LMFDB - Embedded newform 572.2.n.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.2
Root			$-0.601689 + 1.85181i$ of defining polynomial
Character	$\chi$	$=$	572.53
Dual form			572.2.n.a.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57524 + 1.14448i) q^{3} +(-0.125488 - 0.386211i) q^{5} +(-1.28300 - 0.932153i) q^{7} +(0.244502 - 0.752499i) q^{9} +O(q^{10})$	\(q+(-1.57524 + 1.14448i) q^{3} +(-0.125488 - 0.386211i) q^{5} +(-1.28300 - 0.932153i) q^{7} +(0.244502 - 0.752499i) q^{9} +(1.29469 - 3.05349i) q^{11} +(0.309017 - 0.951057i) q^{13} +(0.639685 + 0.464758i) q^{15} +(0.674575 + 2.07613i) q^{17} +(4.69181 - 3.40880i) q^{19} +3.08787 q^{21} -2.28428 q^{23} +(3.91167 - 2.84200i) q^{25} +(-1.32900 - 4.09023i) q^{27} +(5.60500 + 4.07227i) q^{29} +(0.0398609 - 0.122679i) q^{31} +(1.45521 + 6.29173i) q^{33} +(-0.199008 + 0.612483i) q^{35} +(7.33568 + 5.32968i) q^{37} +(0.601689 + 1.85181i) q^{39} +(7.12214 - 5.17454i) q^{41} -6.45033 q^{43} -0.321306 q^{45} +(6.51509 - 4.73349i) q^{47} +(-1.38594 - 4.26549i) q^{49} +(-3.43871 - 2.49837i) q^{51} +(1.94190 - 5.97655i) q^{53} +(-1.34176 - 0.116848i) q^{55} +(-3.48944 + 10.7394i) q^{57} +(1.93858 + 1.40846i) q^{59} +(2.13232 + 6.56260i) q^{61} +(-1.01514 + 0.737542i) q^{63} -0.406087 q^{65} -3.51427 q^{67} +(3.59829 - 2.61431i) q^{69} +(-0.682262 - 2.09979i) q^{71} +(-8.14934 - 5.92084i) q^{73} +(-2.90922 + 8.95367i) q^{75} +(-4.50740 + 2.71078i) q^{77} +(4.72953 - 14.5560i) q^{79} +(8.69502 + 6.31730i) q^{81} +(2.64456 + 8.13913i) q^{83} +(0.717174 - 0.521057i) q^{85} -13.4899 q^{87} -15.7129 q^{89} +(-1.28300 + 0.932153i) q^{91} +(0.0776135 + 0.238870i) q^{93} +(-1.90528 - 1.38427i) q^{95} +(4.51443 - 13.8940i) q^{97} +(-1.98119 - 1.72083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	−1.57524	+	1.14448i	−0.909467	+	0.660766i	−0.940880	−	0.338740i	$-0.889999\pi$
$3$	−1.57524	+	1.14448i	−0.909467	+	0.660766i	0.0314133	+	0.999506i	$0.489999\pi$
$4$		0			0
$5$	−0.125488	−	0.386211i	−0.0561198	−	0.172719i	0.919068	−	0.394100i	$-0.128944\pi$
$5$	−0.125488	−	0.386211i	−0.0561198	−	0.172719i	−0.975187	+	0.221381i	$0.928944\pi$
$6$		0			0
$7$	−1.28300	−	0.932153i	−0.484928	−	0.352321i	0.318302	−	0.947989i	$-0.396887\pi$
$7$	−1.28300	−	0.932153i	−0.484928	−	0.352321i	−0.803230	+	0.595668i	$0.796887\pi$
$8$		0			0
$9$	0.244502	−	0.752499i	0.0815006	−	0.250833i
$10$		0			0
$11$	1.29469	−	3.05349i	0.390363	−	0.920661i
$11$	1.29469	−	3.05349i	0.390363	−	0.920661i
$12$		0			0
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$		0			0
$15$	0.639685	+	0.464758i	0.165166	+	0.120000i
$16$		0			0
$17$	0.674575	+	2.07613i	0.163609	+	0.503535i	0.998931	−	0.0462248i	$-0.0147191\pi$
$17$	0.674575	+	2.07613i	0.163609	+	0.503535i	−0.835322	+	0.549760i	$0.814719\pi$
$18$		0			0
$19$	4.69181	−	3.40880i	1.07638	−	0.782033i	0.0993283	−	0.995055i	$-0.468331\pi$
$19$	4.69181	−	3.40880i	1.07638	−	0.782033i	0.977047	+	0.213022i	$0.0683306\pi$
$20$		0			0
$21$	3.08787			0.673828
$22$		0			0
$23$	−2.28428			−0.476304			−0.238152	−	0.971228i	$-0.576542\pi$
$23$	−2.28428			−0.476304			−0.238152	+	0.971228i	$0.576542\pi$
$24$		0			0
$25$	3.91167	−	2.84200i	0.782335	−	0.568399i
$26$		0			0
$27$	−1.32900	−	4.09023i	−0.255765	−	0.787165i
$28$		0			0
$29$	5.60500	+	4.07227i	1.04082	+	0.756202i	0.970446	−	0.241319i	$-0.0775799\pi$
$29$	5.60500	+	4.07227i	1.04082	+	0.756202i	0.0703765	+	0.997521i	$0.477580\pi$
$30$		0			0
$31$	0.0398609	−	0.122679i	0.00715924	−	0.0220339i	−0.947413	−	0.320013i	$-0.896313\pi$
$31$	0.0398609	−	0.122679i	0.00715924	−	0.0220339i	0.954572	+	0.297979i	$0.0963127\pi$
$32$		0			0
$33$	1.45521	+	6.29173i	0.253320	+	1.09525i
$34$		0			0
$35$	−0.199008	+	0.612483i	−0.0336384	+	0.103528i
$36$		0			0
$37$	7.33568	+	5.32968i	1.20598	+	0.876195i	0.994859	−	0.101266i	$-0.0322892\pi$
$37$	7.33568	+	5.32968i	1.20598	+	0.876195i	0.211119	+	0.977460i	$0.432289\pi$
$38$		0			0
$39$	0.601689	+	1.85181i	0.0963474	+	0.296527i
$40$		0			0
$41$	7.12214	−	5.17454i	1.11229	−	0.808127i	0.129268	−	0.991610i	$-0.458737\pi$
$41$	7.12214	−	5.17454i	1.11229	−	0.808127i	0.983023	+	0.183483i	$0.0587372\pi$
$42$		0			0
$43$	−6.45033			−0.983666			−0.491833	−	0.870690i	$-0.663673\pi$
$43$	−6.45033			−0.983666			−0.491833	+	0.870690i	$0.663673\pi$
$44$		0			0
$45$	−0.321306			−0.0478974
$46$		0			0
$47$	6.51509	−	4.73349i	0.950323	−	0.690450i	−0.000560363	−	1.00000i	$-0.500178\pi$
$47$	6.51509	−	4.73349i	0.950323	−	0.690450i	0.950883	+	0.309550i	$0.100178\pi$
$48$		0			0
$49$	−1.38594	−	4.26549i	−0.197992	−	0.609356i
$50$		0			0
$51$	−3.43871	−	2.49837i	−0.481516	−	0.349842i
$52$		0			0
$53$	1.94190	−	5.97655i	0.266740	−	0.820942i	−0.724547	−	0.689225i	$-0.757951\pi$
$53$	1.94190	−	5.97655i	0.266740	−	0.820942i	0.991287	−	0.131717i	$-0.0420489\pi$
$54$		0			0
$55$	−1.34176	−	0.116848i	−0.180923	−	0.0157557i
$56$		0			0
$57$	−3.48944	+	10.7394i	−0.462187	+	1.42247i
$58$		0			0
$59$	1.93858	+	1.40846i	0.252382	+	0.183366i	0.706782	−	0.707431i	$-0.250146\pi$
$59$	1.93858	+	1.40846i	0.252382	+	0.183366i	−0.454400	+	0.890798i	$0.650146\pi$
$60$		0			0
$61$	2.13232	+	6.56260i	0.273015	+	0.840254i	0.989738	+	0.142896i	$0.0456414\pi$
$61$	2.13232	+	6.56260i	0.273015	+	0.840254i	−0.716723	+	0.697358i	$0.754359\pi$
$62$		0			0
$63$	−1.01514	+	0.737542i	−0.127896	+	0.0929216i
$64$		0			0
$65$	−0.406087			−0.0503689
$66$		0			0
$67$	−3.51427			−0.429336			−0.214668	−	0.976687i	$-0.568867\pi$
$67$	−3.51427			−0.429336			−0.214668	+	0.976687i	$0.568867\pi$
$68$		0			0
$69$	3.59829	−	2.61431i	0.433183	−	0.314726i
$70$		0			0
$71$	−0.682262	−	2.09979i	−0.0809696	−	0.249199i	0.902374	−	0.430953i	$-0.141822\pi$
$71$	−0.682262	−	2.09979i	−0.0809696	−	0.249199i	−0.983344	+	0.181754i	$0.941822\pi$
$72$		0			0
$73$	−8.14934	−	5.92084i	−0.953808	−	0.692982i	−0.00210327	−	0.999998i	$-0.500669\pi$
$73$	−8.14934	−	5.92084i	−0.953808	−	0.692982i	−0.951704	+	0.307016i	$0.900669\pi$
$74$		0			0
$75$	−2.90922	+	8.95367i	−0.335928	+	1.03388i
$76$		0			0
$77$	−4.50740	+	2.71078i	−0.513666	+	0.308922i
$78$		0			0
$79$	4.72953	−	14.5560i	0.532114	−	1.63768i	−0.217690	−	0.976018i	$-0.569852\pi$
$79$	4.72953	−	14.5560i	0.532114	−	1.63768i	0.749804	−	0.661660i	$-0.230148\pi$
$80$		0			0
$81$	8.69502	+	6.31730i	0.966113	+	0.701922i
$82$		0			0
$83$	2.64456	+	8.13913i	0.290279	+	0.893386i	0.984767	+	0.173882i	$0.0556310\pi$
$83$	2.64456	+	8.13913i	0.290279	+	0.893386i	−0.694488	+	0.719504i	$0.744369\pi$
