LMFDB - Embedded newform 1716.2.z.f.313.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8, 0]))

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (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:	$13.7023289869$
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} - 6 x^{19} + 41 x^{18} - 146 x^{17} + 650 x^{16} - 1400 x^{15} + 5756 x^{14} - 2122 x^{13} + \cdots + 4096 $ x^20 - 6x^19 + 41x^18 - 146x^17 + 650x^16 - 1400x^15 + 5756x^14 - 2122x^13 + 27469x^12 + 11286x^11 + 72308x^10 + 48512x^9 + 142448x^8 - 37952x^7 + 295552x^6 + 300160x^5 + 272128x^4 + 194048x^3 + 236544x^2 + 49152*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.3
Root			$-1.24982 - 0.908046i$ of defining polynomial
Character	$\chi$	$=$	1716.313
Dual form			1716.2.z.f.625.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{3} +(-0.465225 + 1.43182i) q^{5} +(1.83500 - 1.33320i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{3} +(-0.465225 + 1.43182i) q^{5} +(1.83500 - 1.33320i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-2.27063 - 2.41749i) q^{11} +(0.309017 + 0.951057i) q^{13} +(-1.21798 + 0.884911i) q^{15} +(-2.05772 + 6.33302i) q^{17} +(0.903606 + 0.656508i) q^{19} +2.26818 q^{21} +7.83420 q^{23} +(2.21142 + 1.60669i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-7.81659 + 5.67909i) q^{29} +(-0.397746 - 1.22414i) q^{31} +(-0.416013 - 3.29043i) q^{33} +(1.05522 + 3.24762i) q^{35} +(0.0492255 - 0.0357645i) q^{37} +(-0.309017 + 0.951057i) q^{39} +(7.87921 + 5.72458i) q^{41} +10.0206 q^{43} -1.50550 q^{45} +(3.94998 + 2.86983i) q^{47} +(-0.573334 + 1.76454i) q^{49} +(-5.38719 + 3.91402i) q^{51} +(-1.77675 - 5.46827i) q^{53} +(4.51775 - 2.12645i) q^{55} +(0.345147 + 1.06225i) q^{57} +(-6.23212 + 4.52790i) q^{59} +(-0.0807210 + 0.248434i) q^{61} +(1.83500 + 1.33320i) q^{63} -1.50550 q^{65} -7.82969 q^{67} +(6.33800 + 4.60483i) q^{69} +(0.399958 - 1.23094i) q^{71} +(7.18319 - 5.21889i) q^{73} +(0.844688 + 2.59968i) q^{75} +(-7.38960 - 1.40887i) q^{77} +(1.48447 + 4.56872i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.03519 - 6.26368i) q^{83} +(-8.11041 - 5.89256i) q^{85} -9.66184 q^{87} -13.8446 q^{89} +(1.83500 + 1.33320i) q^{91} +(0.397746 - 1.22414i) q^{93} +(-1.36038 + 0.988374i) q^{95} +(-0.345886 - 1.06453i) q^{97} +(1.59750 - 2.90654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	−0.465225	+	1.43182i	−0.208055	+	0.640328i	0.791519	+	0.611145i	$0.209291\pi$
$5$	−0.465225	+	1.43182i	−0.208055	+	0.640328i	−0.999574	+	0.0291832i	$0.990709\pi$
$6$		0			0
$7$	1.83500	−	1.33320i	0.693564	−	0.503904i	−0.184266	−	0.982876i	$-0.558991\pi$
$7$	1.83500	−	1.33320i	0.693564	−	0.503904i	0.877830	+	0.478973i	$0.158991\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−2.27063	−	2.41749i	−0.684620	−	0.728900i
$11$	−2.27063	−	2.41749i	−0.684620	−	0.728900i
$12$		0			0
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$		0			0
$15$	−1.21798	+	0.884911i	−0.314480	+	0.228483i
$16$		0			0
$17$	−2.05772	+	6.33302i	−0.499071	+	1.53598i	0.311444	+	0.950264i	$0.399187\pi$
$17$	−2.05772	+	6.33302i	−0.499071	+	1.53598i	−0.810515	+	0.585718i	$0.800813\pi$
$18$		0			0
$19$	0.903606	+	0.656508i	0.207302	+	0.150613i	0.686592	−	0.727043i	$-0.259106\pi$
$19$	0.903606	+	0.656508i	0.207302	+	0.150613i	−0.479290	+	0.877656i	$0.659106\pi$
$20$		0			0
$21$	2.26818			0.494958
$22$		0			0
$23$	7.83420			1.63354			0.816772	−	0.576961i	$-0.195761\pi$
$23$	7.83420			1.63354			0.816772	+	0.576961i	$0.195761\pi$
$24$		0			0
$25$	2.21142	+	1.60669i	0.442284	+	0.321338i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−7.81659	+	5.67909i	−1.45150	+	1.05458i	−0.466028	+	0.884770i	$0.654315\pi$
$29$	−7.81659	+	5.67909i	−1.45150	+	1.05458i	−0.985477	+	0.169810i	$0.945685\pi$
$30$		0			0
$31$	−0.397746	−	1.22414i	−0.0714373	−	0.219861i	0.908963	−	0.416876i	$-0.136875\pi$
$31$	−0.397746	−	1.22414i	−0.0714373	−	0.219861i	−0.980400	+	0.197015i	$0.936875\pi$
$32$		0			0
$33$	−0.416013	−	3.29043i	−0.0724187	−	0.572790i
$34$		0			0
$35$	1.05522	+	3.24762i	0.178364	+	0.548948i
$36$		0			0
$37$	0.0492255	−	0.0357645i	0.00809263	−	0.00587964i	−0.583732	−	0.811947i	$-0.698408\pi$
$37$	0.0492255	−	0.0357645i	0.00809263	−	0.00587964i	0.591824	+	0.806067i	$0.298408\pi$
$38$		0			0
$39$	−0.309017	+	0.951057i	−0.0494823	+	0.152291i
$40$		0			0
$41$	7.87921	+	5.72458i	1.23053	+	0.894029i	0.996930	−	0.0783042i	$-0.0249505\pi$
$41$	7.87921	+	5.72458i	1.23053	+	0.894029i	0.233596	+	0.972334i	$0.424951\pi$
$42$		0			0
$43$	10.0206			1.52813			0.764066	−	0.645138i	$-0.223200\pi$
$43$	10.0206			1.52813			0.764066	+	0.645138i	$0.223200\pi$
$44$		0			0
$45$	−1.50550			−0.224427
$46$		0			0
$47$	3.94998	+	2.86983i	0.576163	+	0.418607i	0.837339	−	0.546684i	$-0.184110\pi$
$47$	3.94998	+	2.86983i	0.576163	+	0.418607i	−0.261176	+	0.965291i	$0.584110\pi$
$48$		0			0
$49$	−0.573334	+	1.76454i	−0.0819048	+	0.252077i
$50$		0			0
$51$	−5.38719	+	3.91402i	−0.754357	+	0.548072i
$52$		0			0
$53$	−1.77675	−	5.46827i	−0.244055	−	0.751124i	−0.995790	−	0.0916594i	$-0.970783\pi$
$53$	−1.77675	−	5.46827i	−0.244055	−	0.751124i	0.751735	−	0.659465i	$-0.229217\pi$
$54$		0			0
$55$	4.51775	−	2.12645i	0.609174	−	0.286730i
$56$		0			0
$57$	0.345147	+	1.06225i	0.0457158	+	0.140699i
$58$		0			0
$59$	−6.23212	+	4.52790i	−0.811353	+	0.589483i	−0.914223	−	0.405212i	$-0.867198\pi$
$59$	−6.23212	+	4.52790i	−0.811353	+	0.589483i	0.102869	+	0.994695i	$0.467198\pi$
$60$		0			0
$61$	−0.0807210	+	0.248434i	−0.0103353	+	0.0318087i	−0.956091	−	0.293069i	$-0.905323\pi$
$61$	−0.0807210	+	0.248434i	−0.0103353	+	0.0318087i	0.945756	+	0.324878i	$0.105323\pi$
$62$		0			0
$63$	1.83500	+	1.33320i	0.231188	+	0.167968i
$64$		0			0
$65$	−1.50550			−0.186734
$66$		0			0
$67$	−7.82969			−0.956549			−0.478274	−	0.878211i	$-0.658738\pi$
$67$	−7.82969			−0.956549			−0.478274	+	0.878211i	$0.658738\pi$
$68$		0			0
$69$	6.33800	+	4.60483i	0.763006	+	0.554356i
$70$		0			0
$71$	0.399958	−	1.23094i	0.0474662	−	0.146086i	−0.924514	−	0.381147i	$-0.875529\pi$
$71$	0.399958	−	1.23094i	0.0474662	−	0.146086i	0.971981	+	0.235061i	$0.0755291\pi$
$72$		0			0
$73$	7.18319	−	5.21889i	0.840728	−	0.610825i	−0.0818457	−	0.996645i	$-0.526081\pi$
$73$	7.18319	−	5.21889i	0.840728	−	0.610825i	0.922574	+	0.385820i	$0.126081\pi$
$74$		0			0
$75$	0.844688	+	2.59968i	0.0975361	+	0.300185i
$76$		0			0
$77$	−7.38960	−	1.40887i	−0.842124	−	0.160556i
$78$		0			0
$79$	1.48447	+	4.56872i	0.167016	+	0.514021i	0.999179	−	0.0405091i	$-0.0128980\pi$
