Properties

Label 567.2.w.a.37.14
Level $567$
Weight $2$
Character 567.37
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (of order \(9\), degree \(6\), not 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.14
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.162149 + 0.919594i) q^{2} +(1.06003 - 0.385818i) q^{4} +(-0.575026 + 3.26114i) q^{5} +(1.06445 + 2.42218i) q^{7} +(1.46046 + 2.52959i) q^{8} +O(q^{10})\) \(q+(0.162149 + 0.919594i) q^{2} +(1.06003 - 0.385818i) q^{4} +(-0.575026 + 3.26114i) q^{5} +(1.06445 + 2.42218i) q^{7} +(1.46046 + 2.52959i) q^{8} -3.09216 q^{10} +(-0.163478 - 0.927130i) q^{11} +(-1.92659 - 1.61660i) q^{13} +(-2.05482 + 1.37161i) q^{14} +(-0.361099 + 0.302998i) q^{16} -2.09645 q^{17} +1.93419 q^{19} +(0.648661 + 3.67874i) q^{20} +(0.826075 - 0.300667i) q^{22} +(-3.45552 - 2.89952i) q^{23} +(-5.60589 - 2.04038i) q^{25} +(1.17422 - 2.03381i) q^{26} +(2.06286 + 2.15689i) q^{28} +(5.49145 - 4.60787i) q^{29} +(-8.64990 + 3.14831i) q^{31} +(4.13791 + 3.47212i) q^{32} +(-0.339938 - 1.92788i) q^{34} +(-8.51114 + 2.07848i) q^{35} +(1.95591 + 3.38773i) q^{37} +(0.313628 + 1.77867i) q^{38} +(-9.08913 + 3.30817i) q^{40} +(6.70881 + 5.62936i) q^{41} +(9.55542 + 3.47789i) q^{43} +(-0.530994 - 0.919708i) q^{44} +(2.10607 - 3.64783i) q^{46} +(10.2711 + 3.73837i) q^{47} +(-4.73391 + 5.15656i) q^{49} +(0.967327 - 5.48599i) q^{50} +(-2.66595 - 0.970325i) q^{52} +(-2.04238 - 3.53751i) q^{53} +3.11750 q^{55} +(-4.57254 + 6.23010i) q^{56} +(5.12781 + 4.30274i) q^{58} +(-6.09905 - 5.11771i) q^{59} +(-5.03423 - 1.83231i) q^{61} +(-4.29774 - 7.44390i) q^{62} +(-2.99336 + 5.18466i) q^{64} +(6.37979 - 5.35328i) q^{65} +(-0.175689 + 0.996384i) q^{67} +(-2.22229 + 0.808848i) q^{68} +(-3.29144 - 7.48977i) q^{70} +(1.14666 - 1.98608i) q^{71} +(8.29219 - 14.3625i) q^{73} +(-2.79818 + 2.34796i) q^{74} +(2.05029 - 0.746246i) q^{76} +(2.07166 - 1.38285i) q^{77} +(-2.47430 - 14.0324i) q^{79} +(-0.780475 - 1.35182i) q^{80} +(-4.08889 + 7.08217i) q^{82} +(-3.77228 + 3.16532i) q^{83} +(1.20552 - 6.83682i) q^{85} +(-1.64884 + 9.35104i) q^{86} +(2.10650 - 1.76757i) q^{88} +1.69093 q^{89} +(1.86495 - 6.38733i) q^{91} +(-4.78163 - 1.74037i) q^{92} +(-1.77233 + 10.0514i) q^{94} +(-1.11221 + 6.30766i) q^{95} +(11.8249 + 4.30390i) q^{97} +(-5.50954 - 3.51714i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.162149 + 0.919594i 0.114657 + 0.650251i 0.986920 + 0.161213i \(0.0515407\pi\)
−0.872263 + 0.489037i \(0.837348\pi\)
\(3\) 0 0
\(4\) 1.06003 0.385818i 0.530013 0.192909i
\(5\) −0.575026 + 3.26114i −0.257160 + 1.45842i 0.533308 + 0.845921i \(0.320949\pi\)
−0.790468 + 0.612503i \(0.790163\pi\)
\(6\) 0 0
\(7\) 1.06445 + 2.42218i 0.402323 + 0.915498i
\(8\) 1.46046 + 2.52959i 0.516350 + 0.894344i
\(9\) 0 0
\(10\) −3.09216 −0.977827
\(11\) −0.163478 0.927130i −0.0492905 0.279540i 0.950194 0.311660i \(-0.100885\pi\)
−0.999484 + 0.0321203i \(0.989774\pi\)
\(12\) 0 0
\(13\) −1.92659 1.61660i −0.534340 0.448364i 0.335257 0.942127i \(-0.391177\pi\)
−0.869597 + 0.493762i \(0.835621\pi\)
\(14\) −2.05482 + 1.37161i −0.549174 + 0.366579i
\(15\) 0 0
\(16\) −0.361099 + 0.302998i −0.0902746 + 0.0757494i
\(17\) −2.09645 −0.508464 −0.254232 0.967143i \(-0.581823\pi\)
−0.254232 + 0.967143i \(0.581823\pi\)
\(18\) 0 0
\(19\) 1.93419 0.443734 0.221867 0.975077i \(-0.428785\pi\)
0.221867 + 0.975077i \(0.428785\pi\)
\(20\) 0.648661 + 3.67874i 0.145045 + 0.822592i
\(21\) 0 0
\(22\) 0.826075 0.300667i 0.176120 0.0641023i
\(23\) −3.45552 2.89952i −0.720526 0.604593i 0.207005 0.978340i \(-0.433628\pi\)
−0.927531 + 0.373747i \(0.878073\pi\)
\(24\) 0 0
\(25\) −5.60589 2.04038i −1.12118 0.408075i
\(26\) 1.17422 2.03381i 0.230284 0.398863i
\(27\) 0 0
\(28\) 2.06286 + 2.15689i 0.389844 + 0.407614i
\(29\) 5.49145 4.60787i 1.01974 0.855661i 0.0301424 0.999546i \(-0.490404\pi\)
0.989594 + 0.143885i \(0.0459595\pi\)
\(30\) 0 0
\(31\) −8.64990 + 3.14831i −1.55357 + 0.565452i −0.969251 0.246073i \(-0.920860\pi\)
−0.584317 + 0.811526i \(0.698637\pi\)
\(32\) 4.13791 + 3.47212i 0.731487 + 0.613790i
\(33\) 0 0
\(34\) −0.339938 1.92788i −0.0582989 0.330629i
\(35\) −8.51114 + 2.07848i −1.43865 + 0.351328i
\(36\) 0 0
\(37\) 1.95591 + 3.38773i 0.321549 + 0.556939i 0.980808 0.194977i \(-0.0624632\pi\)
−0.659259 + 0.751916i \(0.729130\pi\)
\(38\) 0.313628 + 1.77867i 0.0508771 + 0.288539i
\(39\) 0 0
\(40\) −9.08913 + 3.30817i −1.43712 + 0.523068i
\(41\) 6.70881 + 5.62936i 1.04774 + 0.879158i 0.992854 0.119335i \(-0.0380761\pi\)
0.0548856 + 0.998493i \(0.482521\pi\)
\(42\) 0 0
\(43\) 9.55542 + 3.47789i 1.45719 + 0.530373i 0.944589 0.328255i \(-0.106460\pi\)
0.512599 + 0.858628i \(0.328683\pi\)
\(44\) −0.530994 0.919708i −0.0800503 0.138651i
\(45\) 0 0
\(46\) 2.10607 3.64783i 0.310524 0.537843i
\(47\) 10.2711 + 3.73837i 1.49819 + 0.545298i 0.955592 0.294693i \(-0.0952175\pi\)
0.542601 + 0.839991i \(0.317440\pi\)
\(48\) 0 0
