −1.10747 | −0.553734 | − | 0.832694i | \(-0.686798\pi\) | ||||
−0.553734 | + | 0.832694i | \(0.686798\pi\) | |||||||
\(110\) | 4.47214 | + | 11.1352i | 0.426401 | + | 1.06170i | ||||
\(111\) | −12.7639 | −1.21150 | ||||||||
\(112\) | −5.78115 | − | 17.7926i | −0.546268 | − | 1.68124i | ||||
\(113\) | 0.0450850 | + | 0.0327561i | 0.00424124 | + | 0.00308144i | 0.589904 | − | 0.807473i | \(-0.299166\pi\) |
−0.585663 | + | 0.810555i | \(0.699166\pi\) | |||||||
\(114\) | 2.92705 | − | 2.12663i | 0.274143 | − | 0.199177i | ||||
\(115\) | 4.30902 | − | 13.2618i | 0.401818 | − | 1.23667i | ||||
\(116\) | 0.881966 | − | 2.71441i | 0.0818885 | − | 0.252027i | ||||
\(117\) | 8.23607 | − | 5.98385i | 0.761425 | − | 0.553207i | ||||
\(118\) | 5.66312 | + | 4.11450i | 0.521332 | + | 0.378770i | ||||
\(119\) | −1.19098 | − | 3.66547i | −0.109177 | − | 0.336013i | ||||
\(120\) | −11.1803 | −1.02062 | ||||||||
\(121\) | −7.94427 | + | 7.60845i | −0.722207 | + | 0.691677i | ||||
\(122\) | −12.2361 | −1.10780 | ||||||||
\(123\) | 3.61803 | + | 11.1352i | 0.326227 | + | 1.00402i | ||||
\(124\) | 4.61803 | + | 3.35520i | 0.414712 | + | 0.301306i | ||||
\(125\) | −9.04508 | + | 6.57164i | −0.809017 | + | 0.587785i | ||||
\(126\) | −3.85410 | + | 11.8617i | −0.343351 | + | 1.05672i | ||||
\(127\) | 0.0729490 | − | 0.224514i | 0.00647318 | − | 0.0199224i | −0.947768 | − | 0.318961i | \(-0.896666\pi\) |
0.954241 | + | 0.299039i | \(0.0966660\pi\) | |||||||
\(128\) | 11.0172 | − | 8.00448i | 0.973794 | − | 0.707503i | ||||
\(129\) | 16.2812 | + | 11.8290i | 1.43348 | + | 1.04148i | ||||
\(130\) | −5.69098 | − | 17.5150i | −0.499132 | − | 1.53617i | ||||
\(131\) | 3.70820 | 0.323987 | 0.161994 | − | 0.986792i | \(-0.448208\pi\) | ||||
0.161994 | + | 0.986792i | \(0.448208\pi\) | |||||||
\(132\) | 1.70820 | + | 4.25325i | 0.148680 | + | 0.370198i | ||||
\(133\) | 3.85410 | 0.334193 | ||||||||
\(134\) | 3.57295 | + | 10.9964i | 0.308656 | + | 0.949945i | ||||
\(135\) | −4.04508 | − | 2.93893i | −0.348145 | − | 0.252942i | ||||
\(136\) | 1.80902 | − | 1.31433i | 0.155122 | − | 0.112703i | ||||
\(137\) | −2.06231 | + | 6.34712i | −0.176195 | + | 0.542271i | −0.999686 | − | 0.0250574i | \(-0.992023\pi\) |
0.823491 | + | 0.567329i | \(0.192023\pi\) | |||||||
\(138\) | 6.97214 | − | 21.4580i | 0.593508 | − | 1.82663i | ||||
\(139\) | −15.3262 | + | 11.1352i | −1.29995 | + | 0.944472i | −0.999955 | − | 0.00946715i | \(-0.996986\pi\) |
−0.299999 | + | 0.953939i | \(0.596986\pi\) | |||||||
\(140\) | 4.30902 | + | 3.13068i | 0.364178 | + | 0.264591i | ||||
\(141\) | −1.54508 | − | 4.75528i | −0.130120 | − | 0.400467i | ||||
\(142\) | −1.85410 | −0.155593 | ||||||||
\(143\) | 12.9549 | − | 10.8249i | 1.08334 | − | 0.905223i | ||||
\(144\) | −9.70820 | −0.809017 | ||||||||
\(145\) | −3.19098 | − | 9.82084i | −0.264997 | − | 0.815576i | ||||
\(146\) | −17.4443 | − | 12.6740i | −1.44370 | − | 1.04891i | ||||
\(147\) | −14.2082 | + | 10.3229i | −1.17187 | + | 0.851416i | ||||
\(148\) | −1.09017 | + | 3.35520i | −0.0896114 | + | 0.275796i | ||||
\(149\) | 0.354102 | − | 1.08981i | 0.0290092 | − | 0.0892810i | −0.935504 | − | 0.353317i | \(-0.885054\pi\) |
0.964513 | + | 0.264036i | \(0.0850537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.57295 | + | 2.59590i | 0.290762 | + | 0.211251i | 0.723598 | − | 0.690222i | \(-0.242487\pi\) |
−0.432836 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(152\) | 0.690983 | + | 2.12663i | 0.0560461 | + | 0.172492i | ||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −5.04508 | + | 20.0579i | −0.406545 | + | 1.61632i | ||||
\(155\) | 20.6525 | 1.65885 | ||||||||
\(156\) | −2.17376 | − | 6.69015i | −0.174040 | − | 0.535641i | ||||
\(157\) | −0.500000 | − | 0.363271i | −0.0399043 | − | 0.0289922i | 0.567654 | − | 0.823267i | \(-0.307851\pi\) |
−0.607559 | + | 0.794275i | \(0.707851\pi\) | |||||||
\(158\) | 1.30902 | − | 0.951057i | 0.104140 | − | 0.0756620i | ||||
\(159\) | 6.97214 | − | 21.4580i | 0.552926 | − | 1.70173i | ||||
\(160\) | −2.33688 | + | 7.19218i | −0.184747 | + | 0.568592i | ||||
\(161\) | 19.4443 | − | 14.1271i | 1.53242 | − | 1.11337i | ||||
\(162\) | −14.3992 | − | 10.4616i | −1.13131 | − | 0.821943i | ||||
\(163\) | 0.982779 | + | 3.02468i | 0.0769772 | + | 0.236911i | 0.982139 | − | 0.188155i | \(-0.0602507\pi\) |
−0.905162 | + | 0.425066i | \(0.860251\pi\) | |||||||
\(164\) | 3.23607 | 0.252694 | ||||||||
\(165\) | 14.0451 | + | 8.81678i | 1.09341 | + | 0.686385i | ||||
\(166\) | 1.76393 | 0.136908 | ||||||||
\(167\) | −6.07295 | − | 18.6906i | −0.469939 | − | 1.44632i | −0.852663 | − | 0.522461i | \(-0.825014\pi\) |
0.382724 | − | 0.923863i | \(-0.374986\pi\) | |||||||
\(168\) | −15.5902 | − | 11.3269i | −1.20281 | − | 0.873891i | ||||
\(169\) | −10.4443 | + | 7.58821i | −0.803406 | + | 0.583708i | ||||
\(170\) | −1.11803 | + | 3.44095i | −0.0857493 | + | 0.263909i | ||||
\(171\) | 0.618034 | − | 1.90211i | 0.0472622 | − | 0.145458i | ||||
\(172\) | 4.50000 | − | 3.26944i | 0.343122 | − | 0.249293i | ||||
\(173\) | −10.2812 | − | 7.46969i | −0.781662 | − | 0.567910i | 0.123816 | − | 0.992305i | \(-0.460487\pi\) |
−0.905477 | + | 0.424395i | \(0.860487\pi\) | |||||||
\(174\) | −5.16312 | − | 15.8904i | −0.391415 | − | 1.20465i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.0623 | + | 1.08981i | −1.21074 | + | 0.0821478i | ||||
\(177\) | 9.67376 | 0.727124 | ||||||||
\(178\) | −2.04508 | − | 6.29412i | −0.153286 | − | 0.471765i | ||||
\(179\) | 12.4443 | + | 9.04129i | 0.930129 | + | 0.675778i | 0.946024 | − | 0.324096i | \(-0.105060\pi\) |
−0.0158957 | + | 0.999874i | \(0.505060\pi\) | |||||||
\(180\) | 2.23607 | − | 1.62460i | 0.166667 | − | 0.121090i | ||||
\(181\) | −5.35410 | + | 16.4782i | −0.397967 | + | 1.22482i | 0.528659 | + | 0.848834i | \(0.322695\pi\) |
−0.926627 | + | 0.375983i | \(0.877305\pi\) | |||||||
\(182\) | 9.80902 | − | 30.1891i | 0.727093 | − | 2.23776i | ||||
\(183\) | −13.6803 | + | 9.93935i | −1.01128 | + | 0.734738i | ||||
\(184\) | 11.2812 | + | 8.19624i | 0.831658 | + | 0.604235i | ||||
\(185\) | 3.94427 | + | 12.1392i | 0.289989 | + | 0.892493i | ||||
\(186\) | 33.4164 | 2.45021 | ||||||||
\(187\) | −3.30902 | + | 0.224514i | −0.241979 | + | 0.0164181i | ||||
\(188\) | −1.38197 | −0.100790 | ||||||||
\(189\) | −2.66312 | − | 8.19624i | −0.193713 | − | 0.596189i | ||||
\(190\) | −2.92705 | − | 2.12663i | −0.212351 | − | 0.154282i | ||||
\(191\) | −4.28115 | + | 3.11044i | −0.309773 | + | 0.225064i | −0.731799 | − | 0.681520i | \(-0.761319\pi\) |
0.422026 | + | 0.906584i | \(0.361319\pi\) | |||||||
\(192\) | 2.92705 | − | 9.00854i | 0.211242 | − | 0.650135i | ||||
\(193\) | −2.47214 | + | 7.60845i | −0.177948 | + | 0.547668i | −0.999756 | − | 0.0220967i | \(-0.992966\pi\) |
0.821808 | + | 0.569765i | \(0.192966\pi\) | |||||||
\(194\) | 14.0902 | − | 10.2371i | 1.01162 | − | 0.734981i | ||||
\(195\) | −20.5902 | − | 14.9596i | −1.47449 | − | 1.07128i | ||||
\(196\) | 1.50000 | + | 4.61653i | 0.107143 | + | 0.329752i | ||||
\(197\) | −22.6180 | −1.61147 | −0.805734 | − | 0.592277i | \(-0.798229\pi\) | ||||
−0.805734 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(198\) | 9.09017 | + | 5.70634i | 0.646010 | + | 0.405532i | ||||
\(199\) | −12.2361 | −0.867392 | −0.433696 | − | 0.901059i | \(-0.642791\pi\) | ||||
−0.433696 | + | 0.901059i | \(0.642791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9271 | + | 9.39205i | 0.911804 | + | 0.662464i | ||||
\(202\) | −14.8992 | + | 10.8249i | −1.04830 | + | 0.761637i | ||||
\(203\) | 5.50000 | − | 16.9273i | 0.386024 | − | 1.18806i | ||||
\(204\) | −0.427051 | + | 1.31433i | −0.0298995 | + | 0.0920214i | ||||
\(205\) | 9.47214 | − | 6.88191i | 0.661563 | − | 0.480653i | ||||
\(206\) | −19.6353 | − | 14.2658i | −1.36805 | − | 0.993949i | ||||
\(207\) | −3.85410 | − | 11.8617i | −0.267879 | − | 0.824446i | ||||
\(208\) | 24.7082 | 1.71321 | ||||||||
\(209\) | 0.809017 | − | 3.21644i | 0.0559609 | − | 0.222486i | ||||
\(210\) | 31.1803 | 2.15165 | ||||||||
\(211\) | 5.18034 | + | 15.9434i | 0.356629 | + | 1.09759i | 0.955059 | + | 0.296417i | \(0.0957917\pi\) |
−0.598429 | + | 0.801176i | \(0.704208\pi\) | |||||||
\(212\) | −5.04508 | − | 3.66547i | −0.346498 | − | 0.251745i | ||||
\(213\) | −2.07295 | + | 1.50609i | −0.142036 | + | 0.103195i | ||||
\(214\) | 1.50000 | − | 4.61653i | 0.102538 | − | 0.315579i | ||||
\(215\) | 6.21885 | − | 19.1396i | 0.424122 | − | 1.30531i | ||||
\(216\) | 4.04508 | − | 2.93893i | 0.275233 | − | 0.199969i | ||||
\(217\) | 28.7984 | + | 20.9232i | 1.95496 | + | 1.42036i | ||||
\(218\) | 5.78115 | + | 17.7926i | 0.391549 | + | 1.20506i | ||||
