LMFDB - Embedded newform 572.2.b.c.571.4

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			571.4
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.1

$q$-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} +(-3.28678 - 3.34620i) q^{22} +7.77474i q^{23} +(1.30361 + 6.97771i) q^{24} -3.58145 q^{25} +(1.23513 - 4.94717i) 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} +(4.93057 + 4.43729i) 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} +(-1.31297 + 7.09057i) 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} +(-8.39787 + 8.24876i) 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} +(-12.4158 - 3.09978i) 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} +(-7.34576 - 5.83437i) 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	$0.227347\pi$
$5$			2.92941i			1.31007i	−0.755597	+	0.655036i	$0.772653\pi$
$6$	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	$0.214459\pi$
$17$			5.14494i			1.24783i	−0.781492	+	0.623916i	$0.785541\pi$
$18$	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
$22$	−3.28678	−	3.34620i	−0.700745	−	0.713412i
$23$			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
$26$	1.23513	−	4.94717i	0.242229	−	0.970219i
$27$			0.749071i			0.144159i
$28$	−0.304066	−	2.45697i	−0.0574631	−	0.464323i
$29$		−	4.69618i		−	0.872058i	−0.899933	−	0.436029i	$-0.856385\pi$
$29$		−	4.69618i		−	0.872058i	0.899933	−	0.436029i	$-0.143615\pi$
$30$	−10.3774	+	0.639697i	−1.89465	+	0.116792i
$31$	−7.88901			−1.41691			−0.708454	−	0.705757i	$-0.750607\pi$
$31$	−7.88901			−1.41691			−0.708454	+	0.705757i	$0.750607\pi$
$32$	−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	$0.196790\pi$
$37$			7.05110i			1.15919i	−0.814903	+	0.579597i	$0.803210\pi$
$38$	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	$-0.398391\pi$
$43$	4.11572			0.627642			0.313821	+	0.949482i	$0.398391\pi$
$44$	4.93057	+	4.43729i	0.743311	+	0.668946i
$45$		−	9.66258i		−	1.44041i
$46$	−0.676491	−	10.9743i	−0.0997432	−	1.61807i
$47$	5.69467			0.830653			0.415327	−	0.909672i	$-0.363667\pi$
$47$	5.69467			0.830653			0.415327	+	0.909672i	$0.363667\pi$
$48$	−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
$52$	−1.31297	+	7.09057i	−0.182076	+	0.983284i
$53$	−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	$-0.254387\pi$
$59$	10.7121			1.39459			0.697295	+	0.716784i	$0.254387\pi$
$60$	14.5924	−	1.80591i	1.88387	−	0.233142i
$61$		−	5.82597i		−	0.745940i	−0.927844	−	0.372970i	$-0.878340\pi$
$61$		−	5.82597i		−	0.745940i	0.927844	−	0.372970i	$-0.121660\pi$
$62$	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
$66$	−8.39787	+	8.24876i	−1.03371	+	1.01535i
$67$	−7.23336			−0.883695			−0.441848	−	0.897090i	$-0.645677\pi$
$67$	−7.23336			−0.883695			−0.441848	+	0.897090i	$0.645677\pi$
$68$	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	$-0.608478\pi$
$71$	−5.63261			−0.668468			−0.334234	+	0.942490i	$0.608478\pi$
$72$	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
$78$	−12.4158	−	3.09978i	−1.40581	−	0.350980i
$79$	15.4397			1.73711			0.868553	−	0.495597i	$-0.165051\pi$
$79$	15.4397			1.73711			0.868553	+	0.495597i	$0.165051\pi$
$80$	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
$88$	−7.34576	−	5.83437i	−0.783060	−	0.621946i
$89$		−	1.98044i		−	0.209927i	−0.994476	−	0.104963i	$-0.966527\pi$
$89$		−	1.98044i		−	0.209927i	0.994476	−	0.104963i	$-0.0334725\pi$
$90$	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	$-0.916561\pi$
$97$		−	5.10448i		−	0.518281i	0.965840	−	0.259141i	$-0.0834393\pi$
$98$	−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	$0.285504\pi$
$101$			15.7063i			1.56284i	−0.624006	+	0.781420i	$0.714496\pi$
$102$	−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	$0.943304\pi$
$104$	1.23634	−	10.1228i	0.121233	−	0.992624i
