LMFDB - Embedded newform 572.2.b.c.571.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(571,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.571");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.b (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			571.13
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} -1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +O(q^{10})$	\(q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} -1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +(-1.19260 + 1.00935i) q^{10} +(-2.94635 - 1.52284i) q^{11} +(-3.30886 - 0.554581i) q^{12} +(1.61864 - 3.22180i) q^{13} +(-1.37146 + 1.16073i) q^{14} +1.85329 q^{15} +(-3.78141 - 1.30420i) q^{16} +1.40862i q^{17} +(-0.169903 - 0.200750i) q^{18} +0.947603i q^{19} +(2.17917 + 0.365240i) q^{20} +2.13123 q^{21} +(1.04796 + 4.57185i) q^{22} -2.58512i q^{23} +(2.42438 + 4.07856i) q^{24} +3.77945 q^{25} +(-4.95673 + 1.19619i) q^{26} +5.34449i q^{27} +(2.50599 + 0.420015i) q^{28} -9.78308i q^{29} +(-1.69320 - 2.00060i) q^{30} +5.63936 q^{31} +(2.04690 + 5.27354i) q^{32} +(2.55457 - 4.94252i) q^{33} +(1.52059 - 1.28694i) q^{34} -1.40360 q^{35} +(-0.0614803 + 0.366818i) q^{36} -7.85601i q^{37} +(1.02293 - 0.865749i) q^{38} +(5.40460 + 2.71529i) q^{39} +(-1.59666 - 2.68609i) q^{40} +1.57573 q^{41} +(-1.94713 - 2.30064i) q^{42} +4.24023 q^{43} +(3.97783 - 5.30819i) q^{44} -0.205454i q^{45} +(-2.79062 + 2.36182i) q^{46} +0.265145 q^{47} +(2.18781 - 6.34335i) q^{48} +5.38590 q^{49} +(-3.45298 - 4.07988i) q^{50} -2.36297 q^{51} +(5.81984 + 4.25787i) q^{52} +5.33730 q^{53} +(5.76932 - 4.88283i) q^{54} +(-1.68241 + 3.25508i) q^{55} +(-1.83612 - 3.08892i) q^{56} -1.58961 q^{57} +(-10.5607 + 8.93802i) q^{58} +0.801256 q^{59} +(-0.612692 + 3.65558i) q^{60} +4.22552i q^{61} +(-5.15224 - 6.08764i) q^{62} -0.236266i q^{63} +(3.82264 - 7.02762i) q^{64} +(-3.55940 - 1.78825i) q^{65} +(-7.66931 + 1.75795i) q^{66} +10.3107 q^{67} +(-2.77848 - 0.465686i) q^{68} +4.33657 q^{69} +(1.28236 + 1.51517i) q^{70} -11.1238 q^{71} +(0.452146 - 0.268764i) q^{72} -10.0124 q^{73} +(-8.48048 + 7.17740i) q^{74} +6.34006i q^{75} +(-1.86913 - 0.313276i) q^{76} +(-1.93472 + 3.74325i) q^{77} +(-2.00662 - 8.31495i) q^{78} -7.91992 q^{79} +(-1.44086 + 4.17765i) q^{80} -8.40751 q^{81} +(-1.43961 - 1.70098i) q^{82} -12.5969i q^{83} +(-0.704579 + 4.20382i) q^{84} +1.55622 q^{85} +(-3.87396 - 4.57728i) q^{86} +16.4112 q^{87} +(-9.36436 + 0.555636i) q^{88} -5.03112i q^{89} +(-0.221785 + 0.187707i) q^{90} +(-4.09321 - 2.05644i) q^{91} +(5.09913 + 0.854637i) q^{92} +9.46008i q^{93} +(-0.242241 - 0.286221i) q^{94} +1.04690 q^{95} +(-8.84640 + 3.43369i) q^{96} +15.8353i q^{97} +(-4.92067 - 5.81403i) q^{98} +(-0.547924 - 0.283197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^4 - 32 * q^9	$ 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) $ 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$-1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.913620	−	1.07949i	−0.646027	−	0.763315i
$2$	−0.913620	−	1.07949i	−0.646027	−	0.763315i
$3$			1.67751i			0.968510i	0.874927	+	0.484255i	$0.160909\pi$
$3$			1.67751i			0.968510i	−0.874927	+	0.484255i	$0.839091\pi$
$4$	−0.330598	+	1.97249i	−0.165299	+	0.986244i
$5$		−	1.10479i		−	0.494075i	−0.969006	−	0.247038i	$-0.920543\pi$
$5$		−	1.10479i		−	0.494075i	0.969006	−	0.247038i	$-0.0794571\pi$
$6$	1.81085	−	1.53260i	0.739278	−	0.625683i
$7$		−	1.27047i		−	0.480193i	−0.970749	−	0.240097i	$-0.922821\pi$
$7$		−	1.27047i		−	0.480193i	0.970749	−	0.240097i	$-0.0771791\pi$
$8$	2.43132	−	1.44523i	0.859602	−	0.510965i
$9$	0.185967			0.0619890
$10$	−1.19260	+	1.00935i	−0.377135	+	0.319186i
$11$	−2.94635	−	1.52284i	−0.888358	−	0.459152i
$11$	−2.94635	−	1.52284i	−0.888358	−	0.459152i
$12$	−3.30886	−	0.554581i	−0.955186	−	0.160094i
$13$	1.61864	−	3.22180i	0.448931	−	0.893567i
$13$	1.61864	−	3.22180i	0.448931	−	0.893567i
$14$	−1.37146	+	1.16073i	−0.366538	+	0.310218i
$15$	1.85329			0.478516
$16$	−3.78141	−	1.30420i	−0.945353	−	0.326050i
$17$			1.40862i			0.341640i	0.985302	+	0.170820i	$0.0546416\pi$
$17$			1.40862i			0.341640i	−0.985302	+	0.170820i	$0.945358\pi$
$18$	−0.169903	−	0.200750i	−0.0400466	−	0.0473171i
$19$			0.947603i			0.217395i	0.994075	+	0.108698i	$0.0346680\pi$
$19$			0.947603i			0.217395i	−0.994075	+	0.108698i	$0.965332\pi$
$20$	2.17917	+	0.365240i	0.487278	+	0.0816701i
$21$	2.13123			0.465072
$22$	1.04796	+	4.57185i	0.223425	+	0.974721i
$23$		−	2.58512i		−	0.539036i	−0.962995	−	0.269518i	$-0.913136\pi$
$23$		−	2.58512i		−	0.539036i	0.962995	−	0.269518i	$-0.0868643\pi$
$24$	2.42438	+	4.07856i	0.494874	+	0.832533i
$25$	3.77945			0.755890
$26$	−4.95673	+	1.19619i	−0.972094	+	0.234592i
$27$			5.34449i			1.02855i
$28$	2.50599	+	0.420015i	0.473587	+	0.0793754i
$29$		−	9.78308i		−	1.81667i	−0.418241	−	0.908336i	$-0.637353\pi$
$29$		−	9.78308i		−	1.81667i	0.418241	−	0.908336i	$-0.362647\pi$
$30$	−1.69320	−	2.00060i	−0.309134	−	0.365259i
$31$	5.63936			1.01286			0.506430	−	0.862281i	$-0.330965\pi$
$31$	5.63936			1.01286			0.506430	+	0.862281i	$0.330965\pi$
$32$	2.04690	+	5.27354i	0.361844	+	0.932239i
$33$	2.55457	−	4.94252i	0.444694	−	0.860383i
$34$	1.52059	−	1.28694i	0.260779	−	0.220708i
$35$	−1.40360			−0.237251
$36$	−0.0614803	+	0.366818i	−0.0102467	+	0.0611363i
$37$		−	7.85601i		−	1.29152i	−0.763541	−	0.645760i	$-0.776541\pi$
$37$		−	7.85601i		−	1.29152i	0.763541	−	0.645760i	$-0.223459\pi$
$38$	1.02293	−	0.865749i	0.165941	−	0.140443i
$39$	5.40460	+	2.71529i	0.865428	+	0.434794i
$40$	−1.59666	−	2.68609i	−0.252455	−	0.424708i
$41$	1.57573			0.246087			0.123044	−	0.992401i	$-0.460735\pi$
$41$	1.57573			0.246087			0.123044	+	0.992401i	$0.460735\pi$
$42$	−1.94713	−	2.30064i	−0.300449	−	0.354996i
$43$	4.24023			0.646629			0.323314	−	0.946292i	$-0.395203\pi$
$43$	4.24023			0.646629			0.323314	+	0.946292i	$0.395203\pi$
$44$	3.97783	−	5.30819i	0.599681	−	0.800239i
$45$		−	0.205454i		−	0.0306272i
$46$	−2.79062	+	2.36182i	−0.411454	+	0.348232i
$47$	0.265145			0.0386753			0.0193377	−	0.999813i	$-0.493844\pi$
$47$	0.265145			0.0386753			0.0193377	+	0.999813i	$0.493844\pi$
$48$	2.18781	−	6.34335i	0.315783	−	0.915583i
$49$	5.38590			0.769415
$50$	−3.45298	−	4.07988i	−0.488325	−	0.576982i
$51$	−2.36297			−0.330881
$52$	5.81984	+	4.25787i	0.807066	+	0.590461i
$53$	5.33730			0.733135			0.366568	−	0.930391i	$-0.380533\pi$
$53$	5.33730			0.733135			0.366568	+	0.930391i	$0.380533\pi$
$54$	5.76932	−	4.88283i	0.785105	−	0.664469i
$55$	−1.68241	+	3.25508i	−0.226856	+	0.438915i
$56$	−1.83612	−	3.08892i	−0.245362	−	0.412775i
$57$	−1.58961			−0.210549
$58$	−10.5607	+	8.93802i	−1.38669	+	1.17362i
$59$	0.801256			0.104315			0.0521573	−	0.998639i	$-0.483390\pi$
$59$	0.801256			0.104315			0.0521573	+	0.998639i	$0.483390\pi$
$60$	−0.612692	+	3.65558i	−0.0790983	+	0.471934i
$61$			4.22552i			0.541022i	0.962717	+	0.270511i	$0.0871926\pi$
$61$			4.22552i			0.541022i	−0.962717	+	0.270511i	$0.912807\pi$
$62$	−5.15224	−	6.08764i	−0.654335	−	0.773131i
$63$		−	0.236266i		−	0.0297667i
$64$	3.82264	−	7.02762i	0.477830	−	0.878452i
$65$	−3.55940	−	1.78825i	−0.441489	−	0.221805i
$66$	−7.66931	+	1.75795i	−0.944027	+	0.216389i
$67$	10.3107			1.25965			0.629826	−	0.776736i	$-0.283126\pi$
$67$	10.3107			1.25965			0.629826	+	0.776736i	$0.283126\pi$
$68$	−2.77848	−	0.465686i	−0.336940	−	0.0564727i
$69$	4.33657			0.522061
$70$	1.28236	+	1.51517i	0.153271	+	0.181098i
$71$	−11.1238			−1.32015			−0.660074	−	0.751201i	$-0.729475\pi$
$71$	−11.1238			−1.32015			−0.660074	+	0.751201i	$0.729475\pi$
$72$	0.452146	−	0.268764i	0.0532859	−	0.0316742i
$73$	−10.0124			−1.17186			−0.585932	−	0.810360i	$-0.699271\pi$
$73$	−10.0124			−1.17186			−0.585932	+	0.810360i	$0.699271\pi$
$74$	−8.48048	+	7.17740i	−0.985836	+	0.834356i
$75$			6.34006i			0.732087i
$76$	−1.86913	−	0.313276i	−0.214404	−	0.0359352i
$77$	−1.93472	+	3.74325i	−0.220482	+	0.426583i