$79$	1.48447	+	4.56872i	0.167016	+	0.514021i	−0.832164	+	0.554530i	$0.812898\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	2.03519	−	6.26368i	0.223391	−	0.687528i	−0.775060	−	0.631888i	$-0.782280\pi$
$83$	2.03519	−	6.26368i	0.223391	−	0.687528i	0.998451	−	0.0556396i	$-0.0177198\pi$
$84$		0			0
$85$	−8.11041	−	5.89256i	−0.879698	−	0.639138i
$86$		0			0
$87$	−9.66184			−1.03586
$88$		0			0
$89$	−13.8446			−1.46752			−0.733760	−	0.679409i	$-0.762236\pi$
$89$	−13.8446			−1.46752			−0.733760	+	0.679409i	$0.762236\pi$
$90$		0			0
$91$	1.83500	+	1.33320i	0.192360	+	0.139758i
$92$		0			0
$93$	0.397746	−	1.22414i	0.0412443	−	0.126937i
$94$		0			0
$95$	−1.36038	+	0.988374i	−0.139572	+	0.101405i
$96$		0			0
$97$	−0.345886	−	1.06453i	−0.0351194	−	0.108086i	0.931960	−	0.362561i	$-0.118098\pi$
$97$	−0.345886	−	1.06453i	−0.0351194	−	0.108086i	−0.967079	+	0.254475i	$0.918098\pi$
$98$		0			0
$99$	1.59750	−	2.90654i	0.160555	−	0.292118i
$100$		0			0
$101$	4.74486	+	14.6032i	0.472131	+	1.45307i	0.849789	+	0.527124i	$0.176730\pi$
$101$	4.74486	+	14.6032i	0.472131	+	1.45307i	−0.377658	+	0.925945i	$0.623270\pi$
$102$		0			0
$103$	−13.2855	+	9.65250i	−1.30906	+	0.951089i	−0.309062	+	0.951042i	$0.600015\pi$
$103$	−13.2855	+	9.65250i	−1.30906	+	0.951089i	−1.00000		4.76331e-5i	$0.999985\pi$
$104$		0			0
$105$	−1.05522	+	3.24762i	−0.102979	+	0.316935i
$106$		0			0
$107$	−0.0581552	−	0.0422522i	−0.00562208	−	0.00408468i	0.584971	−	0.811054i	$-0.301106\pi$
$107$	−0.0581552	−	0.0422522i	−0.00562208	−	0.00408468i	−0.590593	+	0.806970i	$0.701106\pi$
$108$		0			0
$109$	16.6436			1.59416			0.797082	−	0.603871i	$-0.206376\pi$
$109$	16.6436			1.59416			0.797082	+	0.603871i	$0.206376\pi$
$110$		0			0
$111$	0.0608461			0.00577526
$112$		0			0
$113$	6.34130	+	4.60723i	0.596540	+	0.433411i	0.844649	−	0.535321i	$-0.179809\pi$
$113$	6.34130	+	4.60723i	0.596540	+	0.433411i	−0.248109	+	0.968732i	$0.579809\pi$
$114$		0			0
$115$	−3.64467	+	11.2171i	−0.339867	+	1.04600i
$116$		0			0
$117$	−0.809017	+	0.587785i	−0.0747936	+	0.0543408i
$118$		0			0
$119$	4.66729	+	14.3644i	0.427850	+	1.31679i
$120$		0			0
$121$	−0.688492	+	10.9784i	−0.0625902	+	0.998039i
$122$		0			0
$123$	3.00959	+	9.26257i	0.271366	+	0.835178i
$124$		0			0
$125$	−9.41918	+	6.84343i	−0.842477	+	0.612095i
$126$		0			0
$127$	2.53877	−	7.81352i	0.225279	−	0.693338i	−0.772984	−	0.634426i	$-0.781237\pi$
$127$	2.53877	−	7.81352i	0.225279	−	0.693338i	0.998263	−	0.0589125i	$-0.0187633\pi$
$128$		0			0
$129$	8.10686	+	5.88998i	0.713769	+	0.518584i
$130$		0			0
$131$	−5.30186			−0.463225			−0.231613	−	0.972808i	$-0.574400\pi$
$131$	−5.30186			−0.463225			−0.231613	+	0.972808i	$0.574400\pi$
$132$		0			0
$133$	2.53338			0.219672
$134$		0			0
$135$	−1.21798	−	0.884911i	−0.104827	−	0.0761610i
$136$		0			0
$137$	3.32075	−	10.2202i	0.283711	−	0.873172i	−0.703071	−	0.711119i	$-0.748189\pi$
$137$	3.32075	−	10.2202i	0.283711	−	0.873172i	0.986782	−	0.162053i	$-0.0518114\pi$
$138$		0			0
$139$	7.06440	−	5.13258i	0.599194	−	0.435340i	−0.246398	−	0.969169i	$-0.579247\pi$
$139$	7.06440	−	5.13258i	0.599194	−	0.435340i	0.845593	+	0.533828i	$0.179247\pi$
$140$		0			0
$141$	1.50876	+	4.64348i	0.127060	+	0.391051i
$142$		0			0
$143$	1.59750	−	2.90654i	0.133590	−	0.243057i
$144$		0			0
$145$	−4.49493	−	13.8340i	−0.373284	−	1.14885i
$146$		0			0
$147$	−1.50101	+	1.09055i	−0.123801	+	0.0899467i
$148$		0			0
$149$	3.37591	−	10.3900i	0.276565	−	0.851180i	−0.712236	−	0.701940i	$-0.752317\pi$
$149$	3.37591	−	10.3900i	0.276565	−	0.851180i	0.988801	−	0.149240i	$-0.0476827\pi$
$150$		0			0
$151$	−5.57900	−	4.05338i	−0.454012	−	0.329859i	0.337165	−	0.941445i	$-0.390532\pi$
$151$	−5.57900	−	4.05338i	−0.454012	−	0.329859i	−0.791178	+	0.611586i	$0.790532\pi$
$152$		0			0
$153$	−6.65893			−0.538342
$154$		0			0
$155$	1.93778			0.155646
$156$		0			0
$157$	−7.97772	−	5.79615i	−0.636691	−	0.462583i	0.222021	−	0.975042i	$-0.428735\pi$
$157$	−7.97772	−	5.79615i	−0.636691	−	0.462583i	−0.858712	+	0.512459i	$0.828735\pi$
$158$		0			0
$159$	1.77675	−	5.46827i	0.140905	−	0.433662i
$160$		0			0
$161$	14.3757	−	10.4446i	1.13297	−	0.823149i
$162$		0			0
$163$	−1.37080	−	4.21890i	−0.107370	−	0.330449i	0.882910	−	0.469543i	$-0.155581\pi$
$163$	−1.37080	−	4.21890i	−0.107370	−	0.330449i	−0.990279	+	0.139093i	$0.955581\pi$
$164$		0			0
$165$	4.90483	+	0.935137i	0.381841	+	0.0728003i
$166$		0			0
$167$	2.75833	+	8.48928i	0.213446	+	0.656920i	0.999260	+	0.0384571i	$0.0122443\pi$
$167$	2.75833	+	8.48928i	0.213446	+	0.656920i	−0.785814	+	0.618463i	$0.787756\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	−0.345147	+	1.06225i	−0.0263940	+	0.0812325i
$172$		0			0
$173$	−13.8323	−	10.0498i	−1.05165	−	0.764071i	−0.0791269	−	0.996865i	$-0.525213\pi$
$173$	−13.8323	−	10.0498i	−1.05165	−	0.764071i	−0.972526	+	0.232794i	$0.925213\pi$
$174$		0			0
$175$	6.20000			0.468676
$176$		0			0
$177$	−7.70333			−0.579018
$178$		0			0
$179$	2.89339	+	2.10217i	0.216262	+	0.157124i	0.690643	−	0.723196i	$-0.257328\pi$
$179$	2.89339	+	2.10217i	0.216262	+	0.157124i	−0.474380	+	0.880320i	$0.657328\pi$
$180$		0			0
$181$	3.65697	−	11.2550i	0.271821	−	0.836578i	−0.718222	−	0.695814i	$-0.755044\pi$
$181$	3.65697	−	11.2550i	0.271821	−	0.836578i	0.990043	−	0.140764i	$-0.0449560\pi$
$182$		0			0
$183$	−0.211330	+	0.153540i	−0.0156220	+	0.0113500i
$184$		0			0
$185$	0.0283072	+	0.0871205i	0.00208118	+	0.00640522i
$186$		0			0
$187$	19.9823	−	9.40541i	1.46125	−	0.687792i
$188$		0			0
$189$	0.700907	+	2.15717i	0.0509835	+	0.156911i
$190$		0			0
$191$	2.03418	−	1.47791i	0.147188	−	0.106938i	−0.511754	−	0.859132i	$-0.671004\pi$
$191$	2.03418	−	1.47791i	0.147188	−	0.106938i	0.658942	+	0.752194i	$0.271004\pi$
$192$		0			0
$193$	1.35493	−	4.17006i	0.0975303	−	0.300168i	−0.890375	−	0.455229i	$-0.849557\pi$
$193$	1.35493	−	4.17006i	0.0975303	−	0.300168i	0.987905	+	0.155061i	$0.0495575\pi$
$194$		0			0
$195$	−1.21798	−	0.884911i	−0.0872211	−	0.0633698i
$196$		0			0
$197$	17.3275			1.23453			0.617267	−	0.786754i	$-0.288240\pi$
$197$	17.3275			1.23453			0.617267	+	0.786754i	$0.288240\pi$
$198$		0			0
$199$	−1.23398			−0.0874743			−0.0437372	−	0.999043i	$-0.513926\pi$
$199$	−1.23398			−0.0874743			−0.0437372	+	0.999043i	$0.513926\pi$
$200$		0			0
$201$	−6.33435	−	4.60218i	−0.446791	−	0.324612i
$202$		0			0
$203$	−6.77205	+	20.8422i	−0.475305	+	1.46284i
$204$		0			0
$205$	−11.8622	+	8.61836i	−0.828489	+	0.601933i
$206$		0			0
$207$	2.42090	+	7.45077i	0.168264	+	0.517864i