$105$		−	9.10056i		−	0.888124i
$106$	11.0851	−	0.683322i	1.07668	−	0.0663701i
$107$	−5.82490			−0.563114			−0.281557	−	0.959545i	$-0.590851\pi$
$107$	−5.82490			−0.563114			−0.281557	+	0.959545i	$0.590851\pi$
$108$	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	$0.419001\pi$
$110$	9.80239	−	9.62834i	0.934622	−	0.918027i
$111$	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	$-0.657672\pi$
$127$	−10.7134			−0.950663			−0.475331	+	0.879807i	$0.657672\pi$
$128$	−10.2793	+	4.72619i	−0.908566	+	0.417740i
$129$		−	10.3291i		−	0.909429i
$130$	14.4923	+	3.61820i	1.27106	+	0.317337i
$131$	−7.28004			−0.636060			−0.318030	−	0.948081i	$-0.603021\pi$
$131$	−7.28004			−0.636060			−0.318030	+	0.948081i	$0.603021\pi$
$132$	11.1362	−	12.3741i	0.969278	−	1.07703i
$133$	−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	$0.0226252\pi$
$137$			1.66252i			0.142038i	−0.997475	+	0.0710192i	$0.977375\pi$
$138$	−27.5420	+	1.69777i	−2.34453	+	0.144524i
$139$	1.70917			0.144970			0.0724851	−	0.997369i	$-0.476907\pi$
$139$	1.70917			0.144970			0.0724851	+	0.997369i	$0.476907\pi$
$140$	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
$154$	−4.14211	+	4.06857i	−0.333781	+	0.327854i
$155$		−	23.1102i		−	1.85625i
$156$	17.7950	+	3.29512i	1.42474	+	0.263821i
$157$	−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	$-0.628761\pi$
$163$	−10.0496			−0.787146			−0.393573	+	0.919293i	$0.628761\pi$
$164$	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	$0.132506\pi$
$173$			10.6371i			0.808721i	−0.914600	+	0.404360i	$0.867494\pi$
$174$	16.6362	−	1.02551i	1.26118	−	0.0777434i
$175$			4.43332i			0.335127i
$176$	10.8764	+	7.59624i	0.819843	+	0.572588i
$177$		−	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	$0.741831\pi$
$182$	−6.12388	−	1.52891i	−0.453932	−	0.113331i
$183$	−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	$0.484714\pi$
$198$	10.8414	+	11.0373i	0.770463	+	0.784390i
$199$		−	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
$208$	−0.864334	+	14.3963i	−0.0599308	+	0.998203i
$209$	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	$-0.642491\pi$
$211$	−12.5749			−0.865692			−0.432846	+	0.901468i	$0.642491\pi$
$212$	−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
$220$	−12.9986	+	14.4437i	−0.876368	+	0.973791i
$221$	−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	$-0.115363\pi$
$223$	27.9263			1.87008			0.935041	+	0.354540i	$0.115363\pi$
$224$	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	$0.217421\pi$
$229$			19.1024i			1.26232i	−0.775653	+	0.631159i	$0.782579\pi$
$230$	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	$0.179352\pi$
$233$			16.3056i			1.06821i	−0.845417	+	0.534106i	$0.820648\pi$
$234$	−4.07404	+	16.3181i	−0.266328	+	1.06675i
$235$			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	$0.363460\pi$
$242$	1.23511	−	15.5072i	0.0793960	−	0.996843i
$243$			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
$260$	−20.7712	−	3.84622i	−1.28817	−	0.238533i
$261$			15.4902i			0.958820i
$262$	10.2760	−	0.633447i	0.634855	−	0.0391345i
$263$	22.3720			1.37952			0.689759	−	0.724039i	$-0.257717\pi$
$263$	22.3720			1.37952			0.689759	+	0.724039i	$0.257717\pi$
$264$	−14.6424	+	18.4355i	−0.901176	+	1.13462i
$265$		−	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	$-0.912941\pi$
$277$		−	8.99095i		−	0.540214i	0.962830	−	0.270107i	$-0.0870590\pi$
$278$	−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	$-0.589008\pi$
$283$	−9.28594			−0.551992			−0.275996	+	0.961159i	$0.589008\pi$
$284$	−11.1799	+	1.38359i	−0.663407	+	0.0821010i
$285$		−	2.69151i		−	0.159431i
$286$	15.0762	−	7.66222i	0.891472	−	0.453076i
$287$		−	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	$-0.189689\pi$
$308$	5.49272	−	6.10333i	0.312977	−	0.347770i
