Properties

Label 588.2.e.e.491.4
Level $588$
Weight $2$
Character 588.491
Analytic conductor $4.695$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(491,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.e (of order \(2\), degree \(1\), 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: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.312013725601644544.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{10} - 2x^{8} + 8x^{6} - 8x^{4} - 16x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 491.4
Root \(-1.13556 + 0.842913i\) of defining polynomial
Character \(\chi\) \(=\) 588.491
Dual form 588.2.e.e.491.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13556 + 0.842913i) q^{2} +(1.65140 + 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} -0.499464i q^{5} +(-2.31558 + 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +O(q^{10})\) \(q+(-1.13556 + 0.842913i) q^{2} +(1.65140 + 0.522368i) q^{3} +(0.578995 - 1.91436i) q^{4} -0.499464i q^{5} +(-2.31558 + 0.798808i) q^{6} +(0.956154 + 2.66191i) q^{8} +(2.45426 + 1.72528i) q^{9} +(0.421005 + 0.567172i) q^{10} -1.39050 q^{11} +(1.95615 - 2.85893i) q^{12} +2.75054 q^{13} +(0.260904 - 0.824817i) q^{15} +(-3.32953 - 2.21681i) q^{16} +5.82329i q^{17} +(-4.24123 + 0.109569i) q^{18} -2.48153i q^{19} +(-0.956154 - 0.289187i) q^{20} +(1.57899 - 1.17207i) q^{22} +5.06405 q^{23} +(0.188496 + 4.89535i) q^{24} +4.75054 q^{25} +(-3.12340 + 2.31846i) q^{26} +(3.15174 + 4.13116i) q^{27} +6.32275i q^{29} +(0.398976 + 1.15655i) q^{30} -6.91514i q^{31} +(5.64946 - 0.289187i) q^{32} +(-2.29627 - 0.726352i) q^{33} +(-4.90852 - 6.61269i) q^{34} +(4.72381 - 3.69941i) q^{36} +7.34308 q^{37} +(2.09171 + 2.81793i) q^{38} +(4.54224 + 1.43679i) q^{39} +(1.32953 - 0.477565i) q^{40} -5.74438i q^{41} +3.52627i q^{43} +(-0.805091 + 2.66191i) q^{44} +(0.861717 - 1.22582i) q^{45} +(-5.75054 + 4.26855i) q^{46} -5.06405 q^{47} +(-4.34041 - 5.40008i) q^{48} +(-5.39452 + 4.00429i) q^{50} +(-3.04190 + 9.61659i) q^{51} +(1.59255 - 5.26551i) q^{52} -5.24491i q^{53} +(-7.06121 - 2.03454i) q^{54} +0.694505i q^{55} +(1.29627 - 4.09801i) q^{57} +(-5.32953 - 7.17987i) q^{58} -3.15174 q^{59} +(-1.42793 - 0.977029i) q^{60} -4.90852 q^{61} +(5.82886 + 7.85256i) q^{62} +(-6.17154 + 5.09039i) q^{64} -1.37379i q^{65} +(3.21981 - 1.11074i) q^{66} +10.7439i q^{67} +(11.1479 + 3.37165i) q^{68} +(8.36279 + 2.64530i) q^{69} +4.54224 q^{71} +(-2.24589 + 8.18266i) q^{72} -9.97504 q^{73} +(-8.33851 + 6.18958i) q^{74} +(7.84505 + 2.48153i) q^{75} +(-4.75054 - 1.43679i) q^{76} +(-6.36908 + 2.19715i) q^{78} +2.13130i q^{79} +(-1.10722 + 1.66298i) q^{80} +(3.04681 + 8.46859i) q^{81} +(4.84201 + 6.52309i) q^{82} -12.0165 q^{83} +2.90852 q^{85} +(-2.97234 - 4.00429i) q^{86} +(-3.30281 + 10.4414i) q^{87} +(-1.32953 - 3.70138i) q^{88} +2.45163i q^{89} +(0.0547257 + 2.11834i) q^{90} +(2.93206 - 9.69440i) q^{92} +(3.61225 - 11.4197i) q^{93} +(5.75054 - 4.26855i) q^{94} -1.23944 q^{95} +(9.48059 + 2.47353i) q^{96} +0.526031 q^{97} +(-3.41265 - 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} + 2 q^{9} + 10 q^{10} + 12 q^{12} - 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} + 14 q^{24} + 12 q^{25} + 14 q^{30} - 10 q^{33} - 4 q^{34} + 22 q^{36} + 8 q^{37} - 34 q^{40} + 18 q^{45} - 24 q^{46} + 4 q^{48} - 16 q^{52} - 38 q^{54} - 2 q^{57} - 14 q^{58} - 14 q^{60} - 4 q^{61} - 34 q^{64} - 30 q^{66} + 18 q^{69} - 20 q^{72} - 12 q^{76} - 52 q^{78} - 26 q^{81} + 68 q^{82} - 20 q^{85} + 34 q^{88} - 20 q^{90} + 6 q^{93} + 24 q^{94} + 62 q^{96} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13556 + 0.842913i −0.802962 + 0.596030i
\(3\) 1.65140 + 0.522368i 0.953438 + 0.301590i
\(4\) 0.578995 1.91436i 0.289497 0.957179i
\(5\) 0.499464i 0.223367i −0.993744 0.111684i \(-0.964376\pi\)
0.993744 0.111684i \(-0.0356243\pi\)
\(6\) −2.31558 + 0.798808i −0.945331 + 0.326112i
\(7\) 0 0
\(8\) 0.956154 + 2.66191i 0.338051 + 0.941128i
\(9\) 2.45426 + 1.72528i 0.818087 + 0.575094i
\(10\) 0.421005 + 0.567172i 0.133134 + 0.179356i
\(11\) −1.39050 −0.419251 −0.209626 0.977782i \(-0.567224\pi\)
−0.209626 + 0.977782i \(0.567224\pi\)
\(12\) 1.95615 2.85893i 0.564693 0.825301i
\(13\) 2.75054 0.762861 0.381431 0.924397i \(-0.375432\pi\)
0.381431 + 0.924397i \(0.375432\pi\)
\(14\) 0 0
\(15\) 0.260904 0.824817i 0.0673652 0.212967i
\(16\) −3.32953 2.21681i −0.832383 0.554202i
\(17\) 5.82329i 1.41235i 0.708035 + 0.706177i \(0.249582\pi\)
−0.708035 + 0.706177i \(0.750418\pi\)
\(18\) −4.24123 + 0.109569i −0.999666 + 0.0258256i
\(19\) 2.48153i 0.569302i −0.958631 0.284651i \(-0.908122\pi\)
0.958631 0.284651i \(-0.0918777\pi\)
\(20\) −0.956154 0.289187i −0.213802 0.0646643i
\(21\) 0 0
\(22\) 1.57899 1.17207i 0.336643 0.249886i
\(23\) 5.06405 1.05593 0.527964 0.849267i \(-0.322956\pi\)
0.527964 + 0.849267i \(0.322956\pi\)
\(24\) 0.188496 + 4.89535i 0.0384767 + 0.999259i
\(25\) 4.75054 0.950107
\(26\) −3.12340 + 2.31846i −0.612549 + 0.454688i
\(27\) 3.15174 + 4.13116i 0.606553 + 0.795043i
\(28\) 0 0
\(29\) 6.32275i 1.17411i 0.809549 + 0.587053i \(0.199712\pi\)
−0.809549 + 0.587053i \(0.800288\pi\)
\(30\) 0.398976 + 1.15655i 0.0728428 + 0.211156i
\(31\) 6.91514i 1.24200i −0.783812 0.620998i \(-0.786727\pi\)
0.783812 0.620998i \(-0.213273\pi\)
\(32\) 5.64946 0.289187i 0.998692 0.0511216i
\(33\) −2.29627 0.726352i −0.399730 0.126442i
\(34\) −4.90852 6.61269i −0.841805 1.13407i
\(35\) 0 0
\(36\) 4.72381 3.69941i 0.787302 0.616568i
\(37\) 7.34308 1.20720 0.603598 0.797289i \(-0.293733\pi\)
0.603598 + 0.797289i \(0.293733\pi\)
\(38\) 2.09171 + 2.81793i 0.339321 + 0.457128i
\(39\) 4.54224 + 1.43679i 0.727341 + 0.230071i
\(40\) 1.32953 0.477565i 0.210217 0.0755096i
\(41\) 5.74438i 0.897121i −0.893753 0.448560i \(-0.851937\pi\)
0.893753 0.448560i \(-0.148063\pi\)
\(42\) 0 0
\(43\) 3.52627i 0.537751i 0.963175 + 0.268875i \(0.0866520\pi\)
−0.963175 + 0.268875i \(0.913348\pi\)
\(44\) −0.805091 + 2.66191i −0.121372 + 0.401298i
\(45\) 0.861717 1.22582i 0.128457 0.182734i
\(46\) −5.75054 + 4.26855i −0.847870 + 0.629364i
\(47\) −5.06405 −0.738668 −0.369334 0.929297i \(-0.620414\pi\)
−0.369334 + 0.929297i \(0.620414\pi\)
\(48\) −4.34041 5.40008i −0.626484 0.779435i
\(49\) 0 0
\(50\) −5.39452 + 4.00429i −0.762900 + 0.566292i
\(51\) −3.04190 + 9.61659i −0.425951 + 1.34659i
\(52\) 1.59255 5.26551i 0.220846 0.730195i
\(53\) 5.24491i 0.720444i −0.932867 0.360222i \(-0.882701\pi\)
0.932867 0.360222i \(-0.117299\pi\)
\(54\) −7.06121 2.03454i −0.960909 0.276866i
\(55\) 0.694505i 0.0936470i
\(56\) 0 0
\(57\) 1.29627 4.09801i 0.171696 0.542794i
\(58\) −5.32953 7.17987i −0.699802 0.942763i
\(59\) −3.15174 −0.410322 −0.205161 0.978728i \(-0.565772\pi\)
−0.205161 + 0.978728i \(0.565772\pi\)
\(60\) −1.42793 0.977029i −0.184345 0.126134i