$208$		0			0
$209$	−0.464653	−	3.67514i	−0.0321407	−	0.254215i
$210$		0			0
$211$	−6.73792	−	20.7372i	−0.463858	−	1.42761i	−0.860413	−	0.509597i	$-0.829795\pi$
$211$	−6.73792	−	20.7372i	−0.463858	−	1.42761i	0.396556	−	0.918011i	$-0.370205\pi$
$212$		0			0
$213$	1.04710	−	0.760765i	0.0717463	−	0.0521267i
$214$		0			0
$215$	−4.66185	+	14.3477i	−0.317936	+	0.978505i
$216$		0			0
$217$	−2.36189	−	1.71601i	−0.160335	−	0.116490i
$218$		0			0
$219$	8.87891			0.599981
$220$		0			0
$221$	−6.65893			−0.447928
$222$		0			0
$223$	6.33131	+	4.59997i	0.423976	+	0.308037i	0.779236	−	0.626731i	$-0.215608\pi$
$223$	6.33131	+	4.59997i	0.423976	+	0.308037i	−0.355260	+	0.934768i	$0.615608\pi$
$224$		0			0
$225$	−0.844688	+	2.59968i	−0.0563125	+	0.173312i
$226$		0			0
$227$	−7.54543	+	5.48207i	−0.500808	+	0.363858i	−0.809325	−	0.587361i	$-0.800167\pi$
$227$	−7.54543	+	5.48207i	−0.500808	+	0.363858i	0.308518	+	0.951219i	$0.400167\pi$
$228$		0			0
$229$	−0.132306	−	0.407197i	−0.00874304	−	0.0269083i	0.946590	−	0.322440i	$-0.104503\pi$
$229$	−0.132306	−	0.407197i	−0.00874304	−	0.0269083i	−0.955333	+	0.295532i	$0.904503\pi$
$230$		0			0
$231$	−5.15020	−	5.48330i	−0.338858	−	0.360775i
$232$		0			0
$233$	−1.94320	−	5.98055i	−0.127303	−	0.391799i	0.867011	−	0.498290i	$-0.166038\pi$
$233$	−1.94320	−	5.98055i	−0.127303	−	0.391799i	−0.994314	+	0.106491i	$0.966038\pi$
$234$		0			0
$235$	−5.94669	+	4.32053i	−0.387919	+	0.281840i
$236$		0			0
$237$	−1.48447	+	4.56872i	−0.0964265	+	0.296770i
$238$		0			0
$239$	14.1276	+	10.2643i	0.913835	+	0.663940i	0.941982	−	0.335664i	$-0.108961\pi$
$239$	14.1276	+	10.2643i	0.913835	+	0.663940i	−0.0281465	+	0.999604i	$0.508961\pi$
$240$		0			0
$241$	1.43287			0.0922991			0.0461495	−	0.998935i	$-0.485305\pi$
$241$	1.43287			0.0922991			0.0461495	+	0.998935i	$0.485305\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−2.25977	−	1.64182i	−0.144371	−	0.104892i
$246$		0			0
$247$	−0.345147	+	1.06225i	−0.0219612	+	0.0675895i
$248$		0			0
$249$	5.32820	−	3.87116i	0.337661	−	0.245325i
$250$		0			0
$251$	−0.642832	−	1.97843i	−0.0405752	−	0.124878i	0.928717	−	0.370789i	$-0.120913\pi$
$251$	−0.642832	−	1.97843i	−0.0405752	−	0.124878i	−0.969292	+	0.245911i	$0.920913\pi$
$252$		0			0
$253$	−17.7886	−	18.9391i	−1.11836	−	1.19069i
$254$		0			0
$255$	−3.09790	−	9.53436i	−0.193998	−	0.597065i
$256$		0			0
$257$	−4.69515	+	3.41123i	−0.292875	+	0.212786i	−0.724514	−	0.689260i	$-0.757936\pi$
$257$	−4.69515	+	3.41123i	−0.292875	+	0.212786i	0.431638	+	0.902047i	$0.357936\pi$
$258$		0			0
$259$	0.0426475	−	0.131255i	0.00264998	−	0.00815582i
$260$		0			0
$261$	−7.81659	−	5.67909i	−0.483835	−	0.351527i
$262$		0			0
$263$	0.949567			0.0585528			0.0292764	−	0.999571i	$-0.490680\pi$
$263$	0.949567			0.0585528			0.0292764	+	0.999571i	$0.490680\pi$
$264$		0			0
$265$	8.65614			0.531743
$266$		0			0
$267$	−11.2005	−	8.13763i	−0.685458	−	0.498015i
$268$		0			0
$269$	3.05202	−	9.39315i	0.186085	−	0.572711i	−0.813880	−	0.581032i	$-0.802649\pi$
$269$	3.05202	−	9.39315i	0.186085	−	0.572711i	0.999965	+	0.00832177i	$0.00264893\pi$
$270$		0			0
$271$	16.1609	−	11.7416i	0.981703	−	0.713249i	0.0236143	−	0.999721i	$-0.492483\pi$
$271$	16.1609	−	11.7416i	0.981703	−	0.713249i	0.958089	+	0.286472i	$0.0924826\pi$
$272$		0			0
$273$	0.700907	+	2.15717i	0.0424208	+	0.130558i
$274$		0			0
$275$	−1.13716	−	8.99428i	−0.0685733	−	0.542376i
$276$		0			0
$277$	−9.02568	−	27.7782i	−0.542301	−	1.66903i	−0.727323	−	0.686295i	$-0.759236\pi$
$277$	−9.02568	−	27.7782i	−0.542301	−	1.66903i	0.185022	−	0.982734i	$-0.440764\pi$
$278$		0			0
$279$	1.04131	−	0.756558i	0.0623417	−	0.0452939i
$280$		0			0
$281$	−8.36944	+	25.7585i	−0.499279	+	1.53662i	0.310902	+	0.950442i	$0.399369\pi$
$281$	−8.36944	+	25.7585i	−0.499279	+	1.53662i	−0.810181	+	0.586180i	$0.800631\pi$
$282$		0			0
$283$	18.9196	+	13.7459i	1.12466	+	0.817110i	0.984908	−	0.173078i	$-0.0553711\pi$
$283$	18.9196	+	13.7459i	1.12466	+	0.817110i	0.139747	+	0.990187i	$0.455371\pi$
$284$		0			0
$285$	−1.68152			−0.0996048
$286$		0			0
$287$	22.0904			1.30395
$288$		0			0
$289$	−22.1196	−	16.0708i	−1.30115	−	0.945342i
$290$		0			0
$291$	0.345886	−	1.06453i	0.0202762	−	0.0624037i
$292$		0			0
$293$	9.91299	−	7.20221i	0.579123	−	0.420757i	−0.259285	−	0.965801i	$-0.583487\pi$
$293$	9.91299	−	7.20221i	0.579123	−	0.420757i	0.838408	+	0.545044i	$0.183487\pi$
$294$		0			0
$295$	−3.58378	−	11.0298i	−0.208656	−	0.642177i
$296$		0			0
$297$	3.00083	−	1.41245i	0.174126	−	0.0819587i
$298$		0			0
$299$	2.42090	+	7.45077i	0.140004	+	0.430889i
$300$		0			0
$301$	18.3878	−	13.3595i	1.05986	−	0.770032i
$302$		0			0
$303$	−4.74486	+	14.6032i	−0.272585	+	0.838930i
$304$		0			0
$305$	−0.318158	−	0.231155i	−0.0182177	−	0.0132359i
$306$		0			0
$307$	−1.33666			−0.0762872			−0.0381436	−	0.999272i	$-0.512144\pi$
$307$	−1.33666			−0.0762872			−0.0381436	+	0.999272i	$0.512144\pi$
$308$		0			0
$309$	−16.4218			−0.934205
$310$		0			0
$311$	18.5994	+	13.5132i	1.05467	+	0.766264i	0.973095	−	0.230403i	$-0.0740043\pi$
$311$	18.5994	+	13.5132i	1.05467	+	0.766264i	0.0815771	+	0.996667i	$0.474004\pi$
$312$		0			0
$313$	8.35378	−	25.7103i	0.472184	−	1.45323i	−0.377535	−	0.925995i	$-0.623228\pi$
$313$	8.35378	−	25.7103i	0.472184	−	1.45323i	0.849719	−	0.527236i	$-0.176772\pi$
$314$		0			0
$315$	−2.76259	+	2.00714i	−0.155654	+	0.113090i
$316$		0			0
$317$	−6.06152	−	18.6554i	−0.340449	−	1.04779i	−0.963975	−	0.265991i	$-0.914301\pi$
$317$	−6.06152	−	18.6554i	−0.340449	−	1.04779i	0.623527	−	0.781802i	$-0.285699\pi$
$318$		0			0
$319$	31.4777	+	6.00142i	1.76241	+	0.336015i
$320$		0			0
$321$	−0.0222133	−	0.0683656i	−0.00123983	−	0.00381579i
$322$		0			0
$323$	−6.01705	+	4.37164i	−0.334798	+	0.243245i
$324$		0			0
$325$	−0.844688	+	2.59968i	−0.0468548	+	0.144204i
$326$		0			0
$327$	13.4649	+	9.78284i	0.744612	+	0.540992i
$328$		0			0
$329$	11.0743			0.610544
$330$		0			0
$331$	−22.3645			−1.22927			−0.614633	−	0.788814i	$-0.710696\pi$
$331$	−22.3645			−1.22927			−0.614633	+	0.788814i	$0.710696\pi$
$332$		0			0
$333$	0.0492255	+	0.0357645i	0.00269754	+	0.00195988i
$334$		0			0
$335$	3.64257	−	11.2107i	0.199015	−	0.612505i
$336$		0			0
$337$	−23.0259	+	16.7293i	−1.25430	+	0.911304i	−0.998463	−	0.0554157i	$-0.982352\pi$
$337$	−23.0259	+	16.7293i	−1.25430	+	0.911304i	−0.255839	+	0.966719i	$0.582352\pi$
$338$		0			0
$339$	2.42216	+	7.45465i	0.131554	+	0.404881i
$340$		0			0
$341$	−2.05620	+	3.74110i	−0.111349	+	0.202592i
