LMFDB - Embedded newform 572.2.b.c.571.3

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			571.3
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41153 + 0.0870114i) q^{2} -2.50968i q^{3} +(1.98486 - 0.245639i) q^{4} -2.92941i q^{5} +(0.218370 + 3.54249i) q^{6} -1.23786i q^{7} +(-2.78032 + 0.519434i) q^{8} -3.29847 q^{9} +O(q^{10})$	\(q+(-1.41153 + 0.0870114i) q^{2} -2.50968i q^{3} +(1.98486 - 0.245639i) q^{4} -2.92941i q^{5} +(0.218370 + 3.54249i) q^{6} -1.23786i q^{7} +(-2.78032 + 0.519434i) q^{8} -3.29847 q^{9} +(0.254892 + 4.13496i) q^{10} +(-2.17413 + 2.50463i) q^{11} +(-0.616475 - 4.98135i) q^{12} +(-1.08694 - 3.43781i) q^{13} +(0.107708 + 1.74728i) q^{14} -7.35187 q^{15} +(3.87932 - 0.975118i) q^{16} -5.14494i q^{17} +(4.65591 - 0.287005i) q^{18} -0.366099i q^{19} +(-0.719578 - 5.81447i) q^{20} -3.10662 q^{21} +(2.85092 - 3.72455i) q^{22} +7.77474i q^{23} +(1.30361 + 6.97771i) q^{24} -3.58145 q^{25} +(1.83339 + 4.75801i) q^{26} +0.749071i q^{27} +(-0.304066 - 2.45697i) q^{28} +4.69618i q^{29} +(10.3774 - 0.639697i) q^{30} +7.88901 q^{31} +(-5.39095 + 1.71396i) q^{32} +(6.28581 + 5.45635i) q^{33} +(0.447669 + 7.26226i) q^{34} -3.62619 q^{35} +(-6.54700 + 0.810234i) q^{36} -7.05110i q^{37} +(0.0318548 + 0.516761i) q^{38} +(-8.62779 + 2.72788i) q^{39} +(1.52163 + 8.14471i) q^{40} +9.08665 q^{41} +(4.38510 - 0.270311i) q^{42} -4.11572 q^{43} +(-3.70010 + 5.50539i) q^{44} +9.66258i q^{45} +(-0.676491 - 10.9743i) q^{46} -5.69467 q^{47} +(-2.44723 - 9.73584i) q^{48} +5.46771 q^{49} +(5.05534 - 0.311627i) q^{50} -12.9121 q^{51} +(-3.00189 - 6.55657i) q^{52} -7.85325 q^{53} +(-0.0651777 - 1.05734i) q^{54} +(7.33710 + 6.36891i) q^{55} +(0.642984 + 3.44164i) q^{56} -0.918789 q^{57} +(-0.408621 - 6.62881i) q^{58} -10.7121 q^{59} +(-14.5924 + 1.80591i) q^{60} +5.82597i q^{61} +(-11.1356 + 0.686434i) q^{62} +4.08303i q^{63} +(7.46038 - 2.88838i) q^{64} +(-10.0708 + 3.18411i) q^{65} +(-9.34740 - 7.15489i) q^{66} +7.23336 q^{67} +(-1.26380 - 10.2120i) q^{68} +19.5121 q^{69} +(5.11849 - 0.315520i) q^{70} +5.63261 q^{71} +(9.17082 - 1.71334i) q^{72} -0.631831 q^{73} +(0.613526 + 9.95287i) q^{74} +8.98828i q^{75} +(-0.0899282 - 0.726654i) q^{76} +(3.10037 + 2.69125i) q^{77} +(11.9411 - 4.60121i) q^{78} -15.4397 q^{79} +(-2.85652 - 11.3641i) q^{80} -8.01549 q^{81} +(-12.8261 + 0.790643i) q^{82} -9.80904i q^{83} +(-6.16619 + 0.763107i) q^{84} -15.0716 q^{85} +(5.80948 - 0.358115i) q^{86} +11.7859 q^{87} +(4.74378 - 8.09299i) q^{88} +1.98044i q^{89} +(-0.840755 - 13.6391i) q^{90} +(-4.25552 + 1.34548i) q^{91} +(1.90978 + 15.4318i) q^{92} -19.7989i q^{93} +(8.03823 - 0.495502i) q^{94} -1.07245 q^{95} +(4.30148 + 13.5295i) q^{96} +5.10448i q^{97} +(-7.71786 + 0.475754i) q^{98} +(7.17130 - 8.26146i) 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 $

$2$	−1.41153	+	0.0870114i	−0.998105	+	0.0615264i
$2$	−1.41153	+	0.0870114i	−0.998105	+	0.0615264i
$3$		−	2.50968i		−	1.44896i	−0.689295	−	0.724481i	$-0.742079\pi$
$3$		−	2.50968i		−	1.44896i	0.689295	−	0.724481i	$-0.257921\pi$
$4$	1.98486	−	0.245639i	0.992429	−	0.122820i
$5$		−	2.92941i		−	1.31007i	−0.755597	−	0.655036i	$-0.772653\pi$
$5$		−	2.92941i		−	1.31007i	0.755597	−	0.655036i	$-0.227347\pi$
$6$	0.218370	+	3.54249i	0.0891494	+	1.44622i
$7$		−	1.23786i		−	0.467865i	−0.972253	−	0.233933i	$-0.924840\pi$
$7$		−	1.23786i		−	0.467865i	0.972253	−	0.233933i	$-0.0751596\pi$
$8$	−2.78032	+	0.519434i	−0.982992	+	0.183647i
$9$	−3.29847			−1.09949
$10$	0.254892	+	4.13496i	0.0806040	+	1.30759i
$11$	−2.17413	+	2.50463i	−0.655524	+	0.755175i
$11$	−2.17413	+	2.50463i	−0.655524	+	0.755175i
$12$	−0.616475	−	4.98135i	−0.177961	−	1.43799i
$13$	−1.08694	−	3.43781i	−0.301464	−	0.953478i
$13$	−1.08694	−	3.43781i	−0.301464	−	0.953478i
$14$	0.107708	+	1.74728i	0.0287861	+	0.466979i
$15$	−7.35187			−1.89825
$16$	3.87932	−	0.975118i	0.969831	−	0.243779i
$17$		−	5.14494i		−	1.24783i	−0.781492	−	0.623916i	$-0.785541\pi$
$17$		−	5.14494i		−	1.24783i	0.781492	−	0.623916i	$-0.214459\pi$
$18$	4.65591	−	0.287005i	1.09741	−	0.0676477i
$19$		−	0.366099i		−	0.0839888i	−0.999118	−	0.0419944i	$-0.986629\pi$
$19$		−	0.366099i		−	0.0839888i	0.999118	−	0.0419944i	$-0.0133712\pi$
$20$	−0.719578	−	5.81447i	−0.160903	−	1.30015i
$21$	−3.10662			−0.677919
$22$	2.85092	−	3.72455i	0.607818	−	0.794076i
$23$			7.77474i			1.62115i	0.585638	+	0.810573i	$0.300844\pi$
$23$			7.77474i			1.62115i	−0.585638	+	0.810573i	$0.699156\pi$
$24$	1.30361	+	6.97771i	0.266098	+	1.42432i
$25$	−3.58145			−0.716290
$26$	1.83339	+	4.75801i	0.359557	+	0.933123i
$27$			0.749071i			0.144159i
$28$	−0.304066	−	2.45697i	−0.0574631	−	0.464323i
$29$			4.69618i			0.872058i	0.899933	+	0.436029i	$0.143615\pi$
$29$			4.69618i			0.872058i	−0.899933	+	0.436029i	$0.856385\pi$
$30$	10.3774	−	0.639697i	1.89465	−	0.116792i
$31$	7.88901			1.41691			0.708454	−	0.705757i	$-0.249393\pi$
$31$	7.88901			1.41691			0.708454	+	0.705757i	$0.249393\pi$
$32$	−5.39095	+	1.71396i	−0.952994	+	0.302988i
$33$	6.28581	+	5.45635i	1.09422	+	0.949829i
$34$	0.447669	+	7.26226i	0.0767745	+	1.24547i
$35$	−3.62619			−0.612938
$36$	−6.54700	+	0.810234i	−1.09117	+	0.135039i
$37$		−	7.05110i		−	1.15919i	−0.814903	−	0.579597i	$-0.803210\pi$
$37$		−	7.05110i		−	1.15919i	0.814903	−	0.579597i	$-0.196790\pi$
$38$	0.0318548	+	0.516761i	0.00516753	+	0.0838297i
$39$	−8.62779	+	2.72788i	−1.38155	+	0.436810i
$40$	1.52163	+	8.14471i	0.240592	+	1.28779i
$41$	9.08665			1.41910			0.709548	−	0.704657i	$-0.248899\pi$
$41$	9.08665			1.41910			0.709548	+	0.704657i	$0.248899\pi$
$42$	4.38510	−	0.270311i	0.676635	−	0.0417099i
$43$	−4.11572			−0.627642			−0.313821	−	0.949482i	$-0.601609\pi$
$43$	−4.11572			−0.627642			−0.313821	+	0.949482i	$0.601609\pi$
$44$	−3.70010	+	5.50539i	−0.557810	+	0.829968i
$45$			9.66258i			1.44041i
$46$	−0.676491	−	10.9743i	−0.0997432	−	1.61807i
$47$	−5.69467			−0.830653			−0.415327	−	0.909672i	$-0.636333\pi$
$47$	−5.69467			−0.830653			−0.415327	+	0.909672i	$0.636333\pi$
$48$	−2.44723	−	9.73584i	−0.353227	−	1.40525i
$49$	5.46771			0.781102
$50$	5.05534	−	0.311627i	0.714933	−	0.0440707i
$51$	−12.9121			−1.80806
$52$	−3.00189	−	6.55657i	−0.416287	−	0.909233i
$53$	−7.85325			−1.07873			−0.539363	−	0.842073i	$-0.681335\pi$
$53$	−7.85325			−1.07873			−0.539363	+	0.842073i	$0.681335\pi$
$54$	−0.0651777	−	1.05734i	−0.00886956	−	0.143886i
$55$	7.33710	+	6.36891i	0.989334	+	0.858783i
$56$	0.642984	+	3.44164i	0.0859223	+	0.459908i
$57$	−0.918789			−0.121697
$58$	−0.408621	−	6.62881i	−0.0536546	−	0.870406i
$59$	−10.7121			−1.39459			−0.697295	−	0.716784i	$-0.745613\pi$
$59$	−10.7121			−1.39459			−0.697295	+	0.716784i	$0.745613\pi$
$60$	−14.5924	+	1.80591i	−1.88387	+	0.233142i
$61$			5.82597i			0.745940i	0.927844	+	0.372970i	$0.121660\pi$
$61$			5.82597i			0.745940i	−0.927844	+	0.372970i	$0.878340\pi$
$62$	−11.1356	+	0.686434i	−1.41422	+	0.0871772i
$63$			4.08303i			0.514414i
$64$	7.46038	−	2.88838i	0.932547	−	0.361048i
$65$	−10.0708	+	3.18411i	−1.24912	+	0.394940i
$66$	−9.34740	−	7.15489i	−1.15059	−	0.880706i
$67$	7.23336			0.883695			0.441848	−	0.897090i	$-0.354323\pi$
$67$	7.23336			0.883695			0.441848	+	0.897090i	$0.354323\pi$
$68$	−1.26380	−	10.2120i	−0.153258	−	1.23838i
$69$	19.5121			2.34898
$70$	5.11849	−	0.315520i	0.611777	−	0.0377118i
$71$	5.63261			0.668468			0.334234	−	0.942490i	$-0.391522\pi$
$71$	5.63261			0.668468			0.334234	+	0.942490i	$0.391522\pi$
$72$	9.17082	−	1.71334i	1.08079	−	0.201919i
$73$	−0.631831			−0.0739503			−0.0369751	−	0.999316i	$-0.511772\pi$
$73$	−0.631831			−0.0739503			−0.0369751	+	0.999316i	$0.511772\pi$
$74$	0.613526	+	9.95287i	0.0713210	+	1.15700i
$75$			8.98828i			1.03788i
$76$	−0.0899282	−	0.726654i	−0.0103155	−	0.0833529i
$77$	3.10037	+	2.69125i	0.353320	+	0.306697i
$78$	11.9411	−	4.60121i	1.35206	−	0.520984i
$79$	−15.4397			−1.73711			−0.868553	−	0.495597i	$-0.834949\pi$