$84$		0			0
$85$	0.717174	−	0.521057i	0.0777884	−	0.0565166i
$86$		0			0
$87$	−13.4899			−1.44627
$88$		0			0
$89$	−15.7129			−1.66556			−0.832782	−	0.553601i	$-0.813253\pi$
$89$	−15.7129			−1.66556			−0.832782	+	0.553601i	$0.813253\pi$
$90$		0			0
$91$	−1.28300	+	0.932153i	−0.134495	+	0.0977162i
$92$		0			0
$93$	0.0776135	+	0.238870i	0.00804815	+	0.0247696i
$94$		0			0
$95$	−1.90528	−	1.38427i	−0.195478	−	0.142023i
$96$		0			0
$97$	4.51443	−	13.8940i	0.458371	−	1.41072i	−0.408762	−	0.912641i	$-0.634039\pi$
$97$	4.51443	−	13.8940i	0.458371	−	1.41072i	0.867132	−	0.498078i	$-0.165961\pi$
$98$		0			0
$99$	−1.98119	−	1.72083i	−0.199117	−	0.172950i
$100$		0			0
$101$	−1.98333	+	6.10406i	−0.197349	+	0.607377i	0.802592	+	0.596528i	$0.203453\pi$
$101$	−1.98333	+	6.10406i	−0.197349	+	0.607377i	−0.999941	+	0.0108492i	$0.996547\pi$
$102$		0			0
$103$	−3.22262	−	2.34137i	−0.317534	−	0.230702i	0.417589	−	0.908636i	$-0.362875\pi$
$103$	−3.22262	−	2.34137i	−0.317534	−	0.230702i	−0.735122	+	0.677934i	$0.762875\pi$
$104$		0			0
$105$	−0.387489	−	1.19257i	−0.0378151	−	0.116383i
$106$		0			0
$107$	−12.0791	+	8.77596i	−1.16773	+	0.848404i	−0.990735	−	0.135809i	$-0.956637\pi$
$107$	−12.0791	+	8.77596i	−1.16773	+	0.848404i	−0.176992	+	0.984212i	$0.556637\pi$
$108$		0			0
$109$	0.888745			0.0851263			0.0425632	−	0.999094i	$-0.486448\pi$
$109$	0.888745			0.0851263			0.0425632	+	0.999094i	$0.486448\pi$
$110$		0			0
$111$	−17.6552			−1.67576
$112$		0			0
$113$	−7.38753	+	5.36735i	−0.694960	+	0.504918i	−0.878287	−	0.478134i	$-0.841313\pi$
$113$	−7.38753	+	5.36735i	−0.694960	+	0.504918i	0.183327	+	0.983052i	$0.441313\pi$
$114$		0			0
$115$	0.286648	+	0.882213i	0.0267301	+	0.0822668i
$116$		0			0
$117$	−0.640114	−	0.465070i	−0.0591785	−	0.0429957i
$118$		0			0
$119$	1.06979	−	3.29248i	0.0980677	−	0.301821i
$120$		0			0
$121$	−7.64757	−	7.90662i	−0.695234	−	0.718784i
$122$		0			0
$123$	−5.29694	+	16.3023i	−0.477609	+	1.46993i
$124$		0			0
$125$	−3.23113	−	2.34756i	−0.289001	−	0.209972i
$126$		0			0
$127$	−0.167565	−	0.515711i	−0.0148690	−	0.0457619i	0.943347	−	0.331809i	$-0.107659\pi$
$127$	−0.167565	−	0.515711i	−0.0148690	−	0.0457619i	−0.958216	+	0.286047i	$0.907659\pi$
$128$		0			0
$129$	10.1608	−	7.38227i	0.894611	−	0.649973i
$130$		0			0
$131$	1.23558			0.107953			0.0539766	−	0.998542i	$-0.482810\pi$
$131$	1.23558			0.107953			0.0539766	+	0.998542i	$0.482810\pi$
$132$		0			0
$133$	−9.19712			−0.797491
$134$		0			0
$135$	−1.41292	+	1.02655i	−0.121605	+	0.0883511i
$136$		0			0
$137$	1.73445	+	5.33810i	0.148184	+	0.456065i	0.997407	−	0.0719707i	$-0.0229288\pi$
$137$	1.73445	+	5.33810i	0.148184	+	0.456065i	−0.849222	+	0.528035i	$0.822929\pi$
$138$		0			0
$139$	−7.96108	−	5.78406i	−0.675250	−	0.490598i	0.196529	−	0.980498i	$-0.437033\pi$
$139$	−7.96108	−	5.78406i	−0.675250	−	0.490598i	−0.871778	+	0.489900i	$0.837033\pi$
$140$		0			0
$141$	−4.84545	+	14.9128i	−0.408061	+	1.25588i
$142$		0			0
$143$	−2.50396	−	2.17490i	−0.209392	−	0.181874i
$144$		0			0
$145$	0.869399	−	2.67573i	0.0721996	−	0.222208i
$146$		0			0
$147$	7.06497	+	5.13300i	0.582709	+	0.423363i
$148$		0			0
$149$	6.01821	+	18.5222i	0.493031	+	1.51739i	0.820003	+	0.572360i	$0.193972\pi$
$149$	6.01821	+	18.5222i	0.493031	+	1.51739i	−0.326972	+	0.945034i	$0.606028\pi$
$150$		0			0
$151$	11.1513	−	8.10189i	0.907480	−	0.659323i	−0.0328963	−	0.999459i	$-0.510473\pi$
$151$	11.1513	−	8.10189i	0.907480	−	0.659323i	0.940376	+	0.340136i	$0.110473\pi$
$152$		0			0
$153$	1.72722			0.139637
$154$		0			0
$155$	−0.0523822			−0.00420744
$156$		0			0
$157$	18.5649	−	13.4882i	1.48164	−	1.07647i	0.504615	−	0.863344i	$-0.331634\pi$
$157$	18.5649	−	13.4882i	1.48164	−	1.07647i	0.977024	−	0.213129i	$-0.0683656\pi$
$158$		0			0
$159$	3.78108	+	11.6370i	0.299859	+	0.922872i
$160$		0			0
$161$	2.93072	+	2.12929i	0.230973	+	0.167812i
$162$		0			0
$163$	−4.40718	+	13.5639i	−0.345197	+	1.06241i	0.616281	+	0.787526i	$0.288638\pi$
$163$	−4.40718	+	13.5639i	−0.345197	+	1.06241i	−0.961478	+	0.274881i	$0.911362\pi$
$164$		0			0
$165$	2.24733	−	1.35155i	0.174954	−	0.105218i
$166$		0			0
$167$	2.90533	−	8.94168i	0.224821	−	0.691928i	−0.773489	−	0.633810i	$-0.781490\pi$
$167$	2.90533	−	8.94168i	0.224821	−	0.691928i	0.998310	−	0.0581179i	$-0.0185099\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	−1.41796	−	4.36404i	−0.108434	−	0.333727i
$172$		0			0
$173$	−4.62804	+	3.36247i	−0.351863	+	0.255644i	−0.749650	−	0.661834i	$-0.769778\pi$
$173$	−4.62804	+	3.36247i	−0.351863	+	0.255644i	0.397787	+	0.917478i	$0.369778\pi$
$174$		0			0
$175$	−7.66785			−0.579635
$176$		0			0
$177$	−4.66570			−0.350696
$178$		0			0
$179$	−1.46399	+	1.06365i	−0.109424	+	0.0795009i	−0.641151	−	0.767414i	$-0.721543\pi$
$179$	−1.46399	+	1.06365i	−0.109424	+	0.0795009i	0.531728	+	0.846915i	$0.321543\pi$
$180$		0			0
$181$	−3.43363	−	10.5676i	−0.255220	−	0.785485i	−0.993786	−	0.111305i	$-0.964497\pi$
$181$	−3.43363	−	10.5676i	−0.255220	−	0.785485i	0.738567	−	0.674180i	$-0.235503\pi$
$182$		0			0
$183$	−10.8697	−	7.89728i	−0.803510	−	0.583784i
$184$		0			0
$185$	1.13785	−	3.50193i	0.0836562	−	0.257467i
$186$		0			0
$187$	7.21280	+	0.628130i	0.527452	+	0.0459334i
$188$		0			0
$189$	−2.10762	+	6.48659i	−0.153307	+	0.471830i
$190$		0			0
$191$	21.3645	+	15.5222i	1.54588	+	1.12315i	0.946508	+	0.322680i	$0.104584\pi$
$191$	21.3645	+	15.5222i	1.54588	+	1.12315i	0.599374	+	0.800469i	$0.295416\pi$
$192$		0			0
$193$	−0.264674	−	0.814582i	−0.0190516	−	0.0586349i	0.941079	−	0.338188i	$-0.109814\pi$
$193$	−0.264674	−	0.814582i	−0.0190516	−	0.0586349i	−0.960130	+	0.279553i	$0.909814\pi$
$194$		0			0
$195$	0.639685	−	0.464758i	0.0458088	−	0.0332820i
$196$		0			0
$197$	11.2701			0.802962			0.401481	−	0.915867i	$-0.368496\pi$
$197$	11.2701			0.802962			0.401481	+	0.915867i	$0.368496\pi$
$198$		0			0
$199$	6.26628			0.444205			0.222103	−	0.975023i	$-0.428708\pi$
$199$	6.26628			0.444205			0.222103	+	0.975023i	$0.428708\pi$
$200$		0			0
$201$	5.53582	−	4.02201i	0.390467	−	0.283691i
$202$		0			0
$203$	−3.39523	−	10.4494i	−0.238298	−	0.733407i
$204$		0			0
$205$	−2.89221	−	2.10131i	−0.202000	−	0.146762i
$206$		0			0
$207$	−0.558509	+	1.71891i	−0.0388191	+	0.119473i
$208$		0			0
$209$	−4.33431	−	18.7397i	−0.299810	−	1.29625i
$210$		0			0
$211$	−5.90856	+	18.1847i	−0.406762	+	1.25188i	0.512653	+	0.858596i	$0.328663\pi$
$211$	−5.90856	+	18.1847i	−0.406762	+	1.25188i	−0.919415	+	0.393288i	$0.871337\pi$
$212$		0			0