$309$	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	$-0.277940\pi$
$312$	−25.4050	−	3.10281i	−1.43827	−	0.175662i
$313$	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	$-0.990628\pi$
$317$		−	1.04825i		−	0.0588758i	0.999567	−	0.0294379i	$-0.00937173\pi$
$318$	−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
$330$	−24.1640	−	24.6008i	−1.33019	−	1.35423i
$331$	14.0151			0.770337			0.385169	−	0.922846i	$-0.374143\pi$
$331$	14.0151			0.770337			0.385169	+	0.922846i	$0.374143\pi$
$332$	−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	$-0.732142\pi$
$337$		−	27.3764i		−	1.49129i	0.666345	−	0.745644i	$-0.267858\pi$
$338$	15.6649	+	9.62344i	0.852059	+	0.523446i
$339$		−	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	$-0.871866\pi$
$347$	−34.2779			−1.84013			−0.920067	+	0.391760i	$0.871866\pi$
$348$	−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
$352$	−16.0134	−	9.77598i	−0.853519	−	0.521062i
$353$		−	13.8349i		−	0.736356i	−0.929755	−	0.368178i	$-0.879982\pi$
$353$		−	13.8349i		−	0.736356i	0.929755	−	0.368178i	$-0.120018\pi$
$354$	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
$364$	8.77710	+	1.62526i	0.460045	+	0.0851870i
$365$		−	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	$-0.818719\pi$
$373$		−	20.8282i		−	1.07844i	0.842164	−	0.539221i	$-0.181281\pi$
$374$	17.2160	−	16.9103i	0.890218	−	0.874411i
$375$	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	$-0.406648\pi$
$379$	11.2559			0.578175			0.289088	+	0.957303i	$0.406648\pi$
$380$	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	$-0.513987\pi$
$383$	−1.71937			−0.0878558			−0.0439279	+	0.999035i	$0.513987\pi$
$384$	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	$0.388268\pi$
$390$	9.08052	−	36.3709i	0.459810	−	1.84171i
$391$	−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
$396$	−16.2633	−	14.6363i	−0.817264	−	0.735500i
$397$		−	23.8324i		−	1.19612i	−0.801453	−	0.598058i	$-0.795939\pi$
$397$		−	23.8324i		−	1.19612i	0.801453	−	0.598058i	$-0.204061\pi$
$398$	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	$-0.924538\pi$
$401$		−	9.40594i		−	0.469710i	0.972030	−	0.234855i	$-0.0754616\pi$
$402$	−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
$416$	−0.0326038	−	20.3961i	−0.00159853	−	0.999999i
$417$		−	4.28947i		−	0.210056i
$418$	−1.22504	+	1.20329i	−0.0599186	+	0.0588547i
$419$			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	$-0.920283\pi$
$421$		−	10.1701i		−	0.495660i	0.968804	−	0.247830i	$-0.0797174\pi$
$422$	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	$-0.397902\pi$
$439$	13.2116			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$440$	17.0913	−	21.5187i	0.814794	−	1.02587i
$441$	−18.0351			−0.858814
$442$	25.4529	+	6.35467i	1.21067	+	0.302261i
$443$			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	$-0.865243\pi$
$449$		−	17.4102i		−	0.821638i	0.911717	−	0.410819i	$-0.134757\pi$
$450$	−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	$0.282710\pi$
$462$	10.2108	+	10.3954i	0.475048	+	0.483636i
$463$	−18.1193			−0.842075			−0.421038	−	0.907043i	$-0.638334\pi$
$463$	−18.1193			−0.842075			−0.421038	+	0.907043i	$0.638334\pi$
$464$	−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	$-0.128471\pi$
$468$	4.33079	−	23.3880i	0.200191	−	1.08111i
$469$			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
$484$	−0.394095	+	21.9965i	−0.0179134	+	0.999840i
$485$	14.9531			0.678986
$486$	−1.94588	−	31.5669i	−0.0882669	−	1.43190i
$487$	9.97270			0.451906			0.225953	−	0.974138i	$-0.427450\pi$
$487$	9.97270			0.451906			0.225953	+	0.974138i	$0.427450\pi$
$488$	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	$-0.708996\pi$
$491$	−27.0517			−1.22082			−0.610412	+	0.792084i	$0.708996\pi$
$492$	−5.60169	−	45.2638i	−0.252544	−	2.04065i