\(61\) −4.90852 −0.628472 −0.314236 0.949345i \(-0.601748\pi\)
−0.314236 + 0.949345i \(0.601748\pi\)
\(62\) 5.82886 + 7.85256i 0.740267 + 0.997276i
\(63\) 0 0
\(64\) −6.17154 + 5.09039i −0.771443 + 0.636299i
\(65\) 1.37379i 0.170398i
\(66\) 3.21981 1.11074i 0.396331 0.136723i
\(67\) 10.7439i 1.31257i 0.754513 + 0.656286i \(0.227873\pi\)
−0.754513 + 0.656286i \(0.772127\pi\)
\(68\) 11.1479 + 3.37165i 1.35188 + 0.408873i
\(69\) 8.36279 + 2.64530i 1.00676 + 0.318457i
\(70\) 0 0
\(71\) 4.54224 0.539065 0.269532 0.962991i \(-0.413131\pi\)
0.269532 + 0.962991i \(0.413131\pi\)
\(72\) −2.24589 + 8.18266i −0.264681 + 0.964336i
\(73\) −9.97504 −1.16749 −0.583745 0.811937i \(-0.698413\pi\)
−0.583745 + 0.811937i \(0.698413\pi\)
\(74\) −8.33851 + 6.18958i −0.969332 + 0.719524i
\(75\) 7.84505 + 2.48153i 0.905868 + 0.286542i
\(76\) −4.75054 1.43679i −0.544924 0.164811i
\(77\) 0 0
\(78\) −6.36908 + 2.19715i −0.721156 + 0.248778i
\(79\) 2.13130i 0.239790i 0.992787 + 0.119895i \(0.0382557\pi\)
−0.992787 + 0.119895i \(0.961744\pi\)
\(80\) −1.10722 + 1.66298i −0.123791 + 0.185927i
\(81\) 3.04681 + 8.46859i 0.338534 + 0.940954i
\(82\) 4.84201 + 6.52309i 0.534711 + 0.720354i
\(83\) −12.0165 −1.31899 −0.659493 0.751710i \(-0.729229\pi\)
−0.659493 + 0.751710i \(0.729229\pi\)
\(84\) 0 0
\(85\) 2.90852 0.315474
\(86\) −2.97234 4.00429i −0.320515 0.431794i
\(87\) −3.30281 + 10.4414i −0.354098 + 1.11944i
\(88\) −1.32953 3.70138i −0.141728 0.394569i
\(89\) 2.45163i 0.259873i 0.991522 + 0.129936i \(0.0414773\pi\)
−0.991522 + 0.129936i \(0.958523\pi\)
\(90\) 0.0547257 + 2.11834i 0.00576860 + 0.223293i
\(91\) 0 0
\(92\) 2.93206 9.69440i 0.305688 1.01071i
\(93\) 3.61225 11.4197i 0.374573 1.18417i
\(94\) 5.75054 4.26855i 0.593122 0.440268i
\(95\) −1.23944 −0.127163
\(96\) 9.48059 + 2.47353i 0.967609 + 0.252454i
\(97\) 0.526031 0.0534104 0.0267052 0.999643i \(-0.491498\pi\)
0.0267052 + 0.999643i \(0.491498\pi\)
\(98\) 0 0
\(99\) −3.41265 2.39900i −0.342984 0.241109i
\(100\) 2.75054 9.09422i 0.275054 0.909422i
\(101\) 16.0961i 1.60162i −0.598920 0.800809i \(-0.704403\pi\)
0.598920 0.800809i \(-0.295597\pi\)
\(102\) −4.65169 13.4843i −0.460586 1.33514i
\(103\) 1.87663i 0.184910i 0.995717 + 0.0924550i \(0.0294714\pi\)
−0.995717 + 0.0924550i \(0.970529\pi\)
\(104\) 2.62993 + 7.32168i 0.257886 + 0.717950i
\(105\) 0 0
\(106\) 4.42101 + 5.95591i 0.429406 + 0.578490i
\(107\) −7.27848 −0.703637 −0.351819 0.936068i \(-0.614437\pi\)
−0.351819 + 0.936068i \(0.614437\pi\)
\(108\) 9.73337 3.64164i 0.936594 0.350417i
\(109\) −1.84201 −0.176433 −0.0882163 0.996101i \(-0.528117\pi\)
−0.0882163 + 0.996101i \(0.528117\pi\)
\(110\) −0.585407 0.788652i −0.0558164 0.0751950i
\(111\) 12.1264 + 3.83579i 1.15099 + 0.364077i
\(112\) 0 0
\(113\) 10.2728i 0.966382i −0.875515 0.483191i \(-0.839478\pi\)
0.875515 0.483191i \(-0.160522\pi\)
\(114\) 1.98227 + 5.74618i 0.185656 + 0.538179i
\(115\) 2.52931i 0.235860i
\(116\) 12.1040 + 3.66084i 1.12383 + 0.339900i
\(117\) 6.75054 + 4.74545i 0.624087 + 0.438717i
\(118\) 3.57899 2.65665i 0.329473 0.244564i
\(119\) 0 0
\(120\) 2.44505 0.0941473i 0.223202 0.00859443i
\(121\) −9.06651 −0.824229
\(122\) 5.57393 4.13746i 0.504640 0.374588i
\(123\) 3.00068 9.48628i 0.270562 0.855349i
\(124\) −13.2381 4.00383i −1.18881 0.359555i
\(125\) 4.87005i 0.435590i
\(126\) 0 0
\(127\) 1.51224i 0.134190i 0.997747 + 0.0670949i \(0.0213730\pi\)
−0.997747 + 0.0670949i \(0.978627\pi\)
\(128\) 2.71740 10.9825i 0.240186 0.970727i
\(129\) −1.84201 + 5.82329i −0.162180 + 0.512712i
\(130\) 1.15799 + 1.56003i 0.101562 + 0.136823i
\(131\) −6.65037 −0.581045 −0.290523 0.956868i \(-0.593829\pi\)
−0.290523 + 0.956868i \(0.593829\pi\)
\(132\) −2.72003 + 3.97533i −0.236748 + 0.346008i
\(133\) 0 0
\(134\) −9.05614 12.2003i −0.782331 1.05395i
\(135\) 2.06337 1.57418i 0.177587 0.135484i
\(136\) −15.5011 + 5.56796i −1.32921 + 0.477448i
\(137\) 12.1917i 1.04161i −0.853676 0.520805i \(-0.825632\pi\)
0.853676 0.520805i \(-0.174368\pi\)
\(138\) −11.7262 + 4.04521i −0.998201 + 0.344351i
\(139\) 0.0477837i 0.00405296i 0.999998 + 0.00202648i \(0.000645050\pi\)
−0.999998 + 0.00202648i \(0.999355\pi\)
\(140\) 0 0
\(141\) −8.36279 2.64530i −0.704274 0.222774i
\(142\) −5.15799 + 3.82872i −0.432849 + 0.321299i
\(143\) −3.82461 −0.319830
\(144\) −4.34693 11.1850i −0.362244 0.932083i
\(145\) 3.15799 0.262257
\(146\) 11.3273 8.40809i 0.937451 0.695859i
\(147\) 0 0
\(148\) 4.25161 14.0573i 0.349480 1.15550i
\(149\) 2.29381i 0.187917i 0.995576 + 0.0939583i \(0.0299520\pi\)
−0.995576 + 0.0939583i \(0.970048\pi\)
\(150\) −11.0002 + 3.79477i −0.898166 + 0.309841i
\(151\) 13.1358i 1.06897i −0.845177 0.534487i \(-0.820505\pi\)
0.845177 0.534487i \(-0.179495\pi\)
\(152\) 6.60561 2.37272i 0.535786 0.192453i
\(153\) −10.0468 + 14.2919i −0.812236 + 1.15543i
\(154\) 0 0
\(155\) −3.45387 −0.277421
\(156\) 5.38047 7.86358i 0.430782 0.629590i
\(157\) 8.40960 0.671159 0.335579 0.942012i \(-0.391068\pi\)
0.335579 + 0.942012i \(0.391068\pi\)
\(158\) −1.79650 2.42022i −0.142922 0.192542i
\(159\) 2.73978 8.66146i 0.217278 0.686899i
\(160\) −0.144439 2.82170i −0.0114189 0.223075i
\(161\) 0 0
\(162\) −10.5981 7.04840i −0.832667 0.553774i
\(163\) 12.3599i 0.968099i −0.875041 0.484050i \(-0.839165\pi\)
0.875041 0.484050i \(-0.160835\pi\)
\(164\) −10.9968 3.32596i −0.858705 0.259714i
\(165\) −0.362787 + 1.14691i −0.0282429 + 0.0892866i
\(166\) 13.6455 10.1289i 1.05910 0.786155i
\(167\) 2.36549 0.183047 0.0915237 0.995803i \(-0.470826\pi\)
0.0915237 + 0.995803i \(0.470826\pi\)
\(168\) 0 0
\(169\) −5.43456 −0.418043
\(170\) −3.30281 + 2.45163i −0.253314 + 0.188032i
\(171\) 4.28134 6.09033i 0.327402 0.465739i
\(172\) 6.75054 + 2.04169i 0.514723 + 0.155677i
\(173\) 9.56980i 0.727579i −0.931481 0.363789i \(-0.881483\pi\)
0.931481 0.363789i \(-0.118517\pi\)
\(174\) −5.05067 14.6408i −0.382890 1.10992i
\(175\) 0 0
\(176\) 4.62971 + 3.08247i 0.348977 + 0.232350i
\(177\) −5.20480 1.64637i −0.391217 0.123749i
\(178\) −2.06651 2.78398i −0.154892 0.208668i
\(179\) −20.7541 −1.55124 −0.775619 0.631202i \(-0.782562\pi\)
−0.775619 + 0.631202i \(0.782562\pi\)
\(180\) −1.84772 2.35938i −0.137721 0.175857i
\(181\) −6.43456 −0.478277 −0.239138 0.970985i \(-0.576865\pi\)
−0.239138 + 0.970985i \(0.576865\pi\)
\(182\) 0 0
\(183\) −8.10595 2.56406i −0.599209 0.189541i
\(184\) 4.84201 + 13.4801i 0.356958 + 0.993763i
\(185\) 3.66761i 0.269648i
\(186\) 5.52387 + 16.0126i 0.405030 + 1.17410i
\(187\) 8.09727i 0.592131i
\(188\) −2.93206 + 9.69440i −0.213842 + 0.707037i
\(189\) 0 0
\(190\) 1.40745 1.04474i 0.102107 0.0757932i
\(191\) 17.5338 1.26870 0.634350 0.773046i \(-0.281268\pi\)
0.634350 + 0.773046i \(0.281268\pi\)
\(192\) −12.8508 + 5.18247i −0.927424 + 0.374013i