$213$	3.47789	+	2.52684i	0.238301	+	0.173136i
$214$		0			0
$215$	0.809437	+	2.49119i	0.0552031	+	0.169898i
$216$		0			0
$217$	−0.165498	+	0.120241i	−0.0112347	+	0.00816249i
$218$		0			0
$219$	19.6135			1.32536
$220$		0			0
$221$	2.18297			0.146843
$222$		0			0
$223$	−0.860721	+	0.625351i	−0.0576382	+	0.0418766i	−0.616231	−	0.787565i	$-0.711341\pi$
$223$	−0.860721	+	0.625351i	−0.0576382	+	0.0418766i	0.558593	+	0.829442i	$0.311341\pi$
$224$		0			0
$225$	−1.18219	−	3.63840i	−0.0788126	−	0.242560i
$226$		0			0
$227$	9.65041	+	7.01143i	0.640520	+	0.465365i	0.860029	−	0.510246i	$-0.170445\pi$
$227$	9.65041	+	7.01143i	0.640520	+	0.465365i	−0.219509	+	0.975611i	$0.570445\pi$
$228$		0			0
$229$	8.40482	−	25.8674i	0.555406	−	1.70936i	−0.139462	−	0.990227i	$-0.544537\pi$
$229$	8.40482	−	25.8674i	0.555406	−	1.70936i	0.694868	−	0.719137i	$-0.255463\pi$
$230$		0			0
$231$	3.99782	−	9.42876i	0.263037	−	0.620367i
$232$		0			0
$233$	−6.60059	+	20.3145i	−0.432419	+	1.33085i	0.463290	+	0.886207i	$0.346669\pi$
$233$	−6.60059	+	20.3145i	−0.432419	+	1.33085i	−0.895709	+	0.444641i	$0.853331\pi$
$234$		0			0
$235$	−2.64569	−	1.92221i	−0.172586	−	0.125391i
$236$		0			0
$237$	9.20890	+	28.3421i	0.598182	+	1.84102i
$238$		0			0
$239$	−3.74060	+	2.71770i	−0.241959	+	0.175794i	−0.702156	−	0.712024i	$-0.747779\pi$
$239$	−3.74060	+	2.71770i	−0.241959	+	0.175794i	0.460197	+	0.887817i	$0.347779\pi$
$240$		0			0
$241$	−12.5190			−0.806420			−0.403210	−	0.915107i	$-0.632106\pi$
$241$	−12.5190			−0.806420			−0.403210	+	0.915107i	$0.632106\pi$
$242$		0			0
$243$	−8.02463			−0.514780
$244$		0			0
$245$	−1.47346	+	1.07053i	−0.0941361	+	0.0683939i
$246$		0			0
$247$	−1.79211	−	5.51556i	−0.114029	−	0.350946i
$248$		0			0
$249$	−13.4809	−	9.79445i	−0.854318	−	0.620698i
$250$		0			0
$251$	3.94631	−	12.1455i	0.249089	−	0.766616i	−0.745848	−	0.666116i	$-0.767956\pi$
$251$	3.94631	−	12.1455i	0.249089	−	0.766616i	0.994937	−	0.100500i	$-0.0320443\pi$
$252$		0			0
$253$	−2.95742	+	6.97501i	−0.185931	+	0.438515i
$254$		0			0
$255$	−0.533383	+	1.64158i	−0.0334017	+	0.102800i
$256$		0			0
$257$	13.2560	+	9.63105i	0.826887	+	0.600768i	0.918677	−	0.395010i	$-0.129259\pi$
$257$	13.2560	+	9.63105i	0.826887	+	0.600768i	−0.0917902	+	0.995778i	$0.529259\pi$
$258$		0			0
$259$	−4.44359	−	13.6760i	−0.276111	−	0.849783i
$260$		0			0
$261$	4.43481	−	3.22208i	0.274508	−	0.199442i
$262$		0			0
$263$	−7.72113			−0.476105			−0.238053	−	0.971252i	$-0.576509\pi$
$263$	−7.72113			−0.476105			−0.238053	+	0.971252i	$0.576509\pi$
$264$		0			0
$265$	−2.55189			−0.156762
$266$		0			0
$267$	24.7516	−	17.9831i	1.51477	−	1.10055i
$268$		0			0
$269$	−0.0747168	−	0.229955i	−0.00455556	−	0.0140206i	0.948753	−	0.316019i	$-0.102346\pi$
$269$	−0.0747168	−	0.229955i	−0.00455556	−	0.0140206i	−0.953308	+	0.301998i	$0.902346\pi$
$270$		0			0
$271$	2.81629	+	2.04615i	0.171077	+	0.124295i	0.670029	−	0.742335i	$-0.266282\pi$
$271$	2.81629	+	2.04615i	0.171077	+	0.124295i	−0.498952	+	0.866630i	$0.666282\pi$
$272$		0			0
$273$	0.954203	−	2.93674i	0.0577510	−	0.177739i
$274$		0			0
$275$	−3.61361	−	15.6237i	−0.217909	−	0.942147i
$276$		0			0
$277$	3.55403	−	10.9382i	0.213541	−	0.657211i	−0.785713	−	0.618591i	$-0.787704\pi$
$277$	3.55403	−	10.9382i	0.213541	−	0.657211i	0.999254	−	0.0386201i	$-0.0122962\pi$
$278$		0			0
$279$	−0.0825700	−	0.0599906i	−0.00494334	−	0.00359154i
$280$		0			0
$281$	−2.50238	−	7.70154i	−0.149280	−	0.459436i	0.848257	−	0.529585i	$-0.177652\pi$
$281$	−2.50238	−	7.70154i	−0.149280	−	0.459436i	−0.997536	+	0.0701495i	$0.977652\pi$
$282$		0			0
$283$	−7.78494	+	5.65609i	−0.462767	+	0.336220i	−0.794616	−	0.607113i	$-0.792328\pi$
$283$	−7.78494	+	5.65609i	−0.462767	+	0.336220i	0.331849	+	0.943333i	$0.392328\pi$
$284$		0			0
$285$	4.58555			0.271625
$286$		0			0
$287$	−13.9612			−0.824101
$288$		0			0
$289$	9.89803	−	7.19134i	0.582237	−	0.423020i
$290$		0			0
$291$	8.79007	+	27.0530i	0.515283	+	1.58588i
$292$		0			0
$293$	1.05123	+	0.763765i	0.0614137	+	0.0446196i	0.618069	−	0.786124i	$-0.287915\pi$
$293$	1.05123	+	0.763765i	0.0614137	+	0.0446196i	−0.556655	+	0.830744i	$0.687915\pi$
$294$		0			0
$295$	0.300696	−	0.925448i	0.0175072	−	0.0538817i
$296$		0			0
$297$	−14.2101	−	1.23749i	−0.824554	−	0.0718066i
$298$		0			0
$299$	−0.705880	+	2.17247i	−0.0408221	+	0.125637i
$300$		0			0
$301$	8.27576	+	6.01270i	0.477007	+	0.346566i
$302$		0			0
$303$	−3.86176	−	11.8853i	−0.221852	−	0.682791i
$304$		0			0
$305$	2.26697	−	1.64705i	0.129806	−	0.0943098i
$306$		0			0
$307$	−10.1138			−0.577226			−0.288613	−	0.957446i	$-0.593194\pi$
$307$	−10.1138			−0.577226			−0.288613	+	0.957446i	$0.593194\pi$
$308$		0			0
$309$	7.75605			0.441226
$310$		0			0
$311$	22.7649	−	16.5397i	1.29088	−	0.937879i	0.291057	−	0.956706i	$-0.405993\pi$
$311$	22.7649	−	16.5397i	1.29088	−	0.937879i	0.999823	+	0.0188266i	$0.00599303\pi$
$312$		0			0
$313$	4.77886	+	14.7078i	0.270117	+	0.831335i	0.990470	+	0.137727i	$0.0439797\pi$
$313$	4.77886	+	14.7078i	0.270117	+	0.831335i	−0.720353	+	0.693607i	$0.756020\pi$
$314$		0			0
$315$	0.412235	+	0.299506i	0.0232268	+	0.0168753i
$316$		0			0
$317$	−8.97293	+	27.6158i	−0.503970	+	1.55106i	0.298526	+	0.954402i	$0.403505\pi$
$317$	−8.97293	+	27.6158i	−0.503970	+	1.55106i	−0.802496	+	0.596658i	$0.796495\pi$
$318$		0			0
$319$	19.6913	−	11.8425i	1.10250	−	0.663052i
$320$		0			0
$321$	8.98355	−	27.6485i	0.501413	−	1.54319i
$322$		0			0
$323$	10.2421	+	7.44132i	0.569886	+	0.414046i
$324$		0			0
$325$	−1.49413	−	4.59845i	−0.0828792	−	0.255076i
$326$		0			0
$327$	−1.39999	+	1.01715i	−0.0774195	+	0.0562486i
$328$		0			0
$329$	−12.7712			−0.704098
$330$		0			0
$331$	19.2899			1.06027			0.530134	−	0.847914i	$-0.322142\pi$
$331$	19.2899			1.06027			0.530134	+	0.847914i	$0.322142\pi$
$332$		0			0
$333$	5.80417	−	4.21698i	0.318066	−	0.231089i
$334$		0			0
$335$	0.440997	+	1.35725i	0.0240943	+	0.0741545i
$336$		0			0
$337$	−23.2227	−	16.8722i	−1.26502	−	0.919090i	−0.266026	−	0.963966i	$-0.585711\pi$
$337$	−23.2227	−	16.8722i	−1.26502	−	0.919090i	−0.998993	+	0.0448762i	$0.985711\pi$
$338$		0			0
$339$	5.49432	−	16.9098i	0.298410	−	0.918412i
$340$		0			0
$341$	−0.322992	−	0.280546i	−0.0174910	−	0.0151924i
$342$		0			0
$343$	−5.62836	+	17.3223i	−0.303903	+	0.935318i
$344$		0			0
$345$	−1.46122	−	1.06164i	−0.0786692	−	0.0571566i
$346$		0			0
$347$	−1.18670	−	3.65229i	−0.0637054	−	0.196065i	0.914138	−	0.405403i	$-0.132869\pi$
$347$	−1.18670	−	3.65229i	−0.0637054	−	0.196065i	−0.977843	+	0.209338i	$0.932869\pi$