$78$	−2.00662	−	8.31495i	−0.227205	−	0.941482i
$79$	−7.91992			−0.891061			−0.445530	−	0.895267i	$-0.646985\pi$
$79$	−7.91992			−0.891061			−0.445530	+	0.895267i	$0.646985\pi$
$80$	−1.44086	+	4.17765i	−0.161093	+	0.467075i
$81$	−8.40751			−0.934168
$82$	−1.43961	−	1.70098i	−0.158979	−	0.187842i
$83$		−	12.5969i		−	1.38269i	−0.722525	−	0.691345i	$-0.757019\pi$
$83$		−	12.5969i		−	1.38269i	0.722525	−	0.691345i	$-0.242981\pi$
$84$	−0.704579	+	4.20382i	−0.0768758	+	0.458674i
$85$	1.55622			0.168796
$86$	−3.87396	−	4.57728i	−0.417739	−	0.493581i
$87$	16.4112			1.75946
$88$	−9.36436	+	0.555636i	−0.998244	+	0.0592310i
$89$		−	5.03112i		−	0.533298i	−0.963794	−	0.266649i	$-0.914084\pi$
$89$		−	5.03112i		−	0.533298i	0.963794	−	0.266649i	$-0.0859164\pi$
$90$	−0.221785	+	0.187707i	−0.0233782	+	0.0197860i
$91$	−4.09321	−	2.05644i	−0.429084	−	0.215573i
$92$	5.09913	+	0.854637i	0.531621	+	0.0891020i
$93$			9.46008i			0.980964i
$94$	−0.242241	−	0.286221i	−0.0249853	−	0.0295214i
$95$	1.04690			0.107409
$96$	−8.84640	+	3.43369i	−0.902882	+	0.350450i
$97$			15.8353i			1.60783i	0.594743	+	0.803916i	$0.297254\pi$
$97$			15.8353i			1.60783i	−0.594743	+	0.803916i	$0.702746\pi$
$98$	−4.92067	−	5.81403i	−0.497062	−	0.587306i
$99$	−0.547924	−	0.283197i	−0.0550684	−	0.0284624i
$100$	−1.24948	+	7.45491i	−0.124948	+	0.745491i
$101$		−	2.96407i		−	0.294936i	−0.989067	−	0.147468i	$-0.952888\pi$
$101$		−	2.96407i		−	0.294936i	0.989067	−	0.147468i	$-0.0471123\pi$
$102$	2.15885	+	2.55080i	0.213758	+	0.252567i
$103$			8.90842i			0.877772i	0.898543	+	0.438886i	$0.144627\pi$
$103$			8.90842i			0.877772i	−0.898543	+	0.438886i	$0.855373\pi$
$104$	−0.720789	−	10.1725i	−0.0706792	−	0.997499i
$105$		−	2.35455i		−	0.229780i
$106$	−4.87627	−	5.76157i	−0.473625	−	0.559613i
$107$	−13.6915			−1.32361			−0.661805	−	0.749676i	$-0.730209\pi$
$107$	−13.6915			−1.32361			−0.661805	+	0.749676i	$0.730209\pi$
$108$	−10.5419	−	1.76688i	−1.01440	−	0.170018i
$109$	−7.99559			−0.765839			−0.382919	−	0.923782i	$-0.625081\pi$
$109$	−7.99559			−0.765839			−0.382919	+	0.923782i	$0.625081\pi$
$110$	5.05091	−	1.15777i	0.481585	−	0.110389i
$111$	13.1785			1.25085
$112$	−1.65695	+	4.80417i	−0.156567	+	0.453952i
$113$	4.48064			0.421503			0.210751	−	0.977540i	$-0.432409\pi$
$113$	4.48064			0.421503			0.210751	+	0.977540i	$0.432409\pi$
$114$	1.45230	+	1.71597i	0.136020	+	0.160715i
$115$	−2.85601			−0.266324
$116$	19.2970	+	3.23427i	1.79168	+	0.300294i
$117$	0.301014	−	0.599149i	0.0278288	−	0.0553913i
$118$	−0.732044	−	0.864948i	−0.0673901	−	0.0796249i
$119$	1.78961			0.164053
$120$	4.50593	−	2.67842i	0.411334	−	0.244505i
$121$	6.36194	+	8.97361i	0.578358	+	0.815783i
$122$	4.56140	−	3.86051i	0.412970	−	0.349515i
$123$			2.64329i			0.238338i
$124$	−1.86436	+	11.1236i	−0.167425	+	0.998926i
$125$		−	9.69941i		−	0.867541i
$126$	−0.255047	+	0.215857i	−0.0227214	+	0.0192301i
$127$	17.4581			1.54916			0.774578	−	0.632479i	$-0.217962\pi$
$127$	17.4581			1.54916			0.774578	+	0.632479i	$0.217962\pi$
$128$	−11.0787	+	2.29406i	−0.979227	+	0.202768i
$129$			7.11301i			0.626266i
$130$	1.32153	+	5.47612i	0.115906	+	0.480287i
$131$	−7.08768			−0.619253			−0.309627	−	0.950858i	$-0.600204\pi$
$131$	−7.08768			−0.619253			−0.309627	+	0.950858i	$0.600204\pi$
$132$	8.90453	+	6.67284i	0.775040	+	0.580796i
$133$	1.20390			0.104392
$134$	−9.42005	−	11.1303i	−0.813769	−	0.961511i
$135$	5.90451			0.508179
$136$	2.03577	+	3.42480i	0.174566	+	0.293674i
$137$			14.1974i			1.21296i	0.795098	+	0.606481i	$0.207420\pi$
$137$			14.1974i			1.21296i	−0.795098	+	0.606481i	$0.792580\pi$
$138$	−3.96197	−	4.68128i	−0.337266	−	0.398497i
$139$	9.45130			0.801649			0.400824	−	0.916155i	$-0.368724\pi$
$139$	9.45130			0.801649			0.400824	+	0.916155i	$0.368724\pi$
$140$	0.464027	−	2.76858i	0.0392174	−	0.233988i
$141$			0.444782i			0.0374574i
$142$	10.1629	+	12.0080i	0.852851	+	1.00769i
$143$	−9.67536	+	7.02762i	−0.809094	+	0.587679i
$144$	−0.703218	−	0.242538i	−0.0586015	−	0.0202115i
$145$	−10.8082			−0.897573
$146$	9.14754	+	10.8083i	0.757056	+	0.894501i
$147$			9.03489i			0.745185i
$148$	15.4959	+	2.59718i	1.27375	+	0.213487i
$149$	11.5223			0.943943			0.471972	−	0.881614i	$-0.343543\pi$
$149$	11.5223			0.943943			0.471972	+	0.881614i	$0.343543\pi$
$150$	6.84403	−	5.79240i	0.558813	−	0.472948i
$151$			4.94593i			0.402494i	0.979541	+	0.201247i	$0.0644994\pi$
$151$			4.94593i			0.402494i	−0.979541	+	0.201247i	$0.935501\pi$
$152$	1.36950	+	2.30393i	0.111081	+	0.186873i
$153$			0.261956i			0.0211779i
$154$	5.80840	−	1.33140i	0.468054	−	0.107287i
$155$		−	6.23029i		−	0.500429i
$156$	−7.14261	+	9.76283i	−0.571867	+	0.781652i
$157$	−14.3545			−1.14562			−0.572808	−	0.819690i	$-0.694146\pi$
$157$	−14.3545			−1.14562			−0.572808	+	0.819690i	$0.694146\pi$
$158$	7.23580	+	8.54948i	0.575649	+	0.680160i
$159$			8.95337i			0.710049i
$160$	5.82613	−	2.26139i	0.460596	−	0.178778i
$161$	−3.28433			−0.258841
$162$	7.68127	+	9.07583i	0.603498	+	0.713064i
$163$	−9.26462			−0.725661			−0.362831	−	0.931855i	$-0.618190\pi$
$163$	−9.26462			−0.725661			−0.362831	+	0.931855i	$0.618190\pi$
$164$	−0.520932	+	3.10810i	−0.0406779	+	0.242702i
$165$	−5.46043	−	2.82225i	−0.425094	−	0.219712i
$166$	−13.5982	+	11.5088i	−1.05543	+	0.893254i
$167$			18.2430i			1.41168i	0.708370	+	0.705841i	$0.249431\pi$
$167$			18.2430i			1.41168i	−0.708370	+	0.705841i	$0.750569\pi$
$168$	5.18169	−	3.08010i	0.399776	−	0.237635i
$169$	−7.75999	−	10.4299i	−0.596922	−	0.802299i
$170$	−1.42179	−	1.67992i	−0.109047	−	0.128844i
$171$			0.176223i			0.0134761i
$172$	−1.40181	+	8.36379i	−0.106887	+	0.637733i
$173$			13.9837i			1.06316i	0.847009	+	0.531579i	$0.178401\pi$
$173$			13.9837i			1.06316i	−0.847009	+	0.531579i	$0.821599\pi$
$174$	−14.9936	−	17.7157i	−1.13666	−	1.34303i
$175$		−	4.80168i		−	0.362973i
$176$	9.15527	+	9.60110i	0.690104	+	0.723710i
$177$			1.34411i			0.101030i
$178$	−5.43104	+	4.59653i	−0.407074	+	0.344525i
$179$		−	13.8697i		−	1.03667i	−0.855178	−	0.518334i	$-0.826552\pi$
$179$		−	13.8697i		−	1.03667i	0.855178	−	0.518334i	$-0.173448\pi$
$180$	0.405255	+	0.0679226i	0.0302059	+	0.00506265i
$181$	10.5358			0.783123			0.391561	−	0.920152i	$-0.371935\pi$
$181$	10.5358			0.783123			0.391561	+	0.920152i	$0.371935\pi$
$182$	1.51973	+	6.29738i	0.112650	+	0.466793i
$183$	−7.08834			−0.523985
$184$	−3.73609	−	6.28527i	−0.275428	−	0.463356i
$185$	−8.67920			−0.638108
$186$	10.2121	−	8.64292i	0.748785	−	0.633729i
$187$	2.14509	−	4.15028i	0.156865	−	0.303498i
$188$	−0.0876562	+	0.522994i	−0.00639299	+	0.0381433i
$189$	6.79002			0.493901
$190$	−0.956467	−	1.13012i	−0.0693894	−	0.0819872i
$191$		−	26.4504i		−	1.91388i	−0.290283	−	0.956941i	$-0.593750\pi$
$191$		−	26.4504i		−	1.91388i	0.290283	−	0.956941i	$-0.406250\pi$
$192$	11.7889	+	6.41251i	0.850789	+	0.462783i
$193$	−23.3881			−1.68351			−0.841755	−	0.539860i	$-0.818477\pi$
$193$	−23.3881			−1.68351			−0.841755	+	0.539860i	$0.818477\pi$
$194$	17.0941	−	14.4675i	1.22728	−	1.03870i
$195$	2.99981	−	5.97092i	0.214821	−	0.427586i
$196$	−1.78057	+	10.6236i	−0.127183	+	0.758830i
$197$	18.4367			1.31356			0.656782	−	0.754081i	$-0.271917\pi$
$197$	18.4367			1.31356			0.656782	+	0.754081i	$0.271917\pi$
$198$	0.194885	+	0.850213i	0.0138499	+	0.0604220i
$199$		−	16.5580i		−	1.17377i	−0.809671	−	0.586884i	$-0.800354\pi$
$199$		−	16.5580i		−	1.17377i	0.809671	−	0.586884i	$-0.199646\pi$
$200$	9.18905	−	5.46216i	0.649764	−	0.386233i
$201$			17.2963i			1.21998i
$202$	−3.19968	+	2.70803i	−0.225129	+	0.190536i
$203$	−12.4291			−0.872354
$204$	0.781191	−	4.66092i	0.0546943	−	0.326330i
$205$		−	1.74084i		−	0.121585i
$206$	9.61655	−	8.13890i	0.670017	−	0.567064i
$207$		−	0.480748i		−	0.0334143i
$208$	−10.3226	+	10.0719i	−0.715745	+	0.698362i
$209$	1.44304	−	2.79197i	0.0998175	−	0.193125i
$210$	−2.54171	+	2.15116i	−0.175395	+	0.148444i
$211$	−21.6526			−1.49063			−0.745314	−	0.666714i	$-0.767700\pi$