\(193\) −2.18509 −0.157286 −0.0786432 0.996903i \(-0.525059\pi\)
−0.0786432 + 0.996903i \(0.525059\pi\)
\(194\) −0.597340 + 0.443399i −0.0428865 + 0.0318342i
\(195\) 0.717627 2.26869i 0.0513903 0.162464i
\(196\) 0 0
\(197\) 6.27706i 0.447222i −0.974678 0.223611i \(-0.928215\pi\)
0.974678 0.223611i \(-0.0717845\pi\)
\(198\) 5.89742 0.152355i 0.419111 0.0108274i
\(199\) 0.865522i 0.0613552i 0.999529 + 0.0306776i \(0.00976652\pi\)
−0.999529 + 0.0306776i \(0.990233\pi\)
\(200\) 4.54224 + 12.6455i 0.321185 + 0.894172i
\(201\) −5.61225 + 17.7424i −0.395858 + 1.25145i
\(202\) 13.5676 + 18.2781i 0.954612 + 1.28604i
\(203\) 0 0
\(204\) 16.6484 + 11.3912i 1.16562 + 0.797547i
\(205\) −2.86911 −0.200387
\(206\) −1.58184 2.13103i −0.110212 0.148476i
\(207\) 12.4285 + 8.73691i 0.863841 + 0.607257i
\(208\) −9.15799 6.09740i −0.634992 0.422779i
\(209\) 3.45056i 0.238680i
\(210\) 0 0
\(211\) 3.90417i 0.268774i −0.990929 0.134387i \(-0.957094\pi\)
0.990929 0.134387i \(-0.0429065\pi\)
\(212\) −10.0406 3.03678i −0.689594 0.208567i
\(213\) 7.50107 + 2.37272i 0.513965 + 0.162576i
\(214\) 8.26516 6.13513i 0.564994 0.419389i
\(215\) 1.76124 0.120116
\(216\) −7.98324 + 12.3397i −0.543191 + 0.839609i
\(217\) 0 0
\(218\) 2.09171 1.55265i 0.141669 0.105159i
\(219\) −16.4728 5.21065i −1.11313 0.352103i
\(220\) 1.32953 + 0.402115i 0.0896369 + 0.0271106i
\(221\) 16.0172i 1.07743i
\(222\) −17.0035 + 5.86571i −1.14120 + 0.393681i
\(223\) 23.5017i 1.57379i −0.617085 0.786896i \(-0.711687\pi\)
0.617085 0.786896i \(-0.288313\pi\)
\(224\) 0 0
\(225\) 11.6591 + 8.19601i 0.777271 + 0.546401i
\(226\) 8.65906 + 11.6654i 0.575992 + 0.775968i
\(227\) 19.1678 1.27221 0.636107 0.771601i \(-0.280544\pi\)
0.636107 + 0.771601i \(0.280544\pi\)
\(228\) −7.09451 4.85425i −0.469846 0.321481i
\(229\) 11.4761 0.758363 0.379181 0.925322i \(-0.376206\pi\)
0.379181 + 0.925322i \(0.376206\pi\)
\(230\) 2.13199 + 2.87219i 0.140579 + 0.189386i
\(231\) 0 0
\(232\) −16.8306 + 6.04552i −1.10498 + 0.396908i
\(233\) 20.2174i 1.32449i 0.749288 + 0.662245i \(0.230396\pi\)
−0.749288 + 0.662245i \(0.769604\pi\)
\(234\) −11.6656 + 0.301373i −0.762607 + 0.0197014i
\(235\) 2.52931i 0.164994i
\(236\) −1.82484 + 6.03356i −0.118787 + 0.392752i
\(237\) −1.11332 + 3.51963i −0.0723181 + 0.228625i
\(238\) 0 0
\(239\) 6.90774 0.446824 0.223412 0.974724i \(-0.428280\pi\)
0.223412 + 0.974724i \(0.428280\pi\)
\(240\) −2.69715 + 2.16788i −0.174100 + 0.139936i
\(241\) 8.06651 0.519610 0.259805 0.965661i \(-0.416342\pi\)
0.259805 + 0.965661i \(0.416342\pi\)
\(242\) 10.2956 7.64228i 0.661825 0.491265i
\(243\) 0.607785 + 15.5766i 0.0389894 + 0.999240i
\(244\) −2.84201 + 9.39667i −0.181941 + 0.601560i
\(245\) 0 0
\(246\) 4.58866 + 13.3016i 0.292562 + 0.848076i
\(247\) 6.82553i 0.434298i
\(248\) 18.4075 6.61194i 1.16888 0.419859i
\(249\) −19.8442 6.27706i −1.25757 0.397793i
\(250\) 4.10503 + 5.53023i 0.259625 + 0.349763i
\(251\) −20.4073 −1.28810 −0.644048 0.764985i \(-0.722746\pi\)
−0.644048 + 0.764985i \(0.722746\pi\)
\(252\) 0 0
\(253\) −7.04155 −0.442699
\(254\) −1.27469 1.71724i −0.0799811 0.107749i
\(255\) 4.80315 + 1.51932i 0.300785 + 0.0951436i
\(256\) 6.17154 + 14.7618i 0.385721 + 0.922615i
\(257\) 27.2100i 1.69731i −0.528947 0.848655i \(-0.677413\pi\)
0.528947 0.848655i \(-0.322587\pi\)
\(258\) −2.81681 8.16535i −0.175367 0.508352i
\(259\) 0 0
\(260\) −2.62993 0.795420i −0.163102 0.0493299i
\(261\) −10.9085 + 15.5177i −0.675221 + 0.960521i
\(262\) 7.55189 5.60568i 0.466558 0.346320i
\(263\) 3.60493 0.222290 0.111145 0.993804i \(-0.464548\pi\)
0.111145 + 0.993804i \(0.464548\pi\)
\(264\) −0.262104 6.80698i −0.0161314 0.418941i
\(265\) −2.61965 −0.160924
\(266\) 0 0
\(267\) −1.28066 + 4.04864i −0.0783749 + 0.247772i
\(268\) 20.5676 + 6.22064i 1.25637 + 0.379986i
\(269\) 26.1653i 1.59533i 0.603102 + 0.797664i \(0.293931\pi\)
−0.603102 + 0.797664i \(0.706069\pi\)
\(270\) −1.01618 + 3.52682i −0.0618428 + 0.214636i
\(271\) 23.0619i 1.40091i 0.713696 + 0.700455i \(0.247020\pi\)
−0.713696 + 0.700455i \(0.752980\pi\)
\(272\) 12.9091 19.3888i 0.782729 1.17562i
\(273\) 0 0
\(274\) 10.2766 + 13.8444i 0.620830 + 0.836373i
\(275\) −6.60561 −0.398333
\(276\) 9.90606 14.4778i 0.596275 0.871458i
\(277\) −20.2910 −1.21917 −0.609585 0.792721i \(-0.708664\pi\)
−0.609585 + 0.792721i \(0.708664\pi\)
\(278\) −0.0402775 0.0542613i −0.00241569 0.00325438i
\(279\) 11.9306 16.9716i 0.714264 1.01606i
\(280\) 0 0
\(281\) 27.6637i 1.65028i 0.564929 + 0.825140i \(0.308904\pi\)
−0.564929 + 0.825140i \(0.691096\pi\)
\(282\) 11.7262 4.04521i 0.698286 0.240888i
\(283\) 17.3707i 1.03258i 0.856413 + 0.516291i \(0.172688\pi\)
−0.856413 + 0.516291i \(0.827312\pi\)
\(284\) 2.62993 8.69547i 0.156058 0.515981i
\(285\) −2.04681 0.647442i −0.121242 0.0383512i
\(286\) 4.34308 3.22382i 0.256812 0.190628i
\(287\) 0 0
\(288\) 14.3642 + 9.03716i 0.846417 + 0.532520i
\(289\) −16.9107 −0.994745
\(290\) −3.58609 + 2.66191i −0.210582 + 0.156313i
\(291\) 0.868689 + 0.274782i 0.0509235 + 0.0161080i
\(292\) −5.77550 + 19.0958i −0.337985 + 1.11750i
\(293\) 19.9672i 1.16650i −0.812294 0.583248i \(-0.801782\pi\)
0.812294 0.583248i \(-0.198218\pi\)
\(294\) 0 0
\(295\) 1.57418i 0.0916525i
\(296\) 7.02111 + 19.5466i 0.408094 + 1.13612i
\(297\) −4.38249 5.74438i −0.254298 0.333323i
\(298\) −1.93349 2.60476i −0.112004 0.150890i
\(299\) 13.9288 0.805526
\(300\) 9.29278 13.5814i 0.536519 0.784124i
\(301\) 0 0
\(302\) 11.0723 + 14.9165i 0.637141 + 0.858346i
\(303\) 8.40808 26.5811i 0.483031 1.52704i
\(304\) −5.50107 + 8.26233i −0.315508 + 0.473877i
\(305\) 2.45163i 0.140380i
\(306\) −0.638051 24.6979i −0.0364749 1.41188i
\(307\) 14.1529i 0.807746i 0.914815 + 0.403873i \(0.132336\pi\)
−0.914815 + 0.403873i \(0.867664\pi\)
\(308\) 0 0
\(309\) −0.980294 + 3.09908i −0.0557670 + 0.176300i
\(310\) 3.92208 2.91131i 0.222759 0.165351i
\(311\) −24.5549 −1.39238 −0.696190 0.717857i \(-0.745123\pi\)
−0.696190 + 0.717857i \(0.745123\pi\)
\(312\) 0.518466 + 13.4648i 0.0293524 + 0.762296i
\(313\) 0.0520623 0.00294274 0.00147137 0.999999i \(-0.499532\pi\)
0.00147137 + 0.999999i \(0.499532\pi\)
\(314\) −9.54960 + 7.08856i −0.538915 + 0.400031i
\(315\) 0 0
\(316\) 4.08007 + 1.23401i 0.229522 + 0.0694185i
\(317\) 6.77653i 0.380608i −0.981725 0.190304i \(-0.939053\pi\)
0.981725 0.190304i \(-0.0609473\pi\)
\(318\) 4.18968 + 12.1450i 0.234946 + 0.681058i
\(319\) 8.79177i 0.492245i
\(320\) 2.54247 + 3.08247i 0.142128 + 0.172315i
\(321\) −12.0197 3.80205i −0.670875 0.212210i
\(322\) 0 0
\(323\) 14.4507 0.804056
\(324\) 17.9760 0.929412i 0.998666 0.0516340i
\(325\) 13.0665 0.724800
\(326\) 10.4183 + 14.0354i 0.577016 + 0.777347i
\(327\) −3.04190 0.962208i −0.168218 0.0532102i
\(328\) 15.2910 5.49251i 0.844305 0.303273i
\(329\) 0 0
\(330\) −0.554776 1.60818i −0.0305394 0.0885274i