$342$		0			0
$343$	6.20677	+	19.1025i	0.335134	+	1.03144i
$344$		0			0
$345$	−9.54187	+	6.93257i	−0.513717	+	0.373237i
$346$		0			0
$347$	8.32007	−	25.6066i	0.446645	−	1.37463i	−0.434025	−	0.900901i	$-0.642907\pi$
$347$	8.32007	−	25.6066i	0.446645	−	1.37463i	0.880670	−	0.473731i	$-0.157093\pi$
$348$		0			0
$349$	−5.19255	−	3.77261i	−0.277951	−	0.201943i	0.440072	−	0.897962i	$-0.354953\pi$
$349$	−5.19255	−	3.77261i	−0.277951	−	0.201943i	−0.718023	+	0.696019i	$0.754953\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−26.6873			−1.42042			−0.710210	−	0.703990i	$-0.751400\pi$
$353$	−26.6873			−1.42042			−0.710210	+	0.703990i	$0.751400\pi$
$354$		0			0
$355$	1.57641	+	1.14533i	0.0836674	+	0.0607879i
$356$		0			0
$357$	−4.66729	+	14.3644i	−0.247019	+	0.760247i
$358$		0			0
$359$	6.26712	−	4.55333i	0.330766	−	0.240315i	−0.409990	−	0.912090i	$-0.634468\pi$
$359$	6.26712	−	4.55333i	0.330766	−	0.240315i	0.740755	+	0.671775i	$0.234468\pi$
$360$		0			0
$361$	−5.48582	−	16.8836i	−0.288727	−	0.888612i
$362$		0			0
$363$	−7.00996	+	8.47705i	−0.367928	+	0.444930i
$364$		0			0
$365$	4.13069	+	12.7130i	0.216210	+	0.665427i
$366$		0			0
$367$	−13.0054	+	9.44896i	−0.678875	+	0.493232i	−0.872984	−	0.487748i	$-0.837818\pi$
$367$	−13.0054	+	9.44896i	−0.678875	+	0.493232i	0.194109	+	0.980980i	$0.437818\pi$
$368$		0			0
$369$	−3.00959	+	9.26257i	−0.156673	+	0.482190i
$370$		0			0
$371$	−10.5506	−	7.66549i	−0.547762	−	0.397973i
$372$		0			0
$373$	32.3790			1.67652			0.838260	−	0.545271i	$-0.183573\pi$
$373$	32.3790			1.67652			0.838260	+	0.545271i	$0.183573\pi$
$374$		0			0
$375$	−11.6427			−0.601229
$376$		0			0
$377$	−7.81659	−	5.67909i	−0.402575	−	0.292488i
$378$		0			0
$379$	8.13449	−	25.0354i	0.417841	−	1.28598i	−0.491845	−	0.870683i	$-0.663677\pi$
$379$	8.13449	−	25.0354i	0.417841	−	1.28598i	0.909685	−	0.415298i	$-0.136323\pi$
$380$		0			0
$381$	6.64658	−	4.82902i	0.340515	−	0.247398i
$382$		0			0
$383$	−10.2148	−	31.4380i	−0.521953	−	1.60640i	−0.770264	−	0.637725i	$-0.779876\pi$
$383$	−10.2148	−	31.4380i	−0.521953	−	1.60640i	0.248312	−	0.968680i	$-0.420124\pi$
$384$		0			0
$385$	5.45508	−	9.92511i	0.278017	−	0.505831i
$386$		0			0
$387$	3.09655	+	9.53019i	0.157406	+	0.484447i
$388$		0			0
$389$	−0.196522	+	0.142781i	−0.00996405	+	0.00723931i	−0.592756	−	0.805382i	$-0.701960\pi$
$389$	−0.196522	+	0.142781i	−0.00996405	+	0.00723931i	0.582792	+	0.812621i	$0.301960\pi$
$390$		0			0
$391$	−16.1206	+	49.6141i	−0.815254	+	2.50909i
$392$		0			0
$393$	−4.28929	−	3.11635i	−0.216366	−	0.157199i
$394$		0			0
$395$	−7.23218			−0.363890
$396$		0			0
$397$	16.5772			0.831986			0.415993	−	0.909368i	$-0.363434\pi$
$397$	16.5772			0.831986			0.415993	+	0.909368i	$0.363434\pi$
$398$		0			0
$399$	2.04954	+	1.48908i	0.102606	+	0.0745473i
$400$		0			0
$401$	−10.3449	+	31.8383i	−0.516600	+	1.58993i	0.263752	+	0.964591i	$0.415040\pi$
$401$	−10.3449	+	31.8383i	−0.516600	+	1.58993i	−0.780352	+	0.625341i	$0.784960\pi$
$402$		0			0
$403$	1.04131	−	0.756558i	0.0518714	−	0.0376868i
$404$		0			0
$405$	−0.465225	−	1.43182i	−0.0231172	−	0.0711475i
$406$		0			0
$407$	−0.198233	−	0.0377944i	−0.00982605	−	0.00187340i
$408$		0			0
$409$	−1.60932	−	4.95298i	−0.0795758	−	0.244909i	0.903352	−	0.428899i	$-0.141099\pi$
$409$	−1.60932	−	4.95298i	−0.0795758	−	0.244909i	−0.982928	+	0.183990i	$0.941099\pi$
$410$		0			0
$411$	8.69383	−	6.31644i	0.428835	−	0.311567i
$412$		0			0
$413$	−5.39932	+	16.6174i	−0.265683	+	0.817688i
$414$		0			0
$415$	8.02161	+	5.82804i	0.393765	+	0.286087i
$416$		0			0
$417$	8.73207			0.427612
$418$		0			0
$419$	−35.3250			−1.72574			−0.862868	−	0.505429i	$-0.831334\pi$
$419$	−35.3250			−1.72574			−0.862868	+	0.505429i	$0.831334\pi$
$420$		0			0
$421$	−26.5195	−	19.2676i	−1.29248	−	0.939044i	−0.292630	−	0.956226i	$-0.594531\pi$
$421$	−26.5195	−	19.2676i	−1.29248	−	0.939044i	−0.999852	+	0.0171819i	$0.994531\pi$
$422$		0			0
$423$	−1.50876	+	4.64348i	−0.0733583	+	0.225774i
$424$		0			0
$425$	−14.7257	+	10.6988i	−0.714301	+	0.518970i
$426$		0			0
$427$	0.183090	+	0.563493i	0.00886034	+	0.0272693i
$428$		0			0
$429$	3.00083	−	1.41245i	0.144881	−	0.0681938i
$430$		0			0
$431$	−10.4082	−	32.0331i	−0.501345	−	1.54298i	−0.806829	−	0.590785i	$-0.798818\pi$
$431$	−10.4082	−	32.0331i	−0.501345	−	1.54298i	0.305484	−	0.952197i	$-0.401182\pi$
$432$		0			0
$433$	0.0685117	−	0.0497766i	0.00329246	−	0.00239211i	−0.586138	−	0.810211i	$-0.699352\pi$
$433$	0.0685117	−	0.0497766i	0.00329246	−	0.00239211i	0.589430	+	0.807819i	$0.299352\pi$
$434$		0			0
$435$	4.49493	−	13.8340i	0.215515	−	0.663288i
$436$		0			0
$437$	7.07903	+	5.14322i	0.338636	+	0.246034i
$438$		0			0
$439$	12.1241			0.578654			0.289327	−	0.957230i	$-0.406569\pi$
$439$	12.1241			0.578654			0.289327	+	0.957230i	$0.406569\pi$
$440$		0			0
$441$	−1.85535			−0.0883499
$442$		0			0
$443$	−13.8413	−	10.0563i	−0.657622	−	0.477790i	0.208237	−	0.978078i	$-0.433227\pi$
$443$	−13.8413	−	10.0563i	−0.657622	−	0.477790i	−0.865859	+	0.500288i	$0.833227\pi$
$444$		0			0
$445$	6.44084	−	19.8229i	0.305325	−	0.939694i
$446$		0			0
$447$	8.83825	−	6.42136i	0.418035	−	0.303720i
$448$		0			0
$449$	−12.0491	−	37.0832i	−0.568631	−	1.75007i	−0.656909	−	0.753970i	$-0.728136\pi$
$449$	−12.0491	−	37.0832i	−0.568631	−	1.75007i	0.0882777	−	0.996096i	$-0.471864\pi$
$450$		0			0
$451$	−4.05166	−	32.0463i	−0.190785	−	1.50900i
$452$		0			0
$453$	−2.13099	−	6.55851i	−0.100123	−	0.308146i
$454$		0			0
$455$	−2.76259	+	2.00714i	−0.129512	+	0.0940962i
$456$		0			0
$457$	4.39463	−	13.5253i	0.205572	−	0.632686i	−0.794117	−	0.607764i	$-0.792066\pi$
$457$	4.39463	−	13.5253i	0.205572	−	0.632686i	0.999689	−	0.0249212i	$-0.00793350\pi$
$458$		0			0
$459$	−5.38719	−	3.91402i	−0.251452	−	0.182691i
$460$		0			0
$461$	27.7126			1.29070			0.645352	−	0.763886i	$-0.276711\pi$
$461$	27.7126			1.29070			0.645352	+	0.763886i	$0.276711\pi$
$462$		0			0
$463$	27.0482			1.25704			0.628518	−	0.777795i	$-0.283662\pi$
$463$	27.0482			1.25704			0.628518	+	0.777795i	$0.283662\pi$
$464$		0			0
$465$	1.56770	+	1.13900i	0.0727002	+	0.0528198i
$466$		0			0
$467$	0.321353	−	0.989024i	0.0148705	−	0.0457666i	−0.943346	−	0.331811i	$-0.892340\pi$
$467$	0.321353	−	0.989024i	0.0148705	−	0.0457666i	0.958216	+	0.286044i	$0.0923404\pi$
$468$		0			0
$469$	−14.3675	+	10.4386i	−0.663428	+	0.482009i
$470$		0			0
$471$	−3.04722	−	9.37837i	−0.140408	−	0.432132i
$472$		0			0
$473$	−22.7531	−	24.2248i	−1.04619	−	1.11386i
$474$		0			0
$475$	0.943448	+	2.90363i	0.0432884	+	0.133228i