$79$	−15.4397			−1.73711			−0.868553	+	0.495597i	$0.834949\pi$
$80$	−2.85652	−	11.3641i	−0.319369	−	1.27055i
$81$	−8.01549			−0.890611
$82$	−12.8261	+	0.790643i	−1.41641	+	0.0873119i
$83$		−	9.80904i		−	1.07668i	−0.842727	−	0.538341i	$-0.819051\pi$
$83$		−	9.80904i		−	1.07668i	0.842727	−	0.538341i	$-0.180949\pi$
$84$	−6.16619	+	0.763107i	−0.672787	+	0.0832618i
$85$	−15.0716			−1.63475
$86$	5.80948	−	0.358115i	0.626453	−	0.0386165i
$87$	11.7859			1.26358
$88$	4.74378	−	8.09299i	0.505689	−	0.862716i
$89$			1.98044i			0.209927i	0.994476	+	0.104963i	$0.0334725\pi$
$89$			1.98044i			0.209927i	−0.994476	+	0.104963i	$0.966527\pi$
$90$	−0.840755	−	13.6391i	−0.0886234	−	1.43768i
$91$	−4.25552	+	1.34548i	−0.446099	+	0.141045i
$92$	1.90978	+	15.4318i	0.199108	+	1.60887i
$93$		−	19.7989i		−	2.05305i
$94$	8.03823	−	0.495502i	0.829080	−	0.0511071i
$95$	−1.07245			−0.110031
$96$	4.30148	+	13.5295i	0.439018	+	1.38085i
$97$			5.10448i			0.518281i	0.965840	+	0.259141i	$0.0834393\pi$
$97$			5.10448i			0.518281i	−0.965840	+	0.259141i	$0.916561\pi$
$98$	−7.71786	+	0.475754i	−0.779622	+	0.0480584i
$99$	7.17130	−	8.26146i	0.720742	−	0.830308i
$100$	−7.10867	+	0.879745i	−0.710867	+	0.0879745i
$101$		−	15.7063i		−	1.56284i	−0.624006	−	0.781420i	$-0.714496\pi$
$101$		−	15.7063i		−	1.56284i	0.624006	−	0.781420i	$-0.285504\pi$
$102$	18.2259	−	1.12350i	1.80463	−	0.111243i
$103$			3.59625i			0.354349i	0.984179	+	0.177174i	$0.0566957\pi$
$103$			3.59625i			0.354349i	−0.984179	+	0.177174i	$0.943304\pi$
$104$	4.80777	+	8.99363i	0.471441	+	0.881898i
$105$			9.10056i			0.888124i
$106$	11.0851	−	0.683322i	1.07668	−	0.0663701i
$107$	5.82490			0.563114			0.281557	−	0.959545i	$-0.409149\pi$
$107$	5.82490			0.563114			0.281557	+	0.959545i	$0.409149\pi$
$108$	0.184001	+	1.48680i	0.0177055	+	0.143067i
$109$	5.25625			0.503458			0.251729	−	0.967798i	$-0.419001\pi$
$109$	5.25625			0.503458			0.251729	+	0.967798i	$0.419001\pi$
$110$	−10.9107	−	8.35152i	−1.04030	−	0.796286i
$111$	−17.6960			−1.67963
$112$	−1.20706	−	4.80204i	−0.114056	−	0.453750i
$113$	6.35425			0.597757			0.298879	−	0.954291i	$-0.403387\pi$
$113$	6.35425			0.597757			0.298879	+	0.954291i	$0.403387\pi$
$114$	1.29690	−	0.0799451i	0.121466	−	0.00748755i
$115$	22.7754			2.12382
$116$	1.15356	+	9.32124i	0.107106	+	0.865456i
$117$	3.58526	+	11.3395i	0.331457	+	1.04834i
$118$	15.1204	−	0.932071i	1.39195	−	0.0858041i
$119$	−6.36869			−0.583817
$120$	20.4406	−	3.81881i	1.86596	−	0.348608i
$121$	−1.54635	−	10.8908i	−0.140578	−	0.990070i
$122$	−0.506926	−	8.22356i	−0.0458949	−	0.744526i
$123$		−	22.8046i		−	2.05622i
$124$	15.6586	−	1.93785i	1.40618	−	0.174024i
$125$		−	4.15551i		−	0.371680i
$126$	−0.355271	−	5.76334i	−0.0316500	−	0.513439i
$127$	10.7134			0.950663			0.475331	−	0.879807i	$-0.342328\pi$
$127$	10.7134			0.950663			0.475331	+	0.879807i	$0.342328\pi$
$128$	−10.2793	+	4.72619i	−0.908566	+	0.417740i
$129$			10.3291i			0.909429i
$130$	13.9382	−	5.37075i	1.22246	−	0.471046i
$131$	7.28004			0.636060			0.318030	−	0.948081i	$-0.396979\pi$
$131$	7.28004			0.636060			0.318030	+	0.948081i	$0.396979\pi$
$132$	13.8167	+	9.28604i	1.20259	+	0.808246i
$133$	−0.453177			−0.0392955
$134$	−10.2101	+	0.629385i	−0.882021	+	0.0543706i
$135$	2.19434			0.188858
$136$	2.67245	+	14.3046i	0.229161	+	1.22661i
$137$		−	1.66252i		−	0.142038i	−0.997475	−	0.0710192i	$-0.977375\pi$
$137$		−	1.66252i		−	0.142038i	0.997475	−	0.0710192i	$-0.0226252\pi$
$138$	−27.5420	+	1.69777i	−2.34453	+	0.144524i
$139$	−1.70917			−0.144970			−0.0724851	−	0.997369i	$-0.523093\pi$
$139$	−1.70917			−0.144970			−0.0724851	+	0.997369i	$0.523093\pi$
$140$	−7.19747	+	0.890734i	−0.608297	+	0.0752808i
$141$			14.2918i			1.20359i
$142$	−7.95062	+	0.490101i	−0.667201	+	0.0411284i
$143$	10.9736	+	4.75184i	0.917659	+	0.397369i
$144$	−12.7958	+	3.21640i	−1.06632	+	0.268033i
$145$	13.7570			1.14246
$146$	0.891852	−	0.0549766i	0.0738102	−	0.00454989i
$147$		−	13.7222i		−	1.13179i
$148$	−1.73203	−	13.9954i	−0.142372	−	1.15042i
$149$	−9.26145			−0.758728			−0.379364	−	0.925248i	$-0.623857\pi$
$149$	−9.26145			−0.758728			−0.379364	+	0.925248i	$0.623857\pi$
$150$	−0.782083	−	12.6873i	−0.0638568	−	1.03591i
$151$		−	18.1563i		−	1.47754i	−0.673958	−	0.738770i	$-0.735407\pi$
$151$		−	18.1563i		−	1.47754i	0.673958	−	0.738770i	$-0.264593\pi$
$152$	0.190164	+	1.01787i	0.0154243	+	0.0825603i
$153$			16.9704i			1.37198i
$154$	−4.61045	−	3.52903i	−0.371521	−	0.284377i
$155$		−	23.1102i		−	1.85625i
$156$	−16.4549	+	7.53377i	−1.31744	+	0.603185i
$157$	−1.47056			−0.117363			−0.0586817	−	0.998277i	$-0.518690\pi$
$157$	−1.47056			−0.117363			−0.0586817	+	0.998277i	$0.518690\pi$
$158$	21.7937	−	1.34343i	1.73381	−	0.106878i
$159$			19.7091i			1.56303i
$160$	5.02089	+	15.7923i	0.396936	+	1.24849i
$161$	9.62401			0.758478
$162$	11.3141	−	0.697440i	0.888923	−	0.0547960i
$163$	10.0496			0.787146			0.393573	−	0.919293i	$-0.371239\pi$
$163$	10.0496			0.787146			0.393573	+	0.919293i	$0.371239\pi$
$164$	18.0357	−	2.23204i	1.40835	−	0.174293i
$165$	15.9839	−	18.4137i	1.24434	−	1.43351i
$166$	0.853498	+	13.8458i	0.0662443	+	1.07464i
$167$			13.0686i			1.01128i	0.862745	+	0.505639i	$0.168743\pi$
$167$			13.0686i			1.01128i	−0.862745	+	0.505639i	$0.831257\pi$
$168$	8.63739	−	1.61368i	0.666389	−	0.124498i
$169$	−10.6371	+	7.47342i	−0.818239	+	0.574878i
$170$	21.2741	−	1.31141i	1.63165	−	0.100580i
$171$			1.20757i			0.0923449i
$172$	−8.16912	+	1.01098i	−0.622890	+	0.0770867i
$173$		−	10.6371i		−	0.808721i	−0.914600	−	0.404360i	$-0.867494\pi$
$173$		−	10.6371i		−	0.808721i	0.914600	−	0.404360i	$-0.132506\pi$
$174$	−16.6362	+	1.02551i	−1.26118	+	0.0777434i
$175$			4.43332i			0.335127i
$176$	−5.99182	+	11.8363i	−0.451651	+	0.892195i
$177$			26.8838i			2.02071i
$178$	−0.172321	−	2.79547i	−0.0129160	−	0.209529i
$179$			9.20720i			0.688179i	0.938937	+	0.344089i	$0.111812\pi$
$179$			9.20720i			0.688179i	−0.938937	+	0.344089i	$0.888188\pi$
$180$	2.37351	+	19.1789i	0.176911	+	1.42951i
$181$	−18.5318			−1.37746			−0.688730	−	0.725018i	$-0.741831\pi$
$181$	−18.5318			−1.37746			−0.688730	+	0.725018i	$0.741831\pi$
$182$	5.88973	−	2.26947i	0.436576	−	0.168224i
$183$	14.6213			1.08084
$184$	−4.03846	−	21.6163i	−0.297719	−	1.59357i
$185$	−20.6556			−1.51863
$186$	1.72273	+	27.9468i	0.126316	+	2.04916i
$187$	12.8862	+	11.1857i	0.942331	+	0.817983i
$188$	−11.3031	+	1.39883i	−0.824364	+	0.102021i
$189$	0.927241			0.0674469
$190$	1.51381	−	0.0933157i	0.109823	−	0.00676983i
$191$		−	19.8038i		−	1.43295i	−0.697612	−	0.716475i	$-0.745754\pi$
$191$		−	19.8038i		−	1.43295i	0.697612	−	0.716475i	$-0.254246\pi$
$192$	−7.24891	−	18.7231i	−0.523145	−	1.35123i
$193$	11.7530			0.846001			0.423000	−	0.906129i	$-0.360977\pi$
$193$	11.7530			0.846001			0.423000	+	0.906129i	$0.360977\pi$
$194$	−0.444148	−	7.20515i	−0.0318880	−	0.517299i
$195$	7.99107	+	25.2744i	0.572253	+	1.80993i
$196$	10.8526	−	1.34308i	0.775188	−	0.0959346i
$197$	1.34751			0.0960060			0.0480030	−	0.998847i	$-0.484714\pi$
$197$	1.34751			0.0960060			0.0480030	+	0.998847i	$0.484714\pi$
$198$	−9.40369	+	12.2853i	−0.668291	+	0.873079i
$199$		−	12.9954i		−	0.921219i	−0.887603	−	0.460610i	$-0.847631\pi$
$199$		−	12.9954i		−	0.921219i	0.887603	−	0.460610i	$-0.152369\pi$
$200$	9.95759	−	1.86033i	0.704108	−	0.131545i
$201$		−	18.1534i		−	1.28044i
$202$	1.36663	+	22.1700i	0.0961558	+	1.55988i
$203$	5.81319			0.408006
$204$	−25.6287	+	3.17173i	−1.79437	+	0.222065i
$205$		−	26.6185i		−	1.85912i
$206$	−0.312915	−	5.07623i	−0.0218018	−	0.353678i
$207$		−	25.6448i		−	1.78244i
$208$	−7.56888	−	12.2765i	−0.524807	−	0.851221i
$209$	0.916942	+	0.795945i	0.0634262	+	0.0550566i
$210$	−0.791853	−	12.8458i	−0.0546430	−	0.886441i
$211$	12.5749			0.865692			0.432846	−	0.901468i	$-0.357509\pi$
$211$	12.5749			0.865692			0.432846	+	0.901468i	$0.357509\pi$