\(219\) | −29.7984 | −2.01359 | ||||||||
\(220\) | 3.51722 | − | 2.93893i | 0.237131 | − | 0.198142i | ||||
\(221\) | 5.09017 | 0.342402 | ||||||||
\(222\) | 6.38197 | + | 19.6417i | 0.428330 | + | 1.31826i | ||||
\(223\) | 0.545085 | + | 0.396027i | 0.0365016 | + | 0.0265200i | 0.605886 | − | 0.795551i | \(-0.292819\pi\) |
−0.569385 | + | 0.822071i | \(0.692819\pi\) | |||||||
\(224\) | −10.5451 | + | 7.66145i | −0.704573 | + | 0.511902i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0278640 | − | 0.0857567i | 0.00185349 | − | 0.00570445i | ||||
\(227\) | 4.23607 | − | 3.07768i | 0.281158 | − | 0.204273i | −0.438265 | − | 0.898846i | \(-0.644407\pi\) |
0.719422 | + | 0.694573i | \(0.244407\pi\) | |||||||
\(228\) | −1.11803 | − | 0.812299i | −0.0740436 | − | 0.0537958i | ||||
\(229\) | −4.54508 | − | 13.9883i | −0.300348 | − | 0.924375i | −0.981372 | − | 0.192115i | \(-0.938465\pi\) |
0.681025 | − | 0.732260i | \(-0.261535\pi\) | |||||||
\(230\) | −22.5623 | −1.48771 | ||||||||
\(231\) | 10.6525 | + | 26.5236i | 0.700881 | + | 1.74512i | ||||
\(232\) | 10.3262 | 0.677951 | ||||||||
\(233\) | 5.30902 | + | 16.3395i | 0.347805 | + | 1.07043i | 0.960065 | + | 0.279778i | \(0.0902608\pi\) |
−0.612260 | + | 0.790657i | \(0.709739\pi\) | |||||||
\(234\) | −13.3262 | − | 9.68208i | −0.871163 | − | 0.632937i | ||||
\(235\) | −4.04508 | + | 2.93893i | −0.263872 | + | 0.191714i | ||||
\(236\) | 0.826238 | − | 2.54290i | 0.0537835 | − | 0.165529i | ||||
\(237\) | 0.690983 | − | 2.12663i | 0.0448842 | − | 0.138139i | ||||
\(238\) | −5.04508 | + | 3.66547i | −0.327024 | + | 0.237597i | ||||
\(239\) | −3.85410 | − | 2.80017i | −0.249301 | − | 0.181128i | 0.456116 | − | 0.889920i | \(-0.349240\pi\) |
−0.705417 | + | 0.708793i | \(0.749240\pi\) | |||||||
\(240\) | 7.50000 | + | 23.0826i | 0.484123 | + | 1.48998i | ||||
\(241\) | −6.29180 | −0.405290 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(242\) | 15.6803 | + | 8.42075i | 1.00797 | + | 0.541306i | ||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | 1.44427 | + | 4.44501i | 0.0924600 | + | 0.284563i | ||||
\(245\) | 14.2082 | + | 10.3229i | 0.907729 | + | 0.659504i | ||||
\(246\) | 15.3262 | − | 11.1352i | 0.977165 | − | 0.709952i | ||||
\(247\) | −1.57295 | + | 4.84104i | −0.100084 | + | 0.308028i | ||||
\(248\) | −6.38197 | + | 19.6417i | −0.405255 | + | 1.24725i | ||||
\(249\) | 1.97214 | − | 1.43284i | 0.124979 | − | 0.0908026i | ||||
\(250\) | 14.6353 | + | 10.6331i | 0.925615 | + | 0.672499i | ||||
\(251\) | −2.78115 | − | 8.55951i | −0.175545 | − | 0.540271i | 0.824113 | − | 0.566425i | \(-0.191674\pi\) |
−0.999658 | + | 0.0261539i | \(0.991674\pi\) | |||||||
\(252\) | 4.76393 | 0.300100 | ||||||||
\(253\) | −7.70820 | − | 19.1926i | −0.484611 | − | 1.20663i | ||||
\(254\) | −0.381966 | −0.0239667 | ||||||||
\(255\) | 1.54508 | + | 4.75528i | 0.0967570 | + | 0.297787i | ||||
\(256\) | −10.9721 | − | 7.97172i | −0.685758 | − | 0.498233i | ||||
\(257\) | −8.85410 | + | 6.43288i | −0.552304 | + | 0.401272i | −0.828634 | − | 0.559791i | \(-0.810882\pi\) |
0.276330 | + | 0.961063i | \(0.410882\pi\) | |||||||
\(258\) | 10.0623 | − | 30.9686i | 0.626452 | − | 1.92802i | ||||
\(259\) | −6.79837 | + | 20.9232i | −0.422430 | + | 1.30011i | ||||
\(260\) | −5.69098 | + | 4.13474i | −0.352940 | + | 0.256426i | ||||
\(261\) | −7.47214 | − | 5.42882i | −0.462514 | − | 0.336036i | ||||
\(262\) | −1.85410 | − | 5.70634i | −0.114547 | − | 0.352539i | ||||
\(263\) | 15.6180 | 0.963049 | 0.481525 | − | 0.876433i | \(-0.340083\pi\) | ||||
0.481525 | + | 0.876433i | \(0.340083\pi\) | |||||||
\(264\) | −12.7254 | + | 10.6331i | −0.783196 | + | 0.654424i | ||||
\(265\) | −22.5623 | −1.38599 | ||||||||
\(266\) | −1.92705 | − | 5.93085i | −0.118155 | − | 0.363644i | ||||
\(267\) | −7.39919 | − | 5.37582i | −0.452823 | − | 0.328995i | ||||
\(268\) | 3.57295 | − | 2.59590i | 0.218253 | − | 0.158570i | ||||
\(269\) | −5.97214 | + | 18.3803i | −0.364128 | + | 1.12067i | 0.586398 | + | 0.810023i | \(0.300545\pi\) |
−0.950526 | + | 0.310646i | \(0.899455\pi\) | |||||||
\(270\) | −2.50000 | + | 7.69421i | −0.152145 | + | 0.468255i | ||||
\(271\) | −24.8435 | + | 18.0498i | −1.50913 | + | 1.09645i | −0.542573 | + | 0.840009i | \(0.682550\pi\) |
−0.966560 | + | 0.256440i | \(0.917450\pi\) | |||||||
\(272\) | −3.92705 | − | 2.85317i | −0.238112 | − | 0.172999i | ||||
\(273\) | −13.5557 | − | 41.7202i | −0.820430 | − | 2.52502i | ||||
\(274\) | 10.7984 | 0.652354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.61803 | −0.518745 | ||||||||
\(277\) | 2.26393 | + | 6.96767i | 0.136026 | + | 0.418646i | 0.995748 | − | 0.0921161i | \(-0.0293631\pi\) |
−0.859722 | + | 0.510763i | \(0.829363\pi\) | |||||||
\(278\) | 24.7984 | + | 18.0171i | 1.48731 | + | 1.08059i | ||||
\(279\) | 14.9443 | − | 10.8576i | 0.894690 | − | 0.650030i | ||||
\(280\) | −5.95492 | + | 18.3273i | −0.355874 | + | 1.09527i | ||||
\(281\) | 4.48936 | − | 13.8168i | 0.267813 | − | 0.824242i | −0.723220 | − | 0.690618i | \(-0.757339\pi\) |
0.991032 | − | 0.133624i | \(-0.0426615\pi\) | |||||||
\(282\) | −6.54508 | + | 4.75528i | −0.389754 | + | 0.283173i | ||||
\(283\) | 15.2533 | + | 11.0822i | 0.906714 | + | 0.658766i | 0.940182 | − | 0.340674i | \(-0.110655\pi\) |
−0.0334677 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(284\) | 0.218847 | + | 0.673542i | 0.0129862 | + | 0.0399674i | ||||
\(285\) | −5.00000 | −0.296174 | ||||||||
\(286\) | −23.1353 | − | 14.5231i | −1.36802 | − | 0.858770i | ||||
\(287\) | 20.1803 | 1.19121 | ||||||||
\(288\) | 2.09017 | + | 6.43288i | 0.123164 | + | 0.379061i | ||||
\(289\) | −0.809017 | − | 0.587785i | −0.0475892 | − | 0.0345756i | ||||
\(290\) | −13.5172 | + | 9.82084i | −0.793759 | + | 0.576699i | ||||
\(291\) | 7.43769 | − | 22.8909i | 0.436005 | − | 1.34189i | ||||
\(292\) | −2.54508 | + | 7.83297i | −0.148940 | + | 0.458390i | ||||
\(293\) | −25.6803 | + | 18.6579i | −1.50026 | + | 1.09000i | −0.529984 | + | 0.848007i | \(0.677802\pi\) |
−0.970277 | + | 0.241996i | \(0.922198\pi\) | |||||||
\(294\) | 22.9894 | + | 16.7027i | 1.34077 | + | 0.974124i | ||||
\(295\) | −2.98936 | − | 9.20029i | −0.174047 | − | 0.535662i | ||||
\(296\) | −12.7639 | −0.741888 | ||||||||
\(297\) | −7.39919 | + | 0.502029i | −0.429344 | + | 0.0291307i | ||||
\(298\) | −1.85410 | −0.107405 | ||||||||
\(299\) | 9.80902 | + | 30.1891i | 0.567270 | + | 1.74588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.0623 | − | 20.3885i | 1.61748 | − | 1.17517i | ||||
\(302\) | 2.20820 | − | 6.79615i | 0.127068 | − | 0.391075i | ||||
\(303\) | −7.86475 | + | 24.2052i | −0.451818 | + | 1.39055i | ||||
\(304\) | 3.92705 | − | 2.85317i | 0.225232 | − | 0.163640i | ||||
\(305\) | 13.6803 | + | 9.93935i | 0.783334 | + | 0.569125i | ||||
\(306\) | 1.00000 | + | 3.07768i | 0.0571662 | + | 0.175939i | ||||
\(307\) | 4.32624 | 0.246911 | 0.123456 | − | 0.992350i | \(-0.460602\pi\) | ||||
0.123456 | + | 0.992350i | \(0.460602\pi\) | |||||||
\(308\) | 7.88197 | − | 0.534785i | 0.449117 | − | 0.0304722i | ||||
\(309\) | −33.5410 | −1.90808 | ||||||||
\(310\) | −10.3262 | − | 31.7809i | −0.586491 | − | 1.80503i | ||||
\(311\) | 6.85410 | + | 4.97980i | 0.388660 | + | 0.282378i | 0.764906 | − | 0.644141i | \(-0.222785\pi\) |
−0.376246 | + | 0.926520i | \(0.622785\pi\) | |||||||
\(312\) | 20.5902 | − | 14.9596i | 1.16569 | − | 0.846923i | ||||
\(313\) | 8.01722 | − | 24.6745i | 0.453160 | − | 1.39468i | −0.420122 | − | 0.907468i | \(-0.638013\pi\) |
0.873282 | − | 0.487216i | \(-0.161987\pi\) | |||||||
\(314\) | −0.309017 | + | 0.951057i | −0.0174388 | + | 0.0536712i | ||||
\(315\) | 13.9443 | − | 10.1311i | 0.785671 | − | 0.570823i | ||||
\(316\) | −0.500000 | − | 0.363271i | −0.0281272 | − | 0.0204356i | ||||
\(317\) | −5.05573 | − | 15.5599i | −0.283958 | − | 0.873933i | −0.986709 | − | 0.162497i | \(-0.948045\pi\) |
0.702751 | − | 0.711436i | \(-0.251955\pi\) | |||||||
\(318\) | −36.5066 | −2.04719 | ||||||||
\(319\) | −12.9721 | − | 8.14324i | −0.726300 | − | 0.455934i | ||||
\(320\) | −9.47214 | −0.529508 | ||||||||
\(321\) | −2.07295 | − | 6.37988i | −0.115701 | − | 0.356090i | ||||
\(322\) | −31.4615 | − | 22.8581i | −1.75328 | − | 1.27383i | ||||
\(323\) | 0.809017 | − | 0.587785i | 0.0450149 | − | 0.0327052i | ||||
\(324\) | −2.10081 | + | 6.46564i | −0.116712 | + | 0.359202i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.16312 | − | 3.02468i | 0.230574 | − | 0.167522i | ||||
\(327\) | 20.9164 | + | 15.1967i | 1.15668 | + | 0.840377i | ||||
\(328\) | 3.61803 | + | 11.1352i | 0.199773 | + | 0.614837i | ||||
\(329\) | −8.61803 | −0.475128 | ||||||||