$211$	−21.6526			−1.49063			−0.745314	+	0.666714i	$0.767700\pi$
$212$	−1.76450	+	10.5278i	−0.121186	+	0.723050i
$213$		−	18.6602i		−	1.27858i
$214$	12.5089	+	14.7799i	0.855087	+	1.01033i
$215$		−	4.68454i		−	0.319483i
$216$	7.72399	+	12.9942i	0.525551	+	0.884141i
$217$		−	7.16465i		−	0.486368i
$218$	7.30493	+	8.63116i	0.494752	+	0.584576i
$219$		−	16.7959i		−	1.13496i
$220$	−5.86441	−	4.39465i	−0.395378	−	0.296287i
$221$	4.53828	+	2.28005i	0.305278	+	0.153373i
$222$	−12.0402	−	14.2261i	−0.808082	−	0.954792i
$223$	−4.27837			−0.286501			−0.143251	−	0.989686i	$-0.545755\pi$
$223$	−4.27837			−0.286501			−0.143251	+	0.989686i	$0.545755\pi$
$224$	6.69988	−	2.60053i	0.447655	−	0.173755i
$225$	0.702853			0.0468569
$226$	−4.09360	−	4.83680i	−0.272302	−	0.321739i
$227$		−	1.22344i		−	0.0812028i	−0.999175	−	0.0406014i	$-0.987073\pi$
$227$		−	1.22344i		−	0.0812028i	0.999175	−	0.0406014i	$-0.0129274\pi$
$228$	0.525522	−	3.13549i	0.0348036	−	0.207653i
$229$			11.1604i			0.737498i	0.929529	+	0.368749i	$0.120214\pi$
$229$			11.1604i			0.737498i	−0.929529	+	0.368749i	$0.879786\pi$
$230$	2.60931	+	3.08303i	0.172053	+	0.203289i
$231$	−6.27933	−	3.24551i	−0.413150	−	0.213539i
$232$	−14.1388	−	23.7858i	−0.928255	−	1.56161i
$233$			9.25724i			0.606462i	0.952917	+	0.303231i	$0.0980654\pi$
$233$			9.25724i			0.606462i	−0.952917	+	0.303231i	$0.901935\pi$
$234$	−0.921788	+	0.222452i	−0.0602592	+	0.0145422i
$235$		−	0.292928i		−	0.0191085i
$236$	−0.264894	+	1.58047i	−0.0172431	+	0.102880i
$237$		−	13.2857i		−	0.863001i
$238$	−1.63502	−	1.93186i	−0.105983	−	0.125224i
$239$			20.7938i			1.34504i	0.740079	+	0.672520i	$0.234788\pi$
$239$			20.7938i			1.34504i	−0.740079	+	0.672520i	$0.765212\pi$
$240$	−7.00804	−	2.41706i	−0.452367	−	0.156020i
$241$	−0.892259			−0.0574755			−0.0287377	−	0.999587i	$-0.509149\pi$
$241$	−0.892259			−0.0574755			−0.0287377	+	0.999587i	$0.509149\pi$
$242$	3.87453	−	15.0661i	0.249064	−	0.968487i
$243$			1.92978i			0.123796i
$244$	−8.33478	−	1.39695i	−0.533579	−	0.0894303i
$245$		−	5.95027i		−	0.380149i
$246$	2.85341	−	2.41496i	0.181927	−	0.153973i
$247$	3.05299	+	1.53383i	0.194257	+	0.0975953i
$248$	13.7111	−	8.15016i	0.870656	−	0.517535i
$249$	21.1314			1.33915
$250$	−10.4704	+	8.86157i	−0.662207	+	0.560455i
$251$		−	16.1974i		−	1.02237i	−0.859471	−	0.511185i	$-0.829207\pi$
$251$		−	16.1974i		−	1.02237i	0.859471	−	0.511185i	$-0.170793\pi$
$252$	0.466031	+	0.0781090i	0.0293572	+	0.00492040i
$253$	−3.93672	+	7.61668i	−0.247500	+	0.478856i
$254$	−15.9501	−	18.8458i	−1.00080	−	1.18249i
$255$			2.61057i			0.163480i
$256$	12.5981	+	9.86343i	0.787383	+	0.616464i
$257$	−24.6407			−1.53705			−0.768523	−	0.639822i	$-0.779008\pi$
$257$	−24.6407			−1.53705			−0.768523	+	0.639822i	$0.779008\pi$
$258$	7.67843	−	6.49859i	0.478038	−	0.404585i
$259$	−9.98083			−0.620179
$260$	4.70404	−	6.42967i	0.291732	−	0.398751i
$261$		−	1.81933i		−	0.112614i
$262$	6.47544	+	7.65108i	0.400054	+	0.472685i
$263$	−7.39174			−0.455794			−0.227897	−	0.973685i	$-0.573185\pi$
$263$	−7.39174			−0.455794			−0.227897	+	0.973685i	$0.573185\pi$
$264$	−0.932084	−	15.7088i	−0.0573658	−	0.966809i
$265$		−	5.89658i		−	0.362224i
$266$	−1.09991	−	1.29960i	−0.0674398	−	0.0796836i
$267$	8.43974			0.516504
$268$	−3.40869	+	20.3377i	−0.208219	+	1.24232i
$269$	−17.0000			−1.03651			−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000			−1.03651			−0.518254	+	0.855227i	$0.673418\pi$
$270$	−5.39448	−	6.37386i	−0.328297	−	0.387901i
$271$			7.36919i			0.447647i	0.974630	+	0.223823i	$0.0718539\pi$
$271$			7.36919i			0.447647i	−0.974630	+	0.223823i	$0.928146\pi$
$272$	1.83712	−	5.32656i	0.111392	−	0.322970i
$273$	3.44969	−	6.86638i	0.208785	−	0.415572i
$274$	15.3259	−	12.9710i	0.925872	−	0.783606i
$275$	−11.1356	−	5.75548i	−0.671500	−	0.347069i
$276$	−1.43366	+	8.55382i	−0.0862962	+	0.514880i
$277$			17.7070i			1.06391i	0.846772	+	0.531955i	$0.178543\pi$
$277$			17.7070i			1.06391i	−0.846772	+	0.531955i	$0.821457\pi$
$278$	−8.63490	−	10.2026i	−0.517887	−	0.611910i
$279$	1.04874			0.0627862
$280$	−3.41260	+	2.02852i	−0.203942	+	0.121227i
$281$	13.3348			0.795485			0.397743	−	0.917497i	$-0.369794\pi$
$281$	13.3348			0.795485			0.397743	+	0.917497i	$0.369794\pi$
$282$	0.480138	−	0.406362i	0.0285918	−	0.0241985i
$283$	0.959367			0.0570284			0.0285142	−	0.999593i	$-0.490922\pi$
$283$	0.959367			0.0570284			0.0285142	+	0.999593i	$0.490922\pi$
$284$	3.67749	−	21.9415i	0.218219	−	1.30199i
$285$			1.75618i			0.104027i
$286$	16.4258	+	4.02388i	0.971281	+	0.237937i
$287$		−	2.00191i		−	0.118169i
$288$	0.380656	+	0.980704i	0.0224304	+	0.0577886i
$289$	15.0158			0.883282
$290$	9.87459	+	11.6674i	0.579856	+	0.685130i
$291$	−26.5639			−1.55720
$292$	3.31008	−	19.7494i	0.193708	−	1.15574i
$293$	6.63138			0.387409			0.193705	−	0.981060i	$-0.437950\pi$
$293$	6.63138			0.387409			0.193705	+	0.981060i	$0.437950\pi$
$294$	9.75308	−	8.25446i	0.568811	−	0.481410i
$295$		−	0.885216i		−	0.0515393i
$296$	−11.3537	−	19.1005i	−0.659921	−	1.11019i
$297$	8.13878	−	15.7467i	0.472260	−	0.913717i
$298$	−10.5270	−	12.4382i	−0.609812	−	0.720526i
$299$	−8.32876	−	4.18439i	−0.481664	−	0.241990i
$300$	−12.5057	−	2.09601i	−0.722016	−	0.121013i
$301$		−	5.38709i		−	0.310507i
$302$	5.33908	−	4.51870i	0.307230	−	0.260022i
$303$	4.97225			0.285648
$304$	1.23586	−	3.58328i	0.0708816	−	0.205515i
$305$	4.66829			0.267305
$306$	0.282779	−	0.239328i	0.0161654	−	0.0136815i
$307$		−	7.55650i		−	0.431272i	−0.976474	−	0.215636i	$-0.930818\pi$
$307$		−	7.55650i		−	0.431272i	0.976474	−	0.215636i	$-0.0691825\pi$
$308$	−6.74390	−	5.05372i	−0.384269	−	0.287962i
$309$	−14.9439			−0.850131
$310$	−6.72553	+	5.69211i	−0.381985	+	0.323290i
$311$		−	5.99168i		−	0.339757i	−0.985465	−	0.169879i	$-0.945662\pi$
$311$		−	5.99168i		−	0.339757i	0.985465	−	0.169879i	$-0.0543376\pi$
$312$	17.0645	−	1.20913i	0.966088	−	0.0684535i
$313$	−3.35058			−0.189386			−0.0946931	−	0.995507i	$-0.530187\pi$
$313$	−3.35058			−0.189386			−0.0946931	+	0.995507i	$0.530187\pi$
$314$	13.1146	+	15.4956i	0.740098	+	0.874466i
$315$	−0.261023			−0.0147070
$316$	2.61831	−	15.6219i	0.147291	−	0.878803i
$317$			13.8147i			0.775912i	0.921678	+	0.387956i	$0.126819\pi$
$317$			13.8147i			0.775912i	−0.921678	+	0.387956i	$0.873181\pi$
$318$	9.66508	−	8.17998i	0.541991	−	0.458710i
$319$	−14.8980	+	28.8244i	−0.834129	+	1.61385i
$320$	−7.76401	−	4.22320i	−0.434021	−	0.236084i
$321$		−	22.9676i		−	1.28193i
$322$	3.00063	+	3.54540i	0.167218	+	0.197577i
$323$	−1.33481			−0.0742708
$324$	2.77951	−	16.5837i	0.154417	−	0.921317i
$325$	6.11758	−	12.1766i	0.339342	−	0.675438i
$326$	8.46434	+	10.0011i	0.468797	+	0.553908i
$327$		−	13.4127i		−	0.741722i
$328$	3.83110	−	2.27728i	0.211537	−	0.125742i
$329$		−	0.336859i		−	0.0185716i
$330$	1.94216	+	8.47294i	0.106912	+	0.466420i
$331$	5.70350			0.313493			0.156746	−	0.987639i	$-0.449900\pi$
$331$	5.70350			0.313493			0.156746	+	0.987639i	$0.449900\pi$
$332$	24.8472	+	4.16451i	1.36367	+	0.228557i
$333$		−	1.46096i		−	0.0800600i
$334$	19.6931	−	16.6671i	1.07756	−	0.911984i
$335$		−	11.3911i		−	0.622363i
$336$	−8.05904	−	2.77954i	−0.439657	−	0.151637i
$337$			21.1705i			1.15323i	0.817015	+	0.576616i	$0.195627\pi$
$337$			21.1705i			1.15323i	−0.817015	+	0.576616i	$0.804373\pi$
$338$	−4.16928	+	17.9058i	−0.226779	+	0.973946i
$339$			7.51630i			0.408230i
$340$	−0.514483	+	3.06962i	−0.0279017	+	0.166474i
$341$	−16.6155	−	8.58783i	−0.899782	−	0.465057i
$342$	0.190231	−	0.161001i	0.0102865	−	0.00870593i
$343$		−	15.7359i		−	0.849661i
$344$	10.3094	−	6.12809i	0.555843	−	0.330404i
$345$		−	4.79098i		−	0.257937i
$346$	15.0952	−	12.7758i	0.811525	−	0.686829i
$347$	26.1754			1.40517			0.702584	−	0.711601i	$-0.252030\pi$
$347$	26.1754			1.40517			0.702584	+	0.711601i	$0.252030\pi$
$348$	−5.42551	+	32.3709i	−0.290838	+	1.73526i
$349$	0.953092			0.0510179			0.0255089	−	0.999675i	$-0.491879\pi$