$212$	−15.5876	+	1.92907i	−1.07056	+	0.132489i
$213$		−	14.1360i		−	0.968584i
$214$	−8.22204	+	0.506833i	−0.562047	+	0.0346464i
$215$			12.0566i			0.822256i
$216$	−0.389092	−	2.08266i	−0.0264744	−	0.141707i
$217$		−	9.76545i		−	0.662922i
$218$	−7.41938	+	0.457354i	−0.502504	+	0.0309759i
$219$			1.58569i			0.107151i
$220$	16.1275	+	10.8391i	1.08732	+	0.730772i
$221$	−17.6873	+	5.59226i	−1.18978	+	0.376176i
$222$	24.9785	−	1.53975i	1.67645	−	0.103341i
$223$	−27.9263			−1.87008			−0.935041	−	0.354540i	$-0.884637\pi$
$223$	−27.9263			−1.87008			−0.935041	+	0.354540i	$0.884637\pi$
$224$	2.12163	+	6.67322i	0.141758	+	0.445873i
$225$	11.8133			0.787555
$226$	−8.96924	+	0.552892i	−0.596625	+	0.0367778i
$227$		−	18.1916i		−	1.20742i	−0.797205	−	0.603708i	$-0.793689\pi$
$227$		−	18.1916i		−	1.20742i	0.797205	−	0.603708i	$-0.206311\pi$
$228$	−1.82367	+	0.225691i	−0.120775	+	0.0149467i
$229$		−	19.1024i		−	1.26232i	−0.775653	−	0.631159i	$-0.782579\pi$
$229$		−	19.1024i		−	1.26232i	0.775653	−	0.631159i	$-0.217421\pi$
$230$	−32.1483	+	1.98172i	−2.11979	+	0.130671i
$231$	6.75418	−	7.78093i	0.444392	−	0.511948i
$232$	−2.43935	−	13.0569i	−0.160151	−	0.857226i
$233$		−	16.3056i		−	1.06821i	−0.845417	−	0.534106i	$-0.820648\pi$
$233$		−	16.3056i		−	1.06821i	0.845417	−	0.534106i	$-0.179352\pi$
$234$	−6.04738	−	15.6942i	−0.395330	−	1.02596i
$235$			16.6820i			1.08822i
$236$	−21.2619	+	2.63130i	−1.38403	+	0.171283i
$237$			38.7487i			2.51700i
$238$	8.98963	−	0.554149i	0.582711	−	0.0359202i
$239$		−	1.24972i		−	0.0808378i	−0.999183	−	0.0404189i	$-0.987131\pi$
$239$		−	1.24972i		−	0.0808378i	0.999183	−	0.0404189i	$-0.0128692\pi$
$240$	−28.5203	+	7.16894i	−1.84098	+	0.462753i
$241$	12.9136			0.831835			0.415918	−	0.909402i	$-0.363460\pi$
$241$	12.9136			0.831835			0.415918	+	0.909402i	$0.363460\pi$
$242$	3.13035	+	15.2381i	0.201227	+	0.979545i
$243$			22.3635i			1.43462i
$244$	1.43109	+	11.5637i	0.0916160	+	0.740292i
$245$		−	16.0172i		−	1.02330i
$246$	1.98426	+	32.1894i	0.126512	+	2.05232i
$247$	−1.25858	+	0.397929i	−0.0800814	+	0.0253196i
$248$	−21.9340	+	4.09782i	−1.39281	+	0.260212i
$249$	−24.6175			−1.56007
$250$	0.361577	+	5.86565i	0.0228681	+	0.370976i
$251$		−	0.230732i		−	0.0145637i	−0.999973	−	0.00728183i	$-0.997682\pi$
$251$		−	0.230732i		−	0.0145637i	0.999973	−	0.00728183i	$-0.00231790\pi$
$252$	1.00295	+	8.10424i	0.0631801	+	0.510519i
$253$	−19.4729	−	16.9033i	−1.22425	−	1.06270i
$254$	−15.1224	+	0.932190i	−0.948862	+	0.0584908i
$255$			37.8249i			2.36869i
$256$	14.0983	−	7.56559i	0.881143	−	0.472850i
$257$	25.2667			1.57609			0.788046	−	0.615617i	$-0.211093\pi$
$257$	25.2667			1.57609			0.788046	+	0.615617i	$0.211093\pi$
$258$	−0.898752	−	14.5799i	−0.0559539	−	0.907706i
$259$	−8.72824			−0.542347
$260$	−19.2069	+	8.79377i	−1.19116	+	0.545367i
$261$		−	15.4902i		−	0.958820i
$262$	−10.2760	+	0.633447i	−0.634855	+	0.0391345i
$263$	−22.3720			−1.37952			−0.689759	−	0.724039i	$-0.742283\pi$
$263$	−22.3720			−1.37952			−0.689759	+	0.724039i	$0.742283\pi$
$264$	−20.3108	−	11.9053i	−1.25004	−	0.732724i
$265$			23.0054i			1.41321i
$266$	0.639675	−	0.0394316i	0.0392210	−	0.00241771i
$267$	4.97027			0.304176
$268$	14.3572	−	1.77680i	0.877005	−	0.108535i
$269$	−2.79827			−0.170613			−0.0853066	−	0.996355i	$-0.527187\pi$
$269$	−2.79827			−0.170613			−0.0853066	+	0.996355i	$0.527187\pi$
$270$	−3.09738	+	0.190932i	−0.188501	+	0.0116198i
$271$			13.1789i			0.800563i	0.916392	+	0.400281i	$0.131088\pi$
$271$			13.1789i			0.800563i	−0.916392	+	0.400281i	$0.868912\pi$
$272$	−5.01692	−	19.9589i	−0.304196	−	1.21019i
$273$	3.37672	+	10.6800i	0.204368	+	0.646381i
$274$	0.144658	+	2.34670i	0.00873911	+	0.141769i
$275$	7.78653	−	8.97021i	0.469545	−	0.540924i
$276$	38.7287	−	4.79293i	2.33119	−	0.288501i
$277$			8.99095i			0.540214i	0.962830	+	0.270107i	$0.0870590\pi$
$277$			8.99095i			0.540214i	−0.962830	+	0.270107i	$0.912941\pi$
$278$	2.41256	−	0.148718i	0.144696	−	0.00891949i
$279$	−26.0217			−1.55788
$280$	10.0820	−	1.88356i	0.602513	−	0.112564i
$281$	−12.9059			−0.769904			−0.384952	−	0.922937i	$-0.625782\pi$
$281$	−12.9059			−0.769904			−0.384952	+	0.922937i	$0.625782\pi$
$282$	−1.24355	−	20.1733i	−0.0740522	−	1.20130i
$283$	9.28594			0.551992			0.275996	−	0.961159i	$-0.410992\pi$
$283$	9.28594			0.551992			0.275996	+	0.961159i	$0.410992\pi$
$284$	11.1799	−	1.38359i	0.663407	−	0.0821010i
$285$			2.69151i			0.159431i
$286$	−15.9031	−	5.75256i	−0.940369	−	0.340156i
$287$		−	11.2480i		−	0.663946i
$288$	17.7819	−	5.65344i	1.04781	−	0.333132i
$289$	−9.47041			−0.557083
$290$	−19.4185	+	1.19702i	−1.14029	+	0.0702914i
$291$	12.8106			0.750970
$292$	−1.25410	+	0.155203i	−0.0733904	+	0.00908254i
$293$	−6.49216			−0.379276			−0.189638	−	0.981854i	$-0.560731\pi$
$293$	−6.49216			−0.379276			−0.189638	+	0.981854i	$0.560731\pi$
$294$	1.19399	+	19.3693i	0.0696347	+	1.12964i
$295$			31.3800i			1.82701i
$296$	3.66258	+	19.6043i	0.212883	+	1.13948i
$297$	−1.87615	−	1.62857i	−0.108865	−	0.0944994i
$298$	13.0729	−	0.805852i	0.757290	−	0.0466818i
$299$	26.7281	−	8.45071i	1.54573	−	0.488717i
$300$	2.20787	+	17.8405i	0.127472	+	1.03002i
$301$			5.09467i			0.293652i
$302$	1.57981	+	25.6283i	0.0909077	+	1.47474i
$303$	−39.4178			−2.26449
$304$	−0.356989	−	1.42021i	−0.0204747	−	0.0814549i
$305$	17.0667			0.977235
$306$	−1.47662	−	23.9544i	−0.0844129	−	1.36938i
$307$		−	19.6686i		−	1.12255i	−0.827630	−	0.561274i	$-0.810311\pi$
$307$		−	19.6686i		−	1.12255i	0.827630	−	0.561274i	$-0.189689\pi$
$308$	6.81488	+	4.58018i	0.388314	+	0.260980i
$309$	9.02542			0.513438
$310$	2.01085	+	32.6208i	0.114208	+	1.85274i
$311$		−	27.0302i		−	1.53274i	−0.642397	−	0.766372i	$-0.722060\pi$
$311$		−	27.0302i		−	1.53274i	0.642397	−	0.766372i	$-0.277940\pi$
$312$	22.5711	−	12.0659i	1.27784	−	0.683099i
$313$	20.7119			1.17070			0.585352	−	0.810779i	$-0.300956\pi$
$313$	20.7119			1.17070			0.585352	+	0.810779i	$0.300956\pi$
$314$	2.07575	−	0.127955i	0.117141	−	0.00722095i
$315$	11.9609			0.673920
$316$	−30.6457	+	3.79260i	−1.72395	+	0.213351i
$317$			1.04825i			0.0588758i	0.999567	+	0.0294379i	$0.00937173\pi$
$317$			1.04825i			0.0588758i	−0.999567	+	0.0294379i	$0.990628\pi$
$318$	−1.71492	−	27.8201i	−0.0961678	−	1.56007i
$319$	−11.7622	−	10.2101i	−0.658556	−	0.571654i
$320$	−8.46127	−	21.8545i	−0.472999	−	1.22170i
$321$		−	14.6186i		−	0.815931i
$322$	−13.5846	+	0.837399i	−0.757041	+	0.0466664i
$323$	−1.88356			−0.104804
$324$	−15.9096	+	1.96892i	−0.883868	+	0.109384i
$325$	3.89284	+	12.3124i	0.215936	+	0.682967i
$326$	−14.1854	+	0.874431i	−0.785655	+	0.0484302i
$327$		−	13.1915i		−	0.729491i
$328$	−25.2638	+	4.71991i	−1.39496	+	0.260614i
$329$			7.04918i			0.388634i
$330$	−20.9596	+	27.3824i	−1.15379	+	1.50735i
$331$	−14.0151			−0.770337			−0.385169	−	0.922846i	$-0.625857\pi$
$331$	−14.0151			−0.770337			−0.385169	+	0.922846i	$0.625857\pi$
$332$	−2.40948	−	19.4695i	−0.132238	−	1.06853i
$333$			23.2579i			1.27452i
$334$	−1.13712	−	18.4468i	−0.0622203	−	1.00936i
$335$		−	21.1895i		−	1.15771i
$336$	−12.0516	+	3.02932i	−0.657467	+	0.165263i
$337$			27.3764i			1.49129i	0.666345	+	0.745644i	$0.267858\pi$
$337$			27.3764i			1.49129i	−0.666345	+	0.745644i	$0.732142\pi$
$338$	14.3644	−	11.4745i	0.781319	−	0.624132i
$339$		−	15.9471i		−	0.866127i
$340$	−29.9151	+	3.70219i	−1.62237	+	0.200779i
$341$	−17.1517	+	19.7591i	−0.928816	+	1.07001i
$342$	−0.105072	−	1.70452i	−0.00568165	−	0.0921700i
$343$		−	15.4332i		−	0.833316i
$344$	11.4430	−	2.13784i	0.616967	−	0.115265i
$345$		−	57.1589i		−	3.07733i
$346$	0.925546	+	15.0146i	0.0497576	+	0.807189i
$347$	34.2779			1.84013			0.920067	−	0.391760i	$-0.128134\pi$
$347$	34.2779			1.84013			0.920067	+	0.391760i	$0.128134\pi$
$348$	23.3933	−	2.89507i	1.25401	−	0.155192i
$349$	16.5700			0.886974			0.443487	−	0.896281i	$-0.353741\pi$
$349$	16.5700			0.886974			0.443487	+	0.896281i	$0.353741\pi$