\(49\) −4.73391 + 5.15656i −0.676273 + 0.736651i
\(50\) 0.967327 5.48599i 0.136801 0.775836i
\(51\) 0 0
\(52\) −2.66595 0.970325i −0.369700 0.134560i
\(53\) −2.04238 3.53751i −0.280543 0.485914i 0.690976 0.722878i \(-0.257181\pi\)
−0.971519 + 0.236964i \(0.923848\pi\)
\(54\) 0 0
\(55\) 3.11750 0.420364
\(56\) −4.57254 + 6.23010i −0.611031 + 0.832532i
\(57\) 0 0
\(58\) 5.12781 + 4.30274i 0.673314 + 0.564977i
\(59\) −6.09905 5.11771i −0.794029 0.666269i 0.152710 0.988271i \(-0.451200\pi\)
−0.946739 + 0.322002i \(0.895644\pi\)
\(60\) 0 0
\(61\) −5.03423 1.83231i −0.644567 0.234603i −0.00100763 0.999999i \(-0.500321\pi\)
−0.643559 + 0.765396i \(0.722543\pi\)
\(62\) −4.29774 7.44390i −0.545813 0.945376i
\(63\) 0 0
\(64\) −2.99336 + 5.18466i −0.374170 + 0.648082i
\(65\) 6.37979 5.35328i 0.791316 0.663993i
\(66\) 0 0
\(67\) −0.175689 + 0.996384i −0.0214639 + 0.121728i −0.993657 0.112452i \(-0.964129\pi\)
0.972193 + 0.234180i \(0.0752405\pi\)
\(68\) −2.22229 + 0.808848i −0.269493 + 0.0980873i
\(69\) 0 0
\(70\) −3.29144 7.48977i −0.393402 0.895198i
\(71\) 1.14666 1.98608i 0.136084 0.235704i −0.789927 0.613201i \(-0.789882\pi\)
0.926011 + 0.377497i \(0.123215\pi\)
\(72\) 0 0
\(73\) 8.29219 14.3625i 0.970527 1.68100i 0.276558 0.960997i \(-0.410806\pi\)
0.693969 0.720005i \(-0.255860\pi\)
\(74\) −2.79818 + 2.34796i −0.325282 + 0.272944i
\(75\) 0 0
\(76\) 2.05029 0.746246i 0.235185 0.0856002i
\(77\) 2.07166 1.38285i 0.236088 0.157591i
\(78\) 0 0
\(79\) −2.47430 14.0324i −0.278380 1.57877i −0.728016 0.685560i \(-0.759557\pi\)
0.449636 0.893212i \(-0.351554\pi\)
\(80\) −0.780475 1.35182i −0.0872598 0.151138i
\(81\) 0 0
\(82\) −4.08889 + 7.08217i −0.451543 + 0.782095i
\(83\) −3.77228 + 3.16532i −0.414061 + 0.347439i −0.825898 0.563819i \(-0.809332\pi\)
0.411837 + 0.911257i \(0.364887\pi\)
\(84\) 0 0
\(85\) 1.20552 6.83682i 0.130757 0.741557i
\(86\) −1.64884 + 9.35104i −0.177799 + 1.00835i
\(87\) 0 0
\(88\) 2.10650 1.76757i 0.224554 0.188423i
\(89\) 1.69093 0.179238 0.0896191 0.995976i \(-0.471435\pi\)
0.0896191 + 0.995976i \(0.471435\pi\)
\(90\) 0 0
\(91\) 1.86495 6.38733i 0.195500 0.669574i
\(92\) −4.78163 1.74037i −0.498519 0.181446i
\(93\) 0 0
\(94\) −1.77233 + 10.0514i −0.182802 + 1.03672i
\(95\) −1.11221 + 6.30766i −0.114110 + 0.647153i
\(96\) 0 0
\(97\) 11.8249 + 4.30390i 1.20063 + 0.436995i 0.863446 0.504442i \(-0.168302\pi\)
0.337189 + 0.941437i \(0.390524\pi\)
\(98\) −5.50954 3.51714i −0.556547 0.355285i
\(99\) 0 0
\(100\) −6.72960 −0.672960
\(101\) 2.96186 2.48529i 0.294716 0.247296i −0.483425 0.875386i \(-0.660607\pi\)
0.778141 + 0.628090i \(0.216163\pi\)
\(102\) 0 0
\(103\) −0.923416 + 5.23695i −0.0909868 + 0.516012i 0.904917 + 0.425589i \(0.139933\pi\)
−0.995903 + 0.0904231i \(0.971178\pi\)
\(104\) 1.27563 7.23445i 0.125086 0.709396i
\(105\) 0 0
\(106\) 2.92190 2.45177i 0.283800 0.238137i
\(107\) 4.21924 7.30793i 0.407889 0.706484i −0.586764 0.809758i \(-0.699598\pi\)
0.994653 + 0.103274i \(0.0329317\pi\)
\(108\) 0 0
\(109\) 2.89902 + 5.02125i 0.277676 + 0.480949i 0.970807 0.239863i \(-0.0771025\pi\)
−0.693131 + 0.720812i \(0.743769\pi\)
\(110\) 0.505500 + 2.86683i 0.0481975 + 0.273342i
\(111\) 0 0
\(112\) −1.11828 0.552121i −0.105668 0.0521705i
\(113\) −7.46610 + 2.71744i −0.702352 + 0.255635i −0.668415 0.743789i \(-0.733027\pi\)
−0.0339371 + 0.999424i \(0.510805\pi\)
\(114\) 0 0
\(115\) 11.4428 9.60161i 1.06704 0.895355i
\(116\) 4.04328 7.00316i 0.375409 0.650227i
\(117\) 0 0
\(118\) 3.71726 6.43848i 0.342201 0.592710i
\(119\) −2.23156 5.07799i −0.204567 0.465498i
\(120\) 0 0
\(121\) 9.50377 3.45909i 0.863979 0.314463i
\(122\) 0.868684 4.92655i 0.0786469 0.446029i
\(123\) 0 0
\(124\) −7.95444 + 6.67457i −0.714330 + 0.599394i
\(125\) 1.59887 2.76933i 0.143007 0.247696i
\(126\) 0 0
\(127\) 4.07469 + 7.05757i 0.361570 + 0.626258i 0.988219 0.153043i \(-0.0489074\pi\)
−0.626649 + 0.779302i \(0.715574\pi\)
\(128\) 4.89866 + 1.78297i 0.432984 + 0.157593i
\(129\) 0 0
\(130\) 5.95732 + 4.99879i 0.522492 + 0.438423i
\(131\) −1.11560 0.936099i −0.0974703 0.0817873i 0.592750 0.805386i \(-0.298042\pi\)
−0.690221 + 0.723599i \(0.742487\pi\)
\(132\) 0 0
\(133\) 2.05884 + 4.68496i 0.178524 + 0.406238i
\(134\) −0.944756 −0.0816145
\(135\) 0 0
\(136\) −3.06178 5.30316i −0.262545 0.454742i
\(137\) 1.26758 + 0.461363i 0.108297 + 0.0394169i 0.395600 0.918423i \(-0.370537\pi\)
−0.287303 + 0.957840i \(0.592759\pi\)
\(138\) 0 0
\(139\) 2.03091 11.5179i 0.172260 0.976933i −0.769000 0.639249i \(-0.779245\pi\)
0.941259 0.337684i \(-0.109644\pi\)
\(140\) −8.22011 + 5.48699i −0.694726 + 0.463736i
\(141\) 0 0
\(142\) 2.01231 + 0.732423i 0.168870 + 0.0614635i
\(143\) −1.18384 + 2.05048i −0.0989980 + 0.171469i
\(144\) 0 0
\(145\) 11.8692 + 20.5580i 0.985682 + 1.70725i
\(146\) 14.5522 + 5.29658i 1.20435 + 0.438348i
\(147\) 0 0
\(148\) 3.38035 + 2.83645i 0.277863 + 0.233155i
\(149\) −2.77336 + 1.00942i −0.227203 + 0.0826951i −0.453113 0.891453i \(-0.649687\pi\)
