LMFDB - Embedded newform 552.2.j.b.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.2
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	552.323
Dual form			552.2.j.b.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +4.00000 q^{5} +(-2.00000 - 1.41421i) q^{6} -2.82843i q^{7} -2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +4.00000 q^{5} +(-2.00000 - 1.41421i) q^{6} -2.82843i q^{7} -2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +5.65685i q^{10} +5.65685i q^{11} +(2.00000 - 2.82843i) q^{12} +5.65685i q^{13} +4.00000 q^{14} +(-4.00000 + 5.65685i) q^{15} +4.00000 q^{16} +2.82843i q^{17} +(4.00000 - 1.41421i) q^{18} -2.00000 q^{19} -8.00000 q^{20} +(4.00000 + 2.82843i) q^{21} -8.00000 q^{22} -1.00000 q^{23} +(4.00000 + 2.82843i) q^{24} +11.0000 q^{25} -8.00000 q^{26} +(5.00000 + 1.41421i) q^{27} +5.65685i q^{28} +(-8.00000 - 5.65685i) q^{30} +5.65685i q^{31} +5.65685i q^{32} +(-8.00000 - 5.65685i) q^{33} -4.00000 q^{34} -11.3137i q^{35} +(2.00000 + 5.65685i) q^{36} -2.82843i q^{37} -2.82843i q^{38} +(-8.00000 - 5.65685i) q^{39} -11.3137i q^{40} -5.65685i q^{41} +(-4.00000 + 5.65685i) q^{42} -6.00000 q^{43} -11.3137i q^{44} +(-4.00000 - 11.3137i) q^{45} -1.41421i q^{46} +(-4.00000 + 5.65685i) q^{48} -1.00000 q^{49} +15.5563i q^{50} +(-4.00000 - 2.82843i) q^{51} -11.3137i q^{52} +12.0000 q^{53} +(-2.00000 + 7.07107i) q^{54} +22.6274i q^{55} -8.00000 q^{56} +(2.00000 - 2.82843i) q^{57} -2.82843i q^{59} +(8.00000 - 11.3137i) q^{60} +2.82843i q^{61} -8.00000 q^{62} +(-8.00000 + 2.82843i) q^{63} -8.00000 q^{64} +22.6274i q^{65} +(8.00000 - 11.3137i) q^{66} +2.00000 q^{67} -5.65685i q^{68} +(1.00000 - 1.41421i) q^{69} +16.0000 q^{70} +8.00000 q^{71} +(-8.00000 + 2.82843i) q^{72} -6.00000 q^{73} +4.00000 q^{74} +(-11.0000 + 15.5563i) q^{75} +4.00000 q^{76} +16.0000 q^{77} +(8.00000 - 11.3137i) q^{78} -2.82843i q^{79} +16.0000 q^{80} +(-7.00000 + 5.65685i) q^{81} +8.00000 q^{82} -5.65685i q^{83} +(-8.00000 - 5.65685i) q^{84} +11.3137i q^{85} -8.48528i q^{86} +16.0000 q^{88} -8.48528i q^{89} +(16.0000 - 5.65685i) q^{90} +16.0000 q^{91} +2.00000 q^{92} +(-8.00000 - 5.65685i) q^{93} -8.00000 q^{95} +(-8.00000 - 5.65685i) q^{96} -2.00000 q^{97} -1.41421i q^{98} +(16.0000 - 5.65685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 - 2 * q^9	$ 2 q - 2 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{9} + 4 q^{12} + 8 q^{14} - 8 q^{15} + 8 q^{16} + 8 q^{18} - 4 q^{19} - 16 q^{20} + 8 q^{21} - 16 q^{22} - 2 q^{23} + 8 q^{24} + 22 q^{25} - 16 q^{26} + 10 q^{27} - 16 q^{30} - 16 q^{33} - 8 q^{34} + 4 q^{36} - 16 q^{39} - 8 q^{42} - 12 q^{43} - 8 q^{45} - 8 q^{48} - 2 q^{49} - 8 q^{51} + 24 q^{53} - 4 q^{54} - 16 q^{56} + 4 q^{57} + 16 q^{60} - 16 q^{62} - 16 q^{63} - 16 q^{64} + 16 q^{66} + 4 q^{67} + 2 q^{69} + 32 q^{70} + 16 q^{71} - 16 q^{72} - 12 q^{73} + 8 q^{74} - 22 q^{75} + 8 q^{76} + 32 q^{77} + 16 q^{78} + 32 q^{80} - 14 q^{81} + 16 q^{82} - 16 q^{84} + 32 q^{88} + 32 q^{90} + 32 q^{91} + 4 q^{92} - 16 q^{93} - 16 q^{95} - 16 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 - 2 * q^9 + 4 * q^12 + 8 * q^14 - 8 * q^15 + 8 * q^16 + 8 * q^18 - 4 * q^19 - 16 * q^20 + 8 * q^21 - 16 * q^22 - 2 * q^23 + 8 * q^24 + 22 * q^25 - 16 * q^26 + 10 * q^27 - 16 * q^30 - 16 * q^33 - 8 * q^34 + 4 * q^36 - 16 * q^39 - 8 * q^42 - 12 * q^43 - 8 * q^45 - 8 * q^48 - 2 * q^49 - 8 * q^51 + 24 * q^53 - 4 * q^54 - 16 * q^56 + 4 * q^57 + 16 * q^60 - 16 * q^62 - 16 * q^63 - 16 * q^64 + 16 * q^66 + 4 * q^67 + 2 * q^69 + 32 * q^70 + 16 * q^71 - 16 * q^72 - 12 * q^73 + 8 * q^74 - 22 * q^75 + 8 * q^76 + 32 * q^77 + 16 * q^78 + 32 * q^80 - 14 * q^81 + 16 * q^82 - 16 * q^84 + 32 * q^88 + 32 * q^90 + 32 * q^91 + 4 * q^92 - 16 * q^93 - 16 * q^95 - 16 * q^96 - 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$	−2.00000			−1.00000
$5$	4.00000			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$6$	−2.00000	−	1.41421i	−0.816497	−	0.577350i