$350$	−0.385749	−	6.25778i	−0.0206192	−	0.334493i
$351$	2.57516	−	0.814198i	0.137452	−	0.0434587i
$352$	7.42777	−	17.2287i	0.395902	−	0.918293i
$353$			13.8349i			0.736356i	0.929755	+	0.368178i	$0.120018\pi$
$353$			13.8349i			0.736356i	−0.929755	+	0.368178i	$0.879982\pi$
$354$	−2.33920	−	37.9474i	−0.124327	−	2.01688i
$355$		−	16.5002i		−	0.875741i
$356$	0.486475	+	3.93090i	0.0257831	+	0.208337i
$357$			15.9834i			0.845929i
$358$	−0.801132	−	12.9963i	−0.0423411	−	0.686875i
$359$			35.9171i			1.89563i	0.318819	+	0.947816i	$0.396714\pi$
$359$			35.9171i			1.89563i	−0.318819	+	0.947816i	$0.603286\pi$
$360$	−5.01907	−	26.8651i	−0.264528	−	1.41591i
$361$	18.8660			0.992946
$362$	26.1583	−	1.61248i	1.37485	−	0.0847501i
$363$	−27.3323	+	3.88085i	−1.43457	+	0.203692i
$364$	−8.11609	+	3.71591i	−0.425399	+	0.194767i
$365$			1.85089i			0.0968802i
$366$	−20.6385	+	1.27222i	−1.07879	+	0.0665000i
$367$		−	18.4351i		−	0.962304i	−0.876637	−	0.481152i	$-0.840218\pi$
$367$		−	18.4351i		−	0.962304i	0.876637	−	0.481152i	$-0.159782\pi$
$368$	7.58129	+	30.1607i	0.395202	+	1.57224i
$369$	−29.9721			−1.56028
$370$	29.1560	−	1.79727i	1.51575	−	0.0934357i
$371$			9.72119i			0.504699i
$372$	−4.86337	−	39.2979i	−0.252154	−	2.03750i
$373$			20.8282i			1.07844i	0.842164	+	0.539221i	$0.181281\pi$
$373$			20.8282i			1.07844i	−0.842164	+	0.539221i	$0.818719\pi$
$374$	−19.1626	−	14.6678i	−0.990873	−	0.758455i
$375$	−10.4290			−0.538551
$376$	15.8330	−	2.95800i	0.816526	−	0.152547i
$377$	16.1446	−	5.10448i	0.831488	−	0.262894i
$378$	−1.30883	+	0.0806806i	−0.0673191	+	0.00414976i
$379$	−11.2559			−0.578175			−0.289088	−	0.957303i	$-0.593352\pi$
$379$	−11.2559			−0.578175			−0.289088	+	0.957303i	$0.593352\pi$
$380$	−2.12867	+	0.263437i	−0.109198	+	0.0135140i
$381$		−	26.8872i		−	1.37747i
$382$	1.72315	+	27.9537i	0.0881642	+	1.43024i
$383$	1.71937			0.0878558			0.0439279	−	0.999035i	$-0.486013\pi$
$383$	1.71937			0.0878558			0.0439279	+	0.999035i	$0.486013\pi$
$384$	11.8612	+	25.7976i	0.605290	+	1.31648i
$385$	7.88379	−	9.08227i	0.401795	−	0.462875i
$386$	−16.5898	+	1.02265i	−0.844398	+	0.0520514i
$387$	13.5756			0.690087
$388$	1.25386	+	10.1317i	0.0636551	+	0.514357i
$389$	13.5637			0.687706			0.343853	−	0.939023i	$-0.388268\pi$
$389$	13.5637			0.687706			0.343853	+	0.939023i	$0.388268\pi$
$390$	−13.4788	−	34.9803i	−0.682527	−	1.77130i
$391$	40.0006			2.02292
$392$	−15.2020	+	2.84011i	−0.767817	+	0.143447i
$393$		−	18.2705i		−	0.921627i
$394$	−1.90205	+	0.117249i	−0.0958241	+	0.00590690i
$395$			45.2293i			2.27573i
$396$	12.2047	−	18.1594i	0.613307	−	0.912543i
$397$			23.8324i			1.19612i	0.801453	+	0.598058i	$0.204061\pi$
$397$			23.8324i			1.19612i	−0.801453	+	0.598058i	$0.795939\pi$
$398$	1.13075	+	18.3435i	0.0566793	+	0.919474i
$399$			1.13733i			0.0569376i
$400$	−13.8936	+	3.49234i	−0.694680	+	0.174617i
$401$			9.40594i			0.469710i	0.972030	+	0.234855i	$0.0754616\pi$
$401$			9.40594i			0.469710i	−0.972030	+	0.234855i	$0.924538\pi$
$402$	1.57955	+	25.6241i	0.0787809	+	1.27802i
$403$	−8.57491	−	27.1209i	−0.427147	−	1.35099i
$404$	−3.85809	−	31.1749i	−0.191947	−	1.55101i
$405$			23.4807i			1.16676i
$406$	−8.20551	+	0.505814i	−0.407233	+	0.0251031i
$407$	17.6604	+	15.3300i	0.875394	+	0.759879i
$408$	35.8999	−	6.70699i	1.77731	−	0.332046i
$409$	26.4833			1.30951			0.654756	−	0.755840i	$-0.272771\pi$
$409$	26.4833			1.30951			0.654756	+	0.755840i	$0.272771\pi$
$410$	2.31612	+	37.5730i	0.114385	+	1.85560i
$411$	−4.17238			−0.205808
$412$	0.883380	+	7.13804i	0.0435210	+	0.351666i
$413$			13.2600i			0.652481i
$414$	2.23139	+	36.1985i	0.109667	+	1.77906i
$415$	−28.7347			−1.41053
$416$	11.7519	+	16.6701i	0.576186	+	0.817319i
$417$			4.28947i			0.210056i
$418$	−1.36355	−	1.04372i	−0.0666935	−	0.0510499i
$419$			10.4370i			0.509880i	0.966957	+	0.254940i	$0.0820557\pi$
$419$			10.4370i			0.509880i	−0.966957	+	0.254940i	$0.917944\pi$
$420$	2.23545	+	18.0633i	0.109079	+	0.881400i
$421$			10.1701i			0.495660i	0.968804	+	0.247830i	$0.0797174\pi$
$421$			10.1701i			0.495660i	−0.968804	+	0.247830i	$0.920283\pi$
$422$	−17.7499	+	1.09416i	−0.864052	+	0.0532629i
$423$	18.7837			0.913296
$424$	21.8346	−	4.07924i	1.06038	−	0.198105i
$425$			18.4264i			0.893809i
$426$	1.23000	+	19.9535i	0.0595935	+	0.966749i
$427$	7.21172			0.348999
$428$	11.5616	−	1.43082i	0.558851	−	0.0691614i
$429$	11.9256	−	27.5402i	0.575773	−	1.32965i
$430$	−1.04907	−	17.0184i	−0.0505904	−	0.820699i
$431$		−	1.33759i		−	0.0644295i	−0.999481	−	0.0322148i	$-0.989744\pi$
$431$		−	1.33759i		−	0.0644295i	0.999481	−	0.0322148i	$-0.0102561\pi$
$432$	0.730432	+	2.90589i	0.0351429	+	0.139810i
$433$	−9.35938			−0.449783			−0.224892	−	0.974384i	$-0.572203\pi$
$433$	−9.35938			−0.449783			−0.224892	+	0.974384i	$0.572203\pi$
$434$	0.849706	+	13.7843i	0.0407872	+	0.661666i
$435$		−	34.5257i		−	1.65538i
$436$	10.4329	−	1.29114i	0.499646	−	0.0618345i
$437$	2.84632			0.136158
$438$	−0.137973	−	2.23826i	−0.00659262	−	0.106948i
$439$	−13.2116			−0.630556			−0.315278	−	0.948999i	$-0.602098\pi$
$439$	−13.2116			−0.630556			−0.315278	+	0.948999i	$0.602098\pi$
$440$	−23.7077	−	13.8965i	−1.13022	−	0.662489i
$441$	−18.0351			−0.858814
$442$	24.4797	−	9.43267i	1.16438	−	0.448666i
$443$			18.4463i			0.876411i	0.898875	+	0.438206i	$0.144386\pi$
$443$			18.4463i			0.876411i	−0.898875	+	0.438206i	$0.855614\pi$
$444$	−35.1240	+	4.34683i	−1.66691	+	0.206291i
$445$	5.80154			0.275019
$446$	39.4189	−	2.42990i	1.86654	−	0.115059i
$447$			23.2432i			1.09937i
$448$	−3.57540	−	9.23487i	−0.168922	−	0.436307i
$449$			17.4102i			0.821638i	0.911717	+	0.410819i	$0.134757\pi$
$449$			17.4102i			0.821638i	−0.911717	+	0.410819i	$0.865243\pi$
$450$	−16.6749	+	1.02789i	−0.786063	+	0.0484554i
$451$	−19.7555	+	22.7587i	−0.930251	+	1.07167i
$452$	12.6123	−	1.56085i	0.593232	−	0.0734163i
$453$	−45.5665			−2.14090
$454$	1.58287	+	25.6780i	0.0742879	+	1.20513i
$455$	3.94146	+	12.4662i	0.184779	+	0.584422i
$456$	2.55453	−	0.477250i	0.119627	−	0.0223493i
$457$	−24.2359			−1.13371			−0.566853	−	0.823819i	$-0.691839\pi$
$457$	−24.2359			−1.13371			−0.566853	+	0.823819i	$0.691839\pi$
$458$	1.66212	+	26.9636i	0.0776659	+	1.25993i
$459$	3.85392			0.179886
$460$	45.2060	−	5.59454i	2.10774	−	0.260847i
$461$	27.0895			1.26168			0.630841	−	0.775912i	$-0.282710\pi$
$461$	27.0895			1.26168			0.630841	+	0.775912i	$0.282710\pi$
$462$	−8.85672	+	11.5707i	−0.412052	+	0.538319i
$463$	18.1193			0.842075			0.421038	−	0.907043i	$-0.361666\pi$
$463$	18.1193			0.842075			0.421038	+	0.907043i	$0.361666\pi$
$464$	4.57932	+	18.2180i	0.212590	+	0.845748i
$465$	−57.9990			−2.68964
$466$	1.41877	+	23.0158i	0.0657232	+	1.06619i
$467$		−	16.9741i		−	0.785470i	−0.919652	−	0.392735i	$-0.871529\pi$
$467$		−	16.9741i		−	0.785470i	0.919652	−	0.392735i	$-0.128471\pi$
$468$	9.90166	+	21.6267i	0.457704	+	0.999694i
$469$		−	8.95385i		−	0.413451i
$470$	−1.45153	−	23.5473i	−0.0669540	−	1.08615i
$471$			3.69063i			0.170055i
$472$	29.7829	−	5.56420i	1.37087	−	0.256113i
$473$	8.94810	−	10.3084i	0.411434	−	0.473979i
$474$	−3.37158	−	54.6951i	−0.154862	−	2.51223i
$475$			1.31116i			0.0601604i
$476$	−12.6410	+	1.56440i	−0.579397	+	0.0717042i
$477$	25.9037			1.18605
$478$	0.108740	+	1.76403i	0.00497366	+	0.0806847i
$479$			20.1493i			0.920644i	0.887752	+	0.460322i	$0.152266\pi$
$479$			20.1493i			0.920644i	−0.887752	+	0.460322i	$0.847734\pi$
$480$	39.6336	−	12.6008i	1.80902	−	0.575145i
$481$	−24.2404	+	7.66415i	−1.10527	+	0.349455i
$482$	−18.2279	+	1.12363i	−0.830259	+	0.0511798i
$483$		−	24.1531i		−	1.09901i
$484$	−5.74449	−	21.2368i	−0.261113	−	0.965308i
$485$	14.9531			0.678986
$486$	−1.94588	−	31.5669i	−0.0882669	−	1.43190i
$487$	−9.97270			−0.451906			−0.225953	−	0.974138i	$-0.572550\pi$
$487$	−9.97270			−0.451906			−0.225953	+	0.974138i	$0.572550\pi$
$488$	−3.02621	−	16.1981i	−0.136990	−	0.733253i
$489$		−	25.2213i		−	1.14054i