0.225910 + 0.974148i \(0.427464\pi\)
\(150\) 0 0
\(151\) −2.81725 15.9774i −0.229264 1.30022i −0.854363 0.519677i \(-0.826052\pi\)
0.625098 0.780546i \(-0.285059\pi\)
\(152\) 2.82481 + 4.89271i 0.229122 + 0.396851i
\(153\) 0 0
\(154\) 1.60758 + 1.68086i 0.129543 + 0.135447i
\(155\) −5.29313 30.0189i −0.425155 2.41117i
\(156\) 0 0
\(157\) 1.55569 + 1.30538i 0.124158 + 0.104181i 0.702752 0.711434i \(-0.251954\pi\)
−0.578595 + 0.815615i \(0.696399\pi\)
\(158\) 12.5029 4.55069i 0.994680 0.362034i
\(159\) 0 0
\(160\) −13.7025 + 11.4977i −1.08328 + 0.908976i
\(161\) 3.34496 11.4563i 0.263620 0.902881i
\(162\) 0 0
\(163\) 6.60942 11.4478i 0.517690 0.896665i −0.482099 0.876117i \(-0.660126\pi\)
0.999789 0.0205480i \(-0.00654108\pi\)
\(164\) 9.28341 + 3.37889i 0.724913 + 0.263847i
\(165\) 0 0
\(166\) −3.52248 2.95571i −0.273397 0.229407i
\(167\) −12.3823 + 4.50678i −0.958168 + 0.348745i −0.773316 0.634021i \(-0.781403\pi\)
−0.184853 + 0.982766i \(0.559181\pi\)
\(168\) 0 0
\(169\) −1.15908 6.57345i −0.0891598 0.505650i
\(170\) 6.48257 0.497190
\(171\) 0 0
\(172\) 11.4708 0.874642
\(173\) −7.61204 + 6.38726i −0.578733 + 0.485615i −0.884531 0.466482i \(-0.845521\pi\)
0.305798 + 0.952096i \(0.401077\pi\)
\(174\) 0 0
\(175\) −1.02500 15.7503i −0.0774830 1.19061i
\(176\) 0.339950 + 0.285252i 0.0256247 + 0.0215017i
\(177\) 0 0
\(178\) 0.274183 + 1.55497i 0.0205509 + 0.116550i
\(179\) 3.18668 0.238184 0.119092 0.992883i \(-0.462002\pi\)
0.119092 + 0.992883i \(0.462002\pi\)
\(180\) 0 0
\(181\) 8.86337 + 15.3518i 0.658809 + 1.14109i 0.980924 + 0.194390i \(0.0622729\pi\)
−0.322115 + 0.946701i \(0.604394\pi\)
\(182\) 6.17615 + 0.679294i 0.457806 + 0.0503526i
\(183\) 0 0
\(184\) 2.28796 12.9757i 0.168671 0.956579i
\(185\) −12.1725 + 4.43044i −0.894943 + 0.325733i
\(186\) 0 0
\(187\) 0.342724 + 1.94368i 0.0250625 + 0.142136i
\(188\) 12.3299 0.899254
\(189\) 0 0
\(190\) −5.98083 −0.433895
\(191\) −1.78703 10.1348i −0.129305 0.733326i −0.978657 0.205500i \(-0.934118\pi\)
0.849352 0.527827i \(-0.176993\pi\)
\(192\) 0 0
\(193\) 2.19199 0.797818i 0.157783 0.0574282i −0.261921 0.965089i \(-0.584356\pi\)
0.419704 + 0.907661i \(0.362134\pi\)
\(194\) −2.04045 + 11.5720i −0.146496 + 0.830818i
\(195\) 0 0
\(196\) −3.02858 + 7.29251i −0.216327 + 0.520893i
\(197\) 12.3597 + 21.4077i 0.880596 + 1.52524i 0.850680 + 0.525684i \(0.176191\pi\)
0.0299156 + 0.999552i \(0.490476\pi\)
\(198\) 0 0
\(199\) −1.13809 −0.0806771 −0.0403386 0.999186i \(-0.512844\pi\)
−0.0403386 + 0.999186i \(0.512844\pi\)
\(200\) −3.02585 17.1605i −0.213960 1.21343i
\(201\) 0 0
\(202\) 2.76572 + 2.32072i 0.194596 + 0.163285i
\(203\) 17.0065 + 8.39645i 1.19362 + 0.589315i
\(204\) 0 0
\(205\) −22.2158 + 18.6413i −1.55162 + 1.30197i
\(206\) −4.96560 −0.345970
\(207\) 0 0
\(208\) 1.18551 0.0822006
\(209\) −0.316198 1.79325i −0.0218719 0.124042i
\(210\) 0 0
\(211\) −14.8216 + 5.39463i −1.02036 + 0.371382i −0.797404 0.603446i \(-0.793794\pi\)
−0.222959 + 0.974828i \(0.571572\pi\)
\(212\) −3.52981 2.96186i −0.242428 0.203422i
\(213\) 0 0
\(214\) 7.40447 + 2.69501i 0.506159 + 0.184227i
\(215\) −16.8365 + 29.1617i −1.14824 + 1.98881i
\(216\) 0 0
\(217\) −16.8331 17.6004i −1.14271 1.19479i
\(218\) −4.14744 + 3.48011i −0.280900 + 0.235703i
\(219\) 0 0
\(220\) 3.30463 1.20279i 0.222798 0.0810919i
\(221\) 4.03900 + 3.38913i 0.271693 + 0.227977i
\(222\) 0 0
\(223\) −2.74368 15.5602i −0.183730 1.04199i −0.927576 0.373635i \(-0.878111\pi\)
0.743846 0.668352i \(-0.233000\pi\)
\(224\) −4.00552 + 13.7187i −0.267630 + 0.916616i
\(225\) 0 0
\(226\) −3.70956 6.42515i −0.246756 0.427395i
\(227\) 2.55088 + 14.4667i 0.169308 + 0.960191i 0.944511 + 0.328479i \(0.106536\pi\)
−0.775204 + 0.631711i \(0.782353\pi\)
\(228\) 0 0
\(229\) −8.17259 + 2.97458i −0.540060 + 0.196566i −0.597625 0.801776i \(-0.703889\pi\)
0.0575646 + 0.998342i \(0.481666\pi\)
\(230\) 10.6850 + 8.96579i 0.704549 + 0.591187i
\(231\) 0 0
\(232\) 19.6760 + 7.16150i 1.29180 + 0.470175i
\(233\) −6.13981 10.6345i −0.402233 0.696687i 0.591762 0.806112i \(-0.298432\pi\)
−0.993995 + 0.109425i \(0.965099\pi\)
\(234\) 0 0
\(235\) −18.0975 + 31.3458i −1.18055 + 2.04477i
\(236\) −8.43965 3.07178i −0.549374 0.199956i
\(237\) 0 0
\(238\) 4.30784 2.87552i 0.279236 0.186392i
\(239\) 4.39857 24.9455i 0.284520 1.61359i −0.422475 0.906375i \(-0.638839\pi\)
0.706995 0.707218i \(-0.250050\pi\)
\(240\) 0 0
\(241\) −14.1976 5.16752i −0.914550 0.332869i −0.158482 0.987362i \(-0.550660\pi\)
−0.756068 + 0.654493i \(0.772882\pi\)
\(242\) 4.72199 + 8.17872i 0.303541 + 0.525748i
\(243\) 0 0
\(244\) −6.04335 −0.386886
\(245\) −14.0941 18.4031i −0.900440 1.17573i
\(246\) 0 0
\(247\) −3.72639 3.12682i −0.237105 0.198955i
\(248\) −20.5967 17.2827i −1.30789 1.09745i
\(249\) 0 0
\(250\) 2.80591 + 1.02127i 0.177461 + 0.0645906i
\(251\) −9.55450 16.5489i −0.603075 1.04456i −0.992353 0.123435i \(-0.960609\pi\)