\(331\) 17.8920i 0.983431i 0.870756 + 0.491715i \(0.163630\pi\)
−0.870756 + 0.491715i \(0.836370\pi\)
\(332\) −6.95752 + 23.0040i −0.381843 + 1.26251i
\(333\) 18.0218 + 12.6689i 0.987591 + 0.694250i
\(334\) −2.68616 + 1.99391i −0.146980 + 0.109102i
\(335\) 5.36618 0.293185
\(336\) 0 0
\(337\) 7.09362 0.386414 0.193207 0.981158i \(-0.438111\pi\)
0.193207 + 0.981158i \(0.438111\pi\)
\(338\) 6.17127 4.58086i 0.335673 0.249166i
\(339\) 5.36618 16.9645i 0.291451 0.921385i
\(340\) 1.68402 5.56796i 0.0913288 0.301965i
\(341\) 9.61549i 0.520708i
\(342\) 0.271898 + 10.5247i 0.0147026 + 0.569112i
\(343\) 0 0
\(344\) −9.38661 + 3.37165i −0.506092 + 0.181787i
\(345\) 1.32123 4.17692i 0.0711328 0.224878i
\(346\) 8.06651 + 10.8671i 0.433659 + 0.584218i
\(347\) −9.19079 −0.493387 −0.246694 0.969093i \(-0.579344\pi\)
−0.246694 + 0.969093i \(0.579344\pi\)
\(348\) 18.0763 + 12.3683i 0.968990 + 0.663009i
\(349\) −22.1330 −1.18475 −0.592377 0.805661i \(-0.701810\pi\)
−0.592377 + 0.805661i \(0.701810\pi\)
\(350\) 0 0
\(351\) 8.66898 + 11.3629i 0.462716 + 0.606507i
\(352\) −7.85556 + 0.402115i −0.418703 + 0.0214328i
\(353\) 10.7266i 0.570917i −0.958391 0.285458i \(-0.907854\pi\)
0.958391 0.285458i \(-0.0921459\pi\)
\(354\) 7.29811 2.51764i 0.387890 0.133811i
\(355\) 2.26869i 0.120409i
\(356\) 4.69330 + 1.41948i 0.248745 + 0.0752325i
\(357\) 0 0
\(358\) 23.5676 17.4939i 1.24559 0.924584i
\(359\) 3.60493 0.190261 0.0951305 0.995465i \(-0.469673\pi\)
0.0951305 + 0.995465i \(0.469673\pi\)
\(360\) 4.08695 + 1.12174i 0.215401 + 0.0591211i
\(361\) 12.8420 0.675895
\(362\) 7.30683 5.42377i 0.384038 0.285067i
\(363\) −14.9725 4.73606i −0.785851 0.248579i
\(364\) 0 0
\(365\) 4.98218i 0.260779i
\(366\) 11.3661 3.92097i 0.594114 0.204952i
\(367\) 15.0266i 0.784381i 0.919884 + 0.392190i \(0.128283\pi\)
−0.919884 + 0.392190i \(0.871717\pi\)
\(368\) −16.8609 11.2260i −0.878936 0.585197i
\(369\) 9.91067 14.0982i 0.515929 0.733923i
\(370\) 3.09148 + 4.16479i 0.160718 + 0.216517i
\(371\) 0 0
\(372\) −19.7699 13.5271i −1.02502 0.701346i
\(373\) 2.65692 0.137570 0.0687850 0.997632i \(-0.478088\pi\)
0.0687850 + 0.997632i \(0.478088\pi\)
\(374\) 6.82530 + 9.19494i 0.352928 + 0.475459i
\(375\) 2.54396 8.04241i 0.131369 0.415308i
\(376\) −4.84201 13.4801i −0.249708 0.695181i
\(377\) 17.3909i 0.895679i
\(378\) 0 0
\(379\) 17.7150i 0.909957i −0.890502 0.454979i \(-0.849647\pi\)
0.890502 0.454979i \(-0.150353\pi\)
\(380\) −0.717627 + 2.37272i −0.0368135 + 0.121718i
\(381\) −0.789948 + 2.49732i −0.0404703 + 0.127942i
\(382\) −19.9107 + 14.7795i −1.01872 + 0.756183i
\(383\) −32.9217 −1.68222 −0.841111 0.540862i \(-0.818098\pi\)
−0.841111 + 0.540862i \(0.818098\pi\)
\(384\) 10.2244 16.7171i 0.521764 0.853090i
\(385\) 0 0
\(386\) 2.48130 1.84184i 0.126295 0.0937473i
\(387\) −6.08380 + 8.65438i −0.309257 + 0.439927i
\(388\) 0.304569 1.00701i 0.0154622 0.0511233i
\(389\) 6.82222i 0.345900i −0.984931 0.172950i \(-0.944670\pi\)
0.984931 0.172950i \(-0.0553299\pi\)
\(390\) 1.09740 + 3.18113i 0.0555689 + 0.161083i
\(391\) 29.4894i 1.49134i
\(392\) 0 0
\(393\) −10.9824 3.47394i −0.553991 0.175237i
\(394\) 5.29102 + 7.12798i 0.266558 + 0.359103i
\(395\) 1.06451 0.0535612
\(396\) −6.56845 + 5.14402i −0.330077 + 0.258497i
\(397\) −20.8442 −1.04614 −0.523069 0.852290i \(-0.675213\pi\)
−0.523069 + 0.852290i \(0.675213\pi\)
\(398\) −0.729560 0.982853i −0.0365695 0.0492660i
\(399\) 0 0
\(400\) −15.8170 10.5310i −0.790852 0.526551i
\(401\) 3.82543i 0.191033i −0.995428 0.0955164i \(-0.969550\pi\)
0.995428 0.0955164i \(-0.0304502\pi\)
\(402\) −8.58228 24.8782i −0.428045 1.24081i
\(403\) 19.0203i 0.947471i
\(404\) −30.8136 9.31954i −1.53304 0.463664i
\(405\) 4.22976 1.52177i 0.210178 0.0756175i
\(406\) 0 0
\(407\) −10.2105 −0.506118
\(408\) −28.5070 + 1.09767i −1.41131 + 0.0543427i
\(409\) −3.86911 −0.191315 −0.0956576 0.995414i \(-0.530495\pi\)
−0.0956576 + 0.995414i \(0.530495\pi\)
\(410\) 3.25805 2.41841i 0.160904 0.119437i
\(411\) 6.36857 20.1335i 0.314139 0.993110i
\(412\) 3.59255 + 1.08656i 0.176992 + 0.0535310i
\(413\) 0 0
\(414\) −21.4778 + 0.554862i −1.05558 + 0.0272700i
\(415\) 6.00184i 0.294619i
\(416\) 15.5390 0.795420i 0.761864 0.0389987i
\(417\) −0.0249607 + 0.0789102i −0.00122233 + 0.00386425i
\(418\) −2.90852 3.91832i −0.142261 0.191651i
\(419\) −13.5133 −0.660170 −0.330085 0.943951i \(-0.607077\pi\)
−0.330085 + 0.943951i \(0.607077\pi\)
\(420\) 0 0
\(421\) 11.3825 0.554749 0.277374 0.960762i \(-0.410536\pi\)
0.277374 + 0.960762i \(0.410536\pi\)
\(422\) 3.29087 + 4.43342i 0.160197 + 0.215815i
\(423\) −12.4285 8.73691i −0.604295 0.424803i
\(424\) 13.9615 5.01494i 0.678030 0.243547i
\(425\) 27.6637i 1.34189i
\(426\) −10.5179 + 3.62838i −0.509595 + 0.175796i
\(427\) 0 0
\(428\) −4.21420 + 13.9336i −0.203701 + 0.673507i
\(429\) −6.31598 1.99786i −0.304938 0.0964575i
\(430\) −2.00000 + 1.48458i −0.0964486 + 0.0715926i
\(431\) 25.9245 1.24874 0.624370 0.781129i \(-0.285356\pi\)
0.624370 + 0.781129i \(0.285356\pi\)
\(432\) −1.33583 20.7416i −0.0642704 0.997933i
\(433\) 23.3825 1.12369 0.561845 0.827242i \(-0.310092\pi\)
0.561845 + 0.827242i \(0.310092\pi\)
\(434\) 0 0
\(435\) 5.21511 + 1.64963i 0.250046 + 0.0790939i
\(436\) −1.06651 + 3.52627i −0.0510768 + 0.168878i
\(437\) 12.5666i 0.601142i
\(438\) 23.0980 7.96814i 1.10366 0.380733i
\(439\) 17.6732i 0.843494i −0.906714 0.421747i \(-0.861417\pi\)
0.906714 0.421747i \(-0.138583\pi\)
\(440\) −1.84871 + 0.664053i −0.0881338 + 0.0316575i
\(441\) 0 0
\(442\) −13.5011 18.1884i −0.642180 0.865136i
\(443\) −35.1362 −1.66937 −0.834685 0.550727i \(-0.814350\pi\)
−0.834685 + 0.550727i \(0.814350\pi\)
\(444\) 14.3642 20.9933i 0.681694 0.996299i
\(445\) 1.22450 0.0580471
\(446\) 19.8099 + 26.6876i 0.938027 + 1.26370i
\(447\) −1.19822 + 3.78801i −0.0566737 + 0.179167i
\(448\) 0 0
\(449\) 5.52733i 0.260851i −0.991458 0.130425i \(-0.958366\pi\)
0.991458 0.130425i \(-0.0416343\pi\)
\(450\) −20.1481 + 0.520511i −0.949790 + 0.0245371i
\(451\) 7.98755i 0.376119i
\(452\) −19.6658 5.94789i −0.925000 0.279765i
\(453\) 6.86172 21.6925i 0.322392 1.01920i
\(454\) −21.7662 + 16.1568i −1.02154 + 0.758277i
\(455\) 0 0
\(456\) 12.1480 0.467760i 0.568880 0.0219049i
\(457\) 23.9522 1.12044 0.560219 0.828345i \(-0.310717\pi\)
0.560219 + 0.828345i \(0.310717\pi\)
\(458\) −13.0318 + 9.67336i −0.608937 + 0.452007i
\(459\) −24.0570 + 18.3535i −1.12288 + 0.856668i
\(460\) −4.84201 1.46446i −0.225760 0.0682808i
\(461\) 2.99679i 0.139574i 0.997562 + 0.0697871i \(0.0222320\pi\)
−0.997562 + 0.0697871i \(0.977768\pi\)
\(462\) 0 0
\(463\) 22.4152i 1.04172i −0.853642 0.520861i \(-0.825611\pi\)
0.853642 0.520861i \(-0.174389\pi\)
\(464\) 14.0163 21.0518i 0.650691 0.977305i
\(465\) −5.70373 1.80419i −0.264504 0.0836674i