$348$		0			0
$349$	−5.91882	+	4.30027i	−0.316827	+	0.230188i	−0.734820	−	0.678262i	$-0.762734\pi$
$349$	−5.91882	+	4.30027i	−0.316827	+	0.230188i	0.417993	+	0.908450i	$0.362734\pi$
$350$		0			0
$351$	−4.30072			−0.229556
$352$		0			0
$353$	−2.12954			−0.113344			−0.0566721	−	0.998393i	$-0.518049\pi$
$353$	−2.12954			−0.113344			−0.0566721	+	0.998393i	$0.518049\pi$
$354$		0			0
$355$	−0.725346	+	0.526995i	−0.0384974	+	0.0279700i
$356$		0			0
$357$	2.08300	+	6.41081i	0.110244	+	0.339296i
$358$		0			0
$359$	−1.23387	−	0.896460i	−0.0651212	−	0.0473133i	0.554748	−	0.832018i	$-0.312815\pi$
$359$	−1.23387	−	0.896460i	−0.0651212	−	0.0473133i	−0.619870	+	0.784705i	$0.712815\pi$
$360$		0			0
$361$	4.52186	−	13.9168i	0.237992	−	0.732466i
$362$		0			0
$363$	21.0958	+	3.70234i	1.10724	+	0.194323i
$364$		0			0
$365$	−1.26405	+	3.89036i	−0.0661636	+	0.203631i
$366$		0			0
$367$	1.18955	+	0.864259i	0.0620940	+	0.0451139i	0.618399	−	0.785864i	$-0.287781\pi$
$367$	1.18955	+	0.864259i	0.0620940	+	0.0451139i	−0.556305	+	0.830978i	$0.687781\pi$
$368$		0			0
$369$	−2.15246	−	6.62458i	−0.112052	−	0.344862i
$370$		0			0
$371$	−8.06251	+	5.85776i	−0.418585	+	0.304120i
$372$		0			0
$373$	19.4431			1.00673			0.503363	−	0.864075i	$-0.332096\pi$
$373$	19.4431			1.00673			0.503363	+	0.864075i	$0.332096\pi$
$374$		0			0
$375$	7.77655			0.401579
$376$		0			0
$377$	5.60500	−	4.07227i	0.288672	−	0.209733i
$378$		0			0
$379$	3.38207	+	10.4089i	0.173725	+	0.534672i	0.999573	−	0.0292217i	$-0.00930287\pi$
$379$	3.38207	+	10.4089i	0.173725	+	0.534672i	−0.825848	+	0.563893i	$0.809303\pi$
$380$		0			0
$381$	0.854176	+	0.620595i	0.0437608	+	0.0317941i
$382$		0			0
$383$	−10.7606	+	33.1177i	−0.549841	+	1.69224i	0.159350	+	0.987222i	$0.449060\pi$
$383$	−10.7606	+	33.1177i	−0.549841	+	1.69224i	−0.709192	+	0.705016i	$0.750940\pi$
$384$		0			0
$385$	1.61256	+	1.40064i	0.0821834	+	0.0713833i
$386$		0			0
$387$	−1.57712	+	4.85386i	−0.0801693	+	0.246736i
$388$		0			0
$389$	−0.161651	−	0.117447i	−0.00819606	−	0.00595478i	0.583680	−	0.811984i	$-0.301612\pi$
$389$	−0.161651	−	0.117447i	−0.00819606	−	0.00595478i	−0.591876	+	0.806029i	$0.701612\pi$
$390$		0			0
$391$	−1.54092	−	4.74245i	−0.0779275	−	0.239836i
$392$		0			0
$393$	−1.94634	+	1.41410i	−0.0981798	+	0.0713318i
$394$		0			0
$395$	−6.21519			−0.312720
$396$		0			0
$397$	4.73802			0.237794			0.118897	−	0.992907i	$-0.462064\pi$
$397$	4.73802			0.237794			0.118897	+	0.992907i	$0.462064\pi$
$398$		0			0
$399$	14.4877	−	10.5259i	0.725292	−	0.526955i
$400$		0			0
$401$	7.58213	+	23.3354i	0.378633	+	1.16531i	0.940994	+	0.338422i	$0.109893\pi$
$401$	7.58213	+	23.3354i	0.378633	+	1.16531i	−0.562361	+	0.826892i	$0.690107\pi$
$402$		0			0
$403$	−0.104357	−	0.0758200i	−0.00519841	−	0.00377686i
$404$		0			0
$405$	1.34870	−	4.15086i	0.0670172	−	0.206258i
$406$		0			0
$407$	25.7715	−	15.4991i	1.27745	−	0.768264i
$408$		0			0
$409$	−8.58943	+	26.4355i	−0.424720	+	1.30715i	0.478542	+	0.878065i	$0.341165\pi$
$409$	−8.58943	+	26.4355i	−0.424720	+	1.30715i	−0.903262	+	0.429089i	$0.858835\pi$
$410$		0			0
$411$	−8.84154	−	6.42375i	−0.436121	−	0.316860i
$412$		0			0
$413$	−1.17430	−	3.61412i	−0.0577834	−	0.177839i
$414$		0			0
$415$	2.81157	−	2.04272i	0.138014	−	0.100273i
$416$		0			0
$417$	19.1604			0.938288
$418$		0			0
$419$	21.1838			1.03489			0.517447	−	0.855715i	$-0.326882\pi$
$419$	21.1838			1.03489			0.517447	+	0.855715i	$0.326882\pi$
$420$		0			0
$421$	−0.440700	+	0.320187i	−0.0214784	+	0.0156050i	−0.598473	−	0.801143i	$-0.704225\pi$
$421$	−0.440700	+	0.320187i	−0.0214784	+	0.0156050i	0.576994	+	0.816748i	$0.304225\pi$
$422$		0			0
$423$	−1.96899	−	6.05994i	−0.0957358	−	0.294644i
$424$		0			0
$425$	8.53907	+	6.20400i	0.414206	+	0.300938i
$426$		0			0
$427$	3.38159	−	10.4075i	0.163646	−	0.503652i
$428$		0			0
$429$	6.43347	+	0.560262i	0.310611	+	0.0270497i
$430$		0			0
$431$	−12.5048	+	38.4859i	−0.602336	+	1.85380i	−0.0881793	+	0.996105i	$0.528105\pi$
$431$	−12.5048	+	38.4859i	−0.602336	+	1.85380i	−0.514157	+	0.857696i	$0.671895\pi$
$432$		0			0
$433$	−25.5439	−	18.5587i	−1.22756	−	0.891876i	−0.230857	−	0.972988i	$-0.574153\pi$
$433$	−25.5439	−	18.5587i	−1.22756	−	0.891876i	−0.996705	+	0.0811119i	$0.974153\pi$
$434$		0			0
$435$	1.69281	+	5.20994i	0.0811641	+	0.249798i
$436$		0			0
$437$	−10.7174	+	7.78664i	−0.512682	+	0.372486i
$438$		0			0
$439$	−13.5156			−0.645062			−0.322531	−	0.946559i	$-0.604534\pi$
$439$	−13.5156			−0.645062			−0.322531	+	0.946559i	$0.604534\pi$
$440$		0			0
$441$	−3.54864			−0.168983
$442$		0			0
$443$	−7.90307	+	5.74191i	−0.375486	+	0.272807i	−0.759482	−	0.650528i	$-0.774548\pi$
$443$	−7.90307	+	5.74191i	−0.375486	+	0.272807i	0.383996	+	0.923335i	$0.374548\pi$
$444$		0			0
$445$	1.97178	+	6.06850i	0.0934711	+	0.287675i
$446$		0			0
$447$	−30.6784	−	22.2892i	−1.45104	−	1.05424i
$448$		0			0
$449$	3.91920	−	12.0621i	0.184959	−	0.569244i	−0.814989	−	0.579476i	$-0.803257\pi$
$449$	3.91920	−	12.0621i	0.184959	−	0.569244i	0.999948	+	0.0102325i	$0.00325716\pi$
$450$		0			0
$451$	−6.57945	−	28.4468i	−0.309814	−	1.33951i
$452$		0			0
$453$	−8.29354	+	25.5249i	−0.389665	+	1.19926i
$454$		0			0
$455$	0.521009	+	0.378535i	0.0244253	+	0.0177460i
$456$		0			0
$457$	4.54922	+	14.0011i	0.212804	+	0.654942i	0.999302	+	0.0373503i	$0.0118917\pi$
$457$	4.54922	+	14.0011i	0.212804	+	0.654942i	−0.786499	+	0.617592i	$0.788108\pi$
$458$		0			0
$459$	7.59534	−	5.51834i	0.354520	−	0.257574i
$460$		0			0
$461$	−13.8680			−0.645899			−0.322949	−	0.946416i	$-0.604674\pi$
$461$	−13.8680			−0.645899			−0.322949	+	0.946416i	$0.604674\pi$
$462$		0			0
$463$	24.7632			1.15084			0.575422	−	0.817857i	$-0.304838\pi$
$463$	24.7632			1.15084			0.575422	+	0.817857i	$0.304838\pi$
$464$		0			0
$465$	0.0825147	−	0.0599504i	0.00382653	−	0.00278013i
$466$		0			0
$467$	−10.3142	−	31.7439i	−0.477284	−	1.46893i	−0.842852	−	0.538146i	$-0.819125\pi$
$467$	−10.3142	−	31.7439i	−0.477284	−	1.46893i	0.365567	−	0.930785i	$-0.380875\pi$
$468$		0			0
$469$	4.50880	+	3.27584i	0.208197	+	0.151264i
$470$		0			0
$471$	−13.8072	+	42.4943i	−0.636204	+	1.95803i
$472$		0			0
$473$	−8.35115	+	19.6960i	−0.383986	+	0.905623i
$474$		0			0
$475$	8.66503	−	26.6682i	0.397579	−	1.22362i
$476$		0			0
$477$	−4.02255	−	2.92255i	−0.184180	−	0.133814i
$478$		0			0
$479$	−5.21536	−	16.0512i	−0.238296	−	0.733399i	−0.996667	−	0.0815761i	$-0.974005\pi$
$479$	−5.21536	−	16.0512i	−0.238296	−	0.733399i	0.758371	−	0.651823i	$-0.225995\pi$