$349$	0.953092			0.0510179			0.0255089	+	0.999675i	$0.491879\pi$
$350$	−5.18337	+	4.38691i	−0.277063	+	0.234490i
$351$	17.2189	+	8.65081i	0.919075	+	0.461746i
$352$	1.99985	−	18.6548i	0.106593	−	0.994303i
$353$			34.4757i			1.83496i	0.397786	+	0.917478i	$0.369779\pi$
$353$			34.4757i			1.83496i	−0.397786	+	0.917478i	$0.630221\pi$
$354$	1.45096	−	1.22801i	0.0771175	−	0.0652679i
$355$			12.2894i			0.652252i
$356$	9.92382	+	1.66328i	0.525961	+	0.0881535i
$357$			3.00208i			0.158887i
$358$	−14.9722	+	12.6716i	−0.791304	+	0.669716i
$359$		−	3.10906i		−	0.164090i	−0.996629	−	0.0820450i	$-0.973855\pi$
$359$		−	3.10906i		−	0.164090i	0.996629	−	0.0820450i	$-0.0261451\pi$
$360$	−0.296927	−	0.499524i	−0.0156494	−	0.0263272i
$361$	18.1020			0.952739
$362$	−9.62575	−	11.3733i	−0.505918	−	0.597769i
$363$	−15.0533	+	10.6722i	−0.790094	+	0.560145i
$364$	5.40951	−	7.39394i	0.283535	−	0.387548i
$365$			11.0616i			0.578989i
$366$	6.47604	+	7.65179i	0.338508	+	0.399965i
$367$			15.9489i			0.832526i	0.909244	+	0.416263i	$0.136660\pi$
$367$			15.9489i			0.832526i	−0.909244	+	0.416263i	$0.863340\pi$
$368$	−3.37152	+	9.77542i	−0.175753	+	0.509579i
$369$	0.293033			0.0152547
$370$	7.92949	+	9.36911i	0.412235	+	0.487077i
$371$		−	6.78089i		−	0.352046i
$372$	−18.6599	−	3.12748i	−0.967470	−	0.162152i
$373$		−	12.2599i		−	0.634792i	−0.948293	−	0.317396i	$-0.897192\pi$
$373$		−	12.2599i		−	0.634792i	0.948293	−	0.317396i	$-0.102808\pi$
$374$	−6.43998	+	1.47617i	−0.333003	+	0.0763308i
$375$	16.2708			0.840222
$376$	0.644652	−	0.383194i	0.0332454	−	0.0197617i
$377$	−31.5191	−	15.8353i	−1.62332	−	0.815560i
$378$	−6.20349	−	7.32976i	−0.319073	−	0.377002i
$379$	8.20078			0.421246			0.210623	−	0.977567i	$-0.432451\pi$
$379$	8.20078			0.421246			0.210623	+	0.977567i	$0.432451\pi$
$380$	−0.346102	+	2.06499i	−0.0177547	+	0.105932i
$381$			29.2861i			1.50037i
$382$	−28.5529	+	24.1656i	−1.46089	+	1.23642i
$383$	37.2973			1.90581			0.952903	−	0.303276i	$-0.0980804\pi$
$383$	37.2973			1.90581			0.952903	+	0.303276i	$0.0980804\pi$
$384$	−3.84831	−	18.5846i	−0.196383	−	0.948391i
$385$	4.13549	+	2.13745i	0.210764	+	0.108935i
$386$	21.3678	+	25.2472i	1.08759	+	1.28505i
$387$	0.788543			0.0400839
$388$	−31.2349	−	5.23512i	−1.58571	−	0.265773i
$389$	−8.68887			−0.440543			−0.220272	−	0.975439i	$-0.570694\pi$
$389$	−8.68887			−0.440543			−0.220272	+	0.975439i	$0.570694\pi$
$390$	−9.18623	+	2.21688i	−0.465163	+	0.112256i
$391$	3.64145			0.184156
$392$	13.0949	−	7.78385i	0.661390	−	0.393144i
$393$		−	11.8896i		−	0.599753i
$394$	−16.8442	−	19.9023i	−0.848597	−	1.00266i
$395$			8.74981i			0.440251i
$396$	0.739746	−	0.987148i	0.0371736	−	0.0496061i
$397$			21.4029i			1.07418i	0.843524	+	0.537091i	$0.180477\pi$
$397$			21.4029i			1.07418i	−0.843524	+	0.537091i	$0.819523\pi$
$398$	−17.8742	+	15.1278i	−0.895955	+	0.758286i
$399$			2.01956i			0.101104i
$400$	−14.2916	−	4.92916i	−0.714582	−	0.246458i
$401$		−	13.9031i		−	0.694288i	−0.937812	−	0.347144i	$-0.887152\pi$
$401$		−	13.9031i		−	0.694288i	0.937812	−	0.347144i	$-0.112848\pi$
$402$	18.6712	−	15.8022i	0.931233	−	0.788143i
$403$	9.12812	−	18.1689i	0.454704	−	0.905058i
$404$	5.84658	+	0.979914i	0.290878	+	0.0487526i
$405$			9.28850i			0.461549i
$406$	11.3555	+	13.4171i	0.563564	+	0.665880i
$407$	−11.9634	+	23.1465i	−0.593004	+	1.14733i
$408$	−5.74513	+	3.41502i	−0.284426	+	0.169069i
$409$	35.8638			1.77335			0.886676	−	0.462391i	$-0.153008\pi$
$409$	35.8638			1.77335			0.886676	+	0.462391i	$0.153008\pi$
$410$	−1.87922	+	1.59046i	−0.0928080	+	0.0785475i
$411$	−23.8162			−1.17477
$412$	−17.5717	−	2.94510i	−0.865697	−	0.145095i
$413$		−	1.01797i		−	0.0500912i
$414$	−0.518963	+	0.439221i	−0.0255056	+	0.0215865i
$415$	−13.9169			−0.683152
$416$	20.3035	+	1.94127i	0.995460	+	0.0951786i
$417$			15.8546i			0.776405i
$418$	−4.33230	+	0.993046i	−0.211900	+	0.0485715i
$419$		−	1.60374i		−	0.0783479i	−0.999232	−	0.0391740i	$-0.987527\pi$
$419$		−	1.60374i		−	0.0783479i	0.999232	−	0.0391740i	$-0.0124726\pi$
$420$	4.64431	+	0.778408i	0.226619	+	0.0379824i
$421$		−	6.30644i		−	0.307357i	−0.988121	−	0.153679i	$-0.950888\pi$
$421$		−	6.30644i		−	0.307357i	0.988121	−	0.153679i	$-0.0491120\pi$
$422$	19.7823	+	23.3738i	0.962985	+	1.13782i
$423$	0.0493082			0.00239745
$424$	12.9767	−	7.71361i	0.630204	−	0.374606i
$425$			5.32379i			0.258242i
$426$	−20.1435	+	17.0483i	−0.975956	+	0.825994i
$427$	5.36840			0.259795
$428$	4.52639	−	27.0064i	0.218791	−	1.30540i
$429$	−11.7889	−	16.2305i	−0.569173	−	0.783616i
$430$	−5.05692	+	4.27989i	−0.243866	+	0.206395i
$431$			16.3244i			0.786317i	0.919471	+	0.393158i	$0.128618\pi$
$431$			16.3244i			0.786317i	−0.919471	+	0.393158i	$0.871382\pi$
$432$	6.97028	−	20.2097i	0.335358	−	0.972339i
$433$	19.7915			0.951118			0.475559	−	0.879684i	$-0.342246\pi$
$433$	19.7915			0.951118			0.475559	+	0.879684i	$0.342246\pi$
$434$	−7.73417	+	6.54577i	−0.371252	+	0.314207i
$435$		−	18.1308i		−	0.869308i
$436$	2.64332	−	15.7712i	0.126592	−	0.755303i
$437$	2.44967			0.117184
$438$	−18.1310	+	15.3451i	−0.866333	+	0.733216i
$439$	30.0570			1.43454			0.717272	−	0.696794i	$-0.245391\pi$
$439$	30.0570			1.43454			0.717272	+	0.696794i	$0.245391\pi$
$440$	0.613859	+	10.3456i	0.0292646	+	0.493208i
$441$	1.00160			0.0476953
$442$	−1.68497	−	6.98213i	−0.0801461	−	0.332106i
$443$			10.8198i			0.514065i	0.966403	+	0.257032i	$0.0827447\pi$
$443$			10.8198i			0.514065i	−0.966403	+	0.257032i	$0.917255\pi$
$444$	−4.35679	+	25.9944i	−0.206764	+	1.23364i
$445$	−5.55831			−0.263489
$446$	3.90881	+	4.61846i	0.185087	+	0.218690i
$447$			19.3287i			0.914218i
$448$	−8.92839	−	4.85656i	−0.421827	−	0.229451i
$449$			9.35084i			0.441293i	0.975354	+	0.220647i	$0.0708168\pi$
$449$			9.35084i			0.441293i	−0.975354	+	0.220647i	$0.929183\pi$
$450$	−0.642141	−	0.758723i	−0.0302708	−	0.0357665i
$451$	−4.64264	−	2.39957i	−0.218613	−	0.112991i
$452$	−1.48129	+	8.83800i	−0.0696740	+	0.415704i
$453$	−8.29683			−0.389819
$454$	−1.32070	+	1.11776i	−0.0619833	+	0.0524592i
$455$	−2.27192	+	4.52211i	−0.106509	+	0.212000i
$456$	−3.86486	+	2.29735i	−0.180988	+	0.107583i
$457$	−8.51503			−0.398316			−0.199158	−	0.979967i	$-0.563821\pi$
$457$	−8.51503			−0.398316			−0.199158	+	0.979967i	$0.563821\pi$
$458$	12.0475	−	10.1963i	0.562943	−	0.476443i
$459$	−7.52833			−0.351392
$460$	0.944190	−	5.63344i	0.0440231	−	0.262660i
$461$	−23.3707			−1.08848			−0.544241	−	0.838929i	$-0.683182\pi$
$461$	−23.3707			−1.08848			−0.544241	+	0.838929i	$0.683182\pi$
$462$	2.23343	+	9.74364i	0.103909	+	0.453315i
$463$	23.0963			1.07337			0.536687	−	0.843781i	$-0.319676\pi$
$463$	23.0963			1.07337			0.536687	+	0.843781i	$0.319676\pi$
$464$	−12.7591	+	36.9938i	−0.592326	+	1.71740i
$465$	10.4514			0.484670
$466$	9.99310	−	8.45760i	0.462922	−	0.391791i
$467$			25.7065i			1.18956i	0.803890	+	0.594778i	$0.202760\pi$
$467$			25.7065i			1.18956i	−0.803890	+	0.594778i	$0.797240\pi$
$468$	1.08230	+	0.791824i	0.0500293	+	0.0366021i
$469$		−	13.0994i		−	0.604876i
$470$	−0.316213	+	0.267625i	−0.0145858	+	0.0123446i
$471$		−	24.0798i		−	1.10954i
$472$	1.94811	−	1.15800i	0.0896691	−	0.0533011i
$473$	−12.4932	−	6.45717i	−0.574437	−	0.296901i
$474$	−14.3418	+	12.1381i	−0.658741	+	0.557522i
$475$			3.58142i			0.164327i
$476$	−0.591640	+	3.52998i	−0.0271178	+	0.161796i
$477$	0.992563			0.0454463
$478$	22.4467	−	18.9976i	1.02669	−	0.868932i
$479$		−	6.79360i		−	0.310408i	−0.987882	−	0.155204i	$-0.950397\pi$
$479$		−	6.79360i		−	0.310408i	0.987882	−	0.155204i	$-0.0496034\pi$
$480$	3.79349	+	9.77338i	0.173148	+	0.446092i
$481$	−25.3105	−	12.7161i	−1.15406	−	0.579803i
$482$	0.815186	+	0.963185i	0.0371307	+	0.0438719i
$483$		−	5.50949i		−	0.250690i
$484$	−19.8036	+	9.58219i	−0.900163	+	0.435554i
$485$	17.4946			0.794390
$486$	2.08318	−	1.76309i	0.0944950	−	0.0799753i
$487$	11.9308			0.540638			0.270319	−	0.962771i	$-0.412871\pi$
$487$	11.9308			0.540638			0.270319	+	0.962771i	$0.412871\pi$