\(466\) −17.0416 22.9581i −0.789435 1.06352i
\(467\) 12.0613 0.558130 0.279065 0.960272i \(-0.409975\pi\)
0.279065 + 0.960272i \(0.409975\pi\)
\(468\) 12.9930 10.1753i 0.600602 0.470356i
\(469\) 0 0
\(470\) −2.13199 2.87219i −0.0983414 0.132484i
\(471\) 13.8876 + 4.39291i 0.639908 + 0.202414i
\(472\) −3.01355 8.38966i −0.138710 0.386165i
\(473\) 4.90327i 0.225452i
\(474\) −1.70250 4.93519i −0.0781983 0.226681i
\(475\) 11.7886i 0.540898i
\(476\) 0 0
\(477\) 9.04895 12.8724i 0.414323 0.589386i
\(478\) −7.84415 + 5.82262i −0.358783 + 0.266321i
\(479\) 13.4070 0.612583 0.306292 0.951938i \(-0.400912\pi\)
0.306292 + 0.951938i \(0.400912\pi\)
\(480\) 1.23544 4.73522i 0.0563900 0.216132i
\(481\) 20.1974 0.920922
\(482\) −9.16001 + 6.79937i −0.417227 + 0.309703i
\(483\) 0 0
\(484\) −5.24946 + 17.3566i −0.238612 + 0.788934i
\(485\) 0.262734i 0.0119301i
\(486\) −13.8199 17.1759i −0.626883 0.779113i
\(487\) 12.2083i 0.553212i 0.960983 + 0.276606i \(0.0892096\pi\)
−0.960983 + 0.276606i \(0.910790\pi\)
\(488\) −4.69330 13.0661i −0.212456 0.591473i
\(489\) 6.45640 20.4111i 0.291969 0.923023i
\(490\) 0 0
\(491\) −39.8981 −1.80058 −0.900288 0.435294i \(-0.856644\pi\)
−0.900288 + 0.435294i \(0.856644\pi\)
\(492\) −16.4228 11.2369i −0.740395 0.506598i
\(493\) −36.8192 −1.65825
\(494\) 5.75333 + 7.75081i 0.258855 + 0.348725i
\(495\) −1.19822 + 1.70450i −0.0538558 + 0.0766114i
\(496\) −15.3295 + 23.0242i −0.688316 + 1.03382i
\(497\) 0 0
\(498\) 27.8253 9.59891i 1.24688 0.430138i
\(499\) 8.47517i 0.379401i 0.981842 + 0.189700i \(0.0607516\pi\)
−0.981842 + 0.189700i \(0.939248\pi\)
\(500\) −9.32301 2.81973i −0.416938 0.126102i
\(501\) 3.90638 + 1.23566i 0.174524 + 0.0552052i
\(502\) 23.1737 17.2016i 1.03429 0.767743i
\(503\) 42.5519 1.89730 0.948648 0.316334i \(-0.102452\pi\)
0.948648 + 0.316334i \(0.102452\pi\)
\(504\) 0 0
\(505\) −8.03941 −0.357749
\(506\) 7.99611 5.93542i 0.355470 0.263862i
\(507\) −8.97464 2.83884i −0.398578 0.126077i
\(508\) 2.89497 + 0.875581i 0.128444 + 0.0388476i
\(509\) 17.2071i 0.762692i 0.924432 + 0.381346i \(0.124539\pi\)
−0.924432 + 0.381346i \(0.875461\pi\)
\(510\) −6.73492 + 2.32335i −0.298227 + 0.102880i
\(511\) 0 0
\(512\) −19.4511 11.5609i −0.859626 0.510924i
\(513\) 10.2516 7.82114i 0.452619 0.345312i
\(514\) 22.9356 + 30.8985i 1.01165 + 1.36288i
\(515\) 0.937311 0.0413029
\(516\) 10.0813 + 6.89792i 0.443806 + 0.303664i
\(517\) 7.04155 0.309687
\(518\) 0 0
\(519\) 4.99896 15.8036i 0.219430 0.693701i
\(520\) 3.65692 1.31356i 0.160367 0.0576034i
\(521\) 10.9436i 0.479448i 0.970841 + 0.239724i \(0.0770569\pi\)
−0.970841 + 0.239724i \(0.922943\pi\)
\(522\) −0.692777 26.8162i −0.0303220 1.17371i
\(523\) 5.53433i 0.241999i 0.992653 + 0.121000i \(0.0386100\pi\)
−0.992653 + 0.121000i \(0.961390\pi\)
\(524\) −3.85053 + 12.7312i −0.168211 + 0.556164i
\(525\) 0 0
\(526\) −4.09362 + 3.03864i −0.178490 + 0.132491i
\(527\) 40.2689 1.75414
\(528\) 6.03533 + 7.50880i 0.262654 + 0.326779i
\(529\) 2.64461 0.114983
\(530\) 2.97477 2.20814i 0.129216 0.0959153i
\(531\) −7.73521 5.43764i −0.335679 0.235974i
\(532\) 0 0
\(533\) 15.8001i 0.684379i
\(534\) −1.95839 5.67695i −0.0847476 0.245666i
\(535\) 3.63534i 0.157170i
\(536\) −28.5992 + 10.2728i −1.23530 + 0.443716i
\(537\) −34.2735 10.8413i −1.47901 0.467837i
\(538\) −22.0551 29.7123i −0.950863 1.28099i
\(539\) 0 0
\(540\) −1.81887 4.86147i −0.0782717 0.209204i
\(541\) 12.5282 0.538628 0.269314 0.963052i \(-0.413203\pi\)
0.269314 + 0.963052i \(0.413203\pi\)
\(542\) −19.4392 26.1882i −0.834984 1.12488i
\(543\) −10.6260 3.36121i −0.456007 0.144243i
\(544\) 1.68402 + 32.8984i 0.0722018 + 1.41051i
\(545\) 0.920019i 0.0394093i
\(546\) 0 0
\(547\) 37.4911i 1.60300i 0.597992 + 0.801502i \(0.295966\pi\)
−0.597992 + 0.801502i \(0.704034\pi\)
\(548\) −23.3393 7.05895i −0.997006 0.301543i
\(549\) −12.0468 8.46859i −0.514145 0.361430i
\(550\) 7.50107 5.56796i 0.319847 0.237418i
\(551\) 15.6901 0.668420
\(552\) 0.954556 + 24.7903i 0.0406286 + 1.05515i
\(553\) 0 0
\(554\) 23.0417 17.1036i 0.978947 0.726661i
\(555\) 1.91584 6.05670i 0.0813230 0.257093i
\(556\) 0.0914752 + 0.0276665i 0.00387941 + 0.00117332i
\(557\) 30.0697i 1.27409i −0.770825 0.637046i \(-0.780156\pi\)
0.770825 0.637046i \(-0.219844\pi\)
\(558\) 0.757684 + 29.3287i 0.0320753 + 1.24158i
\(559\) 9.69912i 0.410229i
\(560\) 0 0
\(561\) 4.22976 13.3719i 0.178581 0.564560i
\(562\) −23.3181 31.4138i −0.983616 1.32511i
\(563\) 6.83911 0.288234 0.144117 0.989561i \(-0.453966\pi\)
0.144117 + 0.989561i \(0.453966\pi\)
\(564\) −9.90606 + 14.4778i −0.417120 + 0.609623i
\(565\) −5.13089 −0.215858
\(566\) −14.6420 19.7255i −0.615449 0.829124i
\(567\) 0 0
\(568\) 4.34308 + 12.0910i 0.182232 + 0.507329i
\(569\) 33.4870i 1.40385i −0.712252 0.701924i \(-0.752324\pi\)
0.712252 0.701924i \(-0.247676\pi\)
\(570\) 2.87001 0.990072i 0.120212 0.0414695i
\(571\) 27.9973i 1.17165i 0.810438 + 0.585825i \(0.199229\pi\)
−0.810438 + 0.585825i \(0.800771\pi\)
\(572\) −2.21443 + 7.32168i −0.0925901 + 0.306135i
\(573\) 28.9553 + 9.15909i 1.20963 + 0.382627i
\(574\) 0 0
\(575\) 24.0570 1.00324
\(576\) −23.9289 + 1.84551i −0.997039 + 0.0768964i
\(577\) 37.6362 1.56682 0.783409 0.621507i \(-0.213479\pi\)
0.783409 + 0.621507i \(0.213479\pi\)
\(578\) 19.2031 14.2542i 0.798743 0.592898i
\(579\) −3.60847 1.14142i −0.149963 0.0474359i
\(580\) 1.82846 6.04552i 0.0759227 0.251027i
\(581\) 0 0
\(582\) −1.21807 + 0.420198i −0.0504905 + 0.0174178i
\(583\) 7.29304i 0.302047i
\(584\) −9.53767 26.5527i −0.394672 1.09876i
\(585\) 2.37018 3.37165i 0.0979950 0.139401i
\(586\) 16.8306 + 22.6739i 0.695266 + 0.936652i
\(587\) 19.7791 0.816373 0.408186 0.912899i \(-0.366161\pi\)
0.408186 + 0.912899i \(0.366161\pi\)
\(588\) 0 0
\(589\) −17.1601 −0.707071
\(590\) −1.32690 1.78758i −0.0546276 0.0735935i
\(591\) 3.27894 10.3660i 0.134878 0.426399i
\(592\) −24.4490 16.2782i −1.00485 0.669029i
\(593\) 22.5237i 0.924939i 0.886635 + 0.462469i \(0.153036\pi\)
−0.886635 + 0.462469i \(0.846964\pi\)
\(594\) 9.81860 + 2.82902i 0.402862 + 0.116076i
\(595\) 0 0
\(596\) 4.39118 + 1.32811i 0.179870 + 0.0544013i
\(597\) −0.452122 + 1.42933i −0.0185041 + 0.0584984i
\(598\) −15.8170 + 11.7408i −0.646807 + 0.480117i
\(599\) 26.7316 1.09223 0.546113 0.837712i \(-0.316107\pi\)
0.546113 + 0.837712i \(0.316107\pi\)
\(600\) 0.895459 + 23.2555i 0.0365570 + 0.949403i
\(601\) 31.1478 1.27055 0.635273 0.772288i \(-0.280888\pi\)
0.635273 + 0.772288i \(0.280888\pi\)
\(602\) 0 0
\(603\) −18.5362 + 26.3682i −0.754851 + 1.07380i
\(604\) −25.1466 7.60555i −1.02320 0.309465i
\(605\) 4.52840i 0.184106i
\(606\) 12.8577 + 37.2717i 0.522307 + 1.51406i
\(607\) 12.5787i 0.510552i 0.966868 + 0.255276i \(0.0821664\pi\)
−0.966868 + 0.255276i \(0.917834\pi\)
\(608\) −0.717627 14.0193i −0.0291036 0.568558i