$493$	24.1615			1.08818
$494$	−1.81115	−	0.452179i	−0.0814875	−	0.0203445i
$495$	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	$-0.533234\pi$
$499$	−4.65611			−0.208436			−0.104218	+	0.994554i	$0.533234\pi$
$500$	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	$-0.502481\pi$
$503$	−0.349613			−0.0155885			−0.00779424	+	0.999970i	$0.502481\pi$
$504$	−2.12086	−	11.3521i	−0.0944708	−	0.505665i
$505$	−46.0103			−2.04743
$506$	26.0158	−	25.5539i	1.15654	−	1.13601i
$507$	−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	$-0.781704\pi$
$509$		−	28.5754i		−	1.26658i	0.773914	−	0.633290i	$-0.218296\pi$
$510$	−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
$520$	29.6539	+	3.62175i	1.30041	+	0.158824i
$521$	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	$-0.261239\pi$
$523$	31.1800			1.36341			0.681704	+	0.731628i	$0.261239\pi$
$524$	−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
$528$	19.0641	−	27.2964i	0.829659	−	1.18792i
$529$	−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
$546$	−3.83707	+	15.3689i	−0.164212	+	0.657730i
$547$	43.9235			1.87803			0.939017	−	0.343872i	$-0.111739\pi$
$547$	43.9235			1.87803			0.939017	+	0.343872i	$0.111739\pi$
$548$	0.408380	+	3.29986i	0.0174451	+	0.140963i
$549$			19.2168i			0.820154i
$550$	11.7715	+	11.9842i	0.501937	+	0.511010i
$551$	−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	$-0.794180\pi$
$563$	−37.8757			−1.59627			−0.798136	+	0.602478i	$0.794180\pi$
$564$	−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	$0.0745093\pi$
$569$			11.0656i			0.463892i	−0.972729	+	0.231946i	$0.925491\pi$
$570$	0.234192	+	3.79916i	0.00980923	+	0.159129i
$571$	−7.53391			−0.315284			−0.157642	−	0.987496i	$-0.550389\pi$
$571$	−7.53391			−0.315284			−0.157642	+	0.987496i	$0.550389\pi$
$572$	−20.6138	+	12.1273i	−0.861907	+	0.507067i
$573$	−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	$0.0161415\pi$
$577$			2.43515i			0.101377i	−0.998715	+	0.0506884i	$0.983858\pi$
$578$	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	$-0.598540\pi$
$587$	−14.7623			−0.609305			−0.304652	+	0.952464i	$0.598540\pi$
$588$	−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	$0.588071\pi$
$594$	2.50654	−	2.46203i	0.102845	−	0.101018i
$595$			18.6565i			0.764843i
$596$	−18.3827	+	2.27498i	−0.752983	+	0.0931866i
$597$	−32.6142			−1.33481
$598$	38.4629	+	9.60281i	1.57287	+	0.392688i
$599$		−	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	$0.171898\pi$
$601$			25.2098i			1.02833i	−0.857691	+	0.514165i	$0.828102\pi$
$602$	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	$-0.538773\pi$
$607$	−5.98728			−0.243016			−0.121508	+	0.992590i	$0.538773\pi$
$608$	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
$616$	−7.22210	+	9.09299i	−0.290987	+	0.366367i
$617$			25.5416i			1.02827i	0.857710	+	0.514133i	$0.171886\pi$
$617$			25.5416i			1.02827i	−0.857710	+	0.514133i	$0.828114\pi$
$618$	−12.7397	+	0.785314i	−0.512465	+	0.0315900i
$619$	10.9823			0.441416			0.220708	−	0.975340i	$-0.429163\pi$
$619$	10.9823			0.441416			0.220708	+	0.975340i	$0.429163\pi$
$620$	−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
$624$	36.1300	+	2.16920i	1.44636	+	0.0868374i
$625$	−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	$-0.656911\pi$
$631$	−23.7746			−0.946453			−0.473227	+	0.880941i	$0.656911\pi$
$632$	−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
$638$	−15.7143	+	15.4353i	−0.622137	+	0.611090i
$639$	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	$-0.173037\pi$
$643$	43.4042			1.71169			0.855847	+	0.517229i	$0.173037\pi$
$644$	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
$650$	−4.42356	+	17.7180i	−0.173506	+	0.694959i
$651$	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	$-0.736622\pi$