$488$	6.10683	+	10.2736i	0.276443	+	0.465063i
$489$		−	15.5415i		−	0.702810i
$490$	−6.42325	+	5.43628i	−0.290173	+	0.245586i
$491$	20.2617			0.914398			0.457199	−	0.889364i	$-0.348853\pi$
$491$	20.2617			0.914398			0.457199	+	0.889364i	$0.348853\pi$
$492$	−5.21386	−	0.873867i	−0.235059	−	0.0393970i
$493$	13.7806			0.620647
$494$	−1.13351	−	4.69701i	−0.0509992	−	0.211328i
$495$	−0.312872	+	0.605338i	−0.0140626	+	0.0272079i
$496$	−21.3248	−	7.35486i	−0.957510	−	0.330243i
$497$			14.1324i			0.633926i
$498$	−19.3061	−	22.8111i	−0.865125	−	1.02219i
$499$	−25.9523			−1.16178			−0.580891	−	0.813981i	$-0.697296\pi$
$499$	−25.9523			−1.16178			−0.580891	+	0.813981i	$0.697296\pi$
$500$	19.1320	+	3.20660i	0.855607	+	0.143404i
$501$	−30.6027			−1.36723
$502$	−17.4849	+	14.7983i	−0.780391	+	0.660479i
$503$	21.2219			0.946236			0.473118	−	0.880999i	$-0.343128\pi$
$503$	21.2219			0.946236			0.473118	+	0.880999i	$0.343128\pi$
$504$	−0.341458	−	0.574438i	−0.0152097	−	0.0255875i
$505$	−3.27466			−0.145720
$506$	11.8188	−	2.70910i	0.525410	−	0.120434i
$507$	17.4962	−	13.0174i	0.777034	−	0.578125i
$508$	−5.77161	+	34.4359i	−0.256074	+	1.52784i
$509$			3.90141i			0.172927i	0.996255	+	0.0864635i	$0.0275566\pi$
$509$			3.90141i			0.172927i	−0.996255	+	0.0864635i	$0.972443\pi$
$510$	2.81808	−	2.38507i	0.124787	−	0.105613i
$511$			12.7205i			0.562721i
$512$	−0.862421	−	22.6110i	−0.0381140	−	0.999273i
$513$	−5.06445			−0.223601
$514$	22.5123	+	26.5994i	0.992973	+	1.17325i
$515$	9.84189			0.433685
$516$	−14.0303	−	2.35155i	−0.617651	−	0.103521i
$517$	−0.781208	−	0.403772i	−0.0343575	−	0.0177579i
$518$	9.11869	+	10.7742i	0.400652	+	0.473392i
$519$	−23.4577			−1.02968
$520$	−11.2385	+	0.796317i	−0.492839	+	0.0349208i
$521$	1.17608			0.0515252			0.0257626	−	0.999668i	$-0.491799\pi$
$521$	1.17608			0.0515252			0.0257626	+	0.999668i	$0.491799\pi$
$522$	−1.96395	+	1.66218i	−0.0859597	+	0.0727515i
$523$	37.3218			1.63197			0.815983	−	0.578076i	$-0.196196\pi$
$523$	37.3218			1.63197			0.815983	+	0.578076i	$0.196196\pi$
$524$	2.34317	−	13.9803i	0.102362	−	0.610734i
$525$	8.05486			0.351543
$526$	6.75324	+	7.97931i	0.294455	+	0.347914i
$527$			7.94370i			0.346033i
$528$	−16.1059	+	15.3580i	−0.700920	+	0.668373i
$529$	16.3171			0.709440
$530$	−6.36530	+	5.38723i	−0.276491	+	0.234006i
$531$	0.149007			0.00646637
$532$	−0.398008	+	2.37468i	−0.0172558	+	0.102956i
$533$	2.55054	−	5.07667i	0.110476	−	0.219895i
$534$	−7.71072	−	9.11062i	−0.333675	−	0.394255i
$535$			15.1262i			0.653963i
$536$	25.0686	−	14.9013i	1.08280	−	0.643637i
$537$	23.2665			1.00402
$538$	15.5315	+	18.3513i	0.669612	+	0.791181i
$539$	−15.8687	−	8.20185i	−0.683515	−	0.353279i
$540$	−1.95202	+	11.6466i	−0.0840015	+	0.501188i
$541$	−18.2148			−0.783113			−0.391557	−	0.920154i	$-0.628063\pi$
$541$	−18.2148			−0.783113			−0.391557	+	0.920154i	$0.628063\pi$
$542$	7.95497	−	6.73264i	0.341695	−	0.289192i
$543$			17.6739i			0.758462i
$544$	−7.42839	+	2.88330i	−0.318490	+	0.123620i
$545$			8.83341i			0.378382i
$546$	−10.5639	+	2.54935i	−0.452093	+	0.109102i
$547$	−22.5434			−0.963886			−0.481943	−	0.876203i	$-0.660069\pi$
$547$	−22.5434			−0.963886			−0.481943	+	0.876203i	$0.660069\pi$
$548$	−28.0041	−	4.69362i	−1.19628	−	0.200501i
$549$			0.785807i			0.0335374i
$550$	3.96070	+	17.2791i	0.168885	+	0.736782i
$551$	9.27048			0.394936
$552$	10.5436	−	6.26732i	0.448765	−	0.266755i
$553$			10.0620i			0.427881i
$554$	19.1145	−	16.1775i	0.812099	−	0.687315i
$555$		−	14.5594i		−	0.618013i
$556$	−3.12458	+	18.6426i	−0.132512	+	0.790621i
$557$	−8.53866			−0.361795			−0.180897	−	0.983502i	$-0.557900\pi$
$557$	−8.53866			−0.361795			−0.180897	+	0.983502i	$0.557900\pi$
$558$	−0.958146	−	1.13210i	−0.0405616	−	0.0479256i
$559$	6.86341	−	13.6612i	0.290291	−	0.577806i
$560$	5.30758	+	1.83057i	0.224286	+	0.0773558i
$561$	6.96212	+	3.59841i	0.293941	+	0.151925i
$562$	−12.1829	−	14.3947i	−0.513905	−	0.607206i
$563$	−27.5197			−1.15982			−0.579908	−	0.814682i	$-0.696911\pi$
$563$	−27.5197			−1.15982			−0.579908	+	0.814682i	$0.696911\pi$
$564$	−0.877327	−	0.147044i	−0.0369421	−	0.00619167i
$565$		−	4.95014i		−	0.208254i
$566$	−0.876497	−	1.03563i	−0.0368419	−	0.0435307i
$567$			10.6815i			0.448581i
$568$	−27.0454	+	16.0764i	−1.13480	+	0.674549i
$569$		−	18.7923i		−	0.787815i	−0.919150	−	0.393908i	$-0.871123\pi$
$569$		−	18.7923i		−	0.787815i	0.919150	−	0.393908i	$-0.128877\pi$
$570$	1.89578	−	1.60448i	0.0794054	−	0.0672043i
$571$	−19.1261			−0.800401			−0.400200	−	0.916428i	$-0.631059\pi$
$571$	−19.1261			−0.800401			−0.400200	+	0.916428i	$0.631059\pi$
$572$	−10.6632	−	21.4078i	−0.445852	−	0.895107i
$573$	44.3707			1.85361
$574$	−2.16105	+	1.82899i	−0.0902004	+	0.0763405i
$575$		−	9.77035i		−	0.407452i
$576$	0.710886	−	1.30691i	0.0296202	−	0.0544544i
$577$		−	39.2228i		−	1.63287i	−0.577440	−	0.816433i	$-0.695948\pi$
$577$		−	39.2228i		−	1.63287i	0.577440	−	0.816433i	$-0.304052\pi$
$578$	−13.7187	−	16.2094i	−0.570624	−	0.674222i
$579$		−	39.2337i		−	1.63049i
$580$	3.57317	−	21.3190i	0.148368	−	0.885225i
$581$	−16.0040			−0.663958
$582$	24.2693	+	28.6754i	1.00599	+	1.18863i
$583$	−15.7256	−	8.12784i	−0.651286	−	0.336621i
$584$	−24.3434	+	14.4702i	−1.00734	+	0.598781i
$585$	−0.661931	−	0.332556i	−0.0273675	−	0.0137495i
$586$	−6.05856	−	7.15851i	−0.250277	−	0.295715i
$587$	−30.2126			−1.24701			−0.623504	−	0.781820i	$-0.714291\pi$
$587$	−30.2126			−1.24701			−0.623504	+	0.781820i	$0.714291\pi$
$588$	−17.8212	−	2.98692i	−0.734934	−	0.123178i
$589$			5.34388i			0.220191i
$590$	−0.955582	+	0.808751i	−0.0393407	+	0.0332958i
$591$			30.9278i			1.27220i
$592$	−10.2458	+	29.7068i	−0.421100	+	1.22094i
$593$	−13.8113			−0.567164			−0.283582	−	0.958948i	$-0.591523\pi$
$593$	−13.8113			−0.567164			−0.283582	+	0.958948i	$0.591523\pi$
$594$	−24.4342	+	5.60078i	−1.00255	+	0.229803i
$595$		−	1.97713i		−	0.0810545i
$596$	−3.80925	+	22.7276i	−0.156033	+	0.930958i
$597$	27.7762			1.13681
$598$	3.09230	+	12.8138i	0.126454	+	0.523993i
$599$		−	5.16630i		−	0.211089i	−0.994415	−	0.105545i	$-0.966341\pi$
$599$		−	5.16630i		−	0.211089i	0.994415	−	0.105545i	$-0.0336586\pi$
$600$	9.16281	+	15.4147i	0.374070	+	0.629303i
$601$		−	5.45833i		−	0.222650i	−0.993784	−	0.111325i	$-0.964491\pi$
$601$		−	5.45833i		−	0.222650i	0.993784	−	0.111325i	$-0.0355094\pi$
$602$	−5.81531	+	4.92175i	−0.237014	+	0.200596i
$603$	1.91745			0.0780846
$604$	−9.75578	−	1.63511i	−0.396957	−	0.0665318i
$605$	9.91392	−	7.02858i	0.403058	−	0.285752i
$606$	−4.54274	−	5.36749i	−0.184536	−	0.218039i
$607$	22.9795			0.932709			0.466355	−	0.884598i	$-0.345567\pi$
$607$	22.9795			0.932709			0.466355	+	0.884598i	$0.345567\pi$
$608$	−4.99722	+	1.93965i	−0.202664	+	0.0786631i
$609$		−	20.8500i		−	0.844883i
$610$	−4.26504	−	5.03937i	−0.172686	−	0.204038i
$611$	0.429174	−	0.854243i	0.0173625	−	0.0345590i
$612$	−0.516705	−	0.0866022i	−0.0208866	−	0.00350069i
$613$	−15.8032			−0.638287			−0.319143	−	0.947706i	$-0.603395\pi$
$613$	−15.8032			−0.638287			−0.319143	+	0.947706i	$0.603395\pi$
$614$	−8.15717	+	6.90377i	−0.329196	+	0.278613i
$615$	2.92027			0.117757
$616$	0.705920	+	11.8972i	0.0284423	+	0.479350i
$617$			39.9111i			1.60676i	0.595467	+	0.803380i	$0.296967\pi$
$617$			39.9111i			1.60676i	−0.595467	+	0.803380i	$0.703033\pi$
$618$	13.6531	+	16.1318i	0.549207	+	0.648917i
$619$	30.1748			1.21283			0.606413	−	0.795150i	$-0.292608\pi$
$619$	30.1748			1.21283			0.606413	+	0.795150i	$0.292608\pi$
$620$	12.2892	+	2.05972i	0.493545	+	0.0827203i
$621$	13.8162			0.554423
$622$	−6.46796	+	5.47412i	−0.259342	+	0.219492i
$623$	−6.39189			−0.256086
$624$	−16.8957	−	17.3163i	−0.676370	−	0.693206i
$625$	8.18148			0.327259
$626$	3.06116	+	3.61692i	0.122349	+	0.144561i
$627$	4.68355	+	2.42072i	0.187043	+	0.0966742i
$628$	4.74558	−	28.3141i	0.189369	−	1.12986i
$629$	11.0661			0.441234
$630$	0.238476	+	0.281772i	0.00950111	+	0.0112261i