\(609\) 0 0
\(610\) −2.06651 2.78398i −0.0836707 0.112720i
\(611\) −13.9288 −0.563501
\(612\) 21.5427 + 27.5081i 0.870812 + 1.11195i
\(613\) 4.54262 0.183475 0.0917374 0.995783i \(-0.470758\pi\)
0.0917374 + 0.995783i \(0.470758\pi\)
\(614\) −11.9296 16.0714i −0.481440 0.648590i
\(615\) −4.73806 1.49873i −0.191057 0.0604348i
\(616\) 0 0
\(617\) 35.4652i 1.42777i −0.700261 0.713887i \(-0.746933\pi\)
0.700261 0.713887i \(-0.253067\pi\)
\(618\) −1.49907 4.34549i −0.0603014 0.174801i
\(619\) 41.4572i 1.66631i −0.553042 0.833153i \(-0.686533\pi\)
0.553042 0.833153i \(-0.313467\pi\)
\(620\) −1.99977 + 6.61194i −0.0803128 + 0.265542i
\(621\) 15.9606 + 20.9204i 0.640476 + 0.839508i
\(622\) 27.8836 20.6976i 1.11803 0.829900i
\(623\) 0 0
\(624\) −11.9384 14.8531i −0.477920 0.594600i
\(625\) 21.3203 0.852810
\(626\) −0.0591199 + 0.0438840i −0.00236291 + 0.00175396i
\(627\) −1.80247 + 5.69827i −0.0719835 + 0.227567i
\(628\) 4.86911 16.0990i 0.194299 0.642419i
\(629\) 42.7609i 1.70499i
\(630\) 0 0
\(631\) 22.2919i 0.887428i 0.896168 + 0.443714i \(0.146339\pi\)
−0.896168 + 0.443714i \(0.853661\pi\)
\(632\) −5.67332 + 2.03785i −0.225673 + 0.0810612i
\(633\) 2.03941 6.44735i 0.0810594 0.256259i
\(634\) 5.71202 + 7.69516i 0.226853 + 0.305614i
\(635\) 0.755312 0.0299736
\(636\) −14.9948 10.2599i −0.594583 0.406830i
\(637\) 0 0
\(638\) 7.41070 + 9.98359i 0.293393 + 0.395254i
\(639\) 11.1479 + 7.83664i 0.441002 + 0.310013i
\(640\) −5.48538 1.35724i −0.216829 0.0536498i
\(641\) 34.1111i 1.34731i 0.739048 + 0.673653i \(0.235276\pi\)
−0.739048 + 0.673653i \(0.764724\pi\)
\(642\) 16.8539 5.81411i 0.665170 0.229465i
\(643\) 24.2299i 0.955533i 0.878487 + 0.477766i \(0.158553\pi\)
−0.878487 + 0.477766i \(0.841447\pi\)
\(644\) 0 0
\(645\) 2.90852 + 0.920019i 0.114523 + 0.0362257i
\(646\) −16.4096 + 12.1807i −0.645627 + 0.479241i
\(647\) −1.42818 −0.0561477 −0.0280738 0.999606i \(-0.508937\pi\)
−0.0280738 + 0.999606i \(0.508937\pi\)
\(648\) −19.6294 + 16.2076i −0.771116 + 0.636695i
\(649\) 4.38249 0.172028
\(650\) −14.8378 + 11.0139i −0.581987 + 0.432002i
\(651\) 0 0
\(652\) −23.6612 7.15630i −0.926644 0.280262i
\(653\) 5.02787i 0.196756i 0.995149 + 0.0983778i \(0.0313654\pi\)
−0.995149 + 0.0983778i \(0.968635\pi\)
\(654\) 4.26532 1.47141i 0.166787 0.0575368i
\(655\) 3.32162i 0.129787i
\(656\) −12.7342 + 19.1261i −0.497186 + 0.746748i
\(657\) −24.4814 17.2097i −0.955109 0.671416i
\(658\) 0 0
\(659\) 19.7930 0.771025 0.385512 0.922703i \(-0.374025\pi\)
0.385512 + 0.922703i \(0.374025\pi\)
\(660\) 1.98554 + 1.35856i 0.0772869 + 0.0528818i
\(661\) −22.6612 −0.881419 −0.440709 0.897650i \(-0.645273\pi\)
−0.440709 + 0.897650i \(0.645273\pi\)
\(662\) −15.0814 20.3174i −0.586154 0.789658i
\(663\) −8.36686 + 26.4508i −0.324942 + 1.02726i
\(664\) −11.4897 31.9870i −0.445885 1.24134i
\(665\) 0 0
\(666\) −31.1437 + 0.804573i −1.20679 + 0.0311766i
\(667\) 32.0187i 1.23977i
\(668\) 1.36961 4.52840i 0.0529918 0.175209i
\(669\) 12.2766 38.8108i 0.474639 1.50051i
\(670\) −6.09362 + 4.52322i −0.235417 + 0.174747i
\(671\) 6.82530 0.263488
\(672\) 0 0
\(673\) −11.2766 −0.434680 −0.217340 0.976096i \(-0.569738\pi\)
−0.217340 + 0.976096i \(0.569738\pi\)
\(674\) −8.05523 + 5.97930i −0.310276 + 0.230314i
\(675\) 14.9725 + 19.6252i 0.576291 + 0.755376i
\(676\) −3.14658 + 10.4037i −0.121022 + 0.400142i
\(677\) 10.0890i 0.387750i −0.981026 0.193875i \(-0.937894\pi\)
0.981026 0.193875i \(-0.0621056\pi\)
\(678\) 8.20598 + 23.7874i 0.315149 + 0.913551i
\(679\) 0 0
\(680\) 2.78100 + 7.74223i 0.106646 + 0.296901i
\(681\) 31.6538 + 10.0127i 1.21298 + 0.383686i
\(682\) −8.10503 10.9190i −0.310357 0.418109i
\(683\) −6.23486 −0.238570 −0.119285 0.992860i \(-0.538060\pi\)
−0.119285 + 0.992860i \(0.538060\pi\)
\(684\) −9.18019 11.7223i −0.351013 0.448212i
\(685\) −6.08933 −0.232662
\(686\) 0 0
\(687\) 18.9517 + 5.99476i 0.723052 + 0.228714i
\(688\) 7.81705 11.7408i 0.298022 0.447614i
\(689\) 14.4263i 0.549599i
\(690\) 2.02044 + 5.85682i 0.0769167 + 0.222966i
\(691\) 17.0676i 0.649283i −0.945837 0.324641i \(-0.894756\pi\)
0.945837 0.324641i \(-0.105244\pi\)
\(692\) −18.3200 5.54087i −0.696423 0.210632i
\(693\) 0 0
\(694\) 10.4367 7.74704i 0.396172 0.294074i
\(695\) 0.0238663 0.000905300
\(696\) −30.9521 + 1.19182i −1.17324 + 0.0451757i
\(697\) 33.4511 1.26705
\(698\) 25.1334 18.6562i 0.951313 0.706148i
\(699\) −10.5610 + 33.3872i −0.399452 + 1.26282i
\(700\) 0 0
\(701\) 21.4324i 0.809489i 0.914430 + 0.404744i \(0.132640\pi\)
−0.914430 + 0.404744i \(0.867360\pi\)
\(702\) −19.4221 5.59607i −0.733040 0.211210i
\(703\) 18.2221i 0.687259i
\(704\) 8.58152 7.07818i 0.323428 0.266769i
\(705\) −1.32123 + 4.17692i −0.0497605 + 0.157312i
\(706\) 9.04155 + 12.1807i 0.340283 + 0.458425i
\(707\) 0 0
\(708\) −6.16529 + 9.01060i −0.231706 + 0.338639i
\(709\) −8.54262 −0.320825 −0.160412 0.987050i \(-0.551282\pi\)
−0.160412 + 0.987050i \(0.551282\pi\)
\(710\) 1.91231 + 2.57623i 0.0717676 + 0.0966843i
\(711\) −3.67709 + 5.23076i −0.137902 + 0.196169i
\(712\) −6.52603 + 2.34414i −0.244573 + 0.0878503i
\(713\) 35.0186i 1.31146i
\(714\) 0 0
\(715\) 1.91026i 0.0714396i
\(716\) −12.0165 + 39.7309i −0.449079 + 1.48481i
\(717\) 11.4075 + 3.60838i 0.426019 + 0.134758i
\(718\) −4.09362 + 3.03864i −0.152772 + 0.113401i
\(719\) 27.4731 1.02457 0.512287 0.858814i \(-0.328798\pi\)
0.512287 + 0.858814i \(0.328798\pi\)
\(720\) −5.58651 + 2.17114i −0.208197 + 0.0809134i
\(721\) 0 0
\(722\) −14.5829 + 10.8247i −0.542719 + 0.402854i
\(723\) 13.3211 + 4.21369i 0.495416 + 0.156709i
\(724\) −3.72557 + 12.3180i −0.138460 + 0.457796i
\(725\) 30.0365i 1.11553i
\(726\) 20.9942 7.24241i 0.779169 0.268791i
\(727\) 45.7930i 1.69837i −0.528096 0.849185i \(-0.677094\pi\)
0.528096 0.849185i \(-0.322906\pi\)
\(728\) 0 0
\(729\) −7.13303 + 26.0407i −0.264186 + 0.964472i
\(730\) −4.19954 5.65756i −0.155432 0.209396i
\(731\) −20.5345 −0.759494
\(732\) −9.60183 + 14.0331i −0.354894 + 0.518679i
\(733\) −43.2932 −1.59907 −0.799535 0.600620i \(-0.794920\pi\)
−0.799535 + 0.600620i \(0.794920\pi\)
\(734\) −12.6661 17.0636i −0.467514 0.629828i
\(735\) 0 0
\(736\) 28.6091 1.46446i 1.05455 0.0539807i
\(737\) 14.9393i 0.550297i
\(738\) 0.629405 + 24.3632i 0.0231687 + 0.896822i
\(739\) 5.17590i 0.190399i 0.995458 + 0.0951993i \(0.0303488\pi\)
−0.995458 + 0.0951993i \(0.969651\pi\)
\(740\) −7.02111 2.12353i −0.258101 0.0780624i
\(741\) 3.56544 11.2717i 0.130980 0.414077i
\(742\) 0 0
\(743\) −49.5492 −1.81778 −0.908891 0.417034i \(-0.863070\pi\)
−0.908891 + 0.417034i \(0.863070\pi\)
\(744\) 33.8521 1.30348i 1.24108 0.0477879i
\(745\) 1.14568 0.0419744
\(746\) −3.01709 + 2.23955i −0.110464 + 0.0819958i
\(747\) −29.4917 20.7319i −1.07905 0.758541i
\(748\) −15.5011 4.68828i −0.566775 0.171420i
\(749\) 0 0