$490$	1.39368	+	22.6088i	0.0629599	+	1.02136i
$491$	27.0517			1.22082			0.610412	−	0.792084i	$-0.291004\pi$
$491$	27.0517			1.22082			0.610412	+	0.792084i	$0.291004\pi$
$492$	−5.60169	−	45.2638i	−0.252544	−	2.04065i
$493$	24.1615			1.08818
$494$	1.74190	−	0.671201i	0.0783719	−	0.0301988i
$495$	−24.2012	−	21.0077i	−1.08776	−	0.944225i
$496$	30.6040	−	7.69271i	1.37416	−	0.345413i
$497$		−	6.97236i		−	0.312753i
$498$	34.7485	−	2.14200i	1.55712	−	0.0959855i
$499$	4.65611			0.208436			0.104218	−	0.994554i	$-0.466766\pi$
$499$	4.65611			0.208436			0.104218	+	0.994554i	$0.466766\pi$
$500$	−1.02076	−	8.24810i	−0.0456496	−	0.368866i
$501$	32.7980			1.46530
$502$	0.0200763	+	0.325686i	0.000896049	+	0.0145361i
$503$	0.349613			0.0155885			0.00779424	−	0.999970i	$-0.497519\pi$
$503$	0.349613			0.0155885			0.00779424	+	0.999970i	$0.497519\pi$
$504$	−2.12086	−	11.3521i	−0.0944708	−	0.505665i
$505$	−46.0103			−2.04743
$506$	28.9574	+	22.1652i	1.28731	+	0.985362i
$507$	18.7559	+	26.6957i	0.832977	+	1.18560i
$508$	21.2646	−	2.63164i	0.943465	−	0.116760i
$509$			28.5754i			1.26658i	0.773914	+	0.633290i	$0.218296\pi$
$509$			28.5754i			1.26658i	−0.773914	+	0.633290i	$0.781704\pi$
$510$	−3.29120	−	53.3912i	−0.145737	−	2.36420i
$511$			0.782116i			0.0345988i
$512$	−19.2419	+	11.9058i	−0.850381	+	0.526167i
$513$	0.274234			0.0121077
$514$	−35.6648	+	2.19849i	−1.57311	+	0.0969712i
$515$	10.5349			0.464223
$516$	2.53724	+	20.5019i	0.111696	+	0.902544i
$517$	12.3809	−	14.2631i	0.544513	−	0.627288i
$518$	12.3202	−	0.759457i	0.541319	−	0.0333686i
$519$	−26.6956			−1.17181
$520$	26.3460	−	14.0839i	1.15535	−	0.617621i
$521$	13.0412			0.571346			0.285673	−	0.958327i	$-0.407783\pi$
$521$	13.0412			0.571346			0.285673	+	0.958327i	$0.407783\pi$
$522$	1.34783	+	21.8650i	0.0589927	+	0.957003i
$523$	−31.1800			−1.36341			−0.681704	−	0.731628i	$-0.738761\pi$
$523$	−31.1800			−1.36341			−0.681704	+	0.731628i	$0.738761\pi$
$524$	14.4498	−	1.78826i	0.631245	−	0.0781207i
$525$	11.1262			0.485587
$526$	31.5789	−	1.94662i	1.37690	−	0.0848767i
$527$		−	40.5885i		−	1.76806i
$528$	29.7053	+	15.0375i	1.29276	+	0.654425i
$529$	−37.4466			−1.62811
$530$	−2.00173	−	32.4729i	−0.0869497	−	1.41053i
$531$	35.3334			1.53334
$532$	−0.899493	+	0.111318i	−0.0389980	+	0.00482625i
$533$	−9.87668	−	31.2382i	−0.427807	−	1.35308i
$534$	−7.01571	+	0.432471i	−0.303600	+	0.0187148i
$535$		−	17.0635i		−	0.737720i
$536$	−20.1111	+	3.75725i	−0.868666	+	0.162288i
$537$	23.1071			0.997145
$538$	3.94985	−	0.243481i	0.170290	−	0.0104972i
$539$	−11.8875	+	13.6946i	−0.512031	+	0.589868i
$540$	4.35544	−	0.539015i	0.187429	−	0.0231955i
$541$	24.6573			1.06010			0.530050	−	0.847967i	$-0.322173\pi$
$541$	24.6573			1.06010			0.530050	+	0.847967i	$0.322173\pi$
$542$	−1.14672	−	18.6025i	−0.0492557	−	0.799046i
$543$			46.5089i			1.99589i
$544$	8.81821	+	27.7361i	0.378078	+	1.18918i
$545$		−	15.3977i		−	0.659566i
$546$	−5.69563	−	14.7813i	−0.243751	−	0.632582i
$547$	−43.9235			−1.87803			−0.939017	−	0.343872i	$-0.888261\pi$
$547$	−43.9235			−1.87803			−0.939017	+	0.343872i	$0.888261\pi$
$548$	−0.408380	−	3.29986i	−0.0174451	−	0.140963i
$549$		−	19.2168i		−	0.820154i
$550$	−10.2104	+	13.3393i	−0.435374	+	0.568789i
$551$	1.71926			0.0732431
$552$	−54.2499	+	10.1352i	−2.30903	+	0.431384i
$553$			19.1122i			0.812732i
$554$	−0.782315	−	12.6910i	−0.0332374	−	0.539190i
$555$			51.8388i			2.20043i
$556$	−3.39247	+	0.419840i	−0.143873	+	0.0178052i
$557$	12.1643			0.515417			0.257708	−	0.966223i	$-0.417033\pi$
$557$	12.1643			0.515417			0.257708	+	0.966223i	$0.417033\pi$
$558$	36.7305	−	2.26418i	1.55493	−	0.0958505i
$559$	4.47356	+	14.1491i	0.189211	+	0.598442i
$560$	−14.0672	+	3.53596i	−0.594446	+	0.149422i
$561$	28.0726	−	32.3401i	1.18523	−	1.36540i
$562$	18.2172	−	1.12296i	0.768445	−	0.0473694i
$563$	37.8757			1.59627			0.798136	−	0.602478i	$-0.205820\pi$
$563$	37.8757			1.59627			0.798136	+	0.602478i	$0.205820\pi$
$564$	3.51062	+	28.3672i	0.147824	+	1.19447i
$565$		−	18.6142i		−	0.783105i
$566$	−13.1074	+	0.807983i	−0.550946	+	0.0339621i
$567$			9.92203i			0.416686i
$568$	−15.6605	+	2.92577i	−0.657099	+	0.122762i
$569$		−	11.0656i		−	0.463892i	−0.972729	−	0.231946i	$-0.925491\pi$
$569$		−	11.0656i		−	0.463892i	0.972729	−	0.231946i	$-0.0745093\pi$
$570$	−0.234192	−	3.79916i	−0.00980923	−	0.159129i
$571$	7.53391			0.315284			0.157642	−	0.987496i	$-0.449611\pi$
$571$	7.53391			0.315284			0.157642	+	0.987496i	$0.449611\pi$
$572$	22.9483	+	6.73618i	0.959516	+	0.281654i
$573$	−49.7010			−2.07629
$574$	0.978701	+	15.8769i	0.0408502	+	0.662688i
$575$		−	27.8449i		−	1.16121i
$576$	−24.6079	+	9.52726i	−1.02533	+	0.396969i
$577$		−	2.43515i		−	0.101377i	−0.998715	−	0.0506884i	$-0.983858\pi$
$577$		−	2.43515i		−	0.101377i	0.998715	−	0.0506884i	$-0.0161415\pi$
$578$	13.3678	−	0.824034i	0.556027	−	0.0342753i
$579$		−	29.4963i		−	1.22582i
$580$	27.3058	−	3.37927i	1.13381	−	0.140316i
$581$	−12.1422			−0.503742
$582$	−18.0826	+	1.11467i	−0.749547	+	0.0462045i
$583$	17.0740	−	19.6695i	0.707131	−	0.814627i
$584$	1.75669	−	0.328194i	0.0726925	−	0.0135808i
$585$	33.2182	−	10.5027i	1.37340	−	0.434233i
$586$	9.16390	−	0.564892i	0.378557	−	0.0233355i
$587$	14.7623			0.609305			0.304652	−	0.952464i	$-0.401460\pi$
$587$	14.7623			0.609305			0.304652	+	0.952464i	$0.401460\pi$
$588$	−3.37071	−	27.2366i	−0.139006	−	1.12322i
$589$		−	2.88816i		−	0.119004i
$590$	−2.73042	−	44.2940i	−0.112410	−	1.82355i
$591$		−	3.38181i		−	0.139109i
$592$	−6.87565	−	27.3535i	−0.282588	−	1.12422i
$593$	−13.3041			−0.546333			−0.273167	−	0.961967i	$-0.588071\pi$
$593$	−13.3041			−0.546333			−0.273167	+	0.961967i	$0.588071\pi$
$594$	2.78995	+	2.13554i	0.114473	+	0.0876223i
$595$			18.6565i			0.764843i
$596$	−18.3827	+	2.27498i	−0.752983	+	0.0931866i
$597$	−32.6142			−1.33481
$598$	−36.9923	+	14.2541i	−1.51273	+	0.582894i
$599$		−	29.9135i		−	1.22223i	−0.791541	−	0.611116i	$-0.790721\pi$
$599$		−	29.9135i		−	1.22223i	0.791541	−	0.611116i	$-0.209279\pi$
$600$	−4.66881	−	24.9903i	−0.190604	−	1.02023i
$601$		−	25.2098i		−	1.02833i	−0.857691	−	0.514165i	$-0.828102\pi$
$601$		−	25.2098i		−	1.02833i	0.857691	−	0.514165i	$-0.171898\pi$
$602$	−0.443295	−	7.19130i	−0.0180673	−	0.293096i
$603$	−23.8590			−0.971615
$604$	−4.45990	−	36.0377i	−0.181471	−	1.46635i
$605$	−31.9035	+	4.52991i	−1.29706	+	0.184167i
$606$	55.6396	−	3.42980i	2.26020	−	0.139326i
$607$	5.98728			0.243016			0.121508	−	0.992590i	$-0.461227\pi$
$607$	5.98728			0.243016			0.121508	+	0.992590i	$0.461227\pi$
$608$	0.627478	+	1.97362i	0.0254476	+	0.0800409i
$609$		−	14.5892i		−	0.591185i
$610$	−24.0902	+	1.48500i	−0.975383	+	0.0601257i
$611$	6.18979	+	19.5772i	0.250412	+	0.792009i
$612$	4.16861	+	33.6839i	0.168506	+	1.36159i
$613$	−5.44008			−0.219723			−0.109861	−	0.993947i	$-0.535041\pi$
$613$	−5.44008			−0.219723			−0.109861	+	0.993947i	$0.535041\pi$
$614$	1.71140	+	27.7630i	0.0690663	+	1.12042i
$615$	−66.8039			−2.69379
$616$	−10.0180	−	5.87211i	−0.403635	−	0.236594i
$617$		−	25.5416i		−	1.02827i	−0.857710	−	0.514133i	$-0.828114\pi$
$617$		−	25.5416i		−	1.02827i	0.857710	−	0.514133i	$-0.171886\pi$
$618$	−12.7397	+	0.785314i	−0.512465	+	0.0315900i
$619$	−10.9823			−0.441416			−0.220708	−	0.975340i	$-0.570837\pi$
$619$	−10.9823			−0.441416			−0.220708	+	0.975340i	$0.570837\pi$
$620$	−5.67676	−	45.8704i	−0.227984	−	1.84220i
$621$	−5.82383			−0.233702
$622$	2.35194	+	38.1541i	0.0943042	+	1.52984i
$623$	2.45151			0.0982175
$624$	−30.8100	+	18.9954i	−1.23339	+	0.760426i
$625$	−30.0805			−1.20322
$626$	−29.2355	+	1.80217i	−1.16849	+	0.0720292i
$627$	1.99756	−	2.30123i	0.0797750	−	0.0919022i
$628$	−2.91885	+	0.361227i	−0.116475	+	0.0144145i
$629$	−36.2775			−1.44648
$630$	−16.8832	+	1.04073i	−0.672643	+	0.0414638i
$631$	23.7746			0.946453			0.473227	−	0.880941i	$-0.343089\pi$
$631$	23.7746			0.946453			0.473227	+	0.880941i	$0.343089\pi$