$476$		0			0
$477$	4.65159	−	3.37958i	0.212982	−	0.154740i
$478$		0			0
$479$	3.22824	−	9.93551i	0.147502	−	0.453965i	−0.849822	−	0.527070i	$-0.823291\pi$
$479$	3.22824	−	9.93551i	0.147502	−	0.453965i	0.997324	+	0.0731045i	$0.0232907\pi$
$480$		0			0
$481$	0.0492255	+	0.0357645i	0.00224449	+	0.00163072i
$482$		0			0
$483$	17.7694			0.808536
$484$		0			0
$485$	1.68512			0.0765175
$486$		0			0
$487$	29.4121	+	21.3692i	1.33279	+	0.968329i	0.999676	+	0.0254424i	$0.00809944\pi$
$487$	29.4121	+	21.3692i	1.33279	+	0.968329i	0.333114	+	0.942887i	$0.391901\pi$
$488$		0			0
$489$	1.37080	−	4.21890i	0.0619898	−	0.190785i
$490$		0			0
$491$	−11.4455	+	8.31565i	−0.516529	+	0.375280i	−0.815295	−	0.579046i	$-0.803425\pi$
$491$	−11.4455	+	8.31565i	−0.516529	+	0.375280i	0.298766	+	0.954326i	$0.403425\pi$
$492$		0			0
$493$	−19.8814	−	61.1886i	−0.895412	−	2.75579i
$494$		0			0
$495$	3.41843	+	3.63953i	0.153647	+	0.163585i
$496$		0			0
$497$	−0.907177	−	2.79200i	−0.0406925	−	0.125238i
$498$		0			0
$499$	17.1398	−	12.4528i	0.767281	−	0.557462i	−0.133854	−	0.991001i	$-0.542735\pi$
$499$	17.1398	−	12.4528i	0.767281	−	0.557462i	0.901135	+	0.433539i	$0.142735\pi$
$500$		0			0
$501$	−2.75833	+	8.48928i	−0.123233	+	0.379273i
$502$		0			0
$503$	8.27990	+	6.01570i	0.369183	+	0.268227i	0.756872	−	0.653563i	$-0.226727\pi$
$503$	8.27990	+	6.01570i	0.369183	+	0.268227i	−0.387689	+	0.921790i	$0.626727\pi$
$504$		0			0
$505$	−23.1165			−1.02867
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	21.8714	+	15.8905i	0.969431	+	0.704333i	0.955322	−	0.295567i	$-0.0955087\pi$
$509$	21.8714	+	15.8905i	0.969431	+	0.704333i	0.0141094	+	0.999900i	$0.495509\pi$
$510$		0			0
$511$	6.22329	−	19.1533i	0.275302	−	0.847293i
$512$		0			0
$513$	−0.903606	+	0.656508i	−0.0398952	+	0.0289856i
$514$		0			0
$515$	−7.63985	−	23.5130i	−0.336652	−	1.03611i
$516$		0			0
$517$	−2.03116	−	16.0653i	−0.0893303	−	0.706552i
$518$		0			0
$519$	−5.28348	−	16.2609i	−0.231919	−	0.713774i
$520$		0			0
$521$	−32.2280	+	23.4150i	−1.41193	+	1.02583i	−0.418896	+	0.908034i	$0.637583\pi$
$521$	−32.2280	+	23.4150i	−1.41193	+	1.02583i	−0.993038	+	0.117796i	$0.962417\pi$
$522$		0			0
$523$	−7.67727	+	23.6282i	−0.335704	+	1.03319i	0.630671	+	0.776051i	$0.282780\pi$
$523$	−7.67727	+	23.6282i	−0.335704	+	1.03319i	−0.966374	+	0.257139i	$0.917220\pi$
$524$		0			0
$525$	5.01591	+	3.64427i	0.218912	+	0.159049i
$526$		0			0
$527$	8.57092			0.373355
$528$		0			0
$529$	38.3747			1.66846
$530$		0			0
$531$	−6.23212	−	4.52790i	−0.270451	−	0.196494i
$532$		0			0
$533$	−3.00959	+	9.26257i	−0.130360	+	0.401206i
$534$		0			0
$535$	0.0875528	−	0.0636108i	0.00378524	−	0.00275013i
$536$		0			0
$537$	1.10518	+	3.40139i	0.0476920	+	0.146781i
$538$		0			0
$539$	5.56758	−	2.62059i	0.239813	−	0.112877i
$540$		0			0
$541$	4.08917	+	12.5852i	0.175807	+	0.541079i	0.999669	−	0.0257113i	$-0.00818507\pi$
$541$	4.08917	+	12.5852i	0.175807	+	0.541079i	−0.823862	+	0.566790i	$0.808185\pi$
$542$		0			0
$543$	9.57408	−	6.95598i	0.410863	−	0.298509i
$544$		0			0
$545$	−7.74300	+	23.8305i	−0.331674	+	1.02079i
$546$		0			0
$547$	0.846424	+	0.614963i	0.0361905	+	0.0262939i	0.605733	−	0.795668i	$-0.292880\pi$
$547$	0.846424	+	0.614963i	0.0361905	+	0.0262939i	−0.569543	+	0.821962i	$0.692880\pi$
$548$		0			0
$549$	−0.261219			−0.0111485
$550$		0			0
$551$	−10.7915			−0.459733
$552$		0			0
$553$	8.81503	+	6.40449i	0.374853	+	0.272347i
$554$		0			0
$555$	−0.0283072	+	0.0871205i	−0.00120157	+	0.00369806i
$556$		0			0
$557$	5.51068	−	4.00375i	0.233495	−	0.169644i	−0.464885	−	0.885371i	$-0.653904\pi$
$557$	5.51068	−	4.00375i	0.233495	−	0.169644i	0.698380	+	0.715727i	$0.253904\pi$
$558$		0			0
$559$	3.09655	+	9.53019i	0.130970	+	0.403084i
$560$		0			0
$561$	21.6944	+	4.13617i	0.915938	+	0.174629i
$562$		0			0
$563$	−4.48043	−	13.7894i	−0.188828	−	0.581152i	0.811166	−	0.584817i	$-0.198834\pi$
$563$	−4.48043	−	13.7894i	−0.188828	−	0.581152i	−0.999993	+	0.00366453i	$0.998834\pi$
$564$		0			0
$565$	−9.54684	+	6.93618i	−0.401638	+	0.291807i
$566$		0			0
$567$	−0.700907	+	2.15717i	−0.0294353	+	0.0905926i
$568$		0			0
$569$	−20.0014	−	14.5319i	−0.838502	−	0.609208i	0.0834495	−	0.996512i	$-0.473406\pi$
$569$	−20.0014	−	14.5319i	−0.838502	−	0.609208i	−0.921952	+	0.387304i	$0.873406\pi$
$570$		0			0
$571$	−26.4971			−1.10887			−0.554434	−	0.832228i	$-0.687065\pi$
$571$	−26.4971			−1.10887			−0.554434	+	0.832228i	$0.687065\pi$
$572$		0			0
$573$	2.51438			0.105040
$574$		0			0
$575$	17.3247	+	12.5871i	0.722491	+	0.524920i
$576$		0			0
$577$	−5.85430	+	18.0177i	−0.243718	+	0.750085i	0.752127	+	0.659018i	$0.229028\pi$
$577$	−5.85430	+	18.0177i	−0.243718	+	0.750085i	−0.995845	+	0.0910674i	$0.970972\pi$
$578$		0			0
$579$	3.54727	−	2.57724i	0.147419	−	0.107106i
$580$		0			0
$581$	−4.61619	−	14.2072i	−0.191512	−	0.589412i
$582$		0			0
$583$	−9.18514	+	16.7117i	−0.380409	+	0.692127i
$584$		0			0
$585$	−0.465225	−	1.43182i	−0.0192347	−	0.0591983i
$586$		0			0
$587$	22.5054	−	16.3511i	0.928897	−	0.674883i	−0.0168255	−	0.999858i	$-0.505356\pi$
$587$	22.5054	−	16.3511i	0.928897	−	0.674883i	0.945723	+	0.324975i	$0.105356\pi$
$588$		0			0
$589$	0.444250	−	1.36726i	0.0183050	−	0.0563370i
$590$		0			0
$591$	14.0182	+	10.1849i	0.576633	+	0.418949i
$592$		0			0
$593$	25.9426			1.06534			0.532668	−	0.846324i	$-0.321189\pi$
$593$	25.9426			1.06534			0.532668	+	0.846324i	$0.321189\pi$
$594$		0			0
$595$	−22.7386			−0.932191
$596$		0			0
$597$	−0.998308	−	0.725313i	−0.0408580	−	0.0296851i
$598$		0			0
$599$	2.14239	−	6.59361i	0.0875359	−	0.269408i	−0.897701	−	0.440606i	$-0.854764\pi$
$599$	2.14239	−	6.59361i	0.0875359	−	0.269408i	0.985237	+	0.171198i	$0.0547637\pi$
$600$		0			0
$601$	12.6977	−	9.22544i	0.517951	−	0.376313i	−0.297880	−	0.954603i	$-0.596280\pi$
$601$	12.6977	−	9.22544i	0.517951	−	0.376313i	0.815831	+	0.578290i	$0.196280\pi$
$602$		0			0
$603$	−2.41951	−	7.44648i	−0.0985299	−	0.303244i
$604$		0			0
$605$	−15.3988	−	6.09324i	−0.626050	−	0.247725i
$606$		0			0
$607$	9.47019	+	29.1463i	0.384383	+	1.18301i	0.936927	+	0.349526i	$0.113657\pi$
$607$	9.47019	+	29.1463i	0.384383	+	1.18301i	−0.552543	+	0.833484i	$0.686343\pi$
$608$		0			0
$609$	−17.7295	+	12.8812i	−0.718434	+	0.521973i
$610$		0			0
$611$	−1.50876	+	4.64348i	−0.0610378	+	0.187855i
$612$		0			0
$613$	−16.3433	−	11.8741i	−0.660099	−	0.479590i	0.206597	−	0.978426i	$-0.433761\pi$
$613$	−16.3433	−	11.8741i	−0.660099	−	0.479590i	−0.866696	+	0.498836i	$0.833761\pi$
$614$		0			0