0.389278 0.921120i \(-0.372725\pi\)
\(252\) 0 0
\(253\) −2.12333 + 3.67772i −0.133493 + 0.231216i
\(254\) −5.82939 + 4.89144i −0.365768 + 0.306916i
\(255\) 0 0
\(256\) −2.92446 + 16.5854i −0.182779 + 1.03659i
\(257\) 27.3779 9.96475i 1.70779 0.621584i 0.711114 0.703076i \(-0.248191\pi\)
0.996674 + 0.0814921i \(0.0259685\pi\)
\(258\) 0 0
\(259\) −6.12373 + 8.34361i −0.380510 + 0.518446i
\(260\) 4.69735 8.13605i 0.291317 0.504576i
\(261\) 0 0
\(262\) 0.679937 1.17769i 0.0420066 0.0727576i
\(263\) −13.5286 + 11.3518i −0.834208 + 0.699984i −0.956253 0.292541i \(-0.905499\pi\)
0.122045 + 0.992525i \(0.461055\pi\)
\(264\) 0 0
\(265\) 12.7107 4.62633i 0.780814 0.284193i
\(266\) −3.97442 + 2.65296i −0.243687 + 0.162663i
\(267\) 0 0
\(268\) 0.198187 + 1.12398i 0.0121062 + 0.0686578i
\(269\) −0.462202 0.800557i −0.0281809 0.0488108i 0.851591 0.524207i \(-0.175638\pi\)
−0.879772 + 0.475396i \(0.842305\pi\)
\(270\) 0 0
\(271\) −1.95927 + 3.39355i −0.119017 + 0.206143i −0.919378 0.393374i \(-0.871308\pi\)
0.800361 + 0.599518i \(0.204641\pi\)
\(272\) 0.757026 0.635220i 0.0459014 0.0385159i
\(273\) 0 0
\(274\) −0.218729 + 1.24047i −0.0132139 + 0.0749397i
\(275\) −0.975255 + 5.53095i −0.0588101 + 0.333529i
\(276\) 0 0
\(277\) −18.9191 + 15.8750i −1.13674 + 0.953836i −0.999327 0.0366777i \(-0.988323\pi\)
−0.137411 + 0.990514i \(0.543878\pi\)
\(278\) 10.9211 0.655002
\(279\) 0 0
\(280\) −17.6879 18.4941i −1.05705 1.10524i
\(281\) −2.20028 0.800835i −0.131257 0.0477738i 0.275556 0.961285i \(-0.411138\pi\)
−0.406814 + 0.913511i \(0.633360\pi\)
\(282\) 0 0
\(283\) 1.89733 10.7603i 0.112785 0.639633i −0.875039 0.484053i \(-0.839164\pi\)
0.987823 0.155580i \(-0.0497247\pi\)
\(284\) 0.449227 2.54769i 0.0266567 0.151178i
\(285\) 0 0
\(286\) −2.07756 0.756172i −0.122849 0.0447134i
\(287\) −6.49416 + 22.2421i −0.383338 + 1.31291i
\(288\) 0 0
\(289\) −12.6049 −0.741464
\(290\) −16.9804 + 14.2483i −0.997126 + 0.836688i
\(291\) 0 0
\(292\) 3.24863 18.4239i 0.190111 1.07818i
\(293\) 0.0827719 0.469423i 0.00483559 0.0274240i −0.982294 0.187343i \(-0.940012\pi\)
0.987130 + 0.159919i \(0.0511234\pi\)
\(294\) 0 0
\(295\) 20.1967 16.9470i 1.17590 0.986693i
\(296\) −5.71303 + 9.89526i −0.332063 + 0.575151i
\(297\) 0 0
\(298\) −1.37796 2.38669i −0.0798229 0.138257i
\(299\) 1.96999 + 11.1724i 0.113928 + 0.646116i
\(300\) 0 0
\(301\) 1.74715 + 26.8470i 0.100704 + 1.54743i
\(302\) 14.2359 5.18145i 0.819185 0.298159i
\(303\) 0 0
\(304\) −0.698434 + 0.586056i −0.0400579 + 0.0336126i
\(305\) 8.87022 15.3637i 0.507907 0.879722i
\(306\) 0 0
\(307\) −0.00102554 + 0.00177629i −5.85309e−5 + 0.000101378i −0.866055 0.499949i \(-0.833352\pi\)
0.865996 + 0.500051i \(0.166685\pi\)
\(308\) 1.66249 2.26514i 0.0947289 0.129068i
\(309\) 0 0
\(310\) 26.7469 9.73507i 1.51912 0.552915i
\(311\) −0.483384 + 2.74140i −0.0274102 + 0.155451i −0.995441 0.0953811i \(-0.969593\pi\)
0.968031 + 0.250832i \(0.0807041\pi\)
\(312\) 0 0
\(313\) 13.7935 11.5741i 0.779655 0.654208i −0.163507 0.986542i \(-0.552281\pi\)
0.943162 + 0.332334i \(0.107836\pi\)
\(314\) −0.948167 + 1.64227i −0.0535082 + 0.0926788i
\(315\) 0 0
\(316\) −8.03678 13.9201i −0.452104 0.783067i
\(317\) −8.40466 3.05905i −0.472053 0.171813i 0.0950294 0.995474i \(-0.469705\pi\)
−0.567082 + 0.823661i \(0.691928\pi\)
\(318\) 0 0
\(319\) −5.16983 4.33800i −0.289455 0.242881i
\(320\) −15.1866 12.7431i −0.848957 0.712360i
\(321\) 0 0
\(322\) 11.0775 + 1.21838i 0.617325 + 0.0678975i
\(323\) −4.05494 −0.225623
\(324\) 0 0
\(325\) 7.50177 + 12.9935i 0.416123 + 0.720747i
\(326\) 11.5991 + 4.22172i 0.642413 + 0.233819i
\(327\) 0 0
\(328\) −4.44202 + 25.1919i −0.245270 + 1.39099i
\(329\) 1.87801 + 28.8577i 0.103538 + 1.59098i
\(330\) 0 0
\(331\) 23.6794 + 8.61858i 1.30153 + 0.473720i 0.897496 0.441022i \(-0.145384\pi\)
0.404039 + 0.914742i \(0.367606\pi\)
\(332\) −2.77747 + 4.81072i −0.152434 + 0.264023i
\(333\) 0 0
\(334\) −6.15218 10.6559i −0.336632 0.583064i
\(335\) −3.14832 1.14589i −0.172011 0.0626069i
\(336\) 0 0
\(337\) −7.25619 6.08867i −0.395270 0.331671i 0.423392 0.905947i \(-0.360839\pi\)
−0.818662 + 0.574276i \(0.805284\pi\)
\(338\) 5.85696 2.13176i 0.318577 0.115952i
\(339\) 0 0
\(340\) −1.35989 7.71231i −0.0737503 0.418259i
\(341\) 4.33296 + 7.50490i 0.234643 + 0.406413i
\(342\) 0 0
\(343\) −17.5291 5.97751i −0.946482 0.322755i
\(344\) 5.15767 + 29.2506i 0.278083 + 1.57709i
\(345\) 0 0
\(346\) −7.10797 5.96430i −0.382127 0.320643i
\(347\) 4.55625 1.65834i 0.244592 0.0890242i −0.216815 0.976213i \(-0.569567\pi\)
0.461407 + 0.887188i \(0.347345\pi\)
\(348\) 0 0
\(349\) −14.0136 + 11.7588i −0.750130 + 0.629434i −0.935537 0.353228i \(-0.885084\pi\)
0.185407 + 0.982662i \(0.440640\pi\)
\(350\) 14.3177 3.49649i 0.765314 0.186895i
\(351\) 0 0
\(352\) 2.54265 4.40400i 0.135524 0.234734i
\(353\) −5.51180 2.00613i −0.293364 0.106776i 0.191146 0.981562i \(-0.438780\pi\)
−0.484509 + 0.874786i \(0.661002\pi\)