$631$	−31.8586			−1.26827			−0.634136	−	0.773222i	$-0.718644\pi$
$631$	−31.8586			−1.26827			−0.634136	+	0.773222i	$0.718644\pi$
$632$	−19.2559	+	11.4461i	−0.765957	+	0.455300i
$633$		−	36.3224i		−	1.44369i
$634$	14.9129	−	12.6214i	0.592265	−	0.501260i
$635$		−	19.2874i		−	0.765399i
$636$	−17.6604	−	2.95997i	−0.700281	−	0.117370i
$637$	8.71785	−	17.3523i	0.345414	−	0.687523i
$638$	44.7268	−	10.2522i	1.77075	−	0.405890i
$639$	−2.06865			−0.0818347
$640$	2.53445	+	12.2396i	0.100183	+	0.483811i
$641$	−16.9700			−0.670275			−0.335137	−	0.942169i	$-0.608783\pi$
$641$	−16.9700			−0.670275			−0.335137	+	0.942169i	$0.608783\pi$
$642$	−24.7933	+	20.9837i	−0.978515	+	0.828160i
$643$	16.2635			0.641370			0.320685	−	0.947186i	$-0.396087\pi$
$643$	16.2635			0.641370			0.320685	+	0.947186i	$0.396087\pi$
$644$	1.08579	−	6.47829i	0.0427862	−	0.255281i
$645$	7.85836			0.309422
$646$	1.21951	+	1.44091i	0.0479809	+	0.0566920i
$647$		−	17.5307i		−	0.689205i	−0.938749	−	0.344602i	$-0.888014\pi$
$647$		−	17.5307i		−	0.689205i	0.938749	−	0.344602i	$-0.111986\pi$
$648$	−20.4414	+	12.1508i	−0.803013	+	0.477327i
$649$	−2.36078	−	1.22018i	−0.0926687	−	0.0478963i
$650$	−18.7337	+	4.52094i	−0.734796	+	0.177326i
$651$	12.0188			0.471052
$652$	3.06286	−	18.2743i	0.119951	−	0.715679i
$653$	39.6406			1.55126			0.775628	−	0.631190i	$-0.217433\pi$
$653$	39.6406			1.55126			0.775628	+	0.631190i	$0.217433\pi$
$654$	−14.4788	+	12.2541i	−0.566167	+	0.479172i
$655$			7.83036i			0.305958i
$656$	−5.95847	−	2.05506i	−0.232639	−	0.0802367i
$657$	−1.86198			−0.0726427
$658$	−0.363636	+	0.307761i	−0.0141760	+	0.0119978i
$659$	−15.2238			−0.593036			−0.296518	−	0.955027i	$-0.595825\pi$
$659$	−15.2238			−0.593036			−0.296518	+	0.955027i	$0.595825\pi$
$660$	7.37206	−	9.83759i	0.286957	−	0.382928i
$661$			25.4504i			0.989906i	0.868920	+	0.494953i	$0.164815\pi$
$661$			25.4504i			0.989906i	−0.868920	+	0.494953i	$0.835185\pi$
$662$	−5.21083	−	6.15687i	−0.202525	−	0.239294i
$663$	−3.82480	+	7.61300i	−0.148543	+	0.295665i
$664$	−18.2054	−	30.6271i	−0.706505	−	1.18856i
$665$		−	1.33005i		−	0.0515773i
$666$	−1.57709	+	1.33476i	−0.0611110	+	0.0517209i
$667$	−25.2905			−0.979251
$668$	−35.9840	−	6.03108i	−1.39226	−	0.233350i
$669$		−	7.17700i		−	0.277479i
$670$	−12.2966	+	10.4071i	−0.475059	+	0.402063i
$671$	6.43477	−	12.4498i	0.248411	−	0.480621i
$672$	4.36241	+	11.2391i	0.168283	+	0.433558i
$673$		−	2.38318i		−	0.0918648i	−0.998945	−	0.0459324i	$-0.985374\pi$
$673$		−	2.38318i		−	0.0918648i	0.998945	−	0.0459324i	$-0.0146259\pi$
$674$	22.8534	−	19.3418i	0.880279	−	0.745019i
$675$			20.1992i			0.777468i
$676$	23.1383	−	11.8584i	0.889933	−	0.456092i
$677$			45.9970i			1.76781i	0.467668	+	0.883904i	$0.345094\pi$
$677$			45.9970i			1.76781i	−0.467668	+	0.883904i	$0.654906\pi$
$678$	8.11378	−	6.86704i	0.311608	−	0.263727i
$679$	20.1183			0.772070
$680$	3.78367	−	2.24909i	0.145097	−	0.0862486i
$681$	2.05234			0.0786457
$682$	5.90980	+	25.7823i	0.226298	+	0.987256i
$683$	11.4042			0.436371			0.218186	−	0.975907i	$-0.429986\pi$
$683$	11.4042			0.436371			0.218186	+	0.975907i	$0.429986\pi$
$684$	−0.347598	−	0.0582589i	−0.0132907	−	0.00222759i
$685$	15.6850			0.599295
$686$	−16.9868	+	14.3767i	−0.648559	+	0.548904i
$687$	−18.7216			−0.714274
$688$	−16.0340	−	5.53010i	−0.611292	−	0.210833i
$689$	8.63919	−	17.1957i	0.329127	−	0.655105i
$690$	−5.17181	+	4.37713i	−0.196888	+	0.166635i
$691$	13.8920			0.528478			0.264239	−	0.964457i	$-0.414879\pi$
$691$	13.8920			0.528478			0.264239	+	0.964457i	$0.414879\pi$
$692$	−27.5826	−	4.62297i	−1.04853	−	0.175739i
$693$	−0.359794	+	0.696122i	−0.0136675	+	0.0264435i
$694$	−23.9143	−	28.2561i	−0.907776	−	1.07259i
$695$		−	10.4417i		−	0.396075i
$696$	39.9009	−	23.7179i	1.51244	−	0.899024i
$697$			2.21959i			0.0840731i
$698$	−0.870764	−	1.02885i	−0.0329589	−	0.0389427i
$699$	−15.5291			−0.587364
$700$	9.47126	+	1.58743i	0.357980	+	0.0599991i
$701$			21.5113i			0.812471i	0.913768	+	0.406236i	$0.133159\pi$
$701$			21.5113i			0.812471i	−0.913768	+	0.406236i	$0.866841\pi$
$702$	−6.39303	−	26.4911i	−0.241289	−	0.999844i
$703$	7.44438			0.280770
$704$	−21.9647	+	14.8845i	−0.827828	+	0.560983i
$705$	0.491389			0.0185068
$706$	37.2162	−	31.4977i	1.40065	−	1.18543i
$707$	−3.76576			−0.141626
$708$	−2.65125	−	0.444361i	−0.0996400	−	0.0167001i
$709$		−	43.6867i		−	1.64069i	−0.571871	−	0.820344i	$-0.693782\pi$
$709$		−	43.6867i		−	1.64069i	0.571871	−	0.820344i	$-0.306218\pi$
$710$	13.2663	−	11.2278i	0.497874	−	0.421372i
$711$	−1.47284			−0.0552360
$712$	−7.27110	−	12.2323i	−0.272496	−	0.458424i
$713$		−	14.5785i		−	0.545968i
$714$	3.24072	−	2.74276i	0.121281	−	0.102645i
$715$	7.76401	+	10.6892i	0.290358	+	0.399753i
$716$	27.3578	+	4.58529i	1.02241	+	0.171360i
$717$	−34.8818			−1.30268
$718$	−3.35620	+	2.84050i	−0.125252	+	0.106007i
$719$			30.3223i			1.13083i	0.824806	+	0.565416i	$0.191284\pi$
$719$			30.3223i			1.13083i	−0.824806	+	0.565416i	$0.808716\pi$
$720$	−0.267953	+	0.776905i	−0.00998601	+	0.0289535i
$721$	11.3179			0.421500
$722$	−16.5384	−	19.5410i	−0.615495	−	0.727240i
$723$		−	1.49677i		−	0.0556656i
$724$	−3.48312	+	20.7818i	−0.129449	+	0.772349i
$725$		−	36.9747i		−	1.37320i
$726$	25.2735	+	6.49956i	0.937989	+	0.241221i
$727$			31.9183i			1.18379i	0.806017	+	0.591893i	$0.201619\pi$
$727$			31.9183i			1.18379i	−0.806017	+	0.591893i	$0.798381\pi$
$728$	−12.9239	+	0.915742i	−0.478992	+	0.0339397i
$729$	−28.4598			−1.05407
$730$	11.9409	−	10.1061i	0.441951	−	0.374042i
$731$			5.97285i			0.220914i
$732$	2.34339	−	13.9817i	0.0866141	−	0.516777i
$733$	−17.4514			−0.644582			−0.322291	−	0.946641i	$-0.604453\pi$
$733$	−17.4514			−0.644582			−0.322291	+	0.946641i	$0.604453\pi$
$734$	17.2167	−	14.5712i	0.635480	−	0.537834i
$735$	9.98162			0.368178
$736$	13.6328	−	5.29149i	0.502510	−	0.195047i
$737$	−30.3789	−	15.7015i	−1.11902	−	0.578372i
$738$	−0.267721	−	0.316326i	−0.00985494	−	0.0116441i
$739$			28.6608i			1.05431i	0.849770	+	0.527153i	$0.176740\pi$
$739$			28.6608i			1.05431i	−0.849770	+	0.527153i	$0.823260\pi$
$740$	2.86933	−	17.1196i	0.105479	−	0.629330i
$741$	−2.57301	+	5.12141i	−0.0945220	+	0.188140i
$742$	−7.31991	+	6.19516i	−0.268722	+	0.227431i
$743$			26.5050i			0.972373i	0.873855	+	0.486186i	$0.161612\pi$
$743$			26.5050i			0.972373i	−0.873855	+	0.486186i	$0.838388\pi$
$744$	13.6720	+	23.0005i	0.501238	+	0.843239i
$745$		−	12.7297i		−	0.466379i
$746$	−13.2344	+	11.2009i	−0.484546	+	0.410092i
$747$		−	2.34261i		−	0.0857116i
$748$	7.47720	+	5.60324i	0.273394	+	0.204875i
$749$			17.3947i			0.635588i
$750$	−14.8654	−	17.5642i	−0.542806	−	0.641354i
$751$		−	0.329262i		−	0.0120149i	−0.999982	−	0.00600746i	$-0.998088\pi$
$751$		−	0.329262i		−	0.0120149i	0.999982	−	0.00600746i	$-0.00191225\pi$
$752$	−1.00262	−	0.345802i	−0.0365618	−	0.0126101i
$753$	27.1713			0.990176
$754$	11.7024	+	48.4920i	0.426178	+	1.76598i
$755$	5.46419			0.198862
$756$	−2.24476	+	13.3932i	−0.0816413	+	0.487107i
$757$	−6.45006			−0.234431			−0.117216	−	0.993106i	$-0.537397\pi$
$757$	−6.45006			−0.234431			−0.117216	+	0.993106i	$0.537397\pi$
$758$	−7.49240	−	8.85266i	−0.272136	−	0.321543i
$759$	−12.7770	−	6.60388i	−0.463777	−	0.239706i
$760$	2.54535	−	1.51300i	0.0923294	−	0.0548824i
$761$	29.8226			1.08107			0.540535	−	0.841322i	$-0.318222\pi$
$761$	29.8226			1.08107			0.540535	+	0.841322i	$0.318222\pi$
$762$	31.6140	−	26.7564i	1.14526	−	0.969280i
$763$			10.1582i			0.367750i
$764$	52.1730	+	8.74443i	1.88755	+	0.316363i
$765$	0.289406			0.0104635
$766$	−34.0756	−	40.2621i	−1.23120	−	1.45473i
$767$	1.29695	−	2.58149i	0.0468301	−	0.0932121i
$768$	−16.5460	+	21.1335i	−0.597052	+	0.762588i
$769$	49.1057			1.77080			0.885399	−	0.464832i	$-0.153885\pi$
$769$	49.1057			1.77080			0.885399	+	0.464832i	$0.153885\pi$
$770$	−1.47091	−	6.41704i	−0.0530079	−	0.231254i
$771$		−	41.3350i		−	1.48864i
$772$	7.73204	−	46.1326i	0.278282	−	1.66035i