$615$	−14.6624			−0.591246
$616$		0			0
$617$	47.9803			1.93161			0.965807	−	0.259261i	$-0.0834790\pi$
$617$	47.9803			1.93161			0.965807	+	0.259261i	$0.0834790\pi$
$618$		0			0
$619$	−19.0257	−	13.8230i	−0.764707	−	0.555592i	0.135644	−	0.990758i	$-0.456690\pi$
$619$	−19.0257	−	13.8230i	−0.764707	−	0.555592i	−0.900350	+	0.435166i	$0.856690\pi$
$620$		0			0
$621$	−2.42090	+	7.45077i	−0.0971474	+	0.298989i
$622$		0			0
$623$	−25.4047	+	18.4576i	−1.01782	+	0.739489i
$624$		0			0
$625$	−1.19306	−	3.67186i	−0.0477224	−	0.146874i
$626$		0			0
$627$	1.78428	−	3.24637i	0.0712574	−	0.129648i
$628$		0			0
$629$	0.125204	+	0.385339i	0.00499223	+	0.0153645i
$630$		0			0
$631$	29.2272	−	21.2348i	1.16352	−	0.845344i	0.173298	−	0.984869i	$-0.444558\pi$
$631$	29.2272	−	21.2348i	1.16352	−	0.845344i	0.990219	+	0.139525i	$0.0445575\pi$
$632$		0			0
$633$	6.73792	−	20.7372i	0.267808	−	0.824229i
$634$		0			0
$635$	10.0064	+	7.27010i	0.397093	+	0.288505i
$636$		0			0
$637$	−1.85535			−0.0735115
$638$		0			0
$639$	1.29429			0.0512013
$640$		0			0
$641$	2.93702	+	2.13387i	0.116005	+	0.0842827i	0.644275	−	0.764794i	$-0.277159\pi$
$641$	2.93702	+	2.13387i	0.116005	+	0.0842827i	−0.528270	+	0.849076i	$0.677159\pi$
$642$		0			0
$643$	4.62453	−	14.2329i	0.182374	−	0.561289i	−0.817519	−	0.575901i	$-0.804651\pi$
$643$	4.62453	−	14.2329i	0.182374	−	0.561289i	0.999893	+	0.0146122i	$0.00465136\pi$
$644$		0			0
$645$	−12.2049	+	8.86737i	−0.480567	+	0.349152i
$646$		0			0
$647$	−6.42522	−	19.7748i	−0.252601	−	0.777427i	−0.994293	−	0.106686i	$-0.965976\pi$
$647$	−6.42522	−	19.7748i	−0.252601	−	0.777427i	0.741691	−	0.670741i	$-0.234024\pi$
$648$		0			0
$649$	25.0970	+	4.78490i	0.985143	+	0.187824i
$650$		0			0
$651$	−0.902160	−	2.77656i	−0.0353584	−	0.108822i
$652$		0			0
$653$	21.2194	−	15.4168i	0.830379	−	0.603306i	−0.0892876	−	0.996006i	$-0.528459\pi$
$653$	21.2194	−	15.4168i	0.830379	−	0.603306i	0.919667	+	0.392700i	$0.128459\pi$
$654$		0			0
$655$	2.46656	−	7.59129i	0.0963764	−	0.296616i
$656$		0			0
$657$	7.18319	+	5.21889i	0.280243	+	0.203608i
$658$		0			0
$659$	29.9256			1.16574			0.582868	−	0.812567i	$-0.301931\pi$
$659$	29.9256			1.16574			0.582868	+	0.812567i	$0.301931\pi$
$660$		0			0
$661$	−44.4836			−1.73021			−0.865105	−	0.501591i	$-0.832748\pi$
$661$	−44.4836			−1.73021			−0.865105	+	0.501591i	$0.832748\pi$
$662$		0			0
$663$	−5.38719	−	3.91402i	−0.209221	−	0.152008i
$664$		0			0
$665$	−1.17859	+	3.62733i	−0.0457038	+	0.140662i
$666$		0			0
$667$	−61.2367	+	44.4911i	−2.37110	+	1.72270i
$668$		0			0
$669$	2.41835	+	7.44291i	0.0934987	+	0.287759i
$670$		0			0
$671$	0.783872	−	0.368958i	0.0302611	−	0.0142435i
$672$		0			0
$673$	7.77374	+	23.9251i	0.299655	+	0.922245i	0.981618	+	0.190857i	$0.0611268\pi$
$673$	7.77374	+	23.9251i	0.299655	+	0.922245i	−0.681962	+	0.731387i	$0.738873\pi$
$674$		0			0
$675$	−2.21142	+	1.60669i	−0.0851176	+	0.0618416i
$676$		0			0
$677$	−10.2898	+	31.6688i	−0.395469	+	1.21713i	0.533126	+	0.846036i	$0.321017\pi$
$677$	−10.2898	+	31.6688i	−0.395469	+	1.21713i	−0.928596	+	0.371093i	$0.878983\pi$
$678$		0			0
$679$	−2.05393	−	1.49227i	−0.0788227	−	0.0572680i
$680$		0			0
$681$	−9.32666			−0.357398
$682$		0			0
$683$	14.3590			0.549431			0.274715	−	0.961526i	$-0.411416\pi$
$683$	14.3590			0.549431			0.274715	+	0.961526i	$0.411416\pi$
$684$		0			0
$685$	13.0886	+	9.50941i	0.500089	+	0.363336i
$686$		0			0
$687$	0.132306	−	0.407197i	0.00504780	−	0.0155355i
$688$		0			0
$689$	4.65159	−	3.37958i	0.177211	−	0.128752i
$690$		0			0
$691$	10.5816	+	32.5667i	0.402542	+	1.23890i	0.922930	+	0.384967i	$0.125787\pi$
$691$	10.5816	+	32.5667i	0.402542	+	1.23890i	−0.520389	+	0.853930i	$0.674213\pi$
$692$		0			0
$693$	−0.943595	−	7.46330i	−0.0358442	−	0.283507i
$694$		0			0
$695$	4.06238	+	12.5027i	0.154095	+	0.474256i
$696$		0			0
$697$	−52.4671	+	38.1196i	−1.98733	+	1.44388i
$698$		0			0
$699$	1.94320	−	5.98055i	0.0734985	−	0.226205i
$700$		0			0
$701$	−0.605704	−	0.440070i	−0.0228771	−	0.0166212i	0.576288	−	0.817247i	$-0.304501\pi$
$701$	−0.605704	−	0.440070i	−0.0228771	−	0.0166212i	−0.599165	+	0.800626i	$0.704501\pi$
$702$		0			0
$703$	0.0679602			0.00256317
$704$		0			0
$705$	−7.35052			−0.276836
$706$		0			0
$707$	28.1758	+	20.4709i	1.05966	+	0.769888i
$708$		0			0
$709$	−0.460908	+	1.41853i	−0.0173098	+	0.0532740i	−0.959338	−	0.282259i	$-0.908916\pi$
$709$	−0.460908	+	1.41853i	−0.0173098	+	0.0532740i	0.942029	+	0.335533i	$0.108916\pi$
$710$		0			0
$711$	−3.88638	+	2.82362i	−0.145751	+	0.105894i
$712$		0			0
$713$	−3.11602	−	9.59012i	−0.116696	−	0.359153i
$714$		0			0
$715$	3.41843	+	3.63953i	0.127842	+	0.136111i
$716$		0			0
$717$	5.39625	+	16.6079i	0.201526	+	0.620235i
$718$		0			0
$719$	18.4898	−	13.4336i	0.689552	−	0.500989i	−0.186961	−	0.982367i	$-0.559864\pi$
$719$	18.4898	−	13.4336i	0.689552	−	0.500989i	0.876513	+	0.481378i	$0.159864\pi$
$720$		0			0
$721$	−11.5102	+	35.4247i	−0.428661	+	1.31928i
$722$		0			0
$723$	1.15921	+	0.842218i	0.0431116	+	0.0313224i
$724$		0			0
$725$	−26.4103			−0.980854
$726$		0			0
$727$	−47.1500			−1.74870			−0.874349	−	0.485298i	$-0.838711\pi$
$727$	−47.1500			−1.74870			−0.874349	+	0.485298i	$0.838711\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−20.6197	+	63.4608i	−0.762646	+	2.34718i
$732$		0			0
$733$	25.2036	−	18.3115i	0.930917	−	0.676351i	−0.0153005	−	0.999883i	$-0.504870\pi$
$733$	25.2036	−	18.3115i	0.930917	−	0.676351i	0.946217	+	0.323532i	$0.104870\pi$
$734$		0			0
$735$	−0.863154	−	2.65652i	−0.0318379	−	0.0979871i
$736$		0			0
$737$	17.7783	+	18.9282i	0.654873	+	0.697228i
$738$		0			0
$739$	0.535125	+	1.64695i	0.0196849	+	0.0605839i	0.960416	−	0.278568i	$-0.0898598\pi$
$739$	0.535125	+	1.64695i	0.0196849	+	0.0605839i	−0.940732	+	0.339152i	$0.889860\pi$
$740$		0			0
$741$	−0.903606	+	0.656508i	−0.0331948	+	0.0241174i
$742$		0			0
$743$	7.60350	−	23.4012i	0.278945	−	0.858505i	−0.709203	−	0.705004i	$-0.750945\pi$
$743$	7.60350	−	23.4012i	0.278945	−	0.858505i	0.988148	−	0.153501i	$-0.0490549\pi$
$744$		0			0
$745$	13.3060	+	9.66737i	0.487494	+	0.354185i
$746$		0			0
$747$	6.58602			0.240970
$748$		0			0
$749$	−0.163046			−0.00595756
$750$		0			0
$751$	6.64918	+	4.83091i	0.242632	+	0.176282i	0.702455	−	0.711728i	$-0.252087\pi$
$751$	6.64918	+	4.83091i	0.242632	+	0.176282i	−0.459823	+	0.888011i	$0.652087\pi$
$752$		0			0
$753$	0.642832	−	1.97843i	0.0234261	−	0.0720982i
$754$		0			0
$755$	8.39919	−	6.10237i	0.305678	−	0.222088i
$756$		0			0