$480$		0			0
$481$	7.33568	−	5.32968i	0.334478	−	0.243013i
$482$		0			0
$483$	−7.05354			−0.320947
$484$		0			0
$485$	−5.93252			−0.269382
$486$		0			0
$487$	−8.97183	+	6.51841i	−0.406552	+	0.295377i	−0.772205	−	0.635374i	$-0.780846\pi$
$487$	−8.97183	+	6.51841i	−0.406552	+	0.295377i	0.365652	+	0.930752i	$0.380846\pi$
$488$		0			0
$489$	−8.58125	−	26.4104i	−0.388058	−	1.19432i
$490$		0			0
$491$	−10.8905	−	7.91245i	−0.491484	−	0.357084i	0.314271	−	0.949333i	$-0.398240\pi$
$491$	−10.8905	−	7.91245i	−0.491484	−	0.357084i	−0.805755	+	0.592250i	$0.798240\pi$
$492$		0			0
$493$	−4.67357	+	14.3838i	−0.210487	+	0.647812i
$494$		0			0
$495$	−0.415990	+	0.981103i	−0.0186974	+	0.0440973i
$496$		0			0
$497$	−1.08198	+	3.33000i	−0.0485335	+	0.149371i
$498$		0			0
$499$	22.8720	+	16.6175i	1.02389	+	0.743900i	0.967077	−	0.254485i	$-0.0819060\pi$
$499$	22.8720	+	16.6175i	1.02389	+	0.743900i	0.0568134	+	0.998385i	$0.481906\pi$
$500$		0			0
$501$	5.65698	+	17.4104i	0.252735	+	0.777839i
$502$		0			0
$503$	−21.9182	+	15.9245i	−0.977283	+	0.710038i	−0.957100	−	0.289759i	$-0.906425\pi$
$503$	−21.9182	+	15.9245i	−0.977283	+	0.710038i	−0.0201832	+	0.999796i	$0.506425\pi$
$504$		0			0
$505$	2.60634			0.115981
$506$		0			0
$507$	1.94711			0.0864740
$508$		0			0
$509$	−3.51252	+	2.55200i	−0.155690	+	0.113115i	−0.662903	−	0.748705i	$-0.730676\pi$
$509$	−3.51252	+	2.55200i	−0.155690	+	0.113115i	0.507213	+	0.861821i	$0.330676\pi$
$510$		0			0
$511$	4.93646	+	15.1929i	0.218376	+	0.672093i
$512$		0			0
$513$	−20.1782	−	14.6603i	−0.890889	−	0.647268i
$514$		0			0
$515$	−0.499864	+	1.53842i	−0.0220266	+	0.0677911i
$516$		0			0
$517$	−6.01865	−	26.0221i	−0.264700	−	1.14445i
$518$		0			0
$519$	3.44200	−	10.5934i	0.151087	−	0.464999i
$520$		0			0
$521$	−30.3604	−	22.0581i	−1.33011	−	0.966385i	−0.999746	−	0.0225326i	$-0.992827\pi$
$521$	−30.3604	−	22.0581i	−1.33011	−	0.966385i	−0.330368	−	0.943852i	$-0.607173\pi$
$522$		0			0
$523$	5.91778	+	18.2131i	0.258767	+	0.796402i	0.993064	+	0.117574i	$0.0375117\pi$
$523$	5.91778	+	18.2131i	0.258767	+	0.796402i	−0.734298	+	0.678828i	$0.762488\pi$
$524$		0			0
$525$	12.0787	−	8.77571i	0.527159	−	0.383003i
$526$		0			0
$527$	0.281588			0.0122661
$528$		0			0
$529$	−17.7821			−0.773134
$530$		0			0
$531$	1.53385	−	1.11441i	0.0665636	−	0.0483613i
$532$		0			0
$533$	−2.72041	−	8.37258i	−0.117834	−	0.362657i
$534$		0			0
$535$	4.90515	+	3.56380i	0.212068	+	0.154076i
$536$		0			0
$537$	1.08881	−	3.35101i	0.0469856	−	0.144607i
$538$		0			0
$539$	−14.8190	−	1.29052i	−0.638299	−	0.0555865i
$540$		0			0
$541$	−11.6411	+	35.8275i	−0.500488	+	1.54034i	0.307737	+	0.951472i	$0.400428\pi$
$541$	−11.6411	+	35.8275i	−0.500488	+	1.54034i	−0.808225	+	0.588873i	$0.799572\pi$
$542$		0			0
$543$	17.5032	+	12.7168i	0.751136	+	0.545732i
$544$		0			0
$545$	−0.111527	−	0.343243i	−0.00477727	−	0.0147029i
$546$		0			0
$547$	−31.3717	+	22.7929i	−1.34136	+	0.974552i	−0.341963	+	0.939714i	$0.611092\pi$
$547$	−31.3717	+	22.7929i	−1.34136	+	0.974552i	−0.999393	+	0.0348384i	$0.988908\pi$
$548$		0			0
$549$	5.45970			0.233014
$550$		0			0
$551$	40.1792			1.71169
$552$		0			0
$553$	−19.6364	+	14.2667i	−0.835025	+	0.606681i
$554$		0			0
$555$	2.21551	+	6.81864i	0.0940432	+	0.289435i
$556$		0			0
$557$	−4.37978	−	3.18210i	−0.185577	−	0.134830i	0.491118	−	0.871093i	$-0.336588\pi$
$557$	−4.37978	−	3.18210i	−0.185577	−	0.134830i	−0.676695	+	0.736263i	$0.736588\pi$
$558$		0			0
$559$	−1.99326	+	6.13463i	−0.0843060	+	0.259467i
$560$		0			0
$561$	−12.0808	+	7.26545i	−0.510051	+	0.306748i
$562$		0			0
$563$	1.21044	−	3.72536i	0.0510141	−	0.157005i	−0.922304	−	0.386465i	$-0.873696\pi$
$563$	1.21044	−	3.72536i	0.0510141	−	0.157005i	0.973318	+	0.229460i	$0.0736960\pi$
$564$		0			0
$565$	2.99998	+	2.17961i	0.126210	+	0.0916969i
$566$		0			0
$567$	−5.26701	−	16.2102i	−0.221194	−	0.680764i
$568$		0			0
$569$	19.3304	−	14.0443i	0.810371	−	0.588769i	−0.103567	−	0.994622i	$-0.533026\pi$
$569$	19.3304	−	14.0443i	0.810371	−	0.588769i	0.913938	+	0.405853i	$0.133026\pi$
$570$		0			0
$571$	−36.6420			−1.53342			−0.766709	−	0.641995i	$-0.778107\pi$
$571$	−36.6420			−1.53342			−0.766709	+	0.641995i	$0.778107\pi$
$572$		0			0
$573$	−51.4192			−2.14807
$574$		0			0
$575$	−8.93534	+	6.49190i	−0.372629	+	0.270731i
$576$		0			0
$577$	−2.99017	−	9.20281i	−0.124483	−	0.383118i	0.869324	−	0.494243i	$-0.164555\pi$
$577$	−2.99017	−	9.20281i	−0.124483	−	0.383118i	−0.993806	+	0.111125i	$0.964555\pi$
$578$		0			0
$579$	1.34920	+	0.980250i	0.0560708	+	0.0407378i
$580$		0			0
$581$	4.19395	−	12.9076i	0.173994	−	0.535499i
$582$		0			0
$583$	−15.7352	−	13.6673i	−0.651684	−	0.566042i
$584$		0			0
$585$	−0.0992889	+	0.305580i	−0.00410509	+	0.0126342i
$586$		0			0
$587$	−17.3965	−	12.6393i	−0.718031	−	0.521680i	0.167723	−	0.985834i	$-0.446358\pi$
$587$	−17.3965	−	12.6393i	−0.718031	−	0.521680i	−0.885755	+	0.464154i	$0.846358\pi$
$588$		0			0
$589$	−0.231170	−	0.711467i	−0.00952517	−	0.0293155i
$590$		0			0
$591$	−17.7532	+	12.8984i	−0.730267	+	0.530570i
$592$		0			0
$593$	−38.0335			−1.56185			−0.780924	−	0.624626i	$-0.785251\pi$
$593$	−38.0335			−1.56185			−0.780924	+	0.624626i	$0.785251\pi$
$594$		0			0
$595$	−1.40584			−0.0576338
$596$		0			0
$597$	−9.87092	+	7.17164i	−0.403990	+	0.293516i
$598$		0			0
$599$	7.28046	+	22.4070i	0.297472	+	0.915523i	0.982380	+	0.186894i	$0.0598422\pi$
$599$	7.28046	+	22.4070i	0.297472	+	0.915523i	−0.684908	+	0.728629i	$0.740158\pi$
$600$		0			0
$601$	−15.8262	−	11.4984i	−0.645564	−	0.469030i	0.216193	−	0.976351i	$-0.430636\pi$
$601$	−15.8262	−	11.4984i	−0.645564	−	0.469030i	−0.861757	+	0.507321i	$0.830636\pi$
$602$		0			0
$603$	−0.859244	+	2.64448i	−0.0349911	+	0.107692i
$604$		0			0
$605$	−2.09395	+	3.94576i	−0.0851312	+	0.160418i
$606$		0			0
$607$	−3.06743	+	9.44058i	−0.124503	+	0.383181i	−0.993810	−	0.111091i	$-0.964565\pi$
$607$	−3.06743	+	9.44058i	−0.124503	+	0.383181i	0.869307	+	0.494272i	$0.164565\pi$
$608$		0			0
$609$	17.3075	+	12.5746i	0.701335	+	0.509550i
$610$		0			0
$611$	−2.48854	−	7.65894i	−0.100676	−	0.309848i
$612$		0			0
$613$	9.98527	−	7.25473i	0.403301	−	0.293016i	−0.367583	−	0.929991i	$-0.619815\pi$
$613$	9.98527	−	7.25473i	0.403301	−	0.293016i	0.770884	+	0.636975i	$0.219815\pi$
$614$		0			0
$615$	6.96083			0.280688
$616$		0			0
$617$	−15.4614			−0.622452			−0.311226	−	0.950336i	$-0.600740\pi$
$617$	−15.4614			−0.622452			−0.311226	+	0.950336i	$0.600740\pi$