\(354\) 0 0
\(355\) 5.81751 + 4.88147i 0.308761 + 0.259081i
\(356\) 1.79243 0.652390i 0.0949985 0.0345766i
\(357\) 0 0
\(358\) 0.516717 + 2.93045i 0.0273094 + 0.154879i
\(359\) −17.1710 −0.906253 −0.453126 0.891446i \(-0.649691\pi\)
−0.453126 + 0.891446i \(0.649691\pi\)
\(360\) 0 0
\(361\) −15.2589 −0.803100
\(362\) −12.6802 + 10.6400i −0.666458 + 0.559225i
\(363\) 0 0
\(364\) −0.487452 7.49026i −0.0255494 0.392596i
\(365\) 42.0698 + 35.3008i 2.20203 + 1.84773i
\(366\) 0 0
\(367\) −1.04397 5.92066i −0.0544949 0.309056i 0.945361 0.326025i \(-0.105709\pi\)
−0.999856 + 0.0169692i \(0.994598\pi\)
\(368\) 2.12633 0.110843
\(369\) 0 0
\(370\) −6.04797 10.4754i −0.314419 0.544590i
\(371\) 6.39448 8.71250i 0.331985 0.452331i
\(372\) 0 0
\(373\) −3.65399 + 20.7228i −0.189196 + 1.07299i 0.731248 + 0.682112i \(0.238938\pi\)
−0.920444 + 0.390874i \(0.872173\pi\)
\(374\) −1.73183 + 0.630333i −0.0895506 + 0.0325938i
\(375\) 0 0
\(376\) 5.54396 + 31.4413i 0.285908 + 1.62146i
\(377\) −18.0289 −0.928534
\(378\) 0 0
\(379\) 9.96553 0.511895 0.255947 0.966691i \(-0.417613\pi\)
0.255947 + 0.966691i \(0.417613\pi\)
\(380\) 1.25464 + 7.11539i 0.0643615 + 0.365012i
\(381\) 0 0
\(382\) 9.03011 3.28669i 0.462020 0.168162i
\(383\) 6.58758 37.3600i 0.336610 1.90901i −0.0741152 0.997250i \(-0.523613\pi\)
0.410725 0.911759i \(-0.365276\pi\)
\(384\) 0 0
\(385\) 3.31841 + 7.55115i 0.169122 + 0.384842i
\(386\) 1.08910 + 1.88637i 0.0554336 + 0.0960137i
\(387\) 0 0
\(388\) 14.1952 0.720651
\(389\) 6.53697 + 37.0730i 0.331437 + 1.87967i 0.459916 + 0.887962i \(0.347880\pi\)
−0.128479 + 0.991712i \(0.541009\pi\)
\(390\) 0 0
\(391\) 7.24433 + 6.07872i 0.366362 + 0.307414i
\(392\) −19.9576 4.44391i −1.00801 0.224451i
\(393\) 0 0
\(394\) −17.6823 + 14.8372i −0.890820 + 0.747487i
\(395\) 47.1845 2.37411
\(396\) 0 0
\(397\) −1.75414 −0.0880376 −0.0440188 0.999031i \(-0.514016\pi\)
−0.0440188 + 0.999031i \(0.514016\pi\)
\(398\) −0.184540 1.04658i −0.00925018 0.0524604i
\(399\) 0 0
\(400\) 2.64251 0.961794i 0.132125 0.0480897i
\(401\) −2.12519 1.78324i −0.106127 0.0890510i 0.588180 0.808730i \(-0.299845\pi\)
−0.694307 + 0.719679i \(0.744289\pi\)
\(402\) 0 0
\(403\) 21.7544 + 7.91794i 1.08366 + 0.394421i
\(404\) 2.18077 3.77721i 0.108498 0.187923i
\(405\) 0 0
\(406\) −4.96374 + 17.0005i −0.246346 + 0.843721i
\(407\) 2.82112 2.36720i 0.139838 0.117338i
\(408\) 0 0
\(409\) −16.5654 + 6.02932i −0.819107 + 0.298131i −0.717380 0.696682i \(-0.754659\pi\)
−0.101727 + 0.994812i \(0.532437\pi\)
\(410\) −20.7447 17.4069i −1.02451 0.859664i
\(411\) 0 0
\(412\) 1.04166 + 5.90757i 0.0513191 + 0.291045i
\(413\) 5.90391 20.2205i 0.290512 0.994987i
\(414\) 0 0
\(415\) −8.15337 14.1220i −0.400233 0.693224i
\(416\) −2.35903 13.3787i −0.115661 0.655945i
\(417\) 0 0
\(418\) 1.59779 0.581547i 0.0781504 0.0284444i
\(419\) −27.7705 23.3022i −1.35668 1.13839i −0.976993 0.213270i \(-0.931589\pi\)
−0.379683 0.925117i \(-0.623967\pi\)
\(420\) 0 0
\(421\) 6.59183 + 2.39923i 0.321266 + 0.116931i 0.497619 0.867396i \(-0.334208\pi\)
−0.176353 + 0.984327i \(0.556430\pi\)
\(422\) −7.36418 12.7551i −0.358483 0.620910i
\(423\) 0 0
\(424\) 5.96562 10.3328i 0.289716 0.501803i
\(425\) 11.7525 + 4.27755i 0.570079 + 0.207492i
\(426\) 0 0
\(427\) −0.920479 14.1442i −0.0445451 0.684486i
\(428\) 1.65297 9.37445i 0.0798992 0.453131i
\(429\) 0 0
\(430\) −29.5469 10.7542i −1.42488 0.518613i
\(431\) 5.59564 + 9.69194i 0.269533 + 0.466844i 0.968741 0.248074i \(-0.0797975\pi\)
−0.699209 + 0.714918i \(0.746464\pi\)
\(432\) 0 0
\(433\) 2.32810 0.111881 0.0559406 0.998434i \(-0.482184\pi\)
0.0559406 + 0.998434i \(0.482184\pi\)
\(434\) 13.4558 18.3335i 0.645897 0.880037i
\(435\) 0 0
\(436\) 5.01033 + 4.20416i 0.239951 + 0.201343i
\(437\) −6.68364 5.60824i −0.319722 0.268278i
\(438\) 0 0
\(439\) −19.7599 7.19202i −0.943089 0.343256i −0.175704 0.984443i \(-0.556220\pi\)
−0.767385 + 0.641186i \(0.778443\pi\)
\(440\) 4.55298 + 7.88599i 0.217055 + 0.375950i
\(441\) 0 0
\(442\) −2.46170 + 4.26378i −0.117091 + 0.202808i
\(443\) 13.2231 11.0955i 0.628250 0.527165i −0.272134 0.962259i \(-0.587729\pi\)
0.900385 + 0.435095i \(0.143285\pi\)
\(444\) 0 0
\(445\) −0.972329 + 5.51435i −0.0460928 + 0.261405i
\(446\) 13.8642 5.04614i 0.656487 0.238942i
\(447\) 0 0
\(448\) −15.7444 1.73168i −0.743855 0.0818142i
\(449\) −15.5314 + 26.9012i −0.732972 + 1.26955i 0.222635 + 0.974902i \(0.428534\pi\)
−0.955607 + 0.294643i \(0.904799\pi\)
\(450\) 0 0
\(451\) 4.12240 7.14021i 0.194116 0.336219i
\(452\) −6.86582 + 5.76111i −0.322941 + 0.270980i
\(453\) 0 0
\(454\) −12.8899 + 4.69154i −0.604953 + 0.220185i
\(455\) 19.7576 + 9.75473i 0.926248 + 0.457309i
\(456\) 0 0
\(457\) 5.37599 + 30.4888i 0.251478 + 1.42620i 0.804953 + 0.593339i \(0.202191\pi\)
−0.553474 + 0.832866i \(0.686698\pi\)
\(458\) −4.06058 7.03314i −0.189739 0.328637i
\(459\) 0 0
\(460\) 8.42514 14.5928i 0.392824 0.680392i