$659$	−34.7468			−1.35354			−0.676772	+	0.736192i	$0.736622\pi$
$660$	36.2489	+	32.6224i	1.41099	+	1.26982i
$661$		−	12.9838i		−	0.505012i	−0.967595	−	0.252506i	$-0.918745\pi$
$661$		−	12.9838i		−	0.505012i	0.967595	−	0.252506i	$-0.0812548\pi$
$662$	−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	$-0.680514\pi$
$673$		−	43.7626i		−	1.68692i	0.537188	−	0.843462i	$-0.319486\pi$
$674$	2.38206	+	38.6427i	0.0917535	+	1.48846i
$675$		−	2.68276i		−	0.103259i
$676$	−22.9489	−	12.2208i	−0.882650	−	0.470030i
$677$		−	44.8725i		−	1.72459i	−0.506406	−	0.862295i	$-0.669026\pi$
$677$		−	44.8725i		−	1.72459i	0.506406	−	0.862295i	$-0.330974\pi$
$678$	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
$682$	25.9295	+	26.3982i	0.992891	+	1.01084i
$683$	−35.1245			−1.34400			−0.672001	−	0.740550i	$-0.734565\pi$
$683$	−35.1245			−1.34400			−0.672001	+	0.740550i	$0.734565\pi$
$684$	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	$-0.519391\pi$
$691$	−3.20078			−0.121763			−0.0608817	+	0.998145i	$0.519391\pi$
$692$	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	$-0.927494\pi$
$701$		−	11.9577i		−	0.451637i	0.974169	−	0.225818i	$-0.0725056\pi$
$702$	3.70578	+	0.925199i	0.139866	+	0.0349194i
$703$	2.58140			0.0973593
$704$	23.4541	+	12.4058i	0.883961	+	0.467561i
$705$	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	$-0.915778\pi$
$709$		−	13.9268i		−	0.523031i	0.965199	−	0.261516i	$-0.0842223\pi$
$710$	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
$726$	−38.9181	−	3.09973i	−1.44439	−	0.115042i
$727$			17.5680i			0.651560i	0.945446	+	0.325780i	$0.105627\pi$
$727$			17.5680i			0.651560i	−0.945446	+	0.325780i	$0.894373\pi$
$728$	−12.5306	−	1.53041i	−0.464415	−	0.0567207i
$729$	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
$748$	−22.8296	+	25.3675i	−0.834732	+	0.927527i
$749$			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
$754$	−23.2328	−	5.80039i	−0.846087	−	0.211238i
$755$	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	$0.422514\pi$
$770$	−11.9185	−	12.1339i	−0.429513	−	0.437277i
$771$		−	63.4112i		−	2.28370i
$772$	23.3281	−	2.88700i	0.839596	−	0.103906i
$773$			17.4158i			0.626403i	0.949687	+	0.313202i	$0.101402\pi$
$773$			17.4158i			0.626403i	−0.949687	+	0.313202i	$0.898598\pi$
$774$	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
$780$	−9.65277	+	52.1289i	−0.345625	+	1.86652i
$781$	−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
$792$	24.2298	+	19.2445i	0.860968	+	0.683824i
$793$	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
$806$	−9.74395	+	39.0282i	−0.343216	+	1.37471i
$807$			7.02274i			0.247212i
$808$	−8.15840	−	43.6687i	−0.287011	−	1.53626i
$809$			8.94691i			0.314557i	0.987554	+	0.157278i	$0.0502720\pi$
$809$			8.94691i			0.314557i	−0.987554	+	0.157278i	$0.949728\pi$
$810$	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
$814$	23.5944	−	23.1754i	0.826983	−	0.812299i
$815$		−	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
$832$	1.82071	+	28.7869i	0.0631218	+	0.998006i
$833$			28.1311i			0.974683i
$834$	0.373233	+	6.05474i	0.0129240	+	0.209658i
$835$	−38.2833			−1.32485
$836$	1.62448	−	1.80507i	0.0561840	−	0.0624298i
$837$		−	5.90942i		−	0.204260i
$838$	−0.908136	−	14.7321i	−0.0313710	−	0.508914i
$839$	0.859956			0.0296890			0.0148445	−	0.999890i	$-0.495275\pi$
$839$	0.859956			0.0296890			0.0148445	+	0.999890i	$0.495275\pi$
$840$	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	$0.0129027\pi$
$857$			2.37263i			0.0810476i	−0.999179	+	0.0405238i	$0.987097\pi$
$858$	−19.2297	−	37.8363i	−0.656490	−	1.29171i
$859$		−	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	$-0.380981\pi$
$863$	21.4603			0.730517			0.365259	+	0.930906i	$0.380981\pi$
$864$	−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