$757$	13.0269	+	40.0926i	0.473469	+	1.45719i	0.848011	+	0.529979i	$0.177800\pi$
$757$	13.0269	+	40.0926i	0.473469	+	1.45719i	−0.374541	+	0.927210i	$0.622200\pi$
$758$		0			0
$759$	−3.25913	−	25.7779i	−0.118299	−	0.935678i
$760$		0			0
$761$	−3.93266	−	12.1035i	−0.142559	−	0.438751i	0.854130	−	0.520059i	$-0.174090\pi$
$761$	−3.93266	−	12.1035i	−0.142559	−	0.438751i	−0.996689	+	0.0813084i	$0.974090\pi$
$762$		0			0
$763$	30.5409	−	22.1893i	1.10565	−	0.803305i
$764$		0			0
$765$	3.09790	−	9.53436i	0.112005	−	0.344716i
$766$		0			0
$767$	−6.23212	−	4.52790i	−0.225029	−	0.163493i
$768$		0			0
$769$	−40.5702			−1.46300			−0.731499	−	0.681843i	$-0.761179\pi$
$769$	−40.5702			−1.46300			−0.731499	+	0.681843i	$0.761179\pi$
$770$		0			0
$771$	−5.80352			−0.209009
$772$		0			0
$773$	−1.71787	−	1.24810i	−0.0617873	−	0.0448911i	0.556463	−	0.830872i	$-0.312158\pi$
$773$	−1.71787	−	1.24810i	−0.0617873	−	0.0448911i	−0.618250	+	0.785981i	$0.712158\pi$
$774$		0			0
$775$	1.08723	−	3.34613i	0.0390543	−	0.120197i
$776$		0			0
$777$	0.111653	−	0.0811203i	0.00400551	−	0.00291017i
$778$		0			0
$779$	3.36147	+	10.3455i	0.120437	+	0.370667i
$780$		0			0
$781$	−3.88394	+	1.82812i	−0.138978	+	0.0654153i
$782$		0			0
$783$	−2.98567	−	9.18895i	−0.106699	−	0.328386i
$784$		0			0
$785$	12.0105	−	8.72611i	0.428672	−	0.311448i
$786$		0			0
$787$	−10.8717	+	33.4596i	−0.387533	+	1.19270i	0.547093	+	0.837072i	$0.315734\pi$
$787$	−10.8717	+	33.4596i	−0.387533	+	1.19270i	−0.934626	+	0.355632i	$0.884266\pi$
$788$		0			0
$789$	0.768216	+	0.558141i	0.0273492	+	0.0198704i
$790$		0			0
$791$	17.7787			0.632136
$792$		0			0
$793$	−0.261219			−0.00927614
$794$		0			0
$795$	7.00297	+	5.08795i	0.248370	+	0.180451i
$796$		0			0
$797$	−13.3054	+	40.9498i	−0.471302	+	1.45052i	0.379580	+	0.925159i	$0.376069\pi$
$797$	−13.3054	+	40.9498i	−0.471302	+	1.45052i	−0.850881	+	0.525358i	$0.823931\pi$
$798$		0			0
$799$	−26.3026	+	19.1100i	−0.930519	+	0.676062i
$800$		0			0
$801$	−4.27820	−	13.1670i	−0.151163	−	0.465231i
$802$		0			0
$803$	−28.9269	−	5.51510i	−1.02081	−	0.194624i
$804$		0			0
$805$	8.26677	+	25.4425i	0.291366	+	0.896731i
$806$		0			0
$807$	7.99029	−	5.80529i	0.281272	−	0.204356i
$808$		0			0
$809$	−11.2354	+	34.5790i	−0.395015	+	1.21573i	0.533934	+	0.845526i	$0.320713\pi$
$809$	−11.2354	+	34.5790i	−0.395015	+	1.21573i	−0.928950	+	0.370206i	$0.879287\pi$
$810$		0			0
$811$	13.3021	+	9.66451i	0.467099	+	0.339367i	0.796309	−	0.604889i	$-0.206783\pi$
$811$	13.3021	+	9.66451i	0.467099	+	0.339367i	−0.329211	+	0.944256i	$0.606783\pi$
$812$		0			0
$813$	19.9759			0.700587
$814$		0			0
$815$	6.67842			0.233935
$816$		0			0
$817$	9.05471	+	6.57863i	0.316784	+	0.230157i
$818$		0			0
$819$	−0.700907	+	2.15717i	−0.0244917	+	0.0753776i
$820$		0			0
$821$	33.0445	−	24.0083i	1.15326	−	0.837894i	0.164351	−	0.986402i	$-0.447447\pi$
$821$	33.0445	−	24.0083i	1.15326	−	0.837894i	0.988911	+	0.148508i	$0.0474471\pi$
$822$		0			0
$823$	2.26043	+	6.95690i	0.0787938	+	0.242502i	0.982693	−	0.185244i	$-0.0593076\pi$
$823$	2.26043	+	6.95690i	0.0787938	+	0.242502i	−0.903899	+	0.427747i	$0.859308\pi$
$824$		0			0
$825$	4.36673	−	7.94493i	0.152030	−	0.276607i
$826$		0			0
$827$	5.09216	+	15.6721i	0.177072	+	0.544971i	0.999722	−	0.0235770i	$-0.00750549\pi$
$827$	5.09216	+	15.6721i	0.177072	+	0.544971i	−0.822650	+	0.568548i	$0.807505\pi$
$828$		0			0
$829$	−19.4945	+	14.1636i	−0.677073	+	0.491923i	−0.872385	−	0.488819i	$-0.837428\pi$
$829$	−19.4945	+	14.1636i	−0.677073	+	0.491923i	0.195312	+	0.980741i	$0.437428\pi$
$830$		0			0
$831$	9.02568	−	27.7782i	0.313097	−	0.963615i
$832$		0			0
$833$	−9.99510	−	7.26186i	−0.346310	−	0.251609i
$834$		0			0
$835$	−13.4383			−0.465053
$836$		0			0
$837$	1.28713			0.0444898
$838$		0			0
$839$	−10.1900	−	7.40344i	−0.351797	−	0.255595i	0.397826	−	0.917461i	$-0.369765\pi$
$839$	−10.1900	−	7.40344i	−0.351797	−	0.255595i	−0.749622	+	0.661866i	$0.769765\pi$
$840$		0			0
$841$	19.8856	−	61.2015i	0.685710	−	2.11040i
$842$		0			0
$843$	−21.9115	+	15.9196i	−0.754671	+	0.548301i
$844$		0			0
$845$	−0.465225	−	1.43182i	−0.0160042	−	0.0492560i
$846$		0			0
$847$	13.3731	+	21.0633i	0.459506	+	0.723744i
$848$		0			0
$849$	7.22665	+	22.2414i	0.248018	+	0.763321i
$850$		0			0
$851$	0.385643	−	0.280186i	0.0132197	−	0.00960465i
$852$		0			0
$853$	−7.07481	+	21.7740i	−0.242237	+	0.745528i	0.753842	+	0.657056i	$0.228198\pi$
$853$	−7.07481	+	21.7740i	−0.242237	+	0.745528i	−0.996079	+	0.0884724i	$0.971802\pi$
$854$		0			0
$855$	−1.36038	−	0.988374i	−0.0465240	−	0.0338017i
$856$		0			0
$857$	−26.0696			−0.890522			−0.445261	−	0.895401i	$-0.646889\pi$
$857$	−26.0696			−0.890522			−0.445261	+	0.895401i	$0.646889\pi$
$858$		0			0
$859$	7.54319			0.257370			0.128685	−	0.991685i	$-0.458924\pi$
$859$	7.54319			0.257370			0.128685	+	0.991685i	$0.458924\pi$
$860$		0			0
$861$	17.8715	+	12.9844i	0.609059	+	0.442507i
$862$		0			0
$863$	0.370463	−	1.14017i	0.0126107	−	0.0388118i	−0.944553	−	0.328359i	$-0.893505\pi$
$863$	0.370463	−	1.14017i	0.0126107	−	0.0388118i	0.957164	+	0.289547i	$0.0935046\pi$
$864$		0			0
$865$	20.8246	−	15.1300i	0.708057	−	0.514434i
$866$		0			0
$867$	−8.44893	−	26.0031i	−0.286941	−	0.883113i
$868$		0			0
$869$	7.67415	−	13.9625i	0.260328	−	0.473647i
$870$		0			0
$871$	−2.41951	−	7.44648i	−0.0819819	−	0.252314i
$872$		0			0
$873$	0.905541	−	0.657914i	0.0306479	−	0.0222670i
$874$		0			0
$875$	−8.16048	+	25.1154i	−0.275875	+	0.849055i
$876$		0			0
$877$	0.218773	+	0.158948i	0.00738746	+	0.00536730i	0.591473	−	0.806325i	$-0.298547\pi$
$877$	0.218773	+	0.158948i	0.00738746	+	0.00536730i	−0.584085	+	0.811692i	$0.698547\pi$
$878$		0			0
$879$	12.2531			0.413288
$880$		0			0
$881$	−12.4388			−0.419074			−0.209537	−	0.977801i	$-0.567196\pi$
$881$	−12.4388			−0.419074			−0.209537	+	0.977801i	$0.567196\pi$
$882$		0			0
$883$	29.7885	+	21.6426i	1.00246	+	0.728331i	0.962615	−	0.270874i	$-0.0873128\pi$
$883$	29.7885	+	21.6426i	1.00246	+	0.728331i	0.0398474	+	0.999206i	$0.487313\pi$
$884$		0			0
$885$	3.58378	−	11.0298i	0.120468	−	0.370761i
$886$		0			0
$887$	−12.3977	+	9.00748i	−0.416275	+	0.302442i	−0.776137	−	0.630564i	$-0.782824\pi$
$887$	−12.3977	+	9.00748i	−0.416275	+	0.302442i	0.359862	+	0.933005i	$0.382824\pi$
$888$		0			0
$889$	−5.75839	−	17.7225i	−0.193130	−	0.594394i
$890$		0			0
$891$	3.25794	+	0.621147i	0.109145	+	0.0208092i
$892$		0			0
$893$	1.68516	+	5.18639i	0.0563917	+	0.173556i
$894$		0			0
$895$	−4.35601	+	3.16482i	−0.145605	+	0.105788i
$896$		0			0