\(461\) 2.51229 2.10806i 0.117009 0.0981823i −0.582406 0.812898i \(-0.697888\pi\)
0.699415 + 0.714716i \(0.253444\pi\)
\(462\) 0 0
\(463\) 5.00213 28.3685i 0.232469 1.31840i −0.615410 0.788207i \(-0.711010\pi\)
0.847879 0.530190i \(-0.177879\pi\)
\(464\) −0.586780 + 3.32779i −0.0272406 + 0.154489i
\(465\) 0 0
\(466\) 8.78382 7.37050i 0.406903 0.341432i
\(467\) −2.07669 −0.0960976 −0.0480488 0.998845i \(-0.515300\pi\)
−0.0480488 + 0.998845i \(0.515300\pi\)
\(468\) 0 0
\(469\) −2.60043 + 0.635045i −0.120077 + 0.0293237i
\(470\) −31.7599 11.5596i −1.46497 0.533207i
\(471\) 0 0
\(472\) 4.03829 22.9023i 0.185877 1.05416i
\(473\) 1.66235 9.42768i 0.0764351 0.433485i
\(474\) 0 0
\(475\) −10.8429 3.94648i −0.497505 0.181077i
\(476\) −4.32469 4.52182i −0.198222 0.207257i
\(477\) 0 0
\(478\) 23.6530 1.08186
\(479\) −7.21876 + 6.05726i −0.329834 + 0.276763i −0.792632 0.609700i \(-0.791290\pi\)
0.462798 + 0.886464i \(0.346845\pi\)
\(480\) 0 0
\(481\) 1.70838 9.68868i 0.0778952 0.441766i
\(482\) 2.44988 13.8940i 0.111589 0.632853i
\(483\) 0 0
\(484\) 8.73966 7.33345i 0.397257 0.333339i
\(485\) −20.8352 + 36.0877i −0.946079 + 1.63866i
\(486\) 0 0
\(487\) 4.36325 + 7.55738i 0.197718 + 0.342457i 0.947788 0.318901i \(-0.103314\pi\)
−0.750070 + 0.661358i \(0.769980\pi\)
\(488\) −2.71729 15.4105i −0.123006 0.697602i
\(489\) 0 0
\(490\) 14.6380 15.9449i 0.661278 0.720317i
\(491\) 15.4437 5.62105i 0.696965 0.253674i 0.0308503 0.999524i \(-0.490178\pi\)
0.666114 + 0.745850i \(0.267956\pi\)
\(492\) 0 0
\(493\) −11.5126 + 9.66019i −0.518500 + 0.435073i
\(494\) 2.27117 3.93378i 0.102185 0.176989i
\(495\) 0 0
\(496\) 2.16954 3.75775i 0.0974151 0.168728i
\(497\) 6.03120 + 0.663351i 0.270536 + 0.0297554i
\(498\) 0 0
\(499\) −20.9435 + 7.62282i −0.937561 + 0.341244i −0.765202 0.643790i \(-0.777361\pi\)
−0.172359 + 0.985034i \(0.555139\pi\)
\(500\) 0.626389 3.55243i 0.0280130 0.158869i
\(501\) 0 0
\(502\) 13.6690 11.4696i 0.610077 0.511915i
\(503\) −8.81372 + 15.2658i −0.392984 + 0.680669i −0.992842 0.119438i \(-0.961891\pi\)
0.599857 + 0.800107i \(0.295224\pi\)
\(504\) 0 0
\(505\) 6.40174 + 11.0881i 0.284874 + 0.493415i
\(506\) −3.72631 1.35627i −0.165655 0.0602933i
\(507\) 0 0
\(508\) 7.04221 + 5.90912i 0.312448 + 0.262175i
\(509\) 4.41293 + 3.70288i 0.195599 + 0.164127i 0.735327 0.677712i \(-0.237028\pi\)
−0.539728 + 0.841840i \(0.681473\pi\)
\(510\) 0 0
\(511\) 43.6151 + 4.79708i 1.92942 + 0.212210i
\(512\) −5.29997 −0.234228
\(513\) 0 0
\(514\) 13.6028 + 23.5608i 0.599995 + 1.03922i
\(515\) −16.5474 6.02277i −0.729166 0.265395i
\(516\) 0 0
\(517\) 1.78686 10.1338i 0.0785859 0.445683i
\(518\) −8.66569 4.27844i −0.380748 0.187984i
\(519\) 0 0
\(520\) 22.8590 + 8.32000i 1.00243 + 0.364856i
\(521\) 7.19384 12.4601i 0.315168 0.545887i −0.664305 0.747461i \(-0.731272\pi\)
0.979473 + 0.201575i \(0.0646058\pi\)
\(522\) 0 0
\(523\) 0.204128 + 0.353560i 0.00892588 + 0.0154601i 0.870454 0.492250i \(-0.163825\pi\)
−0.861528 + 0.507710i \(0.830492\pi\)
\(524\) −1.54373 0.561870i −0.0674380 0.0245454i
\(525\) 0 0
\(526\) −12.6327 10.6001i −0.550813 0.462187i
\(527\) 18.1341 6.60027i 0.789934 0.287512i
\(528\) 0 0
\(529\) −0.460540 2.61185i −0.0200235 0.113559i
\(530\) 6.31537 + 10.9385i 0.274322 + 0.475140i
\(531\) 0 0
\(532\) 3.98997 + 4.17184i 0.172987 + 0.180872i
\(533\) −3.82469 21.6909i −0.165666 0.939538i
\(534\) 0 0
\(535\) 21.4060 + 17.9618i 0.925461 + 0.776554i
\(536\) −2.77703 + 1.01076i −0.119949 + 0.0436580i
\(537\) 0 0
\(538\) 0.661242 0.554848i 0.0285082 0.0239212i
\(539\) 5.55469 + 3.54597i 0.239257 + 0.152736i
\(540\) 0 0
\(541\) 7.96991 13.8043i 0.342653 0.593493i −0.642271 0.766477i \(-0.722008\pi\)
0.984925 + 0.172985i \(0.0553411\pi\)
\(542\) −3.43838 1.25147i −0.147691 0.0537551i
\(543\) 0 0
\(544\) −8.67494 7.27914i −0.371935 0.312091i
\(545\) −18.0420 + 6.56675i −0.772835 + 0.281289i
\(546\) 0 0
\(547\) 6.47172 + 36.7030i 0.276711 + 1.56931i 0.733474 + 0.679717i \(0.237898\pi\)
−0.456763 + 0.889588i \(0.650991\pi\)
\(548\) 1.52167 0.0650027
\(549\) 0 0
\(550\) −5.24436 −0.223620
\(551\) 10.6215 8.91252i 0.452492 0.379686i
\(552\) 0 0
\(553\) 31.3553 20.9300i 1.33336 0.890032i
\(554\) −17.6663 14.8238i −0.750568 0.629801i
\(555\) 0 0
\(556\) −2.29098 12.9928i −0.0971592 0.551017i
\(557\) −7.75920 −0.328768 −0.164384 0.986396i \(-0.552564\pi\)
−0.164384 + 0.986396i \(0.552564\pi\)
\(558\) 0 0
\(559\) −12.7870 22.1478i −0.540833 0.936751i
\(560\) 2.44359 3.32939i 0.103260 0.140693i
\(561\) 0 0
\(562\) 0.379670 2.15321i 0.0160154 0.0908278i
\(563\) 4.40208 1.60223i 0.185526 0.0675258i −0.247587 0.968866i \(-0.579638\pi\)
0.433112 + 0.901340i \(0.357415\pi\)
\(564\) 0 0
\(565\) −4.56873 25.9106i −0.192208 1.09007i
\(566\) 10.2028 0.428854
\(567\) 0 0
\(568\) 6.69861 0.281067
\(569\) 3.60604 + 20.4509i 0.151173 + 0.857345i 0.962202 + 0.272338i \(0.0877970\pi\)
−0.811029 + 0.585007i \(0.801092\pi\)
\(570\) 0 0