$773$		−	21.3112i		−	0.766511i	−0.923642	−	0.383256i	$-0.874803\pi$
$773$		−	21.3112i		−	0.766511i	0.923642	−	0.383256i	$-0.125197\pi$
$774$	−0.720428	−	0.851224i	−0.0258953	−	0.0305966i
$775$	21.3137			0.765610
$776$	22.8856	+	38.5007i	0.821545	+	1.38210i
$777$		−	16.7429i		−	0.600649i
$778$	7.93832	+	9.37955i	0.284603	+	0.336273i
$779$			1.49316i			0.0534981i
$780$	10.7858	+	7.89106i	0.386195	+	0.282545i
$781$	32.7745	+	16.9397i	1.17276	+	0.606149i
$782$	−3.32690	−	3.93091i	−0.118970	−	0.140569i
$783$	52.2855			1.86853
$784$	−20.3663	−	7.02429i	−0.727368	−	0.250868i
$785$			15.8587i			0.566020i
$786$	−12.8347	+	10.8626i	−0.457800	+	0.387456i
$787$		−	32.9070i		−	1.17301i	−0.809946	−	0.586504i	$-0.800504\pi$
$787$		−	32.9070i		−	1.17301i	0.809946	−	0.586504i	$-0.199496\pi$
$788$	−6.09515	+	36.3662i	−0.217131	+	1.29549i
$789$		−	12.3997i		−	0.441441i
$790$	9.44534	−	7.99400i	0.336050	−	0.284414i
$791$		−	5.69252i		−	0.202403i
$792$	−1.74146	+	0.103330i	−0.0618802	+	0.00367167i
$793$	13.6138	+	6.83960i	0.483439	+	0.242881i
$794$	23.1043	−	19.5541i	0.819939	−	0.693951i
$795$	9.89155			0.350817
$796$	32.6605	+	5.47405i	1.15762	+	0.194023i
$797$	−51.0946			−1.80986			−0.904931	−	0.425558i	$-0.860078\pi$
$797$	−51.0946			−1.80986			−0.904931	+	0.425558i	$0.860078\pi$
$798$	2.18009	−	1.84511i	0.0771744	−	0.0653161i
$799$			0.373487i			0.0132130i
$800$	7.73615	+	19.9311i	0.273514	+	0.704670i
$801$		−	0.935623i		−	0.0330586i
$802$	−15.0083	+	12.7021i	−0.529960	+	0.448528i
$803$	29.5001	+	15.2473i	1.04103	+	0.538064i
$804$	−34.1167	−	5.71811i	−1.20320	−	0.201662i
$805$			3.62848i			0.127887i
$806$	−27.9528	+	6.74576i	−0.984595	+	0.237609i
$807$		−	28.5176i		−	1.00387i
$808$	−4.28375	−	7.20660i	−0.150702	−	0.253527i
$809$			29.9457i			1.05283i	0.850227	+	0.526417i	$0.176465\pi$
$809$			29.9457i			1.05283i	−0.850227	+	0.526417i	$0.823535\pi$
$810$	10.0268	−	8.48616i	0.352307	−	0.298173i
$811$			33.3267i			1.17026i	0.810940	+	0.585130i	$0.198957\pi$
$811$			33.3267i			1.17026i	−0.810940	+	0.585130i	$0.801043\pi$
$812$	4.10904	−	24.5163i	0.144199	−	0.860353i
$813$	−12.3619			−0.433550
$814$	35.9165	−	8.23275i	1.25887	−	0.288558i
$815$			10.2354i			0.358531i
$816$	8.93534	+	3.08178i	0.312800	+	0.107884i
$817$			4.01805i			0.140574i
$818$	−32.7659	−	38.7146i	−1.14563	−	1.35363i
$819$	−0.761201	−	0.382430i	−0.0265985	−	0.0133632i
$820$	3.43378	+	0.575518i	0.119913	+	0.0200979i
$821$	−24.6890			−0.861652			−0.430826	−	0.902435i	$-0.641778\pi$
$821$	−24.6890			−0.861652			−0.430826	+	0.902435i	$0.641778\pi$
$822$	21.7589	+	25.7093i	0.758930	+	0.896716i
$823$			16.3287i			0.569183i	0.958649	+	0.284592i	$0.0918580\pi$
$823$			16.3287i			0.569183i	−0.958649	+	0.284592i	$0.908142\pi$
$824$	12.8747	+	21.6592i	0.448511	+	0.754535i
$825$	9.65487	−	18.6800i	0.336139	−	0.650355i
$826$	−1.09889	+	0.930041i	−0.0382354	+	0.0323603i
$827$		−	15.4227i		−	0.536299i	−0.963377	−	0.268150i	$-0.913588\pi$
$827$		−	15.4227i		−	0.536299i	0.963377	−	0.268150i	$-0.0864122\pi$
$828$	0.948269	+	0.158934i	0.0329546	+	0.00552335i
$829$	−48.9319			−1.69947			−0.849737	−	0.527207i	$-0.823239\pi$
$829$	−48.9319			−1.69947			−0.849737	+	0.527207i	$0.823239\pi$
$830$	12.7147	+	15.0231i	0.441335	+	0.521460i
$831$	−29.7036			−1.03041
$832$	−16.4541	−	23.6910i	−0.570443	−	0.821337i
$833$			7.58667i			0.262863i
$834$	17.1149	−	14.4851i	0.592641	−	0.501578i
$835$	20.1546			0.697477
$836$	5.03005	+	3.76940i	0.173968	+	0.130368i
$837$			30.1395i			1.04177i
$838$	−1.73122	+	1.46521i	−0.0598041	+	0.0506148i
$839$	4.51783			0.155973			0.0779865	−	0.996954i	$-0.475151\pi$
$839$	4.51783			0.155973			0.0779865	+	0.996954i	$0.475151\pi$
$840$	−3.40285	−	5.72466i	−0.117410	−	0.197520i
$841$	−66.7087			−2.30030
$842$	−6.80774	+	5.76169i	−0.234610	+	0.198561i
$843$			22.3692i			0.770435i
$844$	7.15831	−	42.7095i	0.246399	−	1.47012i
$845$	−11.5228	+	8.57312i	−0.396396	+	0.294924i
$846$	−0.0450489	−	0.0532277i	−0.00154881	−	0.00183001i
$847$	11.4007	−	8.08266i	0.391733	−	0.277724i
$848$	−20.1825	−	6.96091i	−0.693071	−	0.239039i
$849$			1.60935i			0.0552326i
$850$	5.74698	−	4.86392i	0.197120	−	0.166831i
$851$	−20.3088			−0.696175
$852$	36.8070	+	6.16902i	1.26099	+	0.211347i
$853$	37.0817			1.26965			0.634826	−	0.772655i	$-0.281072\pi$
$853$	37.0817			1.26965			0.634826	+	0.772655i	$0.281072\pi$
$854$	−4.90467	−	5.79513i	−0.167834	−	0.198305i
$855$	0.194689			0.00665821
$856$	−33.2885	+	19.7874i	−1.13778	+	0.676318i
$857$			51.0814i			1.74491i	0.488698	+	0.872453i	$0.337472\pi$
$857$			51.0814i			1.74491i	−0.488698	+	0.872453i	$0.662528\pi$
$858$	−6.75010	+	27.5545i	−0.230445	+	0.940695i
$859$			36.8343i			1.25677i	0.777903	+	0.628385i	$0.216284\pi$
$859$			36.8343i			1.25677i	−0.777903	+	0.628385i	$0.783716\pi$
$860$	9.24020	+	1.54870i	0.315088	+	0.0528102i
$861$	3.35823			0.114448
$862$	17.6220	−	14.9143i	0.600207	−	0.507981i
$863$	47.1911			1.60640			0.803202	−	0.595707i	$-0.203128\pi$
$863$	47.1911			1.60640			0.803202	+	0.595707i	$0.203128\pi$
$864$	−28.1843	+	10.9396i	−0.958851	+	0.372174i
$865$	15.4489			0.525280
$866$	−18.0819	−	21.3647i	−0.614448	−	0.726002i
$867$			25.1891i			0.855467i
$868$	14.1322	+	2.36862i	0.479678	+	0.0803962i
$869$	23.3348	+	12.0607i	0.791581	+	0.409133i
$870$	−19.5721	+	16.5647i	−0.663555	+	0.561596i
$871$	16.6893	−	33.2190i	0.565496	−	1.12558i
$872$	−19.4398	+	11.5554i	−0.658316	+	0.391316i
$873$			2.94485i			0.0996680i
$874$	−2.23807	−	2.64440i	−0.0757038	−	0.0894481i
$875$	−12.3228			−0.416587
$876$	33.1297	+	5.55269i	1.11935	+	0.187608i
$877$	30.8744			1.04255			0.521277	−	0.853388i	$-0.325456\pi$
$877$	30.8744			1.04255			0.521277	+	0.853388i	$0.325456\pi$
$878$	−27.4607	−	32.4462i	−0.926753	−	1.09501i
$879$			11.1242i			0.375210i
$880$	10.6072	−	10.1146i	0.357567	−	0.340963i
$881$	−23.1218			−0.778994			−0.389497	−	0.921028i	$-0.627351\pi$
$881$	−23.1218			−0.778994			−0.389497	+	0.921028i	$0.627351\pi$
$882$	−0.915082	−	1.08122i	−0.0308124	−	0.0364065i
$883$		−	2.56715i		−	0.0863915i	−0.999067	−	0.0431958i	$-0.986246\pi$
$883$		−	2.56715i		−	0.0863915i	0.999067	−	0.0431958i	$-0.0137539\pi$
$884$	−5.99771	+	8.19792i	−0.201725	+	0.275726i
$885$	1.48496			0.0499163
$886$	11.6799	−	9.88520i	0.392393	−	0.332100i
$887$	−15.8965			−0.533752			−0.266876	−	0.963731i	$-0.585991\pi$
$887$	−15.8965			−0.533752			−0.266876	+	0.963731i	$0.585991\pi$
$888$	32.0412	−	19.0459i	1.07523	−	0.639140i
$889$		−	22.1800i		−	0.743894i
$890$	5.07818	+	6.00014i	0.170221	+	0.201125i
$891$	24.7715	+	12.8033i	0.829875	+	0.428926i
$892$	1.41442	−	8.43903i	0.0473583	−	0.282560i
$893$			0.251252i			0.00840782i
$894$	20.8652	−	17.6591i	0.697836	−	0.590609i
$895$	−15.3230			−0.512192
$896$	2.91454	+	14.0752i	0.0973680	+	0.470218i
$897$	7.01935	−	13.9716i	0.234369	−	0.466497i
$898$	10.0941	−	8.54311i	0.336846	−	0.285087i
$899$		−	55.1704i		−	1.84003i
$900$	−0.232362	+	1.38637i	−0.00774539	+	0.0462123i
$901$			7.51822i			0.250468i
$902$	1.65129	+	7.20398i	0.0549820	+	0.239866i
$903$	9.03688			0.300729
$904$	10.8939	−	6.47553i	0.362325	−	0.215373i
$905$		−	11.6398i		−	0.386921i
$906$	7.58015	+	8.95635i	0.251834	+	0.297555i
$907$		−	29.8657i		−	0.991674i	−0.868416	−	0.495837i	$-0.834861\pi$
$907$		−	29.8657i		−	0.991674i	0.868416	−	0.495837i	$-0.165139\pi$
$908$	2.41323	+	0.404468i	0.0800858	+	0.0134227i
$909$		−	0.551219i		−	0.0182828i
$910$	6.95725	−	1.67897i	0.230631	−	0.0556574i
$911$		−	8.02735i		−	0.265958i	−0.991119	−	0.132979i	$-0.957546\pi$
$911$		−	8.02735i		−	0.265958i	0.991119	−	0.132979i	$-0.0424543\pi$
$912$	6.01097	+	2.07317i	0.199043	+	0.0686496i
$913$	−19.1830	+	37.1149i	−0.634865	+	1.22832i
$914$	7.77950	+	9.19189i	0.257323	+	0.304041i
$915$			7.83109i			0.258888i
$916$	−22.0137	−	3.68959i	−0.727352	−	0.121908i
$917$			9.00469i			0.297361i
$918$	6.87803	+	8.12676i	0.227009	+	0.268223i