$897$	−2.42090	+	7.45077i	−0.0808315	+	0.248774i
$898$		0			0
$899$	10.0610	+	7.30974i	0.335553	+	0.243793i
$900$		0			0
$901$	38.2867			1.27551
$902$		0			0
$903$	22.7286			0.756361
$904$		0			0
$905$	14.4138	+	10.4722i	0.479130	+	0.348109i
$906$		0			0
$907$	−14.4921	+	44.6022i	−0.481204	+	1.48099i	0.356201	+	0.934409i	$0.384072\pi$
$907$	−14.4921	+	44.6022i	−0.481204	+	1.48099i	−0.837405	+	0.546583i	$0.815928\pi$
$908$		0			0
$909$	−12.4222	+	9.02525i	−0.412018	+	0.299349i
$910$		0			0
$911$	−2.18552	−	6.72634i	−0.0724095	−	0.222854i	0.908302	−	0.418316i	$-0.137379\pi$
$911$	−2.18552	−	6.72634i	−0.0724095	−	0.222854i	−0.980711	+	0.195462i	$0.937379\pi$
$912$		0			0
$913$	−19.7635	+	9.30243i	−0.654077	+	0.307866i
$914$		0			0
$915$	−0.121525	−	0.374017i	−0.00401751	−	0.0123646i
$916$		0			0
$917$	−9.72890	+	7.06846i	−0.321277	+	0.233421i
$918$		0			0
$919$	−9.86942	+	30.3749i	−0.325562	+	1.00198i	0.645624	+	0.763655i	$0.276597\pi$
$919$	−9.86942	+	30.3749i	−0.325562	+	1.00198i	−0.971186	+	0.238322i	$0.923403\pi$
$920$		0			0
$921$	−1.08138	−	0.785669i	−0.0356327	−	0.0258887i
$922$		0			0
$923$	1.29429			0.0426021
$924$		0			0
$925$	0.166321			0.00546860
$926$		0			0
$927$	−13.2855	−	9.65250i	−0.436354	−	0.317030i
$928$		0			0
$929$	−8.37376	+	25.7718i	−0.274734	+	0.845545i	0.714555	+	0.699579i	$0.246629\pi$
$929$	−8.37376	+	25.7718i	−0.274734	+	0.845545i	−0.989290	+	0.145966i	$0.953371\pi$
$930$		0			0
$931$	−1.67650	+	1.21805i	−0.0549452	+	0.0399200i
$932$		0			0
$933$	7.10432	+	21.8648i	0.232585	+	0.715823i
$934$		0			0
$935$	4.17054	+	32.9866i	0.136391	+	1.07878i
$936$		0			0
$937$	−5.99895	−	18.4629i	−0.195977	−	0.603156i	−0.999964	−	0.00850857i	$-0.997292\pi$
$937$	−5.99895	−	18.4629i	−0.195977	−	0.603156i	0.803986	−	0.594648i	$-0.202708\pi$
$938$		0			0
$939$	21.8705	−	15.8898i	0.713716	−	0.518545i
$940$		0			0
$941$	3.72665	−	11.4694i	0.121485	−	0.373893i	−0.871759	−	0.489935i	$-0.837021\pi$
$941$	3.72665	−	11.4694i	0.121485	−	0.373893i	0.993244	+	0.116042i	$0.0370206\pi$
$942$		0			0
$943$	61.7273	+	44.8475i	2.01012	+	1.46044i
$944$		0			0
$945$	−3.41475			−0.111082
$946$		0			0
$947$	−60.8083			−1.97601			−0.988003	−	0.154436i	$-0.950644\pi$
$947$	−60.8083			−1.97601			−0.988003	+	0.154436i	$0.950644\pi$
$948$		0			0
$949$	7.18319	+	5.21889i	0.233176	+	0.169412i
$950$		0			0
$951$	6.06152	−	18.6554i	0.196558	−	0.604944i
$952$		0			0
$953$	14.9198	−	10.8399i	0.483300	−	0.351138i	−0.319302	−	0.947653i	$-0.603448\pi$
$953$	14.9198	−	10.8399i	0.483300	−	0.351138i	0.802602	+	0.596515i	$0.203448\pi$
$954$		0			0
$955$	1.16975	+	3.60013i	0.0378523	+	0.116497i
$956$		0			0
$957$	21.9384	+	23.3574i	0.709169	+	0.755037i
$958$		0			0
$959$	−7.53207	−	23.1813i	−0.243223	−	0.748564i
$960$		0			0
$961$	23.7392	−	17.2476i	0.765781	−	0.556373i
$962$		0			0
$963$	0.0222133	−	0.0683656i	0.000715814	−	0.00220305i
$964$		0			0
$965$	5.34041	+	3.88004i	0.171914	+	0.124903i
$966$		0			0
$967$	43.9100			1.41205			0.706025	−	0.708187i	$-0.250487\pi$
$967$	43.9100			1.41205			0.706025	+	0.708187i	$0.250487\pi$
$968$		0			0
$969$	−7.43748			−0.238926
$970$		0			0
$971$	32.8183	+	23.8439i	1.05319	+	0.765187i	0.972816	−	0.231578i	$-0.0743889\pi$
$971$	32.8183	+	23.8439i	1.05319	+	0.765187i	0.0803728	+	0.996765i	$0.474389\pi$
$972$		0			0
$973$	6.12037	−	18.8366i	0.196210	−	0.603873i
$974$		0			0
$975$	−2.21142	+	1.60669i	−0.0708222	+	0.0514553i
$976$		0			0
$977$	−11.4707	−	35.3033i	−0.366981	−	1.12945i	−0.948731	−	0.316084i	$-0.897632\pi$
$977$	−11.4707	−	35.3033i	−0.366981	−	1.12945i	0.581750	−	0.813368i	$-0.302368\pi$
$978$		0			0
$979$	31.4358	+	33.4690i	1.00469	+	1.06968i
$980$		0			0
$981$	5.14314	+	15.8290i	0.164208	+	0.505380i
$982$		0			0
$983$	28.2345	−	20.5136i	0.900542	−	0.654282i	−0.0380631	−	0.999275i	$-0.512119\pi$
$983$	28.2345	−	20.5136i	0.900542	−	0.654282i	0.938605	+	0.344993i	$0.112119\pi$
$984$		0			0
$985$	−8.06119	+	24.8098i	−0.256851	+	0.790506i
$986$		0			0
$987$	8.95927	+	6.50929i	0.285177	+	0.207193i
$988$		0			0
$989$	78.5036			2.49627
$990$		0			0
$991$	−32.9930			−1.04806			−0.524029	−	0.851700i	$-0.675572\pi$
$991$	−32.9930			−1.04806			−0.524029	+	0.851700i	$0.675572\pi$
$992$		0			0
$993$	−18.0933	−	13.1455i	−0.574173	−	0.417161i
$994$		0			0
$995$	0.574077	−	1.76683i	0.0181995	−	0.0560122i
$996$		0			0
$997$	22.2437	−	16.1610i	0.704466	−	0.511825i	−0.176917	−	0.984226i	$-0.556613\pi$
$997$	22.2437	−	16.1610i	0.704466	−	0.511825i	0.881384	+	0.472401i	$0.156613\pi$
$998$		0			0
$999$	0.0188025	+	0.0578681i	0.000594884	+	0.00183087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.313.3	✓	20
11.9	even	5	inner	1716.2.z.f.625.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.313.3	✓	20	1.1	even	1	trivial
1716.2.z.f.625.3	yes	20	11.9	even	5	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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(-0.465225 + 1.43182i) q^{5} +(1.83500 - 1.33320i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{3} +(-0.465225 + 1.43182i) q^{5} +(1.83500 - 1.33320i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-2.27063 - 2.41749i) q^{11} +(0.309017 + 0.951057i) q^{13} +(-1.21798 + 0.884911i) q^{15} +(-2.05772 + 6.33302i) q^{17} +(0.903606 + 0.656508i) q^{19} +2.26818 q^{21} +7.83420 q^{23} +(2.21142 + 1.60669i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-7.81659 + 5.67909i) q^{29} +(-0.397746 - 1.22414i) q^{31} +(-0.416013 - 3.29043i) q^{33} +(1.05522 + 3.24762i) q^{35} +(0.0492255 - 0.0357645i) q^{37} +(-0.309017 + 0.951057i) q^{39} +(7.87921 + 5.72458i) q^{41} +10.0206 q^{43} -1.50550 q^{45} +(3.94998 + 2.86983i) q^{47} +(-0.573334 + 1.76454i) q^{49} +(-5.38719 + 3.91402i) q^{51} +(-1.77675 - 5.46827i) q^{53} +(4.51775 - 2.12645i) q^{55} +(0.345147 + 1.06225i) q^{57} +(-6.23212 + 4.52790i) q^{59} +(-0.0807210 + 0.248434i) q^{61} +(1.83500 + 1.33320i) q^{63} -1.50550 q^{65} -7.82969 q^{67} +(6.33800 + 4.60483i) q^{69} +(0.399958 - 1.23094i) q^{71} +(7.18319 - 5.21889i) q^{73} +(0.844688 + 2.59968i) q^{75} +(-7.38960 - 1.40887i) q^{77} +(1.48447 + 4.56872i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.03519 - 6.26368i) q^{83} +(-8.11041 - 5.89256i) q^{85} -9.66184 q^{87} -13.8446 q^{89} +(1.83500 + 1.33320i) q^{91} +(0.397746 - 1.22414i) q^{93} +(-1.36038 + 0.988374i) q^{95} +(-0.345886 - 1.06453i) q^{97} +(1.59750 - 2.90654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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