\(750\) 3.89023 + 11.2770i 0.142051 + 0.411777i
\(751\) 30.5879i 1.11617i −0.829784 0.558084i \(-0.811537\pi\)
0.829784 0.558084i \(-0.188463\pi\)
\(752\) 16.8609 + 11.2260i 0.614854 + 0.409371i
\(753\) −33.7006 10.6601i −1.22812 0.388476i
\(754\) −14.6591 19.7485i −0.533851 0.719197i
\(755\) −6.56086 −0.238774
\(756\) 0 0
\(757\) 46.4533 1.68837 0.844187 0.536049i \(-0.180084\pi\)
0.844187 + 0.536049i \(0.180084\pi\)
\(758\) 14.9322 + 20.1164i 0.542362 + 0.730662i
\(759\) −11.6284 3.67829i −0.422086 0.133513i
\(760\) −1.18509 3.29927i −0.0429878 0.119677i
\(761\) 39.4484i 1.43000i −0.699122 0.715002i \(-0.746426\pi\)
0.699122 0.715002i \(-0.253574\pi\)
\(762\) −1.20799 3.50172i −0.0437609 0.126854i
\(763\) 0 0
\(764\) 10.1520 33.5659i 0.367285 1.21437i
\(765\) 7.13828 + 5.01802i 0.258085 + 0.181427i
\(766\) 37.3846 27.7502i 1.35076 1.00265i
\(767\) −8.66898 −0.313019
\(768\) 2.48058 + 27.6016i 0.0895101 + 0.995986i
\(769\) 39.7256 1.43254 0.716270 0.697823i \(-0.245848\pi\)
0.716270 + 0.697823i \(0.245848\pi\)
\(770\) 0 0
\(771\) 14.2136 44.9346i 0.511891 1.61828i
\(772\) −1.26516 + 4.18305i −0.0455340 + 0.150551i
\(773\) 21.9318i 0.788833i 0.918932 + 0.394416i \(0.129053\pi\)
−0.918932 + 0.394416i \(0.870947\pi\)
\(774\) −0.386369 14.9557i −0.0138877 0.537571i
\(775\) 32.8506i 1.18003i
\(776\) 0.502967 + 1.40025i 0.0180554 + 0.0502660i
\(777\) 0 0
\(778\) 5.75054 + 7.74704i 0.206167 + 0.277745i
\(779\) −14.2548 −0.510733
\(780\) −3.92758 2.68735i −0.140630 0.0962227i
\(781\) −6.31598 −0.226004
\(782\) −24.8570 33.4870i −0.888885 1.19749i
\(783\) −26.1203 + 19.9277i −0.933464 + 0.712157i
\(784\) 0 0
\(785\) 4.20029i 0.149915i
\(786\) 15.3994 5.31237i 0.549280 0.189486i
\(787\) 5.04447i 0.179816i −0.995950 0.0899080i \(-0.971343\pi\)
0.995950 0.0899080i \(-0.0286573\pi\)
\(788\) −12.0165 3.63439i −0.428072 0.129470i
\(789\) 5.95319 + 1.88310i 0.211939 + 0.0670402i
\(790\) −1.20881 + 0.897287i −0.0430076 + 0.0319240i
\(791\) 0 0
\(792\) 3.12291 11.3780i 0.110968 0.404299i
\(793\) −13.5011 −0.479437
\(794\) 23.6698 17.5698i 0.840010 0.623529i
\(795\) −4.32609 1.36842i −0.153431 0.0485329i
\(796\) 1.65692 + 0.501133i 0.0587279 + 0.0177622i
\(797\) 28.3335i 1.00362i 0.864977 + 0.501812i \(0.167333\pi\)
−0.864977 + 0.501812i \(0.832667\pi\)
\(798\) 0 0
\(799\) 29.4894i 1.04326i
\(800\) 26.8379 1.37379i 0.948865 0.0485710i
\(801\) −4.22976 + 6.01695i −0.149451 + 0.212599i
\(802\) 3.22450 + 4.34401i 0.113861 + 0.153392i
\(803\) 13.8703 0.489471
\(804\) 30.7159 + 21.0166i 1.08327 + 0.741200i
\(805\) 0 0
\(806\) 16.0325 + 21.5987i 0.564721 + 0.760783i
\(807\) −13.6679 + 43.2095i −0.481134 + 1.52105i
\(808\) 42.8463 15.3903i 1.50733 0.541429i
\(809\) 20.2174i 0.710808i 0.934713 + 0.355404i \(0.115657\pi\)
−0.934713 + 0.355404i \(0.884343\pi\)
\(810\) −3.52042 + 5.29338i −0.123695 + 0.185991i
\(811\) 1.33368i 0.0468317i −0.999726 0.0234158i \(-0.992546\pi\)
0.999726 0.0234158i \(-0.00745418\pi\)
\(812\) 0 0
\(813\) −12.0468 + 38.0845i −0.422500 + 1.33568i
\(814\) 11.5947 8.60660i 0.406394 0.301661i
\(815\) −6.17331 −0.216242
\(816\) 31.4462 25.2754i 1.10084 0.884817i
\(817\) 8.75054 0.306142
\(818\) 4.39361 3.26133i 0.153619 0.114030i
\(819\) 0 0
\(820\) −1.66120 + 5.49251i −0.0580117 + 0.191807i
\(821\) 5.31136i 0.185368i 0.995696 + 0.0926838i \(0.0295446\pi\)
−0.995696 + 0.0926838i \(0.970455\pi\)
\(822\) 9.73885 + 28.2309i 0.339681 + 0.984666i
\(823\) 15.3007i 0.533349i 0.963787 + 0.266675i \(0.0859249\pi\)
−0.963787 + 0.266675i \(0.914075\pi\)
\(824\) −4.99543 + 1.79435i −0.174024 + 0.0625091i
\(825\) −10.9085 3.45056i −0.379786 0.120133i
\(826\) 0 0
\(827\) 0.288306 0.0100254 0.00501270 0.999987i \(-0.498404\pi\)
0.00501270 + 0.999987i \(0.498404\pi\)
\(828\) 23.9216 18.7340i 0.831334 0.651051i
\(829\) −41.1102 −1.42782 −0.713908 0.700239i \(-0.753077\pi\)
−0.713908 + 0.700239i \(0.753077\pi\)
\(830\) −5.05903 6.81545i −0.175601 0.236568i
\(831\) −33.5086 10.5994i −1.16240 0.367689i
\(832\) −16.9750 + 14.0013i −0.588504 + 0.485408i
\(833\) 0 0
\(834\) −0.0381700 0.110647i −0.00132172 0.00383139i
\(835\) 1.18148i 0.0408868i
\(836\) 6.60561 + 1.99786i 0.228460 + 0.0690974i
\(837\) 28.5676 21.7948i 0.987440 0.753337i
\(838\) 15.3452 11.3906i 0.530092 0.393481i
\(839\) 25.7705 0.889695 0.444848 0.895606i \(-0.353258\pi\)
0.444848 + 0.895606i \(0.353258\pi\)
\(840\) 0 0
\(841\) −10.9772 −0.378523
\(842\) −12.9255 + 9.59445i −0.445442 + 0.330647i
\(843\) −14.4507 + 45.6840i −0.497707 + 1.57344i
\(844\) −7.47397 2.26049i −0.257265 0.0778093i
\(845\) 2.71437i 0.0933771i
\(846\) 21.4778 0.554862i 0.738421 0.0190766i
\(847\) 0 0
\(848\) −11.6270 + 17.4631i −0.399271 + 0.599685i
\(849\) −9.07391 + 28.6860i −0.311416 + 0.984502i
\(850\) −23.3181 31.4138i −0.799805 1.07749i
\(851\) 37.1857 1.27471
\(852\) 8.88532 12.9859i 0.304406 0.444891i
\(853\) −51.4656 −1.76215 −0.881074 0.472978i \(-0.843179\pi\)
−0.881074 + 0.472978i \(0.843179\pi\)
\(854\) 0 0
\(855\) −3.04190 2.13838i −0.104031 0.0731309i
\(856\) −6.95935 19.3747i −0.237866 0.662213i
\(857\) 35.5762i 1.21526i 0.794220 + 0.607631i \(0.207880\pi\)
−0.794220 + 0.607631i \(0.792120\pi\)
\(858\) 8.85620 3.05513i 0.302346 0.104301i
\(859\) 51.3072i 1.75058i 0.483598 + 0.875290i \(0.339330\pi\)
−0.483598 + 0.875290i \(0.660670\pi\)
\(860\) 1.01975 3.37165i 0.0347732 0.114972i
\(861\) 0 0
\(862\) −29.4388 + 21.8521i −1.00269 + 0.744286i
\(863\) −11.7830 −0.401099 −0.200550 0.979684i \(-0.564273\pi\)
−0.200550 + 0.979684i \(0.564273\pi\)
\(864\) 19.0003 + 22.4274i 0.646404 + 0.762995i
\(865\) −4.77978 −0.162517
\(866\) −26.5522 + 19.7094i −0.902282 + 0.669753i
\(867\) −27.9263 8.83360i −0.948428 0.300005i
\(868\) 0 0
\(869\) 2.96357i 0.100532i
\(870\) −7.31257 + 2.52263i −0.247919 + 0.0855251i
\(871\) 29.5514i 1.00131i
\(872\) −1.76124 4.90327i −0.0596433 0.166046i
\(873\) 1.29102 + 0.907552i 0.0436944 + 0.0307160i
\(874\) 10.5925 + 14.2701i 0.358298 + 0.482694i
\(875\) 0 0
\(876\) −19.5127 + 28.5179i −0.659273 + 0.963531i
\(877\) 1.32863 0.0448646 0.0224323 0.999748i \(-0.492859\pi\)
0.0224323 + 0.999748i \(0.492859\pi\)
\(878\) 14.8969 + 20.0689i 0.502747 + 0.677294i
\(879\) 10.4302 32.9739i 0.351803 1.11218i
\(880\) 1.53958 2.31237i 0.0518993 0.0779501i
\(881\) 23.8258i 0.802713i −0.915922 0.401356i \(-0.868539\pi\)
0.915922 0.401356i \(-0.131461\pi\)
\(882\) 0 0
\(883\) 30.2235i 1.01710i −0.861032 0.508551i \(-0.830181\pi\)
0.861032 0.508551i \(-0.169819\pi\)
\(884\) 30.6626 + 9.27385i 1.03129 + 0.311913i
\(885\) −0.822304 + 2.59961i −0.0276414 + 0.0873850i
\(886\) 39.8993 29.6167i 1.34044 0.994994i
\(887\) −21.9111 −0.735704 −0.367852 0.929884i \(-0.619907\pi\)
−0.367852 + 0.929884i \(0.619907\pi\)
\(888\) 1.38415 + 35.9470i 0.0464489 + 1.20630i