$618$		0			0
$619$	7.92071	−	5.75473i	0.318360	−	0.231302i	−0.417115	−	0.908854i	$-0.636959\pi$
$619$	7.92071	−	5.75473i	0.318360	−	0.231302i	0.735475	+	0.677551i	$0.236959\pi$
$620$		0			0
$621$	3.03579	+	9.34321i	0.121822	+	0.374930i
$622$		0			0
$623$	20.1596	+	14.6468i	0.807679	+	0.586813i
$624$		0			0
$625$	6.96945	−	21.4497i	0.278778	−	0.857990i
$626$		0			0
$627$	28.2748	+	24.5591i	1.12919	+	0.980795i
$628$		0			0
$629$	−6.11665	+	18.8251i	−0.243887	+	0.750606i
$630$		0			0
$631$	−11.2405	−	8.16668i	−0.447476	−	0.325110i	0.341122	−	0.940019i	$-0.389193\pi$
$631$	−11.2405	−	8.16668i	−0.447476	−	0.325110i	−0.788598	+	0.614909i	$0.789193\pi$
$632$		0			0
$633$	−11.5046	−	35.4075i	−0.457266	−	1.40732i
$634$		0			0
$635$	−0.178146	+	0.129431i	−0.00706951	+	0.00513630i
$636$		0			0
$637$	−4.48500			−0.177702
$638$		0			0
$639$	−1.74690			−0.0691063
$640$		0			0
$641$	32.2281	−	23.4151i	1.27294	−	0.924842i	0.273620	−	0.961838i	$-0.411779\pi$
$641$	32.2281	−	23.4151i	1.27294	−	0.924842i	0.999315	+	0.0369964i	$0.0117790\pi$
$642$		0			0
$643$	9.26111	+	28.5028i	0.365223	+	1.12404i	0.949841	+	0.312732i	$0.101244\pi$
$643$	9.26111	+	28.5028i	0.365223	+	1.12404i	−0.584619	+	0.811308i	$0.698756\pi$
$644$		0			0
$645$	−4.12618	−	2.99784i	−0.162468	−	0.118040i
$646$		0			0
$647$	2.70509	−	8.32540i	0.106348	−	0.327305i	−0.883697	−	0.468060i	$-0.844953\pi$
$647$	2.70509	−	8.32540i	0.106348	−	0.327305i	0.990044	+	0.140755i	$0.0449530\pi$
$648$		0			0
$649$	6.81059	−	4.09592i	0.267339	−	0.160779i
$650$		0			0
$651$	0.123085	−	0.378817i	0.00482409	−	0.0148470i
$652$		0			0
$653$	−13.5641	−	9.85487i	−0.530803	−	0.385651i	0.289855	−	0.957071i	$-0.406393\pi$
$653$	−13.5641	−	9.85487i	−0.530803	−	0.385651i	−0.820658	+	0.571420i	$0.806393\pi$
$654$		0			0
$655$	−0.155050	−	0.477195i	−0.00605831	−	0.0186456i
$656$		0			0
$657$	−6.44795	+	4.68471i	−0.251559	+	0.182768i
$658$		0			0
$659$	38.0509			1.48225			0.741126	−	0.671366i	$-0.234292\pi$
$659$	38.0509			1.48225			0.741126	+	0.671366i	$0.234292\pi$
$660$		0			0
$661$	−33.9627			−1.32100			−0.660499	−	0.750827i	$-0.729655\pi$
$661$	−33.9627			−1.32100			−0.660499	+	0.750827i	$0.729655\pi$
$662$		0			0
$663$	−3.43871	+	2.49837i	−0.133548	+	0.0970286i
$664$		0			0
$665$	1.15413	+	3.55203i	0.0447550	+	0.137742i
$666$		0			0
$667$	−12.8034	−	9.30219i	−0.495748	−	0.360182i
$668$		0			0
$669$	0.640143	−	1.97016i	0.0247494	−	0.0761707i
$670$		0			0
$671$	22.7995	+	1.98550i	0.880164	+	0.0766495i
$672$		0			0
$673$	10.9812	−	33.7965i	0.423293	−	1.30276i	−0.481327	−	0.876541i	$-0.659845\pi$
$673$	10.9812	−	33.7965i	0.423293	−	1.30276i	0.904620	−	0.426220i	$-0.140155\pi$
$674$		0			0
$675$	−16.8230	−	12.2226i	−0.647518	−	0.470450i
$676$		0			0
$677$	8.42758	+	25.9374i	0.323898	+	0.996856i	0.971935	+	0.235248i	$0.0755901\pi$
$677$	8.42758	+	25.9374i	0.323898	+	0.996856i	−0.648037	+	0.761609i	$0.724410\pi$
$678$		0			0
$679$	−18.7433	+	13.6178i	−0.719303	+	0.522604i
$680$		0			0
$681$	−23.2262			−0.890029
$682$		0			0
$683$	28.5618			1.09289			0.546443	−	0.837496i	$-0.315981\pi$
$683$	28.5618			1.09289			0.546443	+	0.837496i	$0.315981\pi$
$684$		0			0
$685$	1.84398	−	1.33973i	0.0704550	−	0.0511885i
$686$		0			0
$687$	16.3651	+	50.3665i	0.624367	+	1.92160i
$688$		0			0
$689$	−5.08395	−	3.69371i	−0.193683	−	0.140719i
$690$		0			0
$691$	−5.66574	+	17.4373i	−0.215535	+	0.663348i	0.783580	+	0.621290i	$0.213391\pi$
$691$	−5.66574	+	17.4373i	−0.215535	+	0.663348i	−0.999115	+	0.0420574i	$0.986609\pi$
$692$		0			0
$693$	0.937788	+	4.05460i	0.0356236	+	0.154022i
$694$		0			0
$695$	−1.23485	+	3.80049i	−0.0468407	+	0.144161i
$696$		0			0
$697$	15.5474	+	11.2959i	0.588901	+	0.427862i
$698$		0			0
$699$	−12.8520	−	39.5545i	−0.486109	−	1.49609i
$700$		0			0
$701$	−11.0655	+	8.03955i	−0.417938	+	0.303650i	−0.776808	−	0.629738i	$-0.783162\pi$
$701$	−11.0655	+	8.03955i	−0.417938	+	0.303650i	0.358870	+	0.933388i	$0.383162\pi$
$702$		0			0
$703$	52.5855			1.98330
$704$		0			0
$705$	6.36753			0.239815
$706$		0			0
$707$	8.23454	−	5.98274i	0.309692	−	0.225004i
$708$		0			0
$709$	−8.45505	−	26.0220i	−0.317536	−	0.977276i	−0.974698	−	0.223526i	$-0.928243\pi$
$709$	−8.45505	−	26.0220i	−0.317536	−	0.977276i	0.657162	−	0.753750i	$-0.271757\pi$
$710$		0			0
$711$	−9.79700	−	7.11793i	−0.367416	−	0.266943i
$712$		0			0
$713$	−0.0910534	+	0.280233i	−0.00340998	+	0.0104948i
$714$		0			0
$715$	−0.525755	+	1.23998i	−0.0196621	+	0.0463726i
$716$		0			0
$717$	2.78199	−	8.56208i	0.103895	−	0.319757i
$718$		0			0
$719$	29.9233	+	21.7405i	1.11595	+	0.810785i	0.983590	−	0.180417i	$-0.0577446\pi$
$719$	29.9233	+	21.7405i	1.11595	+	0.810785i	0.132360	+	0.991202i	$0.457745\pi$
$720$		0			0
$721$	1.95210	+	6.00795i	0.0727000	+	0.223748i
$722$		0			0
$723$	19.7205	−	14.3278i	0.733412	−	0.532855i
$724$		0			0
$725$	33.4983			1.24410
$726$		0			0
$727$	45.3177			1.68074			0.840370	−	0.542013i	$-0.182338\pi$
$727$	45.3177			1.68074			0.840370	+	0.542013i	$0.182338\pi$
$728$		0			0
$729$	−13.4443	+	9.76788i	−0.497938	+	0.361773i
$730$		0			0
$731$	−4.35123	−	13.3917i	−0.160936	−	0.495311i
$732$		0			0
$733$	39.0951	+	28.4042i	1.44401	+	1.04913i	0.987185	+	0.159577i	$0.0510130\pi$
$733$	39.0951	+	28.4042i	1.44401	+	1.04913i	0.456824	+	0.889557i	$0.348987\pi$
$734$		0			0
$735$	1.09586	−	3.37270i	0.0404213	−	0.124404i
$736$		0			0
$737$	−4.54987	+	10.7308i	−0.167597	+	0.395273i
$738$		0			0
$739$	11.2193	−	34.5295i	0.412710	−	1.27019i	−0.501574	−	0.865115i	$-0.667245\pi$
$739$	11.2193	−	34.5295i	0.412710	−	1.27019i	0.914284	−	0.405075i	$-0.132755\pi$
$740$		0			0
$741$	9.13546	+	6.63730i	0.335600	+	0.243827i
$742$		0			0
$743$	−3.54549	−	10.9119i	−0.130072	−	0.400319i	0.864719	−	0.502255i	$-0.167496\pi$
$743$	−3.54549	−	10.9119i	−0.130072	−	0.400319i	−0.994791	+	0.101936i	$0.967496\pi$
$744$		0			0
$745$	6.39825	−	4.64860i	0.234414	−	0.170312i
$746$		0			0
$747$	6.77129			0.247748
$748$		0			0
$749$	23.6780			0.865174
$750$		0			0
$751$	−30.1052	+	21.8727i	−1.09855	+	0.798145i	−0.980823	−	0.194901i	$-0.937562\pi$
$751$	−30.1052	+	21.8727i	−1.09855	+	0.798145i	−0.117730	+	0.993046i	$0.537562\pi$
$752$		0			0
$753$	7.68388	+	23.6486i	0.280016	+	0.861801i
$754$		0			0
$755$	−4.52839	−	3.29007i	−0.164805	−	0.119738i
$756$		0			0
$757$	9.58735	−	29.5068i	0.348458	−	1.07244i	−0.611248	−	0.791439i	$-0.709332\pi$
$757$	9.58735	−	29.5068i	0.348458	−	1.07244i	0.959706	−	0.281005i	$-0.0906678\pi$
$758$		0			0