$632$	42.9274	−	8.01991i	1.70756	−	0.319015i
$633$		−	31.5589i		−	1.25435i
$634$	−0.0912101	−	1.47965i	−0.00362242	−	0.0587643i
$635$		−	31.3840i		−	1.24544i
$636$	4.84133	+	39.1198i	0.191971	+	1.55120i
$637$	−5.94310	−	18.7970i	−0.235474	−	0.744763i
$638$	17.4911	+	13.3884i	0.692480	+	0.530053i
$639$	−18.5790			−0.734974
$640$	13.8450	+	30.1122i	0.547270	+	1.19029i
$641$	−7.75317			−0.306232			−0.153116	−	0.988208i	$-0.548931\pi$
$641$	−7.75317			−0.306232			−0.153116	+	0.988208i	$0.548931\pi$
$642$	1.27199	+	20.6347i	0.0502013	+	0.814385i
$643$	−43.4042			−1.71169			−0.855847	−	0.517229i	$-0.826963\pi$
$643$	−43.4042			−1.71169			−0.855847	+	0.517229i	$0.826963\pi$
$644$	19.1023	−	2.36403i	0.752736	−	0.0931560i
$645$	30.2583			1.19142
$646$	2.65870	−	0.163891i	0.104605	−	0.00644820i
$647$			1.42330i			0.0559556i	0.999609	+	0.0279778i	$0.00890676\pi$
$647$			1.42330i			0.0559556i	−0.999609	+	0.0279778i	$0.991093\pi$
$648$	22.2857	−	4.16352i	0.875463	−	0.163558i
$649$	23.2893	−	26.8297i	0.914187	−	1.05316i
$650$	−6.56619	−	17.0406i	−0.257547	−	0.668387i
$651$	−24.5081			−0.960549
$652$	19.9470	−	2.46858i	0.781187	−	0.0966770i
$653$	36.4169			1.42510			0.712552	−	0.701620i	$-0.247539\pi$
$653$	36.4169			1.42510			0.712552	+	0.701620i	$0.247539\pi$
$654$	1.14781	+	18.6202i	0.0448829	+	0.728109i
$655$		−	21.3262i		−	0.833285i
$656$	35.2501	−	8.86056i	1.37628	−	0.345947i
$657$	2.08408			0.0813077
$658$	−0.613359	−	9.95016i	−0.0239112	−	0.387898i
$659$	34.7468			1.35354			0.676772	−	0.736192i	$-0.263378\pi$
$659$	34.7468			1.35354			0.676772	+	0.736192i	$0.263378\pi$
$660$	27.2026	−	40.4749i	1.05886	−	1.57548i
$661$			12.9838i			0.505012i	0.967595	+	0.252506i	$0.0812548\pi$
$661$			12.9838i			0.505012i	−0.967595	+	0.252506i	$0.918745\pi$
$662$	19.7827	−	1.21947i	0.768878	−	0.0473961i
$663$	14.0348	+	44.3895i	0.545065	+	1.72394i
$664$	5.09514	+	27.2723i	0.197730	+	1.05837i
$665$			1.32754i			0.0514799i
$666$	−2.02370	−	32.8293i	−0.0784168	−	1.27211i
$667$	−36.5116			−1.41373
$668$	3.21016	+	25.9393i	0.124205	+	1.00362i
$669$			70.0859i			2.70968i
$670$	1.84373	+	29.9097i	0.0712294	+	1.15551i
$671$	−14.5919	−	12.6664i	−0.563315	−	0.488981i
$672$	16.7476	−	5.32461i	0.646053	−	0.205401i
$673$			43.7626i			1.68692i	0.537188	+	0.843462i	$0.319486\pi$
$673$			43.7626i			1.68692i	−0.537188	+	0.843462i	$0.680514\pi$
$674$	−2.38206	−	38.6427i	−0.0917535	−	1.48846i
$675$		−	2.68276i		−	0.103259i
$676$	−19.2774	+	17.4466i	−0.741438	+	0.671022i
$677$			44.8725i			1.72459i	0.506406	+	0.862295i	$0.330974\pi$
$677$			44.8725i			1.72459i	−0.506406	+	0.862295i	$0.669026\pi$
$678$	1.38758	+	22.5099i	0.0532897	+	0.864486i
$679$	6.31861			0.242486
$680$	41.9040	−	7.82872i	1.60695	−	0.300218i
$681$	−45.6549			−1.74950
$682$	22.4909	−	29.3830i	0.861223	−	1.12513i
$683$	35.1245			1.34400			0.672001	−	0.740550i	$-0.265435\pi$
$683$	35.1245			1.34400			0.672001	+	0.740550i	$0.265435\pi$
$684$	0.296626	+	2.39685i	0.0113418	+	0.0916458i
$685$	−4.87020			−0.186081
$686$	1.34287	+	21.7845i	0.0512709	+	0.831737i
$687$	−47.9407			−1.82905
$688$	−15.9662	+	4.01331i	−0.608706	+	0.153006i
$689$	8.53604	+	26.9980i	0.325197	+	1.02854i
$690$	4.97348	+	80.6818i	0.189337	+	3.07150i
$691$	3.20078			0.121763			0.0608817	−	0.998145i	$-0.480609\pi$
$691$	3.20078			0.121763			0.0608817	+	0.998145i	$0.480609\pi$
$692$	−2.61288	−	21.1131i	−0.0993268	−	0.802598i
$693$	−10.2265	−	8.87703i	−0.388472	−	0.337210i
$694$	−48.3845	+	2.98257i	−1.83665	+	0.113217i
$695$			5.00687i			0.189922i
$696$	−32.7685	+	6.12198i	−1.24209	+	0.232053i
$697$		−	46.7503i		−	1.77079i
$698$	−23.3892	+	1.44178i	−0.885294	+	0.0545723i
$699$	−40.9216			−1.54780
$700$	1.08900	+	8.79951i	0.0411602	+	0.332590i
$701$			11.9577i			0.451637i	0.974169	+	0.225818i	$0.0725056\pi$
$701$			11.9577i			0.451637i	−0.974169	+	0.225818i	$0.927494\pi$
$702$	−3.56409	+	1.37334i	−0.134518	+	0.0518333i
$703$	−2.58140			−0.0973593
$704$	−8.98546	+	24.9652i	−0.338652	+	0.940912i
$705$	41.8665			1.57678
$706$	−1.20379	−	19.5284i	−0.0453053	−	0.734961i
$707$	−19.4422			−0.731198
$708$	6.60371	+	53.3605i	0.248183	+	2.00541i
$709$			13.9268i			0.523031i	0.965199	+	0.261516i	$0.0842223\pi$
$709$			13.9268i			0.523031i	−0.965199	+	0.261516i	$0.915778\pi$
$710$	1.43571	+	23.2906i	0.0538812	+	0.874082i
$711$	50.9275			1.90993
$712$	−1.02871	−	5.50627i	−0.0385525	−	0.206356i
$713$			61.3350i			2.29701i
$714$	−1.39073	−	22.5611i	−0.0520469	−	0.844326i
$715$	13.9201	−	32.1462i	0.520582	−	1.20220i
$716$	2.26165	+	18.2750i	0.0845218	+	0.682968i
$717$	−3.13640			−0.117131
$718$	−3.12520	−	50.6982i	−0.116631	−	1.89204i
$719$		−	9.22678i		−	0.344101i	−0.985088	−	0.172050i	$-0.944961\pi$
$719$		−	9.22678i		−	0.344101i	0.985088	−	0.172050i	$-0.0550392\pi$
$720$	9.42216	+	37.4843i	0.351143	+	1.39696i
$721$	4.45164			0.165788
$722$	−26.6300	+	1.64156i	−0.991065	+	0.0610924i
$723$		−	32.4088i		−	1.20530i
$724$	−36.7830	+	4.55214i	−1.36703	+	0.169179i
$725$		−	16.8191i		−	0.624647i
$726$	38.2428	−	7.85617i	1.41932	−	0.291570i
$727$			17.5680i			0.651560i	0.945446	+	0.325780i	$0.105627\pi$
$727$			17.5680i			0.651560i	−0.945446	+	0.325780i	$0.894373\pi$
$728$	11.1328	−	5.95132i	0.412610	−	0.220571i
$729$	32.0787			1.18810
$730$	−0.161049	−	2.61260i	−0.00596069	−	0.0966967i
$731$			21.1751i			0.783191i
$732$	29.0212	−	3.59157i	1.07266	−	0.132748i
$733$	36.2315			1.33824			0.669120	−	0.743155i	$-0.266671\pi$
$733$	36.2315			1.33824			0.669120	+	0.743155i	$0.266671\pi$
$734$	1.60406	+	26.0218i	0.0592071	+	0.960481i
$735$	−40.1979			−1.48272
$736$	−13.3256	−	41.9132i	−0.491187	−	1.54494i
$737$	−15.7262	+	18.1169i	−0.579283	+	0.667344i
$738$	42.3066	−	2.60791i	1.55733	−	0.0959986i
$739$			19.6495i			0.722819i	0.932407	+	0.361410i	$0.117704\pi$
$739$			19.6495i			0.722819i	−0.932407	+	0.361410i	$0.882296\pi$
$740$	−40.9984	+	5.07382i	−1.50713	+	0.186517i
$741$	0.998672	+	3.15862i	0.0366871	+	0.116035i
$742$	−0.845855	−	13.7218i	−0.0310523	−	0.503743i
$743$		−	20.3200i		−	0.745469i	−0.927938	−	0.372735i	$-0.878420\pi$
$743$		−	20.3200i		−	0.745469i	0.927938	−	0.372735i	$-0.121580\pi$
$744$	10.2842	+	55.0472i	0.377037	+	2.01813i
$745$			27.1306i			0.993988i
$746$	−1.81229	−	29.3997i	−0.0663526	−	1.07640i
$747$			32.3549i			1.18380i
$748$	28.3249	+	19.0368i	1.03566	+	0.696053i
$749$		−	7.21038i		−	0.263462i
$750$	14.7209	−	0.907441i	0.537530	−	0.0331351i
$751$			50.3750i			1.83821i	0.394013	+	0.919105i	$0.371087\pi$
$751$			50.3750i			1.83821i	−0.394013	+	0.919105i	$0.628913\pi$
$752$	−22.0915	+	5.55298i	−0.805593	+	0.202496i
$753$	−0.579062			−0.0211022
$754$	−22.3445	+	8.60991i	−0.813737	+	0.313554i
$755$	−53.1873			−1.93568
$756$	1.84044	−	0.227767i	0.0669362	−	0.00828380i
$757$	23.4301			0.851582			0.425791	−	0.904821i	$-0.359996\pi$
$757$	23.4301			0.851582			0.425791	+	0.904821i	$0.359996\pi$
$758$	15.8880	−	0.979389i	0.577080	−	0.0355730i
$759$	−42.4217	+	48.8706i	−1.53981	+	1.77389i
$760$	2.98177	−	0.557068i	0.108160	−	0.0202070i
$761$	−4.62839			−0.167779			−0.0838895	−	0.996475i	$-0.526734\pi$
$761$	−4.62839			−0.167779			−0.0838895	+	0.996475i	$0.526734\pi$
$762$	2.33950	+	37.9522i	0.0847510	+	1.37486i
$763$		−	6.50648i		−	0.235550i
$764$	−4.86458	−	39.3077i	−0.175994	−	1.42210i
$765$	49.7134			1.79739
$766$	−2.42695	+	0.149605i	−0.0876894	+	0.00540545i
$767$	11.6434	+	36.8260i	0.420419	+	1.32971i
$768$	−18.9872	−	35.3821i	−0.685141	−	1.27674i
$769$	13.3681			0.482066			0.241033	−	0.970517i	$-0.422514\pi$
$769$	13.3681			0.482066			0.241033	+	0.970517i	$0.422514\pi$
$770$	−10.3380	+	13.5059i	−0.372555	+	0.486719i
$771$		−	63.4112i		−	2.28370i
$772$	23.3281	−	2.88700i	0.839596	−	0.103906i
$773$		−	17.4158i		−	0.626403i	−0.949687	−	0.313202i	$-0.898598\pi$
$773$		−	17.4158i		−	0.626403i	0.949687	−	0.313202i	$-0.101402\pi$