\(330\) | 6.54508 | − | 26.0216i | 0.360295 | − | 1.43244i | ||||
\(331\) | −3.00000 | −0.164895 | −0.0824475 | − | 0.996595i | \(-0.526274\pi\) | ||||
−0.0824475 | + | 0.996595i | \(0.526274\pi\) | |||||||
\(332\) | −0.208204 | − | 0.640786i | −0.0114267 | − | 0.0351677i | ||||
\(333\) | 9.23607 | + | 6.71040i | 0.506133 | + | 0.367727i | ||||
\(334\) | −25.7254 | + | 18.6906i | −1.40763 | + | 1.02270i | ||||
\(335\) | 4.93769 | − | 15.1967i | 0.269775 | − | 0.830282i | ||||
\(336\) | −12.9271 | + | 39.7854i | −0.705228 | + | 2.17047i | ||||
\(337\) | −13.0623 | + | 9.49032i | −0.711549 | + | 0.516971i | −0.883673 | − | 0.468105i | \(-0.844937\pi\) |
0.172124 | + | 0.985075i | \(0.444937\pi\) | |||||||
\(338\) | 16.8992 | + | 12.2780i | 0.919195 | + | 0.667834i | ||||
\(339\) | −0.0385072 | − | 0.118513i | −0.00209142 | − | 0.00643674i | ||||
\(340\) | 1.38197 | 0.0749476 | ||||||||
\(341\) | 23.5066 | − | 19.6417i | 1.27295 | − | 1.06366i | ||||
\(342\) | −3.23607 | −0.174987 | ||||||||
\(343\) | 1.01722 | + | 3.13068i | 0.0549248 | + | 0.169041i | ||||
\(344\) | 16.2812 | + | 11.8290i | 0.877821 | + | 0.637774i | ||||
\(345\) | −25.2254 | + | 18.3273i | −1.35809 | + | 0.986711i | ||||
\(346\) | −6.35410 | + | 19.5559i | −0.341599 | + | 1.05133i | ||||
\(347\) | −3.21885 | + | 9.90659i | −0.172797 | + | 0.531814i | −0.999526 | − | 0.0307863i | \(-0.990199\pi\) |
0.826729 | + | 0.562600i | \(0.190199\pi\) | |||||||
\(348\) | −5.16312 | + | 3.75123i | −0.276772 | + | 0.201087i | ||||
\(349\) | 7.61803 | + | 5.53483i | 0.407784 | + | 0.296272i | 0.772704 | − | 0.634766i | \(-0.218904\pi\) |
−0.364920 | + | 0.931039i | \(0.618904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3820 | 0.607524 | ||||||||
\(352\) | 4.18034 | + | 10.4086i | 0.222813 | + | 0.554781i | ||||
\(353\) | 4.41641 | 0.235062 | 0.117531 | − | 0.993069i | \(-0.462502\pi\) | ||||
0.117531 | + | 0.993069i | \(0.462502\pi\) | |||||||
\(354\) | −4.83688 | − | 14.8864i | −0.257077 | − | 0.791203i | ||||
\(355\) | 2.07295 | + | 1.50609i | 0.110021 | + | 0.0799347i | ||||
\(356\) | −2.04508 | + | 1.48584i | −0.108389 | + | 0.0787494i | ||||
\(357\) | −2.66312 | + | 8.19624i | −0.140947 | + | 0.433791i | ||||
\(358\) | 7.69098 | − | 23.6704i | 0.406481 | − | 1.25102i | ||||
\(359\) | 23.3435 | − | 16.9600i | 1.23202 | − | 0.895115i | 0.234981 | − | 0.972000i | \(-0.424497\pi\) |
0.997040 | + | 0.0768847i | \(0.0244973\pi\) | |||||||
\(360\) | 8.09017 | + | 5.87785i | 0.426389 | + | 0.309790i | ||||
\(361\) | −5.56231 | − | 17.1190i | −0.292753 | − | 0.901001i | ||||
\(362\) | 28.0344 | 1.47346 | ||||||||
\(363\) | 24.3713 | − | 3.32244i | 1.27916 | − | 0.174383i | ||||
\(364\) | −12.1246 | −0.635502 | ||||||||
\(365\) | 9.20820 | + | 28.3399i | 0.481979 | + | 1.48338i | ||||
\(366\) | 22.1353 | + | 16.0822i | 1.15703 | + | 0.840630i | ||||
\(367\) | 17.5623 | − | 12.7598i | 0.916745 | − | 0.666054i | −0.0259668 | − | 0.999663i | \(-0.508266\pi\) |
0.942712 | + | 0.333609i | \(0.108266\pi\) | |||||||
\(368\) | 9.35410 | − | 28.7890i | 0.487616 | − | 1.50073i | ||||
\(369\) | 3.23607 | − | 9.95959i | 0.168463 | − | 0.518476i | ||||
\(370\) | 16.7082 | − | 12.1392i | 0.868618 | − | 0.631088i | ||||
\(371\) | −31.4615 | − | 22.8581i | −1.63340 | − | 1.18673i | ||||
\(372\) | −3.94427 | − | 12.1392i | −0.204501 | − | 0.629389i | ||||
\(373\) | 6.43769 | 0.333331 | 0.166666 | − | 0.986013i | \(-0.446700\pi\) | ||||
0.166666 | + | 0.986013i | \(0.446700\pi\) | |||||||
\(374\) | 2.00000 | + | 4.97980i | 0.103418 | + | 0.257499i | ||||
\(375\) | 25.0000 | 1.29099 | ||||||||
\(376\) | −1.54508 | − | 4.75528i | −0.0796817 | − | 0.245235i | ||||
\(377\) | 19.0172 | + | 13.8168i | 0.979437 | + | 0.711602i | ||||
\(378\) | −11.2812 | + | 8.19624i | −0.580240 | + | 0.421569i | ||||
\(379\) | 9.18034 | − | 28.2542i | 0.471562 | − | 1.45132i | −0.378976 | − | 0.925407i | \(-0.623724\pi\) |
0.850538 | − | 0.525913i | \(-0.176276\pi\) | |||||||
\(380\) | −0.427051 | + | 1.31433i | −0.0219073 | + | 0.0674236i | ||||
\(381\) | −0.427051 | + | 0.310271i | −0.0218785 | + | 0.0158956i | ||||
\(382\) | 6.92705 | + | 5.03280i | 0.354419 | + | 0.257500i | ||||
\(383\) | 0.937694 | + | 2.88593i | 0.0479139 | + | 0.147464i | 0.972151 | − | 0.234355i | \(-0.0752978\pi\) |
−0.924237 | + | 0.381819i | \(0.875298\pi\) | |||||||
\(384\) | −30.4508 | −1.55394 | ||||||||
\(385\) | 21.9336 | − | 18.3273i | 1.11784 | − | 0.934048i | ||||
\(386\) | 12.9443 | 0.658846 | ||||||||
\(387\) | −5.56231 | − | 17.1190i | −0.282748 | − | 0.870209i | ||||
\(388\) | −5.38197 | − | 3.91023i | −0.273228 | − | 0.198512i | ||||
\(389\) | 9.66312 | − | 7.02067i | 0.489940 | − | 0.355962i | −0.315221 | − | 0.949018i | \(-0.602079\pi\) |
0.805161 | + | 0.593056i | \(0.202079\pi\) | |||||||
\(390\) | −12.7254 | + | 39.1648i | −0.644377 | + | 1.98319i | ||||
\(391\) | 1.92705 | − | 5.93085i | 0.0974552 | − | 0.299936i | ||||
\(392\) | −14.2082 | + | 10.3229i | −0.717623 | + | 0.521383i | ||||
\(393\) | −6.70820 | − | 4.87380i | −0.338384 | − | 0.245850i | ||||
\(394\) | 11.3090 | + | 34.8056i | 0.569740 | + | 1.75348i | ||||
\(395\) | −2.23607 | −0.112509 | ||||||||
\(396\) | 1.00000 | − | 3.97574i | 0.0502519 | − | 0.199788i | ||||
\(397\) | −20.4164 | −1.02467 | −0.512335 | − | 0.858786i | \(-0.671219\pi\) | ||||
−0.512335 | + | 0.858786i | \(0.671219\pi\) | |||||||
\(398\) | 6.11803 | + | 18.8294i | 0.306669 | + | 0.943831i | ||||
\(399\) | −6.97214 | − | 5.06555i | −0.349043 | − | 0.253595i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.41641 | − | 22.8254i | 0.370358 | − | 1.13984i | −0.576200 | − | 0.817309i | \(-0.695465\pi\) |
0.946558 | − | 0.322535i | \(-0.104535\pi\) | |||||||
\(402\) | 7.98936 | − | 24.5887i | 0.398473 | − | 1.22637i | ||||
\(403\) | −38.0344 | + | 27.6336i | −1.89463 | + | 1.37653i | ||||
\(404\) | 5.69098 | + | 4.13474i | 0.283137 | + | 0.205711i | ||||
\(405\) | 7.60081 | + | 23.3929i | 0.377687 | + | 1.16240i | ||||
\(406\) | −28.7984 | −1.42924 | ||||||||
\(407\) | 16.0344 | + | 10.0656i | 0.794798 | + | 0.498933i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 0.173762 | + | 0.534785i | 0.00859198 | + | 0.0264434i | 0.955261 | − | 0.295765i | \(-0.0955747\pi\) |
−0.946669 | + | 0.322209i | \(0.895575\pi\) | |||||||
\(410\) | −15.3262 | − | 11.1352i | −0.756909 | − | 0.549927i | ||||
\(411\) | 12.0729 | − | 8.77151i | 0.595515 | − | 0.432667i | ||||
\(412\) | −2.86475 | + | 8.81678i | −0.141136 | + | 0.434372i | ||||
\(413\) | 5.15248 | − | 15.8577i | 0.253537 | − | 0.780306i | ||||
\(414\) | −16.3262 | + | 11.8617i | −0.802391 | + | 0.582971i | ||||
\(415\) | −1.97214 | − | 1.43284i | −0.0968083 | − | 0.0703354i | ||||
\(416\) | −5.31966 | − | 16.3722i | −0.260818 | − | 0.802715i | ||||
\(417\) | 42.3607 | 2.07441 | ||||||||
\(418\) | −5.35410 | + | 0.363271i | −0.261878 | + | 0.0177682i | ||||
\(419\) | −33.5410 | −1.63859 | −0.819293 | − | 0.573375i | \(-0.805634\pi\) | ||||
−0.819293 | + | 0.573375i | \(0.805634\pi\) | |||||||
\(420\) | −3.68034 | − | 11.3269i | −0.179582 | − | 0.552697i | ||||
\(421\) | −18.7082 | − | 13.5923i | −0.911782 | − | 0.662448i | 0.0296829 | − | 0.999559i | \(-0.490550\pi\) |
−0.941465 | + | 0.337111i | \(0.890550\pi\) | |||||||
\(422\) | 21.9443 | − | 15.9434i | 1.06823 | − | 0.776115i | ||||
\(423\) | −1.38197 | + | 4.25325i | −0.0671935 | + | 0.206800i | ||||
\(424\) | 6.97214 | − | 21.4580i | 0.338597 | − | 1.04209i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.35410 | + | 2.43690i | 0.162507 | + | 0.118068i | ||||
\(427\) | 9.00658 | + | 27.7194i | 0.435859 | + | 1.34144i | ||||
\(428\) | −1.85410 | −0.0896214 | ||||||||
\(429\) | −37.6631 | + | 2.55541i | −1.81839 | + | 0.123376i | ||||
\(430\) | −32.5623 | −1.57029 | ||||||||
\(431\) | −10.5279 | − | 32.4014i | −0.507109 | − | 1.56072i | −0.797195 | − | 0.603722i | \(-0.793684\pi\) |
0.290086 | − | 0.957001i | \(-0.406316\pi\) | |||||||
\(432\) | −8.78115 | − | 6.37988i | −0.422483 | − | 0.306952i | ||||
\(433\) | 5.23607 | − | 3.80423i | 0.251629 | − | 0.182819i | −0.454819 | − | 0.890584i | \(-0.650296\pi\) |
0.706449 | + | 0.707764i | \(0.250296\pi\) | |||||||
\(434\) | 17.7984 | − | 54.7778i | 0.854349 | − | 2.62942i | ||||
\(435\) | −7.13525 | + | 21.9601i | −0.342109 | + | 1.05290i | ||||
\(436\) | 5.78115 | − | 4.20025i | 0.276867 | − | 0.201156i | ||||
\(437\) | 5.04508 | + | 3.66547i | 0.241339 | + | 0.175343i | ||||
\(438\) | 14.8992 | + | 45.8550i | 0.711911 | + | 2.19104i | ||||
\(439\) | 35.1246 | 1.67641 | 0.838203 | − | 0.545358i | \(-0.183606\pi\) | ||||
0.838203 | + | 0.545358i | \(0.183606\pi\) | |||||||
\(440\) | 14.0451 | + | 8.81678i | 0.669573 | + | 0.420323i | ||||