$759$	−3.32410	−	14.3720i	−0.120657	−	0.521672i
$760$		0			0
$761$	0.0761884	−	0.234484i	0.00276183	−	0.00850003i	−0.949666	−	0.313264i	$-0.898578\pi$
$761$	0.0761884	−	0.234484i	0.00276183	−	0.00850003i	0.952428	+	0.304764i	$0.0985776\pi$
$762$		0			0
$763$	−1.14026	−	0.828446i	−0.0412801	−	0.0299918i
$764$		0			0
$765$	−0.216745	−	0.667072i	−0.00783643	−	0.0241180i
$766$		0			0
$767$	1.93858	−	1.40846i	0.0699982	−	0.0508567i
$768$		0			0
$769$	−8.64642			−0.311798			−0.155899	−	0.987773i	$-0.549827\pi$
$769$	−8.64642			−0.311798			−0.155899	+	0.987773i	$0.549827\pi$
$770$		0			0
$771$	−31.9040			−1.14899
$772$		0			0
$773$	13.2375	−	9.61762i	0.476120	−	0.345922i	−0.323701	−	0.946159i	$-0.604927\pi$
$773$	13.2375	−	9.61762i	0.476120	−	0.345922i	0.799822	+	0.600238i	$0.204927\pi$
$774$		0			0
$775$	−0.192731	−	0.593166i	−0.00692312	−	0.0213072i
$776$		0			0
$777$	22.6516	+	16.4574i	0.812622	+	0.590404i
$778$		0			0
$779$	15.7768	−	48.5559i	0.565262	−	1.73970i
$780$		0			0
$781$	−7.29499	−	0.635287i	−0.261035	−	0.0227323i
$782$		0			0
$783$	9.20750	−	28.3378i	0.329049	−	1.01271i
$784$		0			0
$785$	−7.53895	−	5.47737i	−0.269077	−	0.195496i
$786$		0			0
$787$	5.98822	+	18.4299i	0.213457	+	0.656953i	0.999260	+	0.0384758i	$0.0122502\pi$
$787$	5.98822	+	18.4299i	0.213457	+	0.656953i	−0.785802	+	0.618478i	$0.787750\pi$
$788$		0			0
$789$	12.1626	−	8.83668i	0.433002	−	0.314594i
$790$		0			0
$791$	14.4814			0.514899
$792$		0			0
$793$	6.90032			0.245038
$794$		0			0
$795$	4.01985	−	2.92059i	0.142569	−	0.103583i
$796$		0			0
$797$	−13.2218	−	40.6924i	−0.468339	−	1.44140i	−0.854734	−	0.519066i	$-0.826280\pi$
$797$	−13.2218	−	40.6924i	−0.468339	−	1.44140i	0.386395	−	0.922334i	$-0.373720\pi$
$798$		0			0
$799$	14.2222	+	10.3331i	0.503147	+	0.365558i
$800$		0			0
$801$	−3.84183	+	11.8239i	−0.135744	+	0.417778i
$802$		0			0
$803$	−28.6300	+	17.2183i	−1.01033	+	0.607619i
$804$		0			0
$805$	0.454588	−	1.39908i	0.0160221	−	0.0493111i
$806$		0			0
$807$	0.380875	+	0.276722i	0.0134075	+	0.00974108i
$808$		0			0
$809$	4.52192	+	13.9170i	0.158982	+	0.489297i	0.998543	−	0.0539692i	$-0.0171873\pi$
$809$	4.52192	+	13.9170i	0.158982	+	0.489297i	−0.839560	+	0.543267i	$0.817187\pi$
$810$		0			0
$811$	13.1336	−	9.54213i	0.461183	−	0.335069i	−0.332812	−	0.942993i	$-0.607997\pi$
$811$	13.1336	−	9.54213i	0.461183	−	0.335069i	0.793995	+	0.607924i	$0.207997\pi$
$812$		0			0
$813$	−6.77812			−0.237719
$814$		0			0
$815$	5.79158			0.202870
$816$		0			0
$817$	−30.2637	+	21.9879i	−1.05879	+	0.769259i
$818$		0			0
$819$	0.387749	+	1.19337i	0.0135490	+	0.0416997i
$820$		0			0
$821$	31.0431	+	22.5541i	1.08341	+	0.787145i	0.978275	−	0.207313i	$-0.0664717\pi$
$821$	31.0431	+	22.5541i	1.08341	+	0.787145i	0.105138	+	0.994458i	$0.466472\pi$
$822$		0			0
$823$	−1.91807	+	5.90320i	−0.0668596	+	0.205773i	−0.978905	−	0.204317i	$-0.934503\pi$
$823$	−1.91807	+	5.90320i	−0.0668596	+	0.205773i	0.912045	+	0.410090i	$0.134503\pi$
$824$		0			0
$825$	23.5734	+	20.4755i	0.820720	+	0.712864i
$826$		0			0
$827$	−6.95834	+	21.4156i	−0.241965	+	0.744692i	0.754156	+	0.656696i	$0.228046\pi$
$827$	−6.95834	+	21.4156i	−0.241965	+	0.744692i	−0.996121	+	0.0879966i	$0.971954\pi$
$828$		0			0
$829$	3.94449	+	2.86584i	0.136998	+	0.0995348i	0.654174	−	0.756344i	$-0.273017\pi$
$829$	3.94449	+	2.86584i	0.136998	+	0.0995348i	−0.517176	+	0.855879i	$0.673017\pi$
$830$		0			0
$831$	6.92007	+	21.2978i	0.240055	+	0.738812i
$832$		0			0
$833$	7.92079	−	5.75479i	0.274439	−	0.199392i
$834$		0			0
$835$	−3.81796			−0.132126
$836$		0			0
$837$	−0.554762			−0.0191754
$838$		0			0
$839$	31.9044	−	23.1799i	1.10146	−	0.800258i	0.120163	−	0.992754i	$-0.461658\pi$
$839$	31.9044	−	23.1799i	1.10146	−	0.800258i	0.981298	+	0.192496i	$0.0616583\pi$
$840$		0			0
$841$	5.87114	+	18.0695i	0.202453	+	0.623087i
$842$		0			0
$843$	12.7561	+	9.26787i	0.439344	+	0.319202i
$844$		0			0
$845$	−0.125488	+	0.386211i	−0.00431691	+	0.0132861i
$846$		0			0
$847$	2.44165	+	17.2729i	0.0838960	+	0.593504i
$848$		0			0
$849$	5.78988	−	17.8194i	0.198708	−	0.611561i
$850$		0			0
$851$	−16.7567	−	12.1745i	−0.574413	−	0.417335i
$852$		0			0
$853$	1.86786	+	5.74867i	0.0639541	+	0.196831i	0.977928	−	0.208943i	$-0.0670022\pi$
$853$	1.86786	+	5.74867i	0.0639541	+	0.196831i	−0.913974	+	0.405773i	$0.867002\pi$
$854$		0			0
$855$	−1.50751	+	1.09527i	−0.0515556	+	0.0374573i
$856$		0			0
$857$	−25.5730			−0.873558			−0.436779	−	0.899569i	$-0.643881\pi$
$857$	−25.5730			−0.873558			−0.436779	+	0.899569i	$0.643881\pi$
$858$		0			0
$859$	10.7934			0.368267			0.184134	−	0.982901i	$-0.441052\pi$
$859$	10.7934			0.368267			0.184134	+	0.982901i	$0.441052\pi$
$860$		0			0
$861$	21.9922	−	15.9783i	0.749492	−	0.544538i
$862$		0			0
$863$	−17.2056	−	52.9533i	−0.585684	−	1.80255i	−0.596504	−	0.802610i	$-0.703444\pi$
$863$	−17.2056	−	52.9533i	−0.585684	−	1.80255i	0.0108198	−	0.999941i	$-0.496556\pi$
$864$		0			0
$865$	1.87938	+	1.36545i	0.0639010	+	0.0464268i
$866$		0			0
$867$	−7.36144	+	22.6562i	−0.250008	+	0.769445i
$868$		0			0
$869$	−38.3233	−	33.2870i	−1.30003	−	1.12918i
$870$		0			0
$871$	−1.08597	+	3.34227i	−0.0367966	+	0.113248i
$872$		0			0
$873$	−9.35142	−	6.79420i	−0.316497	−	0.229949i
$874$		0			0
$875$	1.95726	+	6.02382i	0.0661674	+	0.203642i
$876$		0			0
$877$	24.8728	−	18.0712i	0.839896	−	0.610220i	−0.0824456	−	0.996596i	$-0.526273\pi$
$877$	24.8728	−	18.0712i	0.839896	−	0.610220i	0.922342	+	0.386375i	$0.126273\pi$
$878$		0			0
$879$	−2.53006			−0.0853368
$880$		0			0
$881$	−28.7965			−0.970180			−0.485090	−	0.874464i	$-0.661213\pi$
$881$	−28.7965			−0.970180			−0.485090	+	0.874464i	$0.661213\pi$
$882$		0			0
$883$	−13.8963	+	10.0962i	−0.467646	+	0.339765i	−0.796523	−	0.604608i	$-0.793330\pi$
$883$	−13.8963	+	10.0962i	−0.467646	+	0.339765i	0.328877	+	0.944373i	$0.393330\pi$
$884$		0			0
$885$	0.585488	+	1.80195i	0.0196810	+	0.0605718i
$886$		0			0
$887$	0.409208	+	0.297307i	0.0137399	+	0.00998259i	0.594634	−	0.803997i	$-0.297297\pi$
$887$	0.409208	+	0.297307i	0.0137399	+	0.00998259i	−0.580894	+	0.813979i	$0.697297\pi$
$888$		0			0
$889$	−0.265736	+	0.817853i	−0.00891251	+	0.0274299i
$890$		0			0
$891$	30.5471	−	18.3712i	1.02337	−	0.615459i
$892$		0			0
$893$	14.4320	−	44.4173i	0.482950	−	1.48637i
$894$		0			0
$895$	0.594506	+	0.431934i	0.0198722	+	0.0144380i
$896$		0			0
$897$	−1.37442	−	4.23004i	−0.0458907	−	0.141237i
$898$		0			0
$899$	0.723004	−	0.525293i	0.0241135	−	0.0175195i
$900$		0			0