$919$	−51.9419			−1.71340			−0.856702	−	0.515811i	$-0.827491\pi$
$919$	−51.9419			−1.71340			−0.856702	+	0.515811i	$0.827491\pi$
$920$	−6.94387	+	4.12758i	−0.228933	+	0.136082i
$921$	12.6761			0.417691
$922$	21.3519	+	25.2284i	0.703189	+	0.830855i
$923$	−18.0054	+	35.8385i	−0.592655	+	1.17964i
$924$	8.47766	−	11.3129i	0.278894	−	0.372169i
$925$		−	29.6914i		−	0.976247i
$926$	−21.1012	−	24.9322i	−0.693428	−	0.819322i
$927$			1.65667i			0.0544122i
$928$	51.5914	−	20.0250i	1.69357	−	0.657352i
$929$		−	12.3727i		−	0.405936i	−0.979185	−	0.202968i	$-0.934941\pi$
$929$		−	12.3727i		−	0.405936i	0.979185	−	0.202968i	$-0.0650588\pi$
$930$	−9.54857	−	11.2821i	−0.313110	−	0.369956i
$931$			5.10370i			0.167267i
$932$	−18.2598	−	3.06042i	−0.598119	−	0.100248i
$933$	10.0511			0.329058
$934$	27.7499	−	23.4860i	0.908006	−	0.768485i
$935$	−4.58516	−	2.36987i	−0.149951	−	0.0775029i
$936$	−0.134043	−	1.89176i	−0.00438133	−	0.0618340i
$937$		−	23.1504i		−	0.756292i	−0.925746	−	0.378146i	$-0.876562\pi$
$937$		−	23.1504i		−	0.756292i	0.925746	−	0.378146i	$-0.123438\pi$
$938$	−14.1407	+	11.9679i	−0.461711	+	0.390766i
$939$		−	5.62063i		−	0.183422i
$940$	0.577796	+	0.0968413i	0.0188456	+	0.00315862i
$941$	45.1728			1.47259			0.736296	−	0.676660i	$-0.236573\pi$
$941$	45.1728			1.47259			0.736296	+	0.676660i	$0.236573\pi$
$942$	−25.9939	+	21.9998i	−0.846928	+	0.716793i
$943$		−	4.07345i		−	0.132650i
$944$	−3.02988	−	1.04500i	−0.0986142	−	0.0340118i
$945$		−	7.50151i		−	0.244024i
$946$	4.44357	+	19.3857i	0.144473	+	0.630283i
$947$	−22.7811			−0.740286			−0.370143	−	0.928975i	$-0.620691\pi$
$947$	−22.7811			−0.740286			−0.370143	+	0.928975i	$0.620691\pi$
$948$	26.2059	+	4.39223i	0.851129	+	0.142653i
$949$	−16.2065	+	32.2580i	−0.526086	+	1.04714i
$950$	3.86610	−	3.27205i	0.125433	−	0.106159i
$951$	−23.1743			−0.751478
$952$	4.35111	−	2.58639i	0.141020	−	0.0838253i
$953$		−	32.8772i		−	1.06500i	−0.846431	−	0.532498i	$-0.821253\pi$
$953$		−	32.8772i		−	1.06500i	0.846431	−	0.532498i	$-0.178747\pi$
$954$	−0.906825	−	1.07146i	−0.0293595	−	0.0346899i
$955$	−29.2220			−0.945601
$956$	−41.0155	−	6.87439i	−1.32654	−	0.222334i
$957$	−48.3531	−	24.9916i	−1.56303	−	0.807862i
$958$	−7.33362	+	6.20677i	−0.236939	+	0.200532i
$959$	18.0373			0.582456
$960$	7.08445	−	13.0242i	0.228650	−	0.420354i
$961$	0.802434			0.0258850
$962$	9.39729	+	38.9401i	0.302981	+	1.25548i
$963$	−2.54617			−0.0820493
$964$	0.294979	−	1.75997i	0.00950063	−	0.0566848i
$965$			25.8388i			0.831780i
$966$	−5.94743	+	5.03357i	−0.191356	+	0.161953i
$967$		−	58.8056i		−	1.89106i	−0.325535	−	0.945530i	$-0.605544\pi$
$967$		−	58.8056i		−	1.89106i	0.325535	−	0.945530i	$-0.394456\pi$
$968$	28.4368	+	12.6233i	0.913994	+	0.405728i
$969$		−	2.23915i		−	0.0719320i
$970$	−15.9834	−	18.8853i	−0.513197	−	0.606370i
$971$		−	12.7843i		−	0.410268i	−0.978734	−	0.205134i	$-0.934237\pi$
$971$		−	12.7843i		−	0.410268i	0.978734	−	0.205134i	$-0.0657630\pi$
$972$	−3.80647	−	0.637982i	−0.122093	−	0.0204633i
$973$		−	12.0076i		−	0.384946i
$974$	−10.9003	−	12.8792i	−0.349267	−	0.412677i
$975$	20.4264	+	10.2623i	0.654168	+	0.328656i
$976$	5.51092	−	15.9784i	0.176400	−	0.511456i
$977$			35.1203i			1.12360i	0.827274	+	0.561799i	$0.189891\pi$
$977$			35.1203i			1.12360i	−0.827274	+	0.561799i	$0.810109\pi$
$978$	−16.7769	+	14.1990i	−0.536465	+	0.454034i
$979$	−7.66157	+	14.8234i	−0.244865	+	0.473759i
$980$	11.7368	+	1.96715i	0.374919	+	0.0628381i
$981$	−1.48692			−0.0474736
$982$	−18.5115	−	21.8723i	−0.590726	−	0.697974i
$983$	−11.3212			−0.361090			−0.180545	−	0.983567i	$-0.557786\pi$
$983$	−11.3212			−0.361090			−0.180545	+	0.983567i	$0.557786\pi$
$984$	3.82016	+	6.42669i	0.121782	+	0.204875i
$985$		−	20.3686i		−	0.648999i
$986$	−12.5902	−	14.8760i	−0.400955	−	0.473749i
$987$	0.565083			0.0179868
$988$	−4.03477	+	5.51490i	−0.128363	+	0.175452i
$989$		−	10.9615i		−	0.348556i
$990$	0.939303	−	0.215306i	0.0298530	−	0.00684289i
$991$		−	48.1334i		−	1.52901i	−0.644618	−	0.764505i	$-0.722984\pi$
$991$		−	48.1334i		−	1.52901i	0.644618	−	0.764505i	$-0.277016\pi$
$992$	11.5432	+	29.7394i	0.366497	+	0.944227i
$993$			9.56766i			0.303621i
$994$	15.2558	−	12.9117i	0.483885	−	0.409533i
$995$	−18.2931			−0.579930
$996$	−6.98599	+	41.6814i	−0.221360	+	1.32073i
$997$		−	54.8576i		−	1.73736i	−0.495375	−	0.868679i	$-0.664969\pi$
$997$		−	54.8576i		−	1.73736i	0.495375	−	0.868679i	$-0.335031\pi$
$998$	23.7105	+	28.0152i	0.750543	+	0.886806i
$999$	41.9863			1.32839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.b.c.571.13	✓	56
4.3	odd	2	inner	572.2.b.c.571.15	yes	56
11.10	odd	2	inner	572.2.b.c.571.43	yes	56
13.12	even	2	inner	572.2.b.c.571.44	yes	56
44.43	even	2	inner	572.2.b.c.571.41	yes	56
52.51	odd	2	inner	572.2.b.c.571.42	yes	56
143.142	odd	2	inner	572.2.b.c.571.14	yes	56
572.571	even	2	inner	572.2.b.c.571.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.13	✓	56	1.1	even	1	trivial
572.2.b.c.571.14	yes	56	143.142	odd	2	inner
572.2.b.c.571.15	yes	56	4.3	odd	2	inner
572.2.b.c.571.16	yes	56	572.571	even	2	inner
572.2.b.c.571.41	yes	56	44.43	even	2	inner
572.2.b.c.571.42	yes	56	52.51	odd	2	inner
572.2.b.c.571.43	yes	56	11.10	odd	2	inner
572.2.b.c.571.44	yes	56	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} -1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +O(q^{10})\)	\(q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} -1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +(-1.19260 + 1.00935i) q^{10} +(-2.94635 - 1.52284i) q^{11} +(-3.30886 - 0.554581i) q^{12} +(1.61864 - 3.22180i) q^{13} +(-1.37146 + 1.16073i) q^{14} +1.85329 q^{15} +(-3.78141 - 1.30420i) q^{16} +1.40862i q^{17} +(-0.169903 - 0.200750i) q^{18} +0.947603i q^{19} +(2.17917 + 0.365240i) q^{20} +2.13123 q^{21} +(1.04796 + 4.57185i) q^{22} -2.58512i q^{23} +(2.42438 + 4.07856i) q^{24} +3.77945 q^{25} +(-4.95673 + 1.19619i) q^{26} +5.34449i q^{27} +(2.50599 + 0.420015i) q^{28} -9.78308i q^{29} +(-1.69320 - 2.00060i) q^{30} +5.63936 q^{31} +(2.04690 + 5.27354i) q^{32} +(2.55457 - 4.94252i) q^{33} +(1.52059 - 1.28694i) q^{34} -1.40360 q^{35} +(-0.0614803 + 0.366818i) q^{36} -7.85601i q^{37} +(1.02293 - 0.865749i) q^{38} +(5.40460 + 2.71529i) q^{39} +(-1.59666 - 2.68609i) q^{40} +1.57573 q^{41} +(-1.94713 - 2.30064i) q^{42} +4.24023 q^{43} +(3.97783 - 5.30819i) q^{44} -0.205454i q^{45} +(-2.79062 + 2.36182i) q^{46} +0.265145 q^{47} +(2.18781 - 6.34335i) q^{48} +5.38590 q^{49} +(-3.45298 - 4.07988i) q^{50} -2.36297 q^{51} +(5.81984 + 4.25787i) q^{52} +5.33730 q^{53} +(5.76932 - 4.88283i) q^{54} +(-1.68241 + 3.25508i) q^{55} +(-1.83612 - 3.08892i) q^{56} -1.58961 q^{57} +(-10.5607 + 8.93802i) q^{58} +0.801256 q^{59} +(-0.612692 + 3.65558i) q^{60} +4.22552i q^{61} +(-5.15224 - 6.08764i) q^{62} -0.236266i q^{63} +(3.82264 - 7.02762i) q^{64} +(-3.55940 - 1.78825i) q^{65} +(-7.66931 + 1.75795i) q^{66} +10.3107 q^{67} +(-2.77848 - 0.465686i) q^{68} +4.33657 q^{69} +(1.28236 + 1.51517i) q^{70} -11.1238 q^{71} +(0.452146 - 0.268764i) q^{72} -10.0124 q^{73} +(-8.48048 + 7.17740i) q^{74} +6.34006i q^{75} +(-1.86913 - 0.313276i) q^{76} +(-1.93472 + 3.74325i) q^{77} +(-2.00662 - 8.31495i) q^{78} -7.91992 q^{79} +(-1.44086 + 4.17765i) q^{80} -8.40751 q^{81} +(-1.43961 - 1.70098i) q^{82} -12.5969i q^{83} +(-0.704579 + 4.20382i) q^{84} +1.55622 q^{85} +(-3.87396 - 4.57728i) q^{86} +16.4112 q^{87} +(-9.36436 + 0.555636i) q^{88} -5.03112i q^{89} +(-0.221785 + 0.187707i) q^{90} +(-4.09321 - 2.05644i) q^{91} +(5.09913 + 0.854637i) q^{92} +9.46008i q^{93} +(-0.242241 - 0.286221i) q^{94} +1.04690 q^{95} +(-8.84640 + 3.43369i) q^{96} +15.8353i q^{97} +(-4.92067 - 5.81403i) q^{98} +(-0.547924 - 0.283197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^4 - 32 * q^9	\( 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) \) 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Introduction

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