\(441\) | 15.7082 | 0.748010 | ||||||||
\(442\) | −2.54508 | − | 7.83297i | −0.121057 | − | 0.372576i | ||||
\(443\) | −19.0172 | − | 13.8168i | −0.903535 | − | 0.656457i | 0.0358362 | − | 0.999358i | \(-0.488591\pi\) |
−0.939372 | + | 0.342901i | \(0.888591\pi\) | |||||||
\(444\) | 6.38197 | − | 4.63677i | 0.302875 | − | 0.220051i | ||||
\(445\) | −2.82624 | + | 8.69827i | −0.133977 | + | 0.412337i | ||||
\(446\) | 0.336881 | − | 1.03681i | 0.0159518 | − | 0.0490945i | ||||
\(447\) | −2.07295 | + | 1.50609i | −0.0980471 | + | 0.0712354i | ||||
\(448\) | −13.2082 | − | 9.59632i | −0.624029 | − | 0.453384i | ||||
\(449\) | 0.854102 | + | 2.62866i | 0.0403076 | + | 0.124054i | 0.969185 | − | 0.246332i | \(-0.0792254\pi\) |
−0.928878 | + | 0.370386i | \(0.879225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.23607 | − | 16.8415i | 0.199469 | − | 0.793035i | ||||
\(452\) | −0.0344419 | −0.00162001 | ||||||||
\(453\) | −3.05166 | − | 9.39205i | −0.143380 | − | 0.441277i | ||||
\(454\) | −6.85410 | − | 4.97980i | −0.321679 | − | 0.233713i | ||||
\(455\) | −35.4894 | + | 25.7845i | −1.66377 | + | 1.20880i | ||||
\(456\) | 1.54508 | − | 4.75528i | 0.0723552 | − | 0.222687i | ||||
\(457\) | 0.0450850 | − | 0.138757i | 0.00210899 | − | 0.00649079i | −0.949996 | − | 0.312261i | \(-0.898914\pi\) |
0.952105 | + | 0.305770i | \(0.0989138\pi\) | |||||||
\(458\) | −19.2533 | + | 13.9883i | −0.899647 | + | 0.653632i | ||||
\(459\) | −1.80902 | − | 1.31433i | −0.0844377 | − | 0.0613476i | ||||
\(460\) | 2.66312 | + | 8.19624i | 0.124169 | + | 0.382152i | ||||
\(461\) | 5.09017 | 0.237073 | 0.118536 | − | 0.992950i | \(-0.462180\pi\) | ||||
0.118536 | + | 0.992950i | \(0.462180\pi\) | |||||||
\(462\) | 35.4894 | − | 29.6543i | 1.65111 | − | 1.37964i | ||||
\(463\) | −24.7984 | −1.15248 | −0.576239 | − | 0.817281i | \(-0.695480\pi\) | ||||
−0.576239 | + | 0.817281i | \(0.695480\pi\) | |||||||
\(464\) | −6.92705 | − | 21.3193i | −0.321580 | − | 0.989722i | ||||
\(465\) | −37.3607 | − | 27.1441i | −1.73256 | − | 1.25878i | ||||
\(466\) | 22.4894 | − | 16.3395i | 1.04180 | − | 0.756912i | ||||
\(467\) | −11.1246 | + | 34.2380i | −0.514786 | + | 1.58435i | 0.268886 | + | 0.963172i | \(0.413345\pi\) |
−0.783672 | + | 0.621175i | \(0.786655\pi\) | |||||||
\(468\) | −1.94427 | + | 5.98385i | −0.0898740 | + | 0.276604i | ||||
\(469\) | 22.2812 | − | 16.1882i | 1.02885 | − | 0.747502i | ||||
\(470\) | 6.54508 | + | 4.75528i | 0.301902 | + | 0.219345i | ||||
\(471\) | 0.427051 | + | 1.31433i | 0.0196775 | + | 0.0605610i | ||||
\(472\) | 9.67376 | 0.445271 | ||||||||
\(473\) | −11.1246 | − | 27.6992i | −0.511510 | − | 1.27361i | ||||
\(474\) | −3.61803 | −0.166182 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.92705 | + | 1.40008i | 0.0883262 | + | 0.0641728i | ||||
\(477\) | −16.3262 | + | 11.8617i | −0.747527 | + | 0.543110i | ||||
\(478\) | −2.38197 | + | 7.33094i | −0.108949 | + | 0.335309i | ||||
\(479\) | 2.07295 | − | 6.37988i | 0.0947155 | − | 0.291504i | −0.892464 | − | 0.451119i | \(-0.851025\pi\) |
0.987179 | + | 0.159614i | \(0.0510251\pi\) | |||||||
\(480\) | 13.6803 | − | 9.93935i | 0.624419 | − | 0.453667i | ||||
\(481\) | −23.5066 | − | 17.0785i | −1.07181 | − | 0.778714i | ||||
\(482\) | 3.14590 | + | 9.68208i | 0.143292 | + | 0.441007i | ||||
\(483\) | −53.7426 | −2.44538 | ||||||||
\(484\) | 1.20820 | − | 6.69015i | 0.0549184 | − | 0.304098i | ||||
\(485\) | −24.0689 | −1.09291 | ||||||||
\(486\) | 8.94427 | + | 27.5276i | 0.405720 | + | 1.24868i | ||||
\(487\) | −6.07295 | − | 4.41226i | −0.275192 | − | 0.199938i | 0.441626 | − | 0.897199i | \(-0.354402\pi\) |
−0.716817 | + | 0.697261i | \(0.754402\pi\) | |||||||
\(488\) | −13.6803 | + | 9.93935i | −0.619280 | + | 0.449933i | ||||
\(489\) | 2.19756 | − | 6.76340i | 0.0993771 | − | 0.305851i | ||||
\(490\) | 8.78115 | − | 27.0256i | 0.396692 | − | 1.22089i | ||||
\(491\) | −8.23607 | + | 5.98385i | −0.371689 | + | 0.270048i | −0.757911 | − | 0.652358i | \(-0.773780\pi\) |
0.386222 | + | 0.922406i | \(0.373780\pi\) | |||||||
\(492\) | −5.85410 | − | 4.25325i | −0.263923 | − | 0.191752i | ||||
\(493\) | −1.42705 | − | 4.39201i | −0.0642711 | − | 0.197806i | ||||
\(494\) | 8.23607 | 0.370558 | ||||||||
\(495\) | −5.52786 | − | 13.7638i | −0.248459 | − | 0.618638i | ||||
\(496\) | 44.8328 | 2.01305 | ||||||||
\(497\) | 1.36475 | + | 4.20025i | 0.0612172 | + | 0.188407i | ||||
\(498\) | −3.19098 | − | 2.31838i | −0.142991 | − | 0.103889i | ||||
\(499\) | 22.7705 | − | 16.5437i | 1.01935 | − | 0.740600i | 0.0531989 | − | 0.998584i | \(-0.483058\pi\) |
0.966149 | + | 0.257984i | \(0.0830583\pi\) | |||||||
\(500\) | 2.13525 | − | 6.57164i | 0.0954915 | − | 0.293893i | ||||
\(501\) | −13.5795 | + | 41.7935i | −0.606689 | + | 1.86720i | ||||
\(502\) | −11.7812 | + | 8.55951i | −0.525819 | + | 0.382030i | ||||
\(503\) | −16.2082 | − | 11.7759i | −0.722688 | − | 0.525064i | 0.164554 | − | 0.986368i | \(-0.447382\pi\) |
−0.887242 | + | 0.461304i | \(0.847382\pi\) | |||||||
\(504\) | 5.32624 | + | 16.3925i | 0.237249 | + | 0.730179i | ||||
\(505\) | 25.4508 | 1.13255 | ||||||||
\(506\) | −25.6803 | + | 21.4580i | −1.14163 | + | 0.953926i | ||||
\(507\) | 28.8673 | 1.28204 | ||||||||
\(508\) | 0.0450850 | + | 0.138757i | 0.00200032 | + | 0.00615636i | ||||
\(509\) | −24.2705 | − | 17.6336i | −1.07577 | − | 0.781594i | −0.0988307 | − | 0.995104i | \(-0.531510\pi\) |
−0.976941 | + | 0.213511i | \(0.931510\pi\) | |||||||
\(510\) | 6.54508 | − | 4.75528i | 0.289821 | − | 0.210567i | ||||
\(511\) | −15.8713 | + | 48.8469i | −0.702106 | + | 2.16086i | ||||
\(512\) | 1.63525 | − | 5.03280i | 0.0722687 | − | 0.222420i | ||||
\(513\) | 1.80902 | − | 1.31433i | 0.0798701 | − | 0.0580290i | ||||
\(514\) | 14.3262 | + | 10.4086i | 0.631903 | + | 0.459105i | ||||
\(515\) | 10.3647 | + | 31.8994i | 0.456725 | + | 1.40566i | ||||
\(516\) | −12.4377 | −0.547539 | ||||||||
\(517\) | −1.80902 | + | 7.19218i | −0.0795605 | + | 0.316312i | ||||
\(518\) | 35.5967 | 1.56403 | ||||||||
\(519\) | 8.78115 | + | 27.0256i | 0.385450 | + | 1.18629i | ||||
\(520\) | −20.5902 | − | 14.9596i | −0.902939 | − | 0.656023i | ||||
\(521\) | −10.6353 | + | 7.72696i | −0.465939 | + | 0.338524i | −0.795857 | − | 0.605485i | \(-0.792979\pi\) |
0.329918 | + | 0.944010i | \(0.392979\pi\) | |||||||
\(522\) | −4.61803 | + | 14.2128i | −0.202126 | + | 0.622079i | ||||
\(523\) | 0.746711 | − | 2.29814i | 0.0326514 | − | 0.100491i | −0.933403 | − | 0.358831i | \(-0.883176\pi\) |
0.966054 | + | 0.258340i | \(0.0831755\pi\) | |||||||
\(524\) | −1.85410 | + | 1.34708i | −0.0809968 | + | 0.0588476i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.80902 | − | 24.0337i | −0.340489 | − | 1.04792i | ||||
\(527\) | 9.23607 | 0.402329 | ||||||||
\(528\) | 30.4894 | + | 19.1396i | 1.32688 | + | 0.832946i | ||||
\(529\) | 15.8885 | 0.690806 | ||||||||
\(530\) | 11.2812 | + | 34.7198i | 0.490022 | + | 1.50813i | ||||
\(531\) | −7.00000 | − | 5.08580i | −0.303774 | − | 0.220705i | ||||
\(532\) | −1.92705 | + | 1.40008i | −0.0835483 | + | 0.0607014i | ||||
\(533\) | −8.23607 | + | 25.3480i | −0.356744 | + | 1.09794i | ||||
\(534\) | −4.57295 | + | 14.0741i | −0.197891 | + | 0.609045i | ||||
\(535\) | −5.42705 | + | 3.94298i | −0.234632 | + | 0.170470i | ||||
\(536\) | 12.9271 | + | 9.39205i | 0.558364 | + | 0.405675i | ||||
\(537\) | −10.6287 | − | 32.7117i | −0.458661 | − | 1.41161i | ||||
\(538\) | 31.2705 | 1.34817 | ||||||||
\(539\) | 25.9894 | − | 1.76336i | 1.11944 | − | 0.0759531i | ||||
\(540\) | 3.09017 | 0.132980 | ||||||||
\(541\) | 11.1180 | + | 34.2178i | 0.478002 | + | 1.47114i | 0.841866 | + | 0.539686i | \(0.181457\pi\) |
−0.363865 | + | 0.931452i | \(0.618543\pi\) | |||||||
\(542\) | 40.1976 | + | 29.2052i | 1.72663 | + | 1.25447i | ||||
\(543\) | 31.3435 | − | 22.7724i | 1.34508 | − | 0.977255i | ||||
\(544\) | −1.04508 | + | 3.21644i | −0.0448076 | + | 0.137904i | ||||
\(545\) | 7.98936 | − | 24.5887i | 0.342226 | − | 1.05326i | ||||
\(546\) | −57.4230 | + | 41.7202i | −2.45748 | + | 1.78546i | ||||
\(547\) | −0.590170 | − | 0.428784i | −0.0252338 | − | 0.0183335i | 0.575097 | − | 0.818085i | \(-0.304964\pi\) |
−0.600331 | + | 0.799752i | \(0.704964\pi\) | |||||||
\(548\) | −1.27458 | − | 3.92274i | −0.0544472 | − | 0.167571i | ||||
\(549\) | 15.1246 | 0.645503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.61803 | 0.196735 | ||||||||
\(552\) | −9.63525 | − | 29.6543i | −0.410104 | − | 1.26217i | ||||
\(553\) | −3.11803 | − | 2.26538i | −0.132592 | − | 0.0963339i | ||||
\(554\) | 9.59017 | − | 6.96767i | 0.407447 | − | 0.296028i | ||||