\(571\) 24.6949 8.98821i 1.03345 0.376145i 0.231056 0.972940i \(-0.425782\pi\)
0.802393 + 0.596796i \(0.203560\pi\)
\(572\) −0.463794 + 2.63030i −0.0193922 + 0.109979i
\(573\) 0 0
\(574\) −21.5067 2.36545i −0.897672 0.0987320i
\(575\) 13.4551 + 23.3050i 0.561118 + 0.971885i
\(576\) 0 0
\(577\) 21.8729 0.910580 0.455290 0.890343i \(-0.349536\pi\)
0.455290 + 0.890343i \(0.349536\pi\)
\(578\) −2.04387 11.5914i −0.0850139 0.482138i
\(579\) 0 0
\(580\) 20.5133 + 17.2127i 0.851767 + 0.714718i
\(581\) −11.6823 5.76783i −0.484665 0.239290i
\(582\) 0 0
\(583\) −2.94585 + 2.47186i −0.122004 + 0.102374i
\(584\) 48.4415 2.00453
\(585\) 0 0
\(586\) 0.445100 0.0183869
\(587\) −6.79402 38.5308i −0.280419 1.59034i −0.721204 0.692723i \(-0.756411\pi\)
0.440785 0.897613i \(-0.354700\pi\)
\(588\) 0 0
\(589\) −16.7306 + 6.08943i −0.689371 + 0.250911i
\(590\) 18.8592 + 15.8248i 0.776422 + 0.651496i
\(591\) 0 0
\(592\) −1.73275 0.630669i −0.0712155 0.0259203i
\(593\) 15.6172 27.0498i 0.641322 1.11080i −0.343816 0.939037i \(-0.611720\pi\)
0.985138 0.171765i \(-0.0549471\pi\)
\(594\) 0 0
\(595\) 17.8432 4.35744i 0.731500 0.178638i
\(596\) −2.55038 + 2.14003i −0.104468 + 0.0876589i
\(597\) 0 0
\(598\) −9.95462 + 3.62319i −0.407075 + 0.148163i
\(599\) 4.00860 + 3.36361i 0.163787 + 0.137433i 0.720997 0.692938i \(-0.243684\pi\)
−0.557211 + 0.830371i \(0.688128\pi\)
\(600\) 0 0
\(601\) −7.71508 43.7544i −0.314705 1.78478i −0.573871 0.818946i \(-0.694559\pi\)
0.259166 0.965833i \(-0.416552\pi\)
\(602\) −24.4050 + 5.95989i −0.994674 + 0.242907i
\(603\) 0 0
\(604\) −9.15072 15.8495i −0.372338 0.644908i
\(605\) 5.81565 + 32.9822i 0.236440 + 1.34092i
\(606\) 0 0
\(607\) −21.0134 + 7.64824i −0.852907 + 0.310433i −0.731225 0.682137i \(-0.761051\pi\)
−0.121682 + 0.992569i \(0.538829\pi\)
\(608\) 8.00352 + 6.71575i 0.324586 + 0.272360i
\(609\) 0 0
\(610\) 15.5666 + 5.66579i 0.630275 + 0.229401i
\(611\) −13.7447 23.8066i −0.556052 0.963110i
\(612\) 0 0
\(613\) 19.5149 33.8008i 0.788200 1.36520i −0.138869 0.990311i \(-0.544347\pi\)
0.927069 0.374891i \(-0.122320\pi\)
\(614\) −0.00179976 0.000655059i −7.26324e−5 2.64360e-5i
\(615\) 0 0
\(616\) 6.52362 + 3.22085i 0.262844 + 0.129772i
\(617\) −2.82811 + 16.0390i −0.113855 + 0.645705i 0.873455 + 0.486904i \(0.161874\pi\)
−0.987311 + 0.158801i \(0.949237\pi\)
\(618\) 0 0
\(619\) 13.2292 + 4.81503i 0.531726 + 0.193533i 0.593909 0.804532i \(-0.297584\pi\)
−0.0621826 + 0.998065i \(0.519806\pi\)
\(620\) −17.1927 29.7786i −0.690474 1.19594i
\(621\) 0 0
\(622\) −2.59936 −0.104225
\(623\) 1.79990 + 4.09573i 0.0721115 + 0.164092i
\(624\) 0 0
\(625\) −14.7381 12.3667i −0.589522 0.494668i
\(626\) 12.8801 + 10.8077i 0.514792 + 0.431962i
\(627\) 0 0
\(628\) 2.15271 + 0.783524i 0.0859027 + 0.0312660i
\(629\) −4.10046 7.10221i −0.163496 0.283184i
\(630\) 0 0
\(631\) −15.0249 + 26.0240i −0.598134 + 1.03600i 0.394963 + 0.918697i \(0.370757\pi\)
−0.993096 + 0.117301i \(0.962576\pi\)
\(632\) 31.8826 26.7527i 1.26822 1.06417i
\(633\) 0 0
\(634\) 1.45027 8.22489i 0.0575976 0.326652i
\(635\) −25.3588 + 9.22983i −1.00633 + 0.366275i
\(636\) 0 0
\(637\) 17.4564 2.28172i 0.691648 0.0904052i
\(638\) 3.15092 5.45755i 0.124746 0.216066i
\(639\) 0 0
\(640\) −8.63135 + 14.9499i −0.341184 + 0.590948i
\(641\) 6.71816 5.63721i 0.265351 0.222656i −0.500398 0.865796i \(-0.666813\pi\)
0.765749 + 0.643139i \(0.222368\pi\)
\(642\) 0 0
\(643\) −25.0319 + 9.11085i −0.987160 + 0.359297i −0.784620 0.619977i \(-0.787142\pi\)
−0.202540 + 0.979274i \(0.564920\pi\)
\(644\) −0.874292 13.4345i −0.0344519 0.529393i
\(645\) 0 0
\(646\) −0.657506 3.72890i −0.0258692 0.146712i
\(647\) −21.1893 36.7009i −0.833036 1.44286i −0.895620 0.444820i \(-0.853268\pi\)
0.0625843 0.998040i \(-0.480066\pi\)
\(648\) 0 0
\(649\) −3.74772 + 6.49124i −0.147111 + 0.254804i
\(650\) −10.7323 + 9.00546i −0.420955 + 0.353223i
\(651\) 0 0
\(652\) 2.58937 14.6850i 0.101407 0.575110i
\(653\) −0.630967 + 3.57839i −0.0246917 + 0.140033i −0.994661 0.103192i \(-0.967094\pi\)
0.969970 + 0.243225i \(0.0782055\pi\)
\(654\) 0 0
\(655\) 3.69424 3.09984i 0.144346 0.121121i
\(656\) −4.12822 −0.161180
\(657\) 0 0
\(658\) −26.2329 + 6.40626i −1.02266 + 0.249742i
\(659\) −34.3400 12.4987i −1.33770 0.486882i −0.428611 0.903489i \(-0.640997\pi\)
−0.909087 + 0.416607i \(0.863219\pi\)
\(660\) 0 0
\(661\) −7.34938 + 41.6804i −0.285858 + 1.62118i 0.416347 + 0.909206i \(0.363310\pi\)
−0.702205 + 0.711975i \(0.747801\pi\)
\(662\) −4.08600 + 23.1729i −0.158807 + 0.900639i
\(663\) 0 0
\(664\) −13.5162 4.91949i −0.524530 0.190913i
\(665\) −16.4622 + 4.02019i −0.638376 + 0.155896i
\(666\) 0 0
\(667\) −32.3365 −1.25207
\(668\) −11.3867 + 9.55459i −0.440565 + 0.369678i
\(669\) 0 0
\(670\) 0.543260 3.08098i 0.0209880 0.119029i
\(671\) −0.875803 + 4.96693i −0.0338100 + 0.191746i
\(672\) 0 0
\(673\) −17.6276 + 14.7913i −0.679493 + 0.570163i −0.915858 0.401502i \(-0.868488\pi\)