\(889\) 0 0
\(890\) −1.39050 + 1.03215i −0.0466096 + 0.0345978i
\(891\) −4.23658 11.7756i −0.141931 0.394496i
\(892\) −44.9907 13.6074i −1.50640 0.455609i
\(893\) 12.5666i 0.420525i
\(894\) −1.83232 5.31151i −0.0612819 0.177643i
\(895\) 10.3660i 0.346496i
\(896\) 0 0
\(897\) 23.0021 + 7.27599i 0.768019 + 0.242938i
\(898\) 4.65906 + 6.27662i 0.155475 + 0.209453i
\(899\) 43.7227 1.45823
\(900\) 22.4406 17.5742i 0.748021 0.585805i
\(901\) 30.5426 1.01752
\(902\) −6.73281 9.07034i −0.224178 0.302009i
\(903\) 0 0
\(904\) 27.3452 9.82235i 0.909489 0.326687i
\(905\) 3.21383i 0.106831i
\(906\) 10.4930 + 30.4169i 0.348606 + 1.01053i
\(907\) 48.9638i 1.62581i −0.582393 0.812907i \(-0.697883\pi\)
0.582393 0.812907i \(-0.302117\pi\)
\(908\) 11.0981 36.6941i 0.368302 1.21774i
\(909\) 27.7702 39.5040i 0.921081 1.31026i
\(910\) 0 0
\(911\) 51.8251 1.71704 0.858522 0.512777i \(-0.171383\pi\)
0.858522 + 0.512777i \(0.171383\pi\)
\(912\) −13.4005 + 10.7708i −0.443734 + 0.356658i
\(913\) 16.7090 0.552987
\(914\) −27.1992 + 20.1896i −0.899669 + 0.667814i
\(915\) −1.28066 + 4.04864i −0.0423372 + 0.133844i
\(916\) 6.64461 21.9694i 0.219544 0.725889i
\(917\) 0 0
\(918\) 11.8477 41.1194i 0.391033 1.35714i
\(919\) 50.5037i 1.66596i −0.553301 0.832981i \(-0.686632\pi\)
0.553301 0.832981i \(-0.313368\pi\)
\(920\) 6.73281 2.41841i 0.221974 0.0797327i
\(921\) −7.39300 + 23.3721i −0.243608 + 0.770135i
\(922\) −2.52603 3.40303i −0.0831904 0.112073i
\(923\) 12.4936 0.411232
\(924\) 0 0
\(925\) 34.8836 1.14696
\(926\) 18.8940 + 25.4538i 0.620897 + 0.836463i
\(927\) −3.23772 + 4.60575i −0.106341 + 0.151273i
\(928\) 1.82846 + 35.7201i 0.0600221 + 1.17257i
\(929\) 1.23566i 0.0405407i −0.999795 0.0202703i \(-0.993547\pi\)
0.999795 0.0202703i \(-0.00645269\pi\)
\(930\) 7.99770 2.75898i 0.262255 0.0904705i
\(931\) 0 0
\(932\) 38.7034 + 11.7058i 1.26777 + 0.383436i
\(933\) −40.5500 12.8267i −1.32755 0.419927i
\(934\) −13.6963 + 10.1666i −0.448158 + 0.332662i
\(935\) −4.04430 −0.132263
\(936\) −6.17741 + 22.5067i −0.201915 + 0.735655i
\(937\) −29.4139 −0.960909 −0.480455 0.877020i \(-0.659528\pi\)
−0.480455 + 0.877020i \(0.659528\pi\)
\(938\) 0 0
\(939\) 0.0859759 + 0.0271957i 0.00280572 + 0.000887499i
\(940\) 4.84201 + 1.46446i 0.157929 + 0.0477654i
\(941\) 44.8636i 1.46251i −0.682103 0.731256i \(-0.738934\pi\)
0.682103 0.731256i \(-0.261066\pi\)
\(942\) −19.4731 + 6.71765i −0.634467 + 0.218873i
\(943\) 29.0898i 0.947295i
\(944\) 10.4938 + 6.98680i 0.341545 + 0.227401i
\(945\) 0 0
\(946\) 4.13303 + 5.56796i 0.134376 + 0.181030i
\(947\) 17.5576 0.570547 0.285273 0.958446i \(-0.407916\pi\)
0.285273 + 0.958446i \(0.407916\pi\)
\(948\) 6.09322 + 4.16915i 0.197899 + 0.135408i
\(949\) −27.4367 −0.890633
\(950\) 9.93676 + 13.3867i 0.322391 + 0.434321i
\(951\) 3.53984 11.1908i 0.114787 0.362886i
\(952\) 0 0
\(953\) 37.1546i 1.20356i 0.798663 + 0.601778i \(0.205541\pi\)
−0.798663 + 0.601778i \(0.794459\pi\)
\(954\) 0.574679 + 22.2449i 0.0186059 + 0.720204i
\(955\) 8.75750i 0.283386i
\(956\) 3.99954 13.2239i 0.129354 0.427691i
\(957\) 4.59255 14.5188i 0.148456 0.469325i
\(958\) −15.2245 + 11.3010i −0.491881 + 0.365118i
\(959\) 0 0
\(960\) 2.58846 + 6.41850i 0.0835422 + 0.207156i
\(961\) −16.8192 −0.542555
\(962\) −22.9354 + 17.0247i −0.739466 + 0.548897i
\(963\) −17.8633 12.5574i −0.575637 0.404658i
\(964\) 4.67047 15.4422i 0.150426 0.497360i
\(965\) 1.09138i 0.0351326i
\(966\) 0 0
\(967\) 53.9045i 1.73345i 0.498786 + 0.866725i \(0.333779\pi\)
−0.498786 + 0.866725i \(0.666221\pi\)
\(968\) −8.66898 24.1343i −0.278632 0.775704i
\(969\) 23.8639 + 7.54857i 0.766618 + 0.242495i
\(970\) 0.221462 + 0.298350i 0.00711071 + 0.00957945i
\(971\) 38.3565 1.23092 0.615460 0.788168i \(-0.288970\pi\)
0.615460 + 0.788168i \(0.288970\pi\)
\(972\) 30.1711 + 7.85526i 0.967738 + 0.251957i
\(973\) 0 0
\(974\) −10.2906 13.8633i −0.329731 0.444208i
\(975\) 21.5781 + 6.82553i 0.691052 + 0.218592i
\(976\) 16.3431 + 10.8812i 0.523129 + 0.348300i
\(977\) 18.0025i 0.575952i −0.957638 0.287976i \(-0.907018\pi\)
0.957638 0.287976i \(-0.0929824\pi\)
\(978\) 9.87316 + 28.6202i 0.315709 + 0.915174i
\(979\) 3.40899i 0.108952i
\(980\) 0 0
\(981\) −4.52078 3.17799i −0.144337 0.101465i
\(982\) 45.3067 33.6306i 1.44580 1.07320i
\(983\) −13.7569 −0.438777 −0.219388 0.975638i \(-0.570406\pi\)
−0.219388 + 0.975638i \(0.570406\pi\)
\(984\) 28.1207 1.08279i 0.896457 0.0345182i
\(985\) −3.13517 −0.0998948
\(986\) 41.8104 31.0354i 1.33151 0.988368i
\(987\) 0 0
\(988\) −13.0665 3.95195i −0.415701 0.125728i
\(989\) 17.8572i 0.567826i
\(990\) −0.0760961 2.94555i −0.00241849 0.0936157i
\(991\) 1.85652i 0.0589742i −0.999565 0.0294871i \(-0.990613\pi\)
0.999565 0.0294871i \(-0.00938739\pi\)
\(992\) −1.99977 39.0668i −0.0634928 1.24037i
\(993\) −9.34619 + 29.5468i −0.296593 + 0.937640i
\(994\) 0 0
\(995\) 0.432298 0.0137048
\(996\) −23.5062 + 34.3544i −0.744823 + 1.08856i
\(997\) 60.3495 1.91129 0.955644 0.294524i \(-0.0951612\pi\)
0.955644 + 0.294524i \(0.0951612\pi\)
\(998\) −7.14383 9.62407i −0.226134 0.304644i
\(999\) 23.1435 + 30.3355i 0.732228 + 0.959772i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 588.2.e.e.491.4 12
3.2 odd 2 inner 588.2.e.e.491.9 12
4.3 odd 2 inner 588.2.e.e.491.10 12
7.2 even 3 84.2.n.a.11.11 yes 24
7.3 odd 6 588.2.n.e.275.6 24
7.4 even 3 84.2.n.a.23.6 yes 24
7.5 odd 6 588.2.n.e.263.11 24
7.6 odd 2 588.2.e.d.491.4 12
12.11 even 2 inner 588.2.e.e.491.3 12
21.2 odd 6 84.2.n.a.11.2 24
21.5 even 6 588.2.n.e.263.2 24
21.11 odd 6 84.2.n.a.23.7 yes 24
21.17 even 6 588.2.n.e.275.7 24
21.20 even 2 588.2.e.d.491.9 12
28.3 even 6 588.2.n.e.275.2 24
28.11 odd 6 84.2.n.a.23.2 yes 24
28.19 even 6 588.2.n.e.263.7 24
28.23 odd 6 84.2.n.a.11.7 yes 24
28.27 even 2 588.2.e.d.491.10 12
84.11 even 6 84.2.n.a.23.11 yes 24
84.23 even 6 84.2.n.a.11.6 yes 24
84.47 odd 6 588.2.n.e.263.6 24
84.59 odd 6 588.2.n.e.275.11 24
84.83 odd 2 588.2.e.d.491.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.n.a.11.2 24 21.2 odd 6
84.2.n.a.11.6 yes 24 84.23 even 6
84.2.n.a.11.7 yes 24 28.23 odd 6
84.2.n.a.11.11 yes 24 7.2 even 3
84.2.n.a.23.2 yes 24 28.11 odd 6
84.2.n.a.23.6 yes 24 7.4 even 3
84.2.n.a.23.7 yes 24 21.11 odd 6
84.2.n.a.23.11 yes 24 84.11 even 6
588.2.e.d.491.3 12 84.83 odd 2
588.2.e.d.491.4 12 7.6 odd 2
588.2.e.d.491.9 12 21.20 even 2
588.2.e.d.491.10 12 28.27 even 2
588.2.e.e.491.3 12 12.11 even 2 inner
588.2.e.e.491.4 12 1.1 even 1 trivial
588.2.e.e.491.9 12 3.2 odd 2 inner
588.2.e.e.491.10 12 4.3 odd 2 inner
588.2.n.e.263.2 24 21.5 even 6
588.2.n.e.263.6 24 84.47 odd 6
588.2.n.e.263.7 24 28.19 even 6
588.2.n.e.263.11 24 7.5 odd 6
588.2.n.e.275.2 24 28.3 even 6
588.2.n.e.275.6 24 7.3 odd 6
588.2.n.e.275.7 24 21.17 even 6
588.2.n.e.275.11 24 84.59 odd 6