$901$	13.7180			0.457014
$902$		0			0
$903$	−19.9177			−0.662821
$904$		0			0
$905$	−3.65046	+	2.65221i	−0.121345	+	0.0881625i
$906$		0			0
$907$	9.14845	+	28.1560i	0.303769	+	0.934906i	0.980134	+	0.198338i	$0.0635545\pi$
$907$	9.14845	+	28.1560i	0.303769	+	0.934906i	−0.676364	+	0.736567i	$0.736446\pi$
$908$		0			0
$909$	4.10837	+	2.98491i	0.136266	+	0.0990031i
$910$		0			0
$911$	−3.23497	+	9.95622i	−0.107179	+	0.329864i	−0.990236	−	0.139403i	$-0.955482\pi$
$911$	−3.23497	+	9.95622i	−0.107179	+	0.329864i	0.883056	+	0.469267i	$0.155482\pi$
$912$		0			0
$913$	28.2766	+	2.46248i	0.935820	+	0.0814962i
$914$		0			0
$915$	−1.68601	+	5.18901i	−0.0557378	+	0.171543i
$916$		0			0
$917$	−1.58525	−	1.15175i	−0.0523495	−	0.0380342i
$918$		0			0
$919$	5.15081	+	15.8526i	0.169909	+	0.522928i	0.999364	−	0.0356459i	$-0.0113489\pi$
$919$	5.15081	+	15.8526i	0.169909	+	0.522928i	−0.829455	+	0.558574i	$0.811349\pi$
$920$		0			0
$921$	15.9317	−	11.5751i	0.524967	−	0.381411i
$922$		0			0
$923$	−2.20785			−0.0726721
$924$		0			0
$925$	43.8417			1.44151
$926$		0			0
$927$	−2.54981	+	1.85255i	−0.0837468	+	0.0608456i
$928$		0			0
$929$	−13.1373	−	40.4324i	−0.431020	−	1.32654i	−0.897110	−	0.441807i	$-0.854338\pi$
$929$	−13.1373	−	40.4324i	−0.431020	−	1.32654i	0.466090	−	0.884737i	$-0.345662\pi$
$930$		0			0
$931$	−21.0428	−	15.2885i	−0.689650	−	0.501060i
$932$		0			0
$933$	−16.9309	+	52.1080i	−0.554293	+	1.70594i
$934$		0			0
$935$	−0.662527	−	2.86449i	−0.0216669	−	0.0936788i
$936$		0			0
$937$	15.3292	−	47.1786i	0.500785	−	1.54126i	−0.306959	−	0.951723i	$-0.599311\pi$
$937$	15.3292	−	47.1786i	0.500785	−	1.54126i	0.807744	−	0.589534i	$-0.200689\pi$
$938$		0			0
$939$	−24.3607	−	17.6991i	−0.794980	−	0.577587i
$940$		0			0
$941$	1.12611	+	3.46581i	0.0367101	+	0.112982i	0.967732	−	0.251980i	$-0.0810818\pi$
$941$	1.12611	+	3.46581i	0.0367101	+	0.112982i	−0.931022	+	0.364962i	$0.881082\pi$
$942$		0			0
$943$	−16.2689	+	11.8201i	−0.529789	+	0.384914i
$944$		0			0
$945$	2.76968			0.0900975
$946$		0			0
$947$	9.74479			0.316663			0.158332	−	0.987386i	$-0.449389\pi$
$947$	9.74479			0.316663			0.158332	+	0.987386i	$0.449389\pi$
$948$		0			0
$949$	−8.14934	+	5.92084i	−0.264539	+	0.192199i
$950$		0			0
$951$	−17.4712	−	53.7710i	−0.566544	−	1.74364i
$952$		0			0
$953$	23.3019	+	16.9298i	0.754822	+	0.548410i	0.897318	−	0.441385i	$-0.145513\pi$
$953$	23.3019	+	16.9298i	0.754822	+	0.548410i	−0.142496	+	0.989795i	$0.545513\pi$
$954$		0			0
$955$	3.31388	−	10.1991i	0.107235	−	0.330034i
$956$		0			0
$957$	−17.4652	+	41.1911i	−0.564568	+	1.33152i
$958$		0			0
$959$	2.75063	−	8.46556i	0.0888223	−	0.273367i
$960$		0			0
$961$	25.0661	+	18.2116i	0.808583	+	0.587470i
$962$		0			0
$963$	3.65054	+	11.2352i	0.117637	+	0.362050i
$964$		0			0
$965$	−0.281387	+	0.204440i	−0.00905818	+	0.00658115i
$966$		0			0
$967$	−21.6187			−0.695211			−0.347606	−	0.937641i	$-0.613005\pi$
$967$	−21.6187			−0.695211			−0.347606	+	0.937641i	$0.613005\pi$
$968$		0			0
$969$	−24.6502			−0.791879
$970$		0			0
$971$	−16.4885	+	11.9796i	−0.529140	+	0.384443i	−0.820036	−	0.572312i	$-0.806047\pi$
$971$	−16.4885	+	11.9796i	−0.529140	+	0.384443i	0.290896	+	0.956755i	$0.406047\pi$
$972$		0			0
$973$	4.82242	+	14.8419i	0.154600	+	0.475809i
$974$		0			0
$975$	7.61644	+	5.53367i	0.243921	+	0.177219i
$976$		0			0
$977$	1.52407	−	4.69060i	0.0487593	−	0.150066i	−0.923712	−	0.383087i	$-0.874861\pi$
$977$	1.52407	−	4.69060i	0.0487593	−	0.150066i	0.972472	+	0.233021i	$0.0748611\pi$
$978$		0			0
$979$	−20.3433	+	47.9791i	−0.650174	+	1.53342i
$980$		0			0
$981$	0.217300	−	0.668779i	0.00693784	−	0.0213525i
$982$		0			0
$983$	−14.2681	−	10.3664i	−0.455082	−	0.330636i	0.336517	−	0.941677i	$-0.390751\pi$
$983$	−14.2681	−	10.3664i	−0.455082	−	0.330636i	−0.791599	+	0.611041i	$0.790751\pi$
$984$		0			0
$985$	−1.41426	−	4.35265i	−0.0450621	−	0.138687i
$986$		0			0
$987$	20.1177	−	14.6164i	0.640354	−	0.465244i
$988$		0			0
$989$	14.7343			0.468524
$990$		0			0
$991$	−61.7280			−1.96085			−0.980427	−	0.196885i	$-0.936918\pi$
$991$	−61.7280			−1.96085			−0.980427	+	0.196885i	$0.936918\pi$
$992$		0			0
$993$	−30.3863	+	22.0769i	−0.964279	+	0.700589i
$994$		0			0
$995$	−0.786341	−	2.42011i	−0.0249287	−	0.0767226i
$996$		0			0
$997$	3.39380	+	2.46574i	0.107483	+	0.0780908i	0.640228	−	0.768185i	$-0.278840\pi$
$997$	3.39380	+	2.46574i	0.107483	+	0.0780908i	−0.532746	+	0.846275i	$0.678840\pi$
$998$		0			0
$999$	12.0505	−	37.0878i	0.381262	−	1.17340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.53.2	✓	20
11.4	even	5		6292.2.a.w.1.8		10
11.5	even	5	inner	572.2.n.a.313.2	yes	20
11.7	odd	10		6292.2.a.x.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.53.2	✓	20	1.1	even	1	trivial
572.2.n.a.313.2	yes	20	11.5	even	5	inner
6292.2.a.w.1.8		10	11.4	even	5
6292.2.a.x.1.8		10	11.7	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57524 + 1.14448i) q^{3} +(-0.125488 - 0.386211i) q^{5} +(-1.28300 - 0.932153i) q^{7} +(0.244502 - 0.752499i) q^{9} +O(q^{10})\)	\(q+(-1.57524 + 1.14448i) q^{3} +(-0.125488 - 0.386211i) q^{5} +(-1.28300 - 0.932153i) q^{7} +(0.244502 - 0.752499i) q^{9} +(1.29469 - 3.05349i) q^{11} +(0.309017 - 0.951057i) q^{13} +(0.639685 + 0.464758i) q^{15} +(0.674575 + 2.07613i) q^{17} +(4.69181 - 3.40880i) q^{19} +3.08787 q^{21} -2.28428 q^{23} +(3.91167 - 2.84200i) q^{25} +(-1.32900 - 4.09023i) q^{27} +(5.60500 + 4.07227i) q^{29} +(0.0398609 - 0.122679i) q^{31} +(1.45521 + 6.29173i) q^{33} +(-0.199008 + 0.612483i) q^{35} +(7.33568 + 5.32968i) q^{37} +(0.601689 + 1.85181i) q^{39} +(7.12214 - 5.17454i) q^{41} -6.45033 q^{43} -0.321306 q^{45} +(6.51509 - 4.73349i) q^{47} +(-1.38594 - 4.26549i) q^{49} +(-3.43871 - 2.49837i) q^{51} +(1.94190 - 5.97655i) q^{53} +(-1.34176 - 0.116848i) q^{55} +(-3.48944 + 10.7394i) q^{57} +(1.93858 + 1.40846i) q^{59} +(2.13232 + 6.56260i) q^{61} +(-1.01514 + 0.737542i) q^{63} -0.406087 q^{65} -3.51427 q^{67} +(3.59829 - 2.61431i) q^{69} +(-0.682262 - 2.09979i) q^{71} +(-8.14934 - 5.92084i) q^{73} +(-2.90922 + 8.95367i) q^{75} +(-4.50740 + 2.71078i) q^{77} +(4.72953 - 14.5560i) q^{79} +(8.69502 + 6.31730i) q^{81} +(2.64456 + 8.13913i) q^{83} +(0.717174 - 0.521057i) q^{85} -13.4899 q^{87} -15.7129 q^{89} +(-1.28300 + 0.932153i) q^{91} +(0.0776135 + 0.238870i) q^{93} +(-1.90528 - 1.38427i) q^{95} +(4.51443 - 13.8940i) q^{97} +(-1.98119 - 1.72083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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