0.236365 + 0.971664i \(0.424044\pi\)
\(674\) 4.42251 7.66002i 0.170349 0.295053i
\(675\) 0 0
\(676\) −3.76480 6.52083i −0.144800 0.250801i
\(677\) 1.80122 + 10.2152i 0.0692264 + 0.392603i 0.999658 + 0.0261378i \(0.00832087\pi\)
−0.930432 + 0.366465i \(0.880568\pi\)
\(678\) 0 0
\(679\) 2.16211 + 33.2232i 0.0829741 + 1.27499i
\(680\) 19.0549 6.93543i 0.730723 0.265961i
\(681\) 0 0
\(682\) −6.19887 + 5.20147i −0.237367 + 0.199175i
\(683\) −7.07481 + 12.2539i −0.270710 + 0.468884i −0.969044 0.246888i \(-0.920592\pi\)
0.698334 + 0.715772i \(0.253925\pi\)
\(684\) 0 0
\(685\) −2.23346 + 3.86847i −0.0853362 + 0.147807i
\(686\) 2.65455 17.0889i 0.101351 0.652457i
\(687\) 0 0
\(688\) −4.50424 + 1.63941i −0.171723 + 0.0625019i
\(689\) −1.78391 + 10.1170i −0.0679615 + 0.385429i
\(690\) 0 0
\(691\) −9.84214 + 8.25853i −0.374413 + 0.314169i −0.810504 0.585733i \(-0.800807\pi\)
0.436092 + 0.899902i \(0.356362\pi\)
\(692\) −5.60464 + 9.70752i −0.213056 + 0.369025i
\(693\) 0 0
\(694\) 2.26379 + 3.92100i 0.0859322 + 0.148839i
\(695\) 36.3935 + 13.2462i 1.38049 + 0.502456i
\(696\) 0 0
\(697\) −14.0647 11.8017i −0.532738 0.447021i
\(698\) −13.0856 10.9801i −0.495298 0.415604i
\(699\) 0 0
\(700\) −7.16329 16.3003i −0.270747 0.616093i
\(701\) −10.6569 −0.402504 −0.201252 0.979539i \(-0.564501\pi\)
−0.201252 + 0.979539i \(0.564501\pi\)
\(702\) 0 0
\(703\) 3.78310 + 6.55252i 0.142682 + 0.247133i
\(704\) 5.29620 + 1.92766i 0.199608 + 0.0726514i
\(705\) 0 0
\(706\) 0.951092 5.39391i 0.0357948 0.203003i
\(707\) 9.17257 + 4.52869i 0.344970 + 0.170319i
\(708\) 0 0
\(709\) −13.9753 5.08659i −0.524853 0.191031i 0.0659855 0.997821i \(-0.478981\pi\)
−0.590839 + 0.806790i \(0.701203\pi\)
\(710\) −3.54566 + 6.14127i −0.133066 + 0.230478i
\(711\) 0 0
\(712\) 2.46953 + 4.27735i 0.0925496 + 0.160301i
\(713\) 39.0185 + 14.2016i 1.46125 + 0.531853i
\(714\) 0 0
\(715\) −6.00614 5.03975i −0.224617 0.188476i
\(716\) 3.37796 1.22948i 0.126240 0.0459477i
\(717\) 0 0
\(718\) −2.78427 15.7904i −0.103908 0.589292i
\(719\) −21.0035 36.3791i −0.783298 1.35671i −0.930010 0.367533i \(-0.880202\pi\)
0.146712 0.989179i \(-0.453131\pi\)
\(720\) 0 0
\(721\) −13.6678 + 3.33777i −0.509014 + 0.124305i
\(722\) −2.47422 14.0320i −0.0920808 0.522216i
\(723\) 0 0
\(724\) 15.3184 + 12.8537i 0.569304 + 0.477702i
\(725\) −40.1863 + 14.6266i −1.49248 + 0.543219i
\(726\) 0 0
\(727\) 18.2193 15.2878i 0.675718 0.566994i −0.239034 0.971011i \(-0.576831\pi\)
0.914752 + 0.404017i \(0.132386\pi\)
\(728\) 18.8810 4.61087i 0.699776 0.170890i
\(729\) 0 0
\(730\) −25.6408 + 44.4111i −0.949007 + 1.64373i
\(731\) −20.0325 7.29123i −0.740929 0.269676i
\(732\) 0 0
\(733\) 26.7274 + 22.4270i 0.987200 + 0.828359i 0.985160 0.171639i \(-0.0549063\pi\)
0.00203972 + 0.999998i \(0.499351\pi\)
\(734\) 5.27532 1.92006i 0.194716 0.0708707i
\(735\) 0 0
\(736\) −4.23114 23.9960i −0.155962 0.884503i
\(737\) 0.952499 0.0350857
\(738\) 0 0
\(739\) −8.22260 −0.302473 −0.151237 0.988498i \(-0.548326\pi\)
−0.151237 + 0.988498i \(0.548326\pi\)
\(740\) −11.1939 + 9.39276i −0.411494 + 0.345285i
\(741\) 0 0
\(742\) 9.04882 + 4.46760i 0.332193 + 0.164011i
\(743\) −19.4758 16.3421i −0.714497 0.599534i 0.211360 0.977408i \(-0.432211\pi\)
−0.925857 + 0.377874i \(0.876655\pi\)
\(744\) 0 0
\(745\) −1.69711 9.62476i −0.0621771 0.352624i
\(746\) −19.6490 −0.719402
\(747\) 0 0
\(748\) 1.11320 + 1.92813i 0.0407028 + 0.0704992i
\(749\) 22.1923 + 2.44085i 0.810888 + 0.0891869i
\(750\) 0 0
\(751\) 4.50351 25.5407i 0.164336 0.931993i −0.785411 0.618974i \(-0.787548\pi\)
0.949747 0.313019i \(-0.101340\pi\)
\(752\) −4.84159 + 1.76220i −0.176555 + 0.0642607i
\(753\) 0 0
\(754\) −2.92336 16.5792i −0.106463 0.603780i
\(755\) 53.7245 1.95524
\(756\) 0 0
\(757\) −51.8493 −1.88449 −0.942247 0.334918i \(-0.891291\pi\)
−0.942247 + 0.334918i \(0.891291\pi\)
\(758\) 1.61590 + 9.16423i 0.0586922 + 0.332860i
\(759\) 0 0
\(760\) −17.5801 + 6.39864i −0.637698 + 0.232103i
\(761\) 2.33892 13.2647i 0.0847858 0.480844i −0.912617 0.408816i \(-0.865942\pi\)
0.997403 0.0720282i \(-0.0229472\pi\)
\(762\) 0 0
\(763\) −9.07653 + 12.3668i −0.328592 + 0.447708i
\(764\) −5.80448 10.0536i −0.209999 0.363728i
\(765\) 0 0
\(766\) 35.4242 1.27993
\(767\) 3.47707 + 19.7194i 0.125550 + 0.712028i
\(768\) 0 0
\(769\) 9.94513 + 8.34496i 0.358631 + 0.300927i 0.804245 0.594298i \(-0.202570\pi\)
−0.445614 + 0.895225i \(0.647015\pi\)
\(770\) −6.40591 + 4.27600i −0.230853 + 0.154096i
\(771\) 0 0
\(772\) 2.01575 1.69141i 0.0725484 0.0608753i
\(773\) 33.8415 1.21719 0.608596 0.793480i \(-0.291733\pi\)
0.608596 + 0.793480i \(0.291733\pi\)
\(774\) 0 0
\(775\) 54.9141 1.97257
\(776\) 6.38263 + 36.1977i 0.229123 + 1.29942i
\(777\) 0 0
\(778\) −33.0321 + 12.0227i −1.18426 + 0.431035i
\(779\) 12.9761 + 10.8883i 0.464918 + 0.390112i
\(780\) 0 0
\(781\) −2.02881 0.738425i −0.0725964 0.0264229i
\(782\) −4.41529 + 7.64750i −0.157890 + 0.273474i
\(783\) 0 0