$880$	−22.2525	+	31.8616i	−0.750132	+	1.07405i
$881$	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	$0.893252\pi$
$884$	−36.4805	−	6.75514i	−1.22697	−	0.227200i
$885$	78.7536			2.64727
$886$	−1.60504	−	26.0376i	−0.0539224	−	0.874751i
$887$	25.9829			0.872421			0.436210	−	0.899845i	$-0.356320\pi$
$887$	25.9829			0.872421			0.436210	+	0.899845i	$0.356320\pi$
$888$	−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
$902$	−29.8659	−	30.4057i	−0.994425	−	1.01240i
$903$	−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
$910$	4.47881	−	17.9394i	0.148471	−	0.594684i
$911$		−	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	$-0.665331\pi$
$919$	−30.0944			−0.992722			−0.496361	+	0.868116i	$0.665331\pi$
$920$	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
$924$	−15.3174	−	13.7849i	−0.503905	−	0.453492i
$925$		−	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	$0.219610\pi$
$929$			38.7992i			1.27296i	−0.771293	+	0.636480i	$0.780390\pi$
$930$	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
$936$	−4.07803	+	33.3898i	−0.133295	+	1.09138i
$937$		−	17.0554i		−	0.557174i	−0.960411	−	0.278587i	$-0.910134\pi$
$937$		−	17.0554i		−	0.557174i	0.960411	−	0.278587i	$-0.0898661\pi$
$938$	−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
$946$	−13.5275	−	13.7720i	−0.439817	−	0.447767i
$947$	−28.1580			−0.915012			−0.457506	−	0.889207i	$-0.651257\pi$
$947$	−28.1580			−0.915012			−0.457506	+	0.889207i	$0.651257\pi$
$948$	−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	$-0.616747\pi$
$953$		−	57.6350i		−	1.86698i	0.358602	−	0.933490i	$-0.383253\pi$
$954$	−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
$962$	34.8830	+	8.70902i	1.12467	+	0.280790i
$963$	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	$0.615885\pi$
$968$	−1.35767	−	31.0831i	−0.0436370	−	0.999047i
$969$		−	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	$0.169675\pi$
$977$			31.7673i			1.01633i	−0.861261	+	0.508163i	$0.830325\pi$
$978$	−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	$-0.784071\pi$
$983$	−48.8227			−1.55720			−0.778602	+	0.627518i	$0.784071\pi$
$984$	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
$988$	2.59585	+	0.480676i	0.0825849	+	0.0152923i
$989$			31.9987i			1.01750i
$990$	−32.3329	+	31.7588i	−1.02761	+	1.00936i
$991$			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	$0.0153651\pi$
$997$			3.04715i			0.0965042i	−0.998835	+	0.0482521i	$0.984635\pi$
$998$	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.571.4	yes	56
4.3	odd	2	inner	572.2.b.c.571.2	yes	56
11.10	odd	2	inner	572.2.b.c.571.54	yes	56
13.12	even	2	inner	572.2.b.c.571.53	yes	56
44.43	even	2	inner	572.2.b.c.571.56	yes	56
52.51	odd	2	inner	572.2.b.c.571.55	yes	56
143.142	odd	2	inner	572.2.b.c.571.3	yes	56
572.571	even	2	inner	572.2.b.c.571.1	✓	56

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

\(f(q)\)	\(=\)	\(q+(-1.41153 + 0.0870114i) q^{2} -2.50968i q^{3} +(1.98486 - 0.245639i) q^{4} +2.92941i q^{5} +(0.218370 + 3.54249i) q^{6} -1.23786i q^{7} +(-2.78032 + 0.519434i) q^{8} -3.29847 q^{9} +O(q^{10})\)	\(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} +(-3.28678 - 3.34620i) q^{22} +7.77474i q^{23} +(1.30361 + 6.97771i) q^{24} -3.58145 q^{25} +(1.23513 - 4.94717i) 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} +(4.93057 + 4.43729i) 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} +(-1.31297 + 7.09057i) 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} +(-8.39787 + 8.24876i) 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} +(-12.4158 - 3.09978i) 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} +(-7.34576 - 5.83437i) 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

L-functions

Modular forms

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