\(555\) | 8.81966 | − | 27.1441i | 0.374374 | − | 1.15220i | ||||
\(556\) | 3.61803 | − | 11.1352i | 0.153439 | − | 0.472236i | ||||
\(557\) | −25.2533 | + | 18.3476i | −1.07002 | + | 0.777412i | −0.975915 | − | 0.218150i | \(-0.929998\pi\) |
−0.0941010 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(558\) | −24.1803 | − | 17.5680i | −1.02364 | − | 0.743715i | ||||
\(559\) | 14.1565 | + | 43.5694i | 0.598758 | + | 1.84279i | ||||
\(560\) | 41.8328 | 1.76776 | ||||||||
\(561\) | 6.28115 | + | 3.94298i | 0.265190 | + | 0.166473i | ||||
\(562\) | −23.5066 | −0.991565 | ||||||||
\(563\) | −1.30902 | − | 4.02874i | −0.0551685 | − | 0.169791i | 0.919676 | − | 0.392679i | \(-0.128452\pi\) |
−0.974844 | + | 0.222888i | \(0.928452\pi\) | |||||||
\(564\) | 2.50000 | + | 1.81636i | 0.105269 | + | 0.0764824i | ||||
\(565\) | −0.100813 | + | 0.0732450i | −0.00424124 | + | 0.00308144i | ||||
\(566\) | 9.42705 | − | 29.0135i | 0.396249 | − | 1.21953i | ||||
\(567\) | −13.1008 | + | 40.3202i | −0.550182 | + | 1.69329i | ||||
\(568\) | −2.07295 | + | 1.50609i | −0.0869790 | + | 0.0631939i | ||||
\(569\) | 14.1353 | + | 10.2699i | 0.592581 | + | 0.430535i | 0.843238 | − | 0.537541i | \(-0.180647\pi\) |
−0.250657 | + | 0.968076i | \(0.580647\pi\) | |||||||
\(570\) | 2.50000 | + | 7.69421i | 0.104713 | + | 0.322275i | ||||
\(571\) | 7.56231 | 0.316473 | 0.158236 | − | 0.987401i | \(-0.449419\pi\) | ||||
0.158236 | + | 0.987401i | \(0.449419\pi\) | |||||||
\(572\) | −2.54508 | + | 10.1186i | −0.106415 | + | 0.423080i | ||||
\(573\) | 11.8328 | 0.494323 | ||||||||
\(574\) | −10.0902 | − | 31.0543i | −0.421156 | − | 1.29618i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.85410 | + | 4.97980i | −0.285588 | + | 0.207492i | ||||
\(577\) | −11.1976 | + | 34.4625i | −0.466161 | + | 1.43469i | 0.391357 | + | 0.920239i | \(0.372006\pi\) |
−0.857517 | + | 0.514456i | \(0.827994\pi\) | |||||||
\(578\) | −0.500000 | + | 1.53884i | −0.0207973 | + | 0.0640074i | ||||
\(579\) | 14.4721 | − | 10.5146i | 0.601441 | − | 0.436973i | ||||
\(580\) | 5.16312 | + | 3.75123i | 0.214387 | + | 0.155761i | ||||
\(581\) | −1.29837 | − | 3.99598i | −0.0538656 | − | 0.165781i | ||||
\(582\) | −38.9443 | −1.61429 | ||||||||
\(583\) | −25.6803 | + | 21.4580i | −1.06357 | + | 0.888701i | ||||
\(584\) | −29.7984 | −1.23307 | ||||||||
\(585\) | 7.03444 | + | 21.6498i | 0.290838 | + | 0.895108i | ||||
\(586\) | 41.5517 | + | 30.1891i | 1.71648 | + | 1.24710i | ||||
\(587\) | −11.7812 | + | 8.55951i | −0.486260 | + | 0.353289i | −0.803744 | − | 0.594975i | \(-0.797162\pi\) |
0.317484 | + | 0.948264i | \(0.397162\pi\) | |||||||
\(588\) | 3.35410 | − | 10.3229i | 0.138321 | − | 0.425708i | ||||
\(589\) | −2.85410 | + | 8.78402i | −0.117601 | + | 0.361939i | ||||
\(590\) | −12.6631 | + | 9.20029i | −0.521332 | + | 0.378770i | ||||
\(591\) | 40.9164 | + | 29.7275i | 1.68308 | + | 1.22283i | ||||
\(592\) | 8.56231 | + | 26.3521i | 0.351909 | + | 1.08306i | ||||
\(593\) | 35.3050 | 1.44980 | 0.724900 | − | 0.688854i | \(-0.241886\pi\) | ||||
0.724900 | + | 0.688854i | \(0.241886\pi\) | |||||||
\(594\) | 4.47214 | + | 11.1352i | 0.183494 | + | 0.456881i | ||||
\(595\) | 8.61803 | 0.353305 | ||||||||
\(596\) | 0.218847 | + | 0.673542i | 0.00896432 | + | 0.0275894i | ||||
\(597\) | 22.1353 | + | 16.0822i | 0.905936 | + | 0.658201i | ||||
\(598\) | 41.5517 | − | 30.1891i | 1.69917 | − | 1.23452i | ||||
\(599\) | 6.65248 | − | 20.4742i | 0.271813 | − | 0.836554i | −0.718232 | − | 0.695803i | \(-0.755048\pi\) |
0.990045 | − | 0.140750i | \(-0.0449515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8262 | − | 13.6781i | 0.767938 | − | 0.557940i | −0.133397 | − | 0.991063i | \(-0.542588\pi\) |
0.901335 | + | 0.433123i | \(0.142588\pi\) | |||||||
\(602\) | −45.4058 | − | 32.9892i | −1.85060 | − | 1.34454i | ||||
\(603\) | −4.41641 | − | 13.5923i | −0.179850 | − | 0.553521i | ||||
\(604\) | −2.72949 | −0.111061 | ||||||||
\(605\) | −10.6910 | − | 22.1518i | −0.434650 | − | 0.900599i | ||||
\(606\) | 41.1803 | 1.67284 | ||||||||
\(607\) | −1.80244 | − | 5.54734i | −0.0731587 | − | 0.225159i | 0.907790 | − | 0.419424i | \(-0.137768\pi\) |
−0.980949 | + | 0.194265i | \(0.937768\pi\) | |||||||
\(608\) | −2.73607 | − | 1.98787i | −0.110962 | − | 0.0806188i | ||||
\(609\) | −32.1976 | + | 23.3929i | −1.30471 | + | 0.947928i | ||||
\(610\) | 8.45492 | − | 26.0216i | 0.342330 | − | 1.05358i | ||||
\(611\) | 3.51722 | − | 10.8249i | 0.142292 | − | 0.437928i | ||||
\(612\) | 1.00000 | − | 0.726543i | 0.0404226 | − | 0.0293687i | ||||
\(613\) | 3.32624 | + | 2.41665i | 0.134345 | + | 0.0976077i | 0.652928 | − | 0.757420i | \(-0.273540\pi\) |
−0.518583 | + | 0.855027i | \(0.673540\pi\) | |||||||
\(614\) | −2.16312 | − | 6.65740i | −0.0872964 | − | 0.268671i | ||||
\(615\) | −26.1803 | −1.05569 | ||||||||
\(616\) | 10.6525 | + | 26.5236i | 0.429200 | + | 1.06867i | ||||
\(617\) | 27.0132 | 1.08751 | 0.543754 | − | 0.839244i | \(-0.317002\pi\) | ||||
0.543754 | + | 0.839244i | \(0.317002\pi\) | |||||||
\(618\) | 16.7705 | + | 51.6143i | 0.674609 | + | 2.07623i | ||||
\(619\) | −21.5623 | − | 15.6659i | −0.866662 | − | 0.629667i | 0.0630270 | − | 0.998012i | \(-0.479925\pi\) |
−0.929689 | + | 0.368345i | \(0.879925\pi\) | |||||||
\(620\) | −10.3262 | + | 7.50245i | −0.414712 | + | 0.301306i | ||||
\(621\) | 4.30902 | − | 13.2618i | 0.172915 | − | 0.532177i | ||||
\(622\) | 4.23607 | − | 13.0373i | 0.169851 | − | 0.522747i | ||||
\(623\) | −12.7533 | + | 9.26581i | −0.510950 | + | 0.371227i | ||||
\(624\) | −44.6976 | − | 32.4747i | −1.78933 | − | 1.30003i | ||||
\(625\) | −7.72542 | − | 23.7764i | −0.309017 | − | 0.951057i | ||||
\(626\) | −41.9787 | −1.67781 | ||||||||
\(627\) | −5.69098 | + | 4.75528i | −0.227276 | + | 0.189908i | ||||
\(628\) | 0.381966 | 0.0152421 | ||||||||
\(629\) | 1.76393 | + | 5.42882i | 0.0703326 | + | 0.216461i | ||||
\(630\) | −22.5623 | − | 16.3925i | −0.898904 | − | 0.653092i | ||||
\(631\) | −14.3262 | + | 10.4086i | −0.570319 | + | 0.414361i | −0.835221 | − | 0.549915i | \(-0.814660\pi\) |
0.264902 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(632\) | 0.690983 | − | 2.12663i | 0.0274858 | − | 0.0845927i | ||||
\(633\) | 11.5836 | − | 35.6506i | 0.460406 | − | 1.41699i | ||||
\(634\) | −21.4164 | + | 15.5599i | −0.850554 | + | 0.617964i | ||||
\(635\) | 0.427051 | + | 0.310271i | 0.0169470 | + | 0.0123127i | ||||
\(636\) | 4.30902 | + | 13.2618i | 0.170864 | + | 0.525864i | ||||
\(637\) | −39.9787 | −1.58401 | ||||||||
\(638\) | −6.04508 | + | 24.0337i | −0.239327 | + | 0.951503i | ||||
\(639\) | 2.29180 | 0.0906621 | ||||||||
\(640\) | 9.40983 | + | 28.9605i | 0.371956 | + | 1.14476i | ||||
\(641\) | −28.2254 | − | 20.5070i | −1.11484 | − | 0.809977i | −0.131419 | − | 0.991327i | \(-0.541953\pi\) |
−0.983419 | + | 0.181350i | \(0.941953\pi\) | |||||||
\(642\) | −8.78115 | + | 6.37988i | −0.346564 | + | 0.251794i | ||||
\(643\) | 14.1287 | − | 43.4836i | 0.557181 | − | 1.71483i | −0.132933 | − | 0.991125i | \(-0.542440\pi\) |
0.690114 | − | 0.723701i | \(-0.257560\pi\) | |||||||
\(644\) | −4.59017 | + | 14.1271i | −0.180878 | + | 0.556685i | ||||
\(645\) | −36.4058 | + | 26.4503i | −1.43348 | + | 1.04148i | ||||
\(646\) | −1.30902 | − | 0.951057i | −0.0515026 | − | 0.0374188i | ||||
\(647\) | −9.23607 | − | 28.4257i | −0.363107 | − | 1.11753i | −0.951158 | − | 0.308705i | \(-0.900104\pi\) |
0.588050 | − | 0.808824i | \(-0.299896\pi\) | |||||||
\(648\) | −24.5967 | −0.966252 | ||||||||
\(649\) | −12.1525 | − | 7.62870i | −0.477026 | − | 0.299453i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.5967 | − | 75.7010i | −0.964023 | − | 2.96696i | ||||
\(652\) | −1.59017 | − | 1.15533i | −0.0622759 | − | 0.0452461i | ||||
\(653\) | 28.9615 | − | 21.0418i | 1.13335 | − | 0.823428i | 0.147172 | − | 0.989111i | \(-0.452983\pi\) |
0.986179 | + | 0.165683i | \(0.0529830\pi\) | |||||||
\(654\) | 12.9271 | − | 39.7854i | 0.505488 | − | 1.55573i | ||||
\(655\) | −2.56231 | + | 7.88597i | −0.100118 | + | 0.308130i | ||||
\(656\) | 20.5623 | − | 14.9394i | 0.802823 | − | 0.583285i | ||||
\(657\) | 21.5623 | + | 15.6659i | 0.841226 | + | 0.611186i | ||||
\(658\) | 4.30902 | + | 13.2618i | 0.167983 | + | 0.516998i | ||||
\(659\) | 26.1246 | 1.01767 | 0.508835 | − | 0.860864i | \(-0.330076\pi\) | ||||
0.508835 | + | 0.860864i | \(0.330076\pi\) | |||||||
\(660\) | −10.2254 | + | 0.693786i | −0.398024 | + | 0.0270056i | ||||
\(661\) | −9.83282 | −0.382452 | −0.191226 | − | 0.981546i | \(-0.561246\pi\) | ||||
−0.191226 | + | 0.981546i | \(0.561246\pi\) | |||||||
\(662\) | 1.50000 | + | 4.61653i | 0.0582992 | + | 0.179426i | ||||