$774$	−19.1624	+	1.18123i	−0.688779	+	0.0424585i
$775$	−28.2541			−1.01492
$776$	−2.65144	−	14.1921i	−0.0951811	−	0.509467i
$777$			21.9051i			0.785840i
$778$	−19.1456	+	1.18020i	−0.686403	+	0.0423121i
$779$		−	3.32661i		−	0.119188i
$780$	22.0695	+	48.2031i	0.790216	+	1.72595i
$781$	−12.2460	+	14.1076i	−0.438196	+	0.504810i
$782$	−56.4622	+	3.48051i	−2.01908	+	0.124463i
$783$	−3.51777			−0.125715
$784$	21.2110	−	5.33167i	0.757537	−	0.190417i
$785$			4.30787i			0.153755i
$786$	1.58975	+	25.7895i	0.0567044	+	0.919881i
$787$			20.2730i			0.722655i	0.932439	+	0.361327i	$0.117676\pi$
$787$			20.2730i			0.722655i	−0.932439	+	0.361327i	$0.882324\pi$
$788$	2.67461	−	0.331001i	0.0952791	−	0.0117914i
$789$			56.1465i			1.99887i
$790$	−3.93547	−	63.8427i	−0.140018	−	2.27142i
$791$		−	7.86564i		−	0.279670i
$792$	−15.6472	+	26.6945i	−0.556000	+	0.948549i
$793$	20.0286	−	6.33251i	0.711237	−	0.224874i
$794$	−2.07369	−	33.6403i	−0.0735926	−	1.19385i
$795$	57.7361			2.04769
$796$	−3.19218	−	25.7940i	−0.113144	−	0.914245i
$797$	−26.9598			−0.954965			−0.477482	−	0.878641i	$-0.658451\pi$
$797$	−26.9598			−0.954965			−0.477482	+	0.878641i	$0.658451\pi$
$798$	−0.0989606	−	1.60538i	−0.00350317	−	0.0568298i
$799$			29.2987i			1.03652i
$800$	19.3074	−	6.13846i	0.682621	−	0.217027i
$801$		−	6.53244i		−	0.230813i
$802$	−0.818424	−	13.2768i	−0.0288996	−	0.468820i
$803$	1.37368	−	1.58250i	0.0484761	−	0.0558454i
$804$	−4.45918	−	36.0319i	−0.157263	−	1.27075i
$805$		−	28.1927i		−	0.993661i
$806$	14.4636	+	37.5360i	0.509459	+	1.32215i
$807$			7.02274i			0.247212i
$808$	8.15840	+	43.6687i	0.287011	+	1.53626i
$809$		−	8.94691i		−	0.314557i	−0.987554	−	0.157278i	$-0.949728\pi$
$809$		−	8.94691i		−	0.314557i	0.987554	−	0.157278i	$-0.0502720\pi$
$810$	−2.04309	−	33.1438i	−0.0717868	−	1.16455i
$811$		−	20.8363i		−	0.731663i	−0.930681	−	0.365831i	$-0.880785\pi$
$811$		−	20.8363i		−	0.731663i	0.930681	−	0.365831i	$-0.119215\pi$
$812$	11.5384	−	1.42795i	0.404917	−	0.0501111i
$813$	33.0748			1.15999
$814$	−26.2622	−	20.1021i	−0.920488	−	0.704579i
$815$		−	29.4394i		−	1.03122i
$816$	−50.0903	+	12.5909i	−1.75351	+	0.440768i
$817$			1.50676i			0.0527149i
$818$	−37.3820	+	2.30435i	−1.30703	+	0.0805696i
$819$	14.0367	−	4.43803i	0.490482	−	0.155077i
$820$	−6.53856	−	52.8340i	−0.228336	−	1.84504i
$821$	−43.8781			−1.53136			−0.765679	−	0.643223i	$-0.777597\pi$
$821$	−43.8781			−1.53136			−0.765679	+	0.643223i	$0.777597\pi$
$822$	5.88946	−	0.363045i	0.205418	−	0.0126626i
$823$		−	14.7243i		−	0.513258i	−0.966510	−	0.256629i	$-0.917388\pi$
$823$		−	14.7243i		−	0.513258i	0.966510	−	0.256629i	$-0.0826118\pi$
$824$	−1.86801	−	9.99873i	−0.0650753	−	0.348322i
$825$	−22.5123	−	19.5417i	−0.783779	−	0.680353i
$826$	−1.15377	−	18.7169i	−0.0401448	−	0.651245i
$827$			5.53677i			0.192532i	0.995356	+	0.0962662i	$0.0306900\pi$
$827$			5.53677i			0.192532i	−0.995356	+	0.0962662i	$0.969310\pi$
$828$	−6.29936	−	50.9012i	−0.218918	−	1.76894i
$829$	−14.4923			−0.503338			−0.251669	−	0.967813i	$-0.580980\pi$
$829$	−14.4923			−0.503338			−0.251669	+	0.967813i	$0.580980\pi$
$830$	40.5600	−	2.50025i	1.40786	−	0.0867849i
$831$	22.5644			0.782749
$832$	−18.0387	−	22.5079i	−0.625381	−	0.780320i
$833$		−	28.1311i		−	0.974683i
$834$	−0.373233	−	6.05474i	−0.0129240	−	0.209658i
$835$	38.2833			1.32485
$836$	2.01552	+	1.35460i	0.0697081	+	0.0468498i
$837$			5.90942i			0.204260i
$838$	−0.908136	−	14.7321i	−0.0313710	−	0.508914i
$839$	−0.859956			−0.0296890			−0.0148445	−	0.999890i	$-0.504725\pi$
$839$	−0.859956			−0.0296890			−0.0148445	+	0.999890i	$0.504725\pi$
$840$	−4.72714	−	25.3025i	−0.163102	−	0.873019i
$841$	6.94594			0.239515
$842$	−0.884914	−	14.3554i	−0.0304962	−	0.494721i
$843$			32.3897i			1.11556i
$844$	24.9594	−	3.08889i	0.859138	−	0.106324i
$845$	21.8927	+	31.1605i	0.753132	+	1.07195i
$846$	−26.5139	+	1.63440i	−0.911566	+	0.0561918i
$847$	−13.4812	+	1.91416i	−0.463219	+	0.0657715i
$848$	−30.4653	+	7.65784i	−1.04618	+	0.262971i
$849$		−	23.3047i		−	0.799815i
$850$	−1.60330	−	26.0094i	−0.0549928	−	0.892116i
$851$	54.8205			1.87922
$852$	−3.47236	−	28.0580i	−0.118961	−	0.961251i
$853$	−14.6167			−0.500466			−0.250233	−	0.968186i	$-0.580507\pi$
$853$	−14.6167			−0.500466			−0.250233	+	0.968186i	$0.580507\pi$
$854$	−10.1796	+	0.627502i	−0.348338	+	0.0214727i
$855$	3.53746			0.120979
$856$	−16.1951	+	3.02565i	−0.553537	+	0.103414i
$857$		−	2.37263i		−	0.0810476i	−0.999179	−	0.0405238i	$-0.987097\pi$
$857$		−	2.37263i		−	0.0810476i	0.999179	−	0.0405238i	$-0.0129027\pi$
$858$	−14.4371	+	39.9116i	−0.492873	+	1.36256i
$859$		−	4.90111i		−	0.167224i	−0.996498	−	0.0836118i	$-0.973354\pi$
$859$		−	4.90111i		−	0.167224i	0.996498	−	0.0836118i	$-0.0266456\pi$
$860$	2.96158	+	23.9307i	0.100989	+	0.816031i
$861$	−28.2287			−0.962033
$862$	0.116386	+	1.88806i	0.00396412	+	0.0643075i
$863$	−21.4603			−0.730517			−0.365259	−	0.930906i	$-0.619019\pi$
$863$	−21.4603			−0.730517			−0.365259	+	0.930906i	$0.619019\pi$
$864$	−1.28388	−	4.03820i	−0.0436783	−	0.137382i
$865$	−31.1603			−1.05948
$866$	13.2111	−	0.814373i	0.448931	−	0.0276735i
$867$			23.7677i			0.807192i
$868$	−2.39878	−	19.3830i	−0.0814198	−	0.657903i
$869$	33.5679	−	38.6708i	1.13871	−	1.31182i
$870$	3.00413	+	48.7342i	0.101850	+	1.65224i
$871$	−7.86225	−	24.8669i	−0.266402	−	0.842584i
$872$	−14.6141	+	2.73027i	−0.494895	+	0.0924587i
$873$		−	16.8370i		−	0.569846i
$874$	−4.01768	+	0.247663i	−0.135900	+	0.00837731i
$875$	−5.14393			−0.173896
$876$	0.389508	+	3.14737i	0.0131603	+	0.106340i
$877$	−47.5053			−1.60414			−0.802070	−	0.597230i	$-0.796268\pi$
$877$	−47.5053			−1.60414			−0.802070	+	0.597230i	$0.796268\pi$
$878$	18.6487	−	1.14956i	0.629362	−	0.0387958i
$879$			16.2932i			0.549556i
$880$	34.6734	+	17.5525i	1.16884	+	0.591695i
$881$	25.7375			0.867120			0.433560	−	0.901125i	$-0.357257\pi$
$881$	25.7375			0.867120			0.433560	+	0.901125i	$0.357257\pi$
$882$	25.4572	−	1.56926i	0.857187	−	0.0528397i
$883$			19.5591i			0.658215i	0.944292	+	0.329108i	$0.106748\pi$
$883$			19.5591i			0.658215i	−0.944292	+	0.329108i	$0.893252\pi$
$884$	−33.7332	+	15.4445i	−1.13457	+	0.519456i
$885$	78.7536			2.64727
$886$	−1.60504	−	26.0376i	−0.0539224	−	0.874751i
$887$	−25.9829			−0.872421			−0.436210	−	0.899845i	$-0.643680\pi$
$887$	−25.9829			−0.872421			−0.436210	+	0.899845i	$0.643680\pi$
$888$	49.2005	−	9.19188i	1.65106	−	0.308459i
$889$		−	13.2617i		−	0.444782i
$890$	−8.18907	+	0.504800i	−0.274498	+	0.0169209i
$891$	17.4267	−	20.0759i	0.583816	−	0.672567i
$892$	−55.4297	+	6.85979i	−1.85592	+	0.229683i
$893$			2.08481i			0.0697656i
$894$	−2.02243	−	32.8086i	−0.0676401	−	1.09728i
$895$	26.9717			0.901564
$896$	5.85034	+	12.7242i	0.195446	+	0.425087i
$897$	−21.2085	−	67.0789i	−0.708133	−	2.23970i
$898$	−1.51489	−	24.5751i	−0.0505524	−	0.820081i
$899$			37.0482i			1.23563i
$900$	23.4478	−	2.90181i	0.781592	−	0.0967272i
$901$			40.4045i			1.34607i
$902$	25.9053	−	33.8437i	0.862553	−	1.12687i
$903$	12.7860			0.425491
$904$	−17.6668	+	3.30061i	−0.587591	+	0.109777i
$905$			54.2873i			1.80457i
$906$	64.3186	−	3.96480i	2.13684	−	0.131722i
$907$		−	41.9544i		−	1.39307i	−0.717522	−	0.696536i	$-0.754724\pi$
$907$		−	41.9544i		−	1.39307i	0.717522	−	0.696536i	$-0.245276\pi$
$908$	−4.46856	−	36.1077i	−0.148294	−	1.19827i
$909$			51.8069i			1.71833i
$910$	−6.64821	−	17.2535i	−0.220386	−	0.571946i
$911$		−	36.7603i		−	1.21792i	−0.793200	−	0.608961i	$-0.791587\pi$
$911$		−	36.7603i		−	1.21792i	0.793200	−	0.608961i	$-0.208413\pi$
$912$	−3.56428	+	0.895928i	−0.118025	+	0.0296671i
$913$	24.5680	+	21.3261i	0.813083	+	0.705790i
$914$	34.2097	−	2.10880i	1.13156	−	0.0697528i
$915$		−	42.8318i		−	1.41598i
$916$	−4.69229	−	37.9155i	−0.155038	−	1.25276i
$917$		−	9.01164i		−	0.297591i
$918$	−5.43994	+	0.335335i	−0.179545	+	0.0110677i
$919$	30.0944			0.992722			0.496361	−	0.868116i	$-0.334669\pi$