\(663\) | −9.20820 | − | 6.69015i | −0.357617 | − | 0.259824i | ||||
\(664\) | 1.97214 | − | 1.43284i | 0.0765337 | − | 0.0556050i | ||||
\(665\) | −2.66312 | + | 8.19624i | −0.103271 | + | 0.317836i | ||||
\(666\) | 5.70820 | − | 17.5680i | 0.221188 | − | 0.680748i | ||||
\(667\) | 23.2984 | − | 16.9273i | 0.902117 | − | 0.655426i | ||||
\(668\) | 9.82624 | + | 7.13918i | 0.380189 | + | 0.276223i | ||||
\(669\) | −0.465558 | − | 1.43284i | −0.0179995 | − | 0.0553968i | ||||
\(670\) | −25.8541 | −0.998831 | ||||||||
\(671\) | 25.0238 | − | 1.69784i | 0.966033 | − | 0.0655445i | ||||
\(672\) | 29.1459 | 1.12433 | ||||||||
\(673\) | 2.64590 | + | 8.14324i | 0.101992 | + | 0.313899i | 0.989013 | − | 0.147831i | \(-0.0472291\pi\) |
−0.887021 | + | 0.461729i | \(0.847229\pi\) | |||||||
\(674\) | 21.1353 | + | 15.3557i | 0.814100 | + | 0.591478i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.46556 | − | 7.58821i | 0.0948292 | − | 0.291854i | ||||
\(677\) | −13.9377 | + | 42.8958i | −0.535669 | + | 1.64862i | 0.206530 | + | 0.978440i | \(0.433783\pi\) |
−0.742199 | + | 0.670180i | \(0.766217\pi\) | |||||||
\(678\) | −0.163119 | + | 0.118513i | −0.00626455 | + | 0.00455146i | ||||
\(679\) | −33.5623 | − | 24.3844i | −1.28800 | − | 0.935789i | ||||
\(680\) | 1.54508 | + | 4.75528i | 0.0592513 | + | 0.182357i | ||||
\(681\) | −11.7082 | −0.448659 | ||||||||
\(682\) | −41.9787 | − | 26.3521i | −1.60745 | − | 1.00907i | ||||
\(683\) | 25.8541 | 0.989280 | 0.494640 | − | 0.869098i | \(-0.335300\pi\) | ||||
0.494640 | + | 0.869098i | \(0.335300\pi\) | |||||||
\(684\) | 0.381966 | + | 1.17557i | 0.0146048 | + | 0.0449491i | ||||
\(685\) | −12.0729 | − | 8.77151i | −0.461284 | − | 0.335142i | ||||
\(686\) | 4.30902 | − | 3.13068i | 0.164519 | − | 0.119530i | ||||
\(687\) | −10.1631 | + | 31.2789i | −0.387747 | + | 1.19336i | ||||
\(688\) | 13.5000 | − | 41.5487i | 0.514683 | − | 1.58403i | ||||
\(689\) | 41.5517 | − | 30.1891i | 1.58299 | − | 1.15011i | ||||
\(690\) | 40.8156 | + | 29.6543i | 1.55382 | + | 1.12892i | ||||
\(691\) | 14.5902 | + | 44.9039i | 0.555036 | + | 1.70823i | 0.695848 | + | 0.718189i | \(0.255029\pi\) |
−0.140811 | + | 0.990036i | \(0.544971\pi\) | |||||||
\(692\) | 7.85410 | 0.298568 | ||||||||
\(693\) | 6.23607 | − | 24.7930i | 0.236889 | − | 0.941807i | ||||
\(694\) | 16.8541 | 0.639773 | ||||||||
\(695\) | −13.0902 | − | 40.2874i | −0.496538 | − | 1.52819i | ||||
\(696\) | −18.6803 | − | 13.5721i | −0.708076 | − | 0.514448i | ||||
\(697\) | 4.23607 | − | 3.07768i | 0.160453 | − | 0.116576i | ||||
\(698\) | 4.70820 | − | 14.4904i | 0.178208 | − | 0.548468i | ||||
\(699\) | 11.8713 | − | 36.5362i | 0.449015 | − | 1.38193i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.04508 | − | 6.57164i | −0.341628 | − | 0.248207i | 0.403720 | − | 0.914882i | \(-0.367717\pi\) |
−0.745348 | + | 0.666675i | \(0.767717\pi\) | |||||||
\(702\) | −5.69098 | − | 17.5150i | −0.214792 | − | 0.661063i | ||||
\(703\) | −5.70820 | −0.215289 | ||||||||
\(704\) | −10.7812 | + | 9.00854i | −0.406330 | + | 0.339522i | ||||
\(705\) | 11.1803 | 0.421076 | ||||||||
\(706\) | −2.20820 | − | 6.79615i | −0.0831069 | − | 0.255777i | ||||
\(707\) | 35.4894 | + | 25.7845i | 1.33471 | + | 0.969727i | ||||
\(708\) | −4.83688 | + | 3.51420i | −0.181781 | + | 0.132072i | ||||
\(709\) | −1.63525 | + | 5.03280i | −0.0614133 | + | 0.189011i | −0.977056 | − | 0.212982i | \(-0.931682\pi\) |
0.915643 | + | 0.401993i | \(0.131682\pi\) | |||||||
\(710\) | 1.28115 | − | 3.94298i | 0.0480808 | − | 0.147978i | ||||
\(711\) | −1.61803 | + | 1.17557i | −0.0606810 | + | 0.0440873i | ||||
\(712\) | −7.39919 | − | 5.37582i | −0.277296 | − | 0.201468i | ||||
\(713\) | 17.7984 | + | 54.7778i | 0.666554 | + | 2.05144i | ||||
\(714\) | 13.9443 | 0.521851 | ||||||||
\(715\) | 14.0689 | + | 35.0301i | 0.526146 | + | 1.31005i | ||||
\(716\) | −9.50658 | −0.355277 | ||||||||
\(717\) | 3.29180 | + | 10.1311i | 0.122934 | + | 0.378353i | ||||
\(718\) | −37.7705 | − | 27.4419i | −1.40958 | − | 1.02412i | ||||
\(719\) | −42.3607 | + | 30.7768i | −1.57979 | + | 1.14778i | −0.662848 | + | 0.748754i | \(0.730653\pi\) |
−0.916939 | + | 0.399029i | \(0.869347\pi\) | |||||||
\(720\) | 6.70820 | − | 20.6457i | 0.250000 | − | 0.769421i | ||||
\(721\) | −17.8647 | + | 54.9820i | −0.665318 | + | 2.04764i | ||||
\(722\) | −23.5623 | + | 17.1190i | −0.876898 | + | 0.637104i | ||||
\(723\) | 11.3820 | + | 8.26948i | 0.423300 | + | 0.307545i | ||||
\(724\) | −3.30902 | − | 10.1841i | −0.122979 | − | 0.378489i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −17.2984 | − | 35.8424i | −0.642003 | − | 1.33024i | ||||
\(727\) | 24.0000 | 0.890111 | 0.445055 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445055 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(728\) | −13.5557 | − | 41.7202i | −0.502409 | − | 1.54626i | ||||
\(729\) | 5.66312 | + | 4.11450i | 0.209745 | + | 0.152389i | ||||
\(730\) | 39.0066 | − | 28.3399i | 1.44370 | − | 1.04891i | ||||
\(731\) | 2.78115 | − | 8.55951i | 0.102865 | − | 0.316585i | ||||
\(732\) | 3.22949 | − | 9.93935i | 0.119365 | − | 0.367369i | ||||
\(733\) | −8.57295 | + | 6.22861i | −0.316649 | + | 0.230059i | −0.734744 | − | 0.678344i | \(-0.762698\pi\) |
0.418095 | + | 0.908403i | \(0.362698\pi\) | |||||||
\(734\) | −28.4164 | − | 20.6457i | −1.04887 | − | 0.762048i | ||||
\(735\) | −12.1353 | − | 37.3485i | −0.447616 | − | 1.37762i | ||||
\(736\) | −21.0902 | −0.777394 | ||||||||
\(737\) | −8.83282 | − | 21.9928i | −0.325361 | − | 0.810116i | ||||
\(738\) | −16.9443 | −0.623727 | ||||||||
\(739\) | −0.281153 | − | 0.865300i | −0.0103424 | − | 0.0318306i | 0.945752 | − | 0.324889i | \(-0.105327\pi\) |
−0.956095 | + | 0.293058i | \(0.905327\pi\) | |||||||
\(740\) | −6.38197 | − | 4.63677i | −0.234606 | − | 0.170451i | ||||
\(741\) | 9.20820 | − | 6.69015i | 0.338272 | − | 0.245769i | ||||
\(742\) | −19.4443 | + | 59.8433i | −0.713822 | + | 2.19692i | ||||
\(743\) | −11.7148 | + | 36.0544i | −0.429774 | + | 1.32271i | 0.468575 | + | 0.883424i | \(0.344768\pi\) |
−0.898348 | + | 0.439284i | \(0.855232\pi\) | |||||||
\(744\) | 37.3607 | − | 27.1441i | 1.36971 | − | 0.995152i | ||||
\(745\) | 2.07295 | + | 1.50609i | 0.0759470 | + | 0.0551787i | ||||
\(746\) | −3.21885 | − | 9.90659i | −0.117850 | − | 0.362706i | ||||
\(747\) | −2.18034 | −0.0797745 | ||||||||
\(748\) | 1.57295 | − | 1.31433i | 0.0575127 | − | 0.0480566i | ||||
\(749\) | −11.5623 | −0.422477 | ||||||||
\(750\) | −12.5000 | − | 38.4710i | −0.456435 | − | 1.40476i | ||||
\(751\) | 34.0795 | + | 24.7602i | 1.24358 | + | 0.903513i | 0.997831 | − | 0.0658203i | \(-0.0209664\pi\) |
0.245748 | + | 0.969334i | \(0.420966\pi\) | |||||||
\(752\) | −8.78115 | + | 6.37988i | −0.320216 | + | 0.232650i | ||||
\(753\) | −6.21885 | + | 19.1396i | −0.226627 | + | 0.697487i | ||||
\(754\) | 11.7533 | − | 36.1729i | 0.428030 | − | 1.31734i | ||||
\(755\) | −7.98936 | + | 5.80461i | −0.290762 | + | 0.211251i | ||||
\(756\) | 4.30902 | + | 3.13068i | 0.156717 | + | 0.113862i | ||||
\(757\) | 12.3262 | + | 37.9363i | 0.448005 | + | 1.37882i | 0.879155 | + | 0.476537i | \(0.158108\pi\) |
−0.431150 | + | 0.902280i | \(0.641892\pi\) | |||||||
\(758\) | −48.0689 | −1.74594 | ||||||||
\(759\) | −11.2812 | + | 44.8509i | −0.409480 | + | 1.62799i | ||||
\(760\) | −5.00000 | −0.181369 | ||||||||
\(761\) | 5.51064 | + | 16.9600i | 0.199761 | + | 0.614800i | 0.999888 | + | 0.0149698i | \(0.00476523\pi\) |
−0.800127 | + | 0.599830i | \(0.795235\pi\) | |||||||
\(762\) | 0.690983 | + | 0.502029i | 0.0250317 | + | 0.0181866i | ||||
\(763\) | 36.0517 | − | 26.1931i | 1.30516 | − | 0.948253i | ||||
\(764\) | 1.01064 | − | 3.11044i | 0.0365638 | − | 0.112532i | ||||
\(765\) | 1.38197 | − | 4.25325i | 0.0499651 | − | 0.153777i | ||||
\(766\) | 3.97214 | − | 2.88593i | 0.143519 | − | 0.104273i | ||||
\(767\) | 17.8156 | + | 12.9438i | 0.643284 | + | 0.467373i | ||||
\(768\) | 9.37132 | + | 28.8420i | 0.338158 | + | 1.04074i | ||||
\(769\) | −31.8541 | −1.14869 | −0.574344 | − | 0.818614i | \(-0.694743\pi\) | ||||
−0.574344 | + | 0.818614i | \(0.694743\pi\) | |||||||
\(770\) | −39.1697 | − | 24.5887i | −1.41158 | − | 0.886116i | ||||
\(771\) | 24.4721 | 0.881342 | ||||||||
\(772\) | −1.52786 | − | 4.70228i | −0.0549890 | − | 0.169239i | ||||
\(773\) | −40.1697 | − | 29.1850i | −1.44480 | − | 1.04971i | −0.987011 | − | 0.160652i | \(-0.948640\pi\) |
−0.457792 | − | 0.889059i | \(-0.651360\pi\) | |||||||
\(774\) | −23.5623 | + | 17.1190i | −0.846930 | + | 0.615330i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.43769 | − | 22.8909i | 0.266998 | − | 0.821734i | ||||
\(777\) | 39.7984 | − | 28.9152i | 1.42776 | − | 1.03733i | ||||
\(778\) | −15.6353 | − | 11.3597i | −0.560551 | − | 0.407264i | ||||
\(779\) | 1.61803 | + | 4.97980i | 0.0579721 | + | 0.178420i | ||||
\(780\) | 15.7295 | 0.563206 | ||||||||
\(781\) | 3.79180 | − | 0.257270i | 0.135681 | − | 0.00920585i | ||||
\(782\) | −10.0902 | −0.360824 | ||||||||
\(783\) | −3.19098 | − | 9.82084i | −0.114036 | − | 0.350968i | ||||
\(784\) | 30.8435 | + | 22.4091i | 1.10155 | + | 0.800324i | ||||
\(785\) | 1.11803 | − | 0.812299i | 0.0399043 | − | 0.0289922i | ||||
\(786\) | −4.14590 | + | 12.7598i | −0.147879 | + | 0.455126i | ||||
\(787\) | 10.3885 | − | 31.9727i | 0.370312 | − | 1.13970i | −0.576276 | − | 0.817255i | \(-0.695495\pi\) |
0.946588 | − | 0.322447i | \(-0.104505\pi\) | |||||||
\(788\) | 11.3090 | − | 8.21648i | 0.402867 | − | 0.292700i | ||||
\(789\) | −28.2533 | − | 20.5272i | −1.00584 | − | 0.730788i | ||||
\(790\) | 1.11803 | + | 3.44095i | 0.0397779 | + | 0.122424i | ||||
\(791\) | −0.214782 | −0.00763676 | ||||||||
\(792\) | 14.7984 | − | 1.00406i | 0.525837 | − | 0.0356776i | ||||
\(793\) | −38.4934 | −1.36694 | ||||||||
\(794\) | 10.2082 | + | 31.4176i | 0.362276 | + | 1.11497i | ||||
\(795\) | 40.8156 | + | 29.6543i | 1.44758 | + | 1.05173i | ||||
\(796\) | 6.11803 | − | 4.44501i | 0.216848 | − | 0.157549i | ||||
\(797\) | 4.06231 | − | 12.5025i | 0.143894 | − | 0.442861i | −0.852973 | − | 0.521955i | \(-0.825203\pi\) |
0.996867 | + | 0.0790942i | \(0.0252028\pi\) | |||||||
\(798\) | −4.30902 | + | 13.2618i | −0.152538 | + | 0.469462i | ||||
\(799\) | −1.80902 | + | 1.31433i | −0.0639984 | + | 0.0464976i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.52786 | + | 7.77997i | 0.0893177 | + | 0.274892i | ||||
\(802\) | −38.8328 | −1.37123 | ||||||||
\(803\) | 37.4336 | + | 23.4989i | 1.32100 | + | 0.829258i | ||||
\(804\) | −9.87539 | −0.348278 | ||||||||
\(805\) | 16.6074 | + | 51.1123i | 0.585334 | + | 1.80147i | ||||
\(806\) | 61.5410 | + | 44.7122i | 2.16769 | + | 1.57492i | ||||
\(807\) | 34.9615 | − | 25.4010i | 1.23070 | − | 0.894158i | ||||
\(808\) | −7.86475 | + | 24.2052i | −0.276681 | + | 0.851536i | ||||
\(809\) | −5.91641 | + | 18.2088i | −0.208010 | + | 0.640188i | 0.791567 | + | 0.611083i | \(0.209266\pi\) |
−0.999576 | + | 0.0291054i | \(0.990734\pi\) | |||||||
\(810\) | 32.1976 | − | 23.3929i | 1.13131 | − | 0.821943i | ||||
\(811\) | −2.88197 | − | 2.09387i | −0.101200 | − | 0.0735258i | 0.536035 | − | 0.844196i | \(-0.319922\pi\) |
−0.637234 | + | 0.770670i | \(0.719922\pi\) | |||||||
\(812\) | 3.39919 | + | 10.4616i | 0.119288 | + | 0.367131i | ||||
\(813\) | 68.6656 | 2.40821 | ||||||||
\(814\) | 7.47214 | − | 29.7073i | 0.261898 | − | 1.04124i | ||||
\(815\) | −7.11146 | −0.249103 | ||||||||
\(816\) | 3.35410 | + | 10.3229i | 0.117417 | + | 0.361373i | ||||
\(817\) | 7.28115 | + | 5.29007i | 0.254735 | + | 0.185076i | ||||
\(818\) | 0.736068 | − | 0.534785i | 0.0257360 | − | 0.0186983i | ||||
\(819\) | −12.1246 | + | 37.3157i | −0.423668 | + | 1.30392i | ||||
\(820\) | −2.23607 | + | 6.88191i | −0.0780869 | + | 0.240327i | ||||
\(821\) | −5.00000 | + | 3.63271i | −0.174501 | + | 0.126783i | −0.671608 | − | 0.740907i | \(-0.734396\pi\) |
0.497106 | + | 0.867690i | \(0.334396\pi\) | |||||||
\(822\) | −19.5344 | − | 14.1926i | −0.681342 | − | 0.495024i | ||||
\(823\) | −6.18034 | − | 19.0211i | −0.215433 | − | 0.663035i | −0.999123 | − | 0.0418821i | \(-0.986665\pi\) |
0.783689 | − | 0.621153i | \(-0.213335\pi\) | |||||||
\(824\) | −33.5410 | −1.16846 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.9787 | −0.938710 | ||||||||
\(827\) | 0.375388 | + | 1.15533i | 0.0130535 | + | 0.0401746i | 0.957371 | − | 0.288861i | \(-0.0932765\pi\) |
−0.944318 | + | 0.329035i | \(0.893276\pi\) | |||||||
\(828\) | 6.23607 | + | 4.53077i | 0.216718 | + | 0.157455i | ||||
\(829\) | 21.9443 | − | 15.9434i | 0.762156 | − | 0.553739i | −0.137415 | − | 0.990514i | \(-0.543879\pi\) |
0.899571 | + | 0.436775i | \(0.143879\pi\) | |||||||
\(830\) | −1.21885 | + | 3.75123i | −0.0423068 | + | 0.130207i | ||||
\(831\) | 5.06231 | − | 15.5802i | 0.175609 | − | 0.540470i | ||||
\(832\) | 17.4443 | − | 12.6740i | 0.604771 | − | 0.439392i | ||||
\(833\) | 6.35410 | + | 4.61653i | 0.220157 | + | 0.159953i | ||||
\(834\) | −21.1803 | − | 65.1864i | −0.733415 | − | 2.25722i | ||||
\(835\) | 43.9443 | 1.52075 | ||||||||
\(836\) | 0.763932 | + | 1.90211i | 0.0264211 | + | 0.0657860i | ||||
\(837\) | 20.6525 | 0.713854 | ||||||||
\(838\) | 16.7705 | + | 51.6143i | 0.579328 | + | 1.78299i | ||||
\(839\) | −6.85410 | − | 4.97980i | −0.236630 | − | 0.171922i | 0.463151 | − | 0.886280i | \(-0.346719\pi\) |
−0.699781 | + | 0.714358i | \(0.746719\pi\) | |||||||
\(840\) | 34.8607 | − | 25.3278i | 1.20281 | − | 0.873891i | ||||
\(841\) | −2.37132 | + | 7.29818i | −0.0817698 | + | 0.251661i | ||||
\(842\) | −11.5623 | + | 35.5851i | −0.398463 | + | 1.22634i | ||||
\(843\) | −26.2812 | + | 19.0944i | −0.905171 | + | 0.657645i | ||||
\(844\) | −8.38197 | − | 6.08985i | −0.288519 | − | 0.209621i | ||||
\(845\) | −8.92047 | − | 27.4544i | −0.306874 | − | 0.944460i | ||||
\(846\) | 7.23607 | 0.248781 | ||||||||
\(847\) | 7.53444 | − | 41.7202i | 0.258886 | − | 1.43352i | ||||
\(848\) | −48.9787 | −1.68194 | ||||||||
\(849\) | −13.0279 | − | 40.0956i | −0.447115 | − | 1.37608i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7984 | + | 20.9232i | −0.987196 | + | 0.717240i | ||||
\(852\) | 0.489357 | − | 1.50609i | 0.0167651 | − | 0.0515976i | ||||
\(853\) | −3.13525 | + | 9.64932i | −0.107349 | + | 0.330387i | −0.990275 | − | 0.139127i | \(-0.955571\pi\) |
0.882926 | + | 0.469513i | \(0.155571\pi\) | |||||||
\(854\) | 38.1525 | − | 27.7194i | 1.30555 | − | 0.948538i | ||||
\(855\) | 3.61803 | + | 2.62866i | 0.123734 | + | 0.0898981i | ||||
\(856\) | −2.07295 | − | 6.37988i | −0.0708519 | − | 0.218060i | ||||
\(857\) | −40.3394 | −1.37797 | −0.688984 | − | 0.724777i | \(-0.741943\pi\) | ||||
−0.688984 | + | 0.724777i | \(0.741943\pi\) | |||||||
\(858\) | 22.7639 | + | 56.6799i | 0.777148 | + | 1.93502i | ||||
\(859\) | 26.4164 | 0.901316 | 0.450658 | − | 0.892697i | \(-0.351189\pi\) | ||||
0.450658 | + | 0.892697i | \(0.351189\pi\) | |||||||
\(860\) | 3.84346 | + | 11.8290i | 0.131061 | + | 0.403364i | ||||
\(861\) | −36.5066 | − | 26.5236i | −1.24414 | − | 0.903921i | ||||
\(862\) | −44.5967 | + | 32.4014i | −1.51897 | + | 1.10360i | ||||
\(863\) | 8.23607 | − | 25.3480i | 0.280359 | − | 0.862856i | −0.707392 | − | 0.706821i | \(-0.750129\pi\) |
0.987751 | − | 0.156035i | \(-0.0498714\pi\) | |||||||
\(864\) | −2.33688 | + | 7.19218i | −0.0795023 | + | 0.244683i | ||||
\(865\) | 22.9894 | − | 16.7027i | 0.781662 | − | 0.567910i | ||||
\(866\) | −8.47214 | − | 6.15537i | −0.287895 | − | 0.209168i | ||||
\(867\) | 0.690983 | + | 2.12663i | 0.0234670 | + | 0.0722240i | ||||
\(868\) | −22.0000 | −0.746729 | ||||||||
\(869\) | −2.54508 | + | 2.12663i | −0.0863361 | + | 0.0721409i | ||||
\(870\) | 37.3607 | 1.26665 | ||||||||
\(871\) | 11.2401 | + | 34.5936i | 0.380857 | + | 1.17216i | ||||
\(872\) | 20.9164 | + | 15.1967i | 0.708319 | + | 0.514624i | ||||
\(873\) | −17.4164 | + | 12.6538i | −0.589456 | + | 0.428265i | ||||
\(874\) | 3.11803 | − | 9.59632i | 0.105469 | − | 0.324600i | ||||
\(875\) | 13.3156 | − | 40.9812i | 0.450149 | − | 1.38542i | ||||
\(876\) | 14.8992 | − | 10.8249i | 0.503397 | − | 0.365739i | ||||
\(877\) | −14.8992 | − | 10.8249i | −0.503110 | − | 0.365531i | 0.307094 | − | 0.951679i | \(-0.400643\pi\) |
−0.810204 | + | 0.586149i | \(0.800643\pi\) | |||||||
\(878\) | −17.5623 | − | 54.0512i | −0.592699 | − | 1.82414i | ||||
\(879\) | 70.9787 | 2.39405 | ||||||||
\(880\) | 8.78115 | − | 34.9116i | 0.296013 | − | 1.17687i | ||||
\(881\) | −41.2148 | −1.38856 | −0.694281 | − | 0.719704i | \(-0.744277\pi\) | ||||
−0.694281 | + | 0.719704i | \(0.744277\pi\) | |||||||
\(882\) | −7.85410 | − | 24.1724i | −0.264461 | − | 0.813928i | ||||
\(883\) | 37.3885 | + | 27.1644i | 1.25822 | + | 0.914154i | 0.998669 | − | 0.0515744i | \(-0.0164239\pi\) |
0.259556 | + | 0.965728i | \(0.416424\pi\) | |||||||
\(884\) | −2.54508 | + | 1.84911i | −0.0856005 | + | 0.0621924i | ||||
\(885\) | −6.68441 | + | 20.5725i | −0.224694 | + | 0.691536i | ||||
\(886\) | −11.7533 | + | 36.1729i | −0.394859 | + | 1.21525i | ||||
\(887\) | 20.8262 | − | 15.1311i | 0.699277 | − | 0.508054i | −0.180420 | − | 0.983590i | \(-0.557746\pi\) |
0.879697 | + | 0.475535i | \(0.157746\pi\) | |||||||
\(888\) | 23.0902 | + | 16.7760i | 0.774855 | + | 0.562965i | ||||
\(889\) | 0.281153 | + | 0.865300i | 0.00942957 | + | 0.0290212i | ||||
\(890\) | 14.7984 | 0.496043 | ||||||||