$919$	30.0944			0.992722			0.496361	+	0.868116i	$0.334669\pi$
$920$	−63.3230	+	11.8303i	−2.08770	+	0.390034i
$921$	−49.3619			−1.62653
$922$	−38.2377	+	2.35709i	−1.25929	+	0.0776268i
$923$	−6.12233	−	19.3639i	−0.201519	−	0.637369i
$924$	11.4948	−	17.1031i	0.378150	−	0.562652i
$925$			25.2532i			0.830319i
$926$	−25.5760	+	1.57659i	−0.840480	+	0.0518098i
$927$		−	11.8621i		−	0.389603i
$928$	−8.04905	−	25.3168i	−0.264223	−	0.831066i
$929$		−	38.7992i		−	1.27296i	−0.771293	−	0.636480i	$-0.780390\pi$
$929$		−	38.7992i		−	1.27296i	0.771293	−	0.636480i	$-0.219610\pi$
$930$	81.8676	−	5.04657i	2.68454	−	0.165484i
$931$		−	2.00172i		−	0.0656038i
$932$	−4.00528	−	32.3642i	−0.131197	−	1.06012i
$933$	−67.8372			−2.22089
$934$	1.47694	+	23.9596i	0.0483271	+	0.783982i
$935$	32.7677	−	37.7489i	1.07162	−	1.23452i
$936$	−15.8583	−	29.6652i	−0.518345	−	0.969639i
$937$			17.0554i			0.557174i	0.960411	+	0.278587i	$0.0898661\pi$
$937$			17.0554i			0.557174i	−0.960411	+	0.278587i	$0.910134\pi$
$938$	0.779088	+	12.6387i	0.0254381	+	0.412667i
$939$		−	51.9801i		−	1.69631i
$940$	4.09776	+	33.1115i	0.133654	+	1.07998i
$941$	43.7885			1.42747			0.713733	−	0.700418i	$-0.247003\pi$
$941$	43.7885			1.42747			0.713733	+	0.700418i	$0.247003\pi$
$942$	−0.321127	−	5.20945i	−0.0104629	−	0.169733i
$943$			70.6464i			2.30056i
$944$	−41.5555	+	10.4455i	−1.35252	+	0.339973i
$945$		−	2.71627i		−	0.0883603i
$946$	−11.7336	+	15.3292i	−0.381492	+	0.498395i
$947$	28.1580			0.915012			0.457506	−	0.889207i	$-0.348743\pi$
$947$	28.1580			0.915012			0.457506	+	0.889207i	$0.348743\pi$
$948$	9.51820	+	76.9107i	0.309137	+	2.49794i
$949$	0.686765	+	2.17212i	0.0222933	+	0.0705099i
$950$	−0.114086	−	1.85075i	−0.00370145	−	0.0600464i
$951$	2.63078			0.0853089
$952$	17.7070	−	3.30811i	0.573888	−	0.107217i
$953$			57.6350i			1.86698i	0.358602	+	0.933490i	$0.383253\pi$
$953$			57.6350i			1.86698i	−0.358602	+	0.933490i	$0.616747\pi$
$954$	−36.5640	+	2.25392i	−1.18380	+	0.0729734i
$955$	−58.0134			−1.87727
$956$	−0.306981	−	2.48052i	−0.00992847	−	0.0802258i
$957$	−25.6240	+	29.5193i	−0.828306	+	0.954223i
$958$	−1.75322	−	28.4414i	−0.0566439	−	0.918900i
$959$	−2.05796			−0.0664549
$960$	−54.8478	+	21.2350i	−1.77020	+	0.685358i
$961$	31.2364			1.00763
$962$	33.5492	−	12.9274i	1.08167	−	0.416796i
$963$	−19.2133			−0.619139
$964$	25.6316	−	3.17208i	0.825538	−	0.102166i
$965$		−	34.4294i		−	1.10832i
$966$	2.10160	+	34.0930i	0.0676179	+	1.09692i
$967$			58.1170i			1.86892i	0.356073	+	0.934458i	$0.384115\pi$
$967$			58.1170i			1.86892i	−0.356073	+	0.934458i	$0.615885\pi$
$968$	9.95639	+	29.4766i	0.320011	+	0.947414i
$969$			4.72711i			0.151857i
$970$	−21.1068	+	1.30109i	−0.677700	+	0.0417756i
$971$		−	14.7215i		−	0.472436i	−0.971700	−	0.236218i	$-0.924092\pi$
$971$		−	14.7215i		−	0.472436i	0.971700	−	0.236218i	$-0.0759080\pi$
$972$	5.49335	+	44.3884i	0.176199	+	1.42376i
$973$			2.11571i			0.0678266i
$974$	14.0768	−	0.867738i	0.451050	−	0.0278041i
$975$	30.9000	−	9.76976i	0.989593	−	0.312883i
$976$	5.68101	+	22.6008i	0.181845	+	0.723435i
$977$		−	31.7673i		−	1.01633i	−0.861261	−	0.508163i	$-0.830325\pi$
$977$		−	31.7673i		−	1.01633i	0.861261	−	0.508163i	$-0.169675\pi$
$978$	2.19454	+	35.6007i	0.0701736	+	1.13838i
$979$	−4.96028	−	4.30574i	−0.158531	−	0.137612i
$980$	−3.93445	−	31.7918i	−0.125681	−	1.01555i
$981$	−17.3376			−0.553547
$982$	−38.1844	+	2.35380i	−1.21851	+	0.0751129i
$983$	48.8227			1.55720			0.778602	−	0.627518i	$-0.215929\pi$
$983$	48.8227			1.55720			0.778602	+	0.627518i	$0.215929\pi$
$984$	11.8454	+	63.4040i	0.377619	+	2.02125i
$985$		−	3.94741i		−	0.125775i
$986$	−34.1048	+	2.10233i	−1.08612	+	0.0669518i
$987$	17.6912			0.563116
$988$	−2.40035	+	1.09899i	−0.0763654	+	0.0349635i
$989$		−	31.9987i		−	1.01750i
$990$	35.9887	+	27.5473i	1.14380	+	0.875510i
$991$			23.0130i			0.731031i	0.930805	+	0.365515i	$0.119107\pi$
$991$			23.0130i			0.731031i	−0.930805	+	0.365515i	$0.880893\pi$
$992$	−42.5293	+	13.5214i	−1.35031	+	0.429306i
$993$			35.1733i			1.11619i
$994$	0.606675	+	9.84172i	0.0192426	+	0.312160i
$995$	−38.0689			−1.20686
$996$	−48.8623	+	6.04703i	−1.54826	+	0.191607i
$997$		−	3.04715i		−	0.0965042i	−0.998835	−	0.0482521i	$-0.984635\pi$
$997$		−	3.04715i		−	0.0965042i	0.998835	−	0.0482521i	$-0.0153651\pi$
$998$	−6.57227	+	0.405135i	−0.208041	+	0.0128243i
$999$	5.28177			0.167108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.b.c.571.3	yes	56
4.3	odd	2	inner	572.2.b.c.571.1	✓	56
11.10	odd	2	inner	572.2.b.c.571.53	yes	56
13.12	even	2	inner	572.2.b.c.571.54	yes	56
44.43	even	2	inner	572.2.b.c.571.55	yes	56
52.51	odd	2	inner	572.2.b.c.571.56	yes	56
143.142	odd	2	inner	572.2.b.c.571.4	yes	56
572.571	even	2	inner	572.2.b.c.571.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.1	✓	56	4.3	odd	2	inner
572.2.b.c.571.2	yes	56	572.571	even	2	inner
572.2.b.c.571.3	yes	56	1.1	even	1	trivial
572.2.b.c.571.4	yes	56	143.142	odd	2	inner
572.2.b.c.571.53	yes	56	11.10	odd	2	inner
572.2.b.c.571.54	yes	56	13.12	even	2	inner
572.2.b.c.571.55	yes	56	44.43	even	2	inner
572.2.b.c.571.56	yes	56	52.51	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.41153 + 0.0870114i) q^{2} -2.50968i q^{3} +(1.98486 - 0.245639i) q^{4} -2.92941i q^{5} +(0.218370 + 3.54249i) q^{6} -1.23786i q^{7} +(-2.78032 + 0.519434i) q^{8} -3.29847 q^{9} +O(q^{10})\)	\(q+(-1.41153 + 0.0870114i) q^{2} -2.50968i q^{3} +(1.98486 - 0.245639i) q^{4} -2.92941i q^{5} +(0.218370 + 3.54249i) q^{6} -1.23786i q^{7} +(-2.78032 + 0.519434i) q^{8} -3.29847 q^{9} +(0.254892 + 4.13496i) q^{10} +(-2.17413 + 2.50463i) q^{11} +(-0.616475 - 4.98135i) q^{12} +(-1.08694 - 3.43781i) q^{13} +(0.107708 + 1.74728i) q^{14} -7.35187 q^{15} +(3.87932 - 0.975118i) q^{16} -5.14494i q^{17} +(4.65591 - 0.287005i) q^{18} -0.366099i q^{19} +(-0.719578 - 5.81447i) q^{20} -3.10662 q^{21} +(2.85092 - 3.72455i) q^{22} +7.77474i q^{23} +(1.30361 + 6.97771i) q^{24} -3.58145 q^{25} +(1.83339 + 4.75801i) q^{26} +0.749071i q^{27} +(-0.304066 - 2.45697i) q^{28} +4.69618i q^{29} +(10.3774 - 0.639697i) q^{30} +7.88901 q^{31} +(-5.39095 + 1.71396i) q^{32} +(6.28581 + 5.45635i) q^{33} +(0.447669 + 7.26226i) q^{34} -3.62619 q^{35} +(-6.54700 + 0.810234i) q^{36} -7.05110i q^{37} +(0.0318548 + 0.516761i) q^{38} +(-8.62779 + 2.72788i) q^{39} +(1.52163 + 8.14471i) q^{40} +9.08665 q^{41} +(4.38510 - 0.270311i) q^{42} -4.11572 q^{43} +(-3.70010 + 5.50539i) q^{44} +9.66258i q^{45} +(-0.676491 - 10.9743i) q^{46} -5.69467 q^{47} +(-2.44723 - 9.73584i) q^{48} +5.46771 q^{49} +(5.05534 - 0.311627i) q^{50} -12.9121 q^{51} +(-3.00189 - 6.55657i) q^{52} -7.85325 q^{53} +(-0.0651777 - 1.05734i) q^{54} +(7.33710 + 6.36891i) q^{55} +(0.642984 + 3.44164i) q^{56} -0.918789 q^{57} +(-0.408621 - 6.62881i) q^{58} -10.7121 q^{59} +(-14.5924 + 1.80591i) q^{60} +5.82597i q^{61} +(-11.1356 + 0.686434i) q^{62} +4.08303i q^{63} +(7.46038 - 2.88838i) q^{64} +(-10.0708 + 3.18411i) q^{65} +(-9.34740 - 7.15489i) q^{66} +7.23336 q^{67} +(-1.26380 - 10.2120i) q^{68} +19.5121 q^{69} +(5.11849 - 0.315520i) q^{70} +5.63261 q^{71} +(9.17082 - 1.71334i) q^{72} -0.631831 q^{73} +(0.613526 + 9.95287i) q^{74} +8.98828i q^{75} +(-0.0899282 - 0.726654i) q^{76} +(3.10037 + 2.69125i) q^{77} +(11.9411 - 4.60121i) q^{78} -15.4397 q^{79} +(-2.85652 - 11.3641i) q^{80} -8.01549 q^{81} +(-12.8261 + 0.790643i) q^{82} -9.80904i q^{83} +(-6.16619 + 0.763107i) q^{84} -15.0716 q^{85} +(5.80948 - 0.358115i) q^{86} +11.7859 q^{87} +(4.74378 - 8.09299i) q^{88} +1.98044i q^{89} +(-0.840755 - 13.6391i) q^{90} +(-4.25552 + 1.34548i) q^{91} +(1.90978 + 15.4318i) q^{92} -19.7989i q^{93} +(8.03823 - 0.495502i) q^{94} -1.07245 q^{95} +(4.30148 + 13.5295i) q^{96} +5.10448i q^{97} +(-7.71786 + 0.475754i) q^{98} +(7.17130 - 8.26146i) 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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