\(891\) | 30.8992 | + | 19.3969i | 1.03516 | + | 0.649821i | ||||
\(892\) | −0.416408 | −0.0139424 | ||||||||
\(893\) | −0.690983 | − | 2.12663i | −0.0231229 | − | 0.0711649i | ||||
\(894\) | 3.35410 | + | 2.43690i | 0.112178 | + | 0.0815021i | ||||
\(895\) | −27.8262 | + | 20.2169i | −0.930129 | + | 0.675778i | ||||
\(896\) | −16.2188 | + | 49.9165i | −0.541834 | + | 1.66759i | ||||
\(897\) | 21.9336 | − | 67.5048i | 0.732343 | − | 2.25392i | ||||
\(898\) | 3.61803 | − | 2.62866i | 0.120735 | − | 0.0877194i | ||||
\(899\) | 34.5066 | + | 25.0705i | 1.15086 | + | 0.836148i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0902 | −0.336152 | ||||||||
\(902\) | −28.0344 | + | 1.90211i | −0.933445 | + | 0.0633334i | ||||
\(903\) | −77.5623 | −2.58111 | ||||||||
\(904\) | −0.0385072 | − | 0.118513i | −0.00128073 | − | 0.00394168i | ||||
\(905\) | −31.3435 | − | 22.7724i | −1.04189 | − | 0.756979i | ||||
\(906\) | −12.9271 | + | 9.39205i | −0.429473 | + | 0.312030i | ||||
\(907\) | −6.83688 | + | 21.0418i | −0.227015 | + | 0.698680i | 0.771066 | + | 0.636755i | \(0.219724\pi\) |
−0.998081 | + | 0.0619247i | \(0.980276\pi\) | |||||||
\(908\) | −1.00000 | + | 3.07768i | −0.0331862 | + | 0.102137i | ||||
\(909\) | 18.4164 | − | 13.3803i | 0.610834 | − | 0.443797i | ||||
\(910\) | 57.4230 | + | 41.7202i | 1.90355 | + | 1.38301i | ||||
\(911\) | −16.9894 | − | 52.2879i | −0.562883 | − | 1.73237i | −0.674160 | − | 0.738585i | \(-0.735494\pi\) |
0.111278 | − | 0.993789i | \(-0.464506\pi\) | |||||||
\(912\) | −10.8541 | −0.359415 | ||||||||
\(913\) | −3.60739 | + | 0.244758i | −0.119387 | + | 0.00810032i | ||||
\(914\) | −0.236068 | −0.00780843 | ||||||||
\(915\) | −11.6844 | − | 35.9609i | −0.386275 | − | 1.18883i | ||||
\(916\) | 7.35410 | + | 5.34307i | 0.242986 | + | 0.176540i | ||||
\(917\) | −11.5623 | + | 8.40051i | −0.381821 | + | 0.277409i | ||||
\(918\) | −1.11803 | + | 3.44095i | −0.0369006 | + | 0.113568i | ||||
\(919\) | −15.3090 | + | 47.1163i | −0.504998 | + | 1.55422i | 0.295776 | + | 0.955257i | \(0.404422\pi\) |
−0.800774 | + | 0.598966i | \(0.795578\pi\) | |||||||
\(920\) | −25.2254 | + | 18.3273i | −0.831658 | + | 0.604235i | ||||
\(921\) | −7.82624 | − | 5.68609i | −0.257883 | − | 0.187363i | ||||
\(922\) | −2.54508 | − | 7.83297i | −0.0838179 | − | 0.257965i | ||||
\(923\) | −5.83282 | −0.191989 | ||||||||
\(924\) | −14.9615 | − | 9.39205i | −0.492197 | − | 0.308976i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.3992 | + | 38.1608i | 0.407463 | + | 1.25404i | ||||
\(927\) | 24.2705 | + | 17.6336i | 0.797148 | + | 0.579162i | ||||
\(928\) | −12.6353 | + | 9.18005i | −0.414773 | + | 0.301350i | ||||
\(929\) | −1.99342 | + | 6.13512i | −0.0654021 | + | 0.201287i | −0.978417 | − | 0.206638i | \(-0.933748\pi\) |
0.913015 | + | 0.407925i | \(0.133748\pi\) | |||||||
\(930\) | −23.0902 | + | 71.0642i | −0.757157 | + | 2.33029i | ||||
\(931\) | −6.35410 | + | 4.61653i | −0.208247 | + | 0.151301i | ||||
\(932\) | −8.59017 | − | 6.24112i | −0.281380 | − | 0.204435i | ||||
\(933\) | −5.85410 | − | 18.0171i | −0.191655 | − | 0.589852i | ||||
\(934\) | 58.2492 | 1.90597 | ||||||||
\(935\) | 1.80902 | − | 7.19218i | 0.0591612 | − | 0.235209i | ||||
\(936\) | −22.7639 | −0.744062 | ||||||||
\(937\) | −7.37539 | − | 22.6991i | −0.240943 | − | 0.741548i | −0.996277 | − | 0.0862074i | \(-0.972525\pi\) |
0.755334 | − | 0.655340i | \(-0.227475\pi\) | |||||||
\(938\) | −36.0517 | − | 26.1931i | −1.17713 | − | 0.855234i | ||||
\(939\) | −46.9336 | + | 34.0993i | −1.53162 | + | 1.11279i | ||||
\(940\) | 0.954915 | − | 2.93893i | 0.0311459 | − | 0.0958572i | ||||
\(941\) | −0.236068 | + | 0.726543i | −0.00769560 | + | 0.0236846i | −0.954831 | − | 0.297151i | \(-0.903964\pi\) |
0.947135 | + | 0.320835i | \(0.103964\pi\) | |||||||
\(942\) | 1.80902 | − | 1.31433i | 0.0589410 | − | 0.0428231i | ||||
\(943\) | 26.4164 | + | 19.1926i | 0.860237 | + | 0.624998i | ||||
\(944\) | −6.48936 | − | 19.9722i | −0.211211 | − | 0.650039i | ||||
\(945\) | 19.2705 | 0.626870 | ||||||||
\(946\) | −37.0623 | + | 30.9686i | −1.20500 | + | 1.00688i | ||||
\(947\) | −42.4853 | −1.38059 | −0.690293 | − | 0.723530i | \(-0.742518\pi\) | ||||
−0.690293 | + | 0.723530i | \(0.742518\pi\) | |||||||
\(948\) | 0.427051 | + | 1.31433i | 0.0138700 | + | 0.0426874i | ||||
\(949\) | −54.8779 | − | 39.8711i | −1.78141 | − | 1.29427i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.3050 | + | 34.7931i | −0.366588 | + | 1.12824i | ||||
\(952\) | −2.66312 | + | 8.19624i | −0.0863122 | + | 0.265642i | ||||
\(953\) | −30.3992 | + | 22.0863i | −0.984726 | + | 0.715446i | −0.958760 | − | 0.284217i | \(-0.908266\pi\) |
−0.0259664 | + | 0.999663i | \(0.508266\pi\) | |||||||
\(954\) | 26.4164 | + | 19.1926i | 0.855263 | + | 0.621385i | ||||
\(955\) | −3.65654 | − | 11.2537i | −0.118323 | − | 0.364160i | ||||
\(956\) | 2.94427 | 0.0952246 | ||||||||
\(957\) | 12.7639 | + | 31.7809i | 0.412599 | + | 1.02733i | ||||
\(958\) | −10.8541 | −0.350680 | ||||||||
\(959\) | −7.94834 | − | 24.4625i | −0.256665 | − | 0.789934i | ||||
\(960\) | 17.1353 | + | 12.4495i | 0.553038 | + | 0.401806i | ||||
\(961\) | −43.9336 | + | 31.9196i | −1.41721 | + | 1.02967i | ||||
\(962\) | −14.5279 | + | 44.7122i | −0.468397 | + | 1.44158i | ||||
\(963\) | −1.85410 | + | 5.70634i | −0.0597476 | + | 0.183884i | ||||
\(964\) | 3.14590 | − | 2.28563i | 0.101323 | − | 0.0736151i | ||||
\(965\) | −14.4721 | − | 10.5146i | −0.465875 | − | 0.338478i | ||||
\(966\) | 26.8713 | + | 82.7014i | 0.864571 | + | 2.66087i | ||||
\(967\) | −57.4508 | −1.84749 | −0.923747 | − | 0.383002i | \(-0.874890\pi\) | ||||
−0.923747 | + | 0.383002i | \(0.874890\pi\) | |||||||
\(968\) | 24.3713 | − | 3.32244i | 0.783324 | − | 0.106787i | ||||
\(969\) | −2.23607 | −0.0718329 | ||||||||
\(970\) | 12.0344 | + | 37.0382i | 0.386403 | + | 1.18923i | ||||
\(971\) | 2.00000 | + | 1.45309i | 0.0641831 | + | 0.0466317i | 0.619414 | − | 0.785064i | \(-0.287370\pi\) |
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(972\) | 8.94427 | − | 6.49839i | 0.286888 | − | 0.208436i | ||||
\(973\) | 22.5623 | − | 69.4396i | 0.723314 | − | 2.22613i | ||||
\(974\) | −3.75329 | + | 11.5514i | −0.120263 | + | 0.370132i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.6976 | + | 21.5765i | 0.950596 | + | 0.690648i | ||||
\(977\) | −7.47214 | − | 22.9969i | −0.239055 | − | 0.735735i | −0.996558 | − | 0.0829031i | \(-0.973581\pi\) |
0.757503 | − | 0.652832i | \(-0.226419\pi\) | |||||||
\(978\) | −11.5066 | −0.367940 | ||||||||
\(979\) | 5.05573 | + | 12.5882i | 0.161582 | + | 0.402322i | ||||
\(980\) | −10.8541 | −0.346722 | ||||||||
\(981\) | −7.14590 | − | 21.9928i | −0.228151 | − | 0.702176i | ||||
\(982\) | 13.3262 | + | 9.68208i | 0.425257 | + | 0.308968i | ||||
\(983\) | −11.5623 | + | 8.40051i | −0.368780 | + | 0.267935i | −0.756705 | − | 0.653757i | \(-0.773192\pi\) |
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(984\) | 8.09017 | − | 24.8990i | 0.257905 | − | 0.793751i | ||||
\(985\) | 15.6287 | − | 48.1001i | 0.497971 | − | 1.53260i | ||||
\(986\) | −6.04508 | + | 4.39201i | −0.192515 | + | 0.139870i | ||||
\(987\) | 15.5902 | + | 11.3269i | 0.496241 | + | 0.360540i | ||||
\(988\) | −0.972136 | − | 2.99193i | −0.0309278 | − | 0.0951859i | ||||
\(989\) | 56.1246 | 1.78466 | ||||||||
\(990\) | −18.4164 | + | 15.3884i | −0.585312 | + | 0.489076i | ||||
\(991\) | −23.2148 | −0.737442 | −0.368721 | − | 0.929540i | \(-0.620204\pi\) | ||||
−0.368721 | + | 0.929540i | \(0.620204\pi\) | |||||||
\(992\) | −9.65248 | − | 29.7073i | −0.306466 | − | 0.943207i | ||||
\(993\) | 5.42705 | + | 3.94298i | 0.172222 | + | 0.125127i | ||||
\(994\) | 5.78115 | − | 4.20025i | 0.183367 | − | 0.133224i | ||||
\(995\) | 8.45492 | − | 26.0216i | 0.268039 | − | 0.824939i | ||||
\(996\) | −0.465558 | + | 1.43284i | −0.0147518 | + | 0.0454013i | ||||
\(997\) | 32.0066 | − | 23.2541i | 1.01366 | − | 0.736466i | 0.0486852 | − | 0.998814i | \(-0.484497\pi\) |
0.964973 | + | 0.262348i | \(0.0844969\pi\) | |||||||
\(998\) | −36.8435 | − | 26.7683i | −1.16626 | − | 0.847337i | ||||
\(999\) | 3.94427 | + | 12.1392i | 0.124791 | + | 0.384068i |
(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 | 187.2.g.a.137.1 | yes | 4 | |
11.3 | even | 5 | 2057.2.a.g.1.1 | 2 | |||
11.8 | odd | 10 | 2057.2.a.l.1.2 | 2 | |||
11.9 | even | 5 | inner | 187.2.g.a.86.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.g.a.86.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
187.2.g.a.137.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2057.2.a.g.1.1 | 2 | 11.3 | even | 5 | |||
2057.2.a.l.1.2 | 2 | 11.8 | odd | 10 |