$7$		−	2.82843i		−	1.06904i	−0.845154	−	0.534522i	$-0.820491\pi$
$7$		−	2.82843i		−	1.06904i	0.845154	−	0.534522i	$-0.179509\pi$
$8$		−	2.82843i		−	1.00000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$			5.65685i			1.78885i
$11$			5.65685i			1.70561i	0.522233	+	0.852803i	$0.325099\pi$
$11$			5.65685i			1.70561i	−0.522233	+	0.852803i	$0.674901\pi$
$12$	2.00000	−	2.82843i	0.577350	−	0.816497i
$13$			5.65685i			1.56893i	0.620174	+	0.784465i	$0.287062\pi$
$13$			5.65685i			1.56893i	−0.620174	+	0.784465i	$0.712938\pi$
$14$	4.00000			1.06904
$15$	−4.00000	+	5.65685i	−1.03280	+	1.46059i
$16$	4.00000			1.00000
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$	4.00000	−	1.41421i	0.942809	−	0.333333i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	−8.00000			−1.78885
$21$	4.00000	+	2.82843i	0.872872	+	0.617213i
$22$	−8.00000			−1.70561
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	4.00000	+	2.82843i	0.816497	+	0.577350i
$25$	11.0000			2.20000
$26$	−8.00000			−1.56893
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$			5.65685i			1.06904i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−8.00000	−	5.65685i	−1.46059	−	1.03280i
$31$			5.65685i			1.01600i	0.861357	+	0.508001i	$0.169615\pi$
$31$			5.65685i			1.01600i	−0.861357	+	0.508001i	$0.830385\pi$
$32$			5.65685i			1.00000i
$33$	−8.00000	−	5.65685i	−1.39262	−	0.984732i
$34$	−4.00000			−0.685994
$35$		−	11.3137i		−	1.91237i
$36$	2.00000	+	5.65685i	0.333333	+	0.942809i
$37$		−	2.82843i		−	0.464991i	−0.972598	−	0.232495i	$-0.925311\pi$
$37$		−	2.82843i		−	0.464991i	0.972598	−	0.232495i	$-0.0746890\pi$
$38$		−	2.82843i		−	0.458831i
$39$	−8.00000	−	5.65685i	−1.28103	−	0.905822i
$40$		−	11.3137i		−	1.78885i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	−4.00000	+	5.65685i	−0.617213	+	0.872872i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		−	11.3137i		−	1.70561i
$45$	−4.00000	−	11.3137i	−0.596285	−	1.68655i
$46$		−	1.41421i		−	0.208514i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−4.00000	+	5.65685i	−0.577350	+	0.816497i
$49$	−1.00000			−0.142857
$50$			15.5563i			2.20000i
$51$	−4.00000	−	2.82843i	−0.560112	−	0.396059i
$52$		−	11.3137i		−	1.56893i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	−2.00000	+	7.07107i	−0.272166	+	0.962250i
$55$			22.6274i			3.05108i
$56$	−8.00000			−1.06904
$57$	2.00000	−	2.82843i	0.264906	−	0.374634i
$58$		0			0
$59$		−	2.82843i		−	0.368230i	−0.982905	−	0.184115i	$-0.941058\pi$
$59$		−	2.82843i		−	0.368230i	0.982905	−	0.184115i	$-0.0589419\pi$
$60$	8.00000	−	11.3137i	1.03280	−	1.46059i
$61$			2.82843i			0.362143i	0.983470	+	0.181071i	$0.0579565\pi$
$61$			2.82843i			0.362143i	−0.983470	+	0.181071i	$0.942043\pi$
$62$	−8.00000			−1.01600
$63$	−8.00000	+	2.82843i	−1.00791	+	0.356348i
$64$	−8.00000			−1.00000
$65$			22.6274i			2.80659i
$66$	8.00000	−	11.3137i	0.984732	−	1.39262i
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$		−	5.65685i		−	0.685994i
$69$	1.00000	−	1.41421i	0.120386	−	0.170251i
$70$	16.0000			1.91237
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−8.00000	+	2.82843i	−0.942809	+	0.333333i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	4.00000			0.464991
$75$	−11.0000	+	15.5563i	−1.27017	+	1.79629i
$76$	4.00000			0.458831
$77$	16.0000			1.82337
$78$	8.00000	−	11.3137i	0.905822	−	1.28103i
$79$		−	2.82843i		−	0.318223i	−0.987261	−	0.159111i	$-0.949137\pi$
$79$		−	2.82843i		−	0.318223i	0.987261	−	0.159111i	$-0.0508629\pi$
$80$	16.0000			1.78885
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	8.00000			0.883452
$83$		−	5.65685i		−	0.620920i	−0.950586	−	0.310460i	$-0.899517\pi$
$83$		−	5.65685i		−	0.620920i	0.950586	−	0.310460i	$-0.100483\pi$
$84$	−8.00000	−	5.65685i	−0.872872	−	0.617213i
$85$			11.3137i			1.22714i
$86$		−	8.48528i		−	0.914991i
$87$		0			0
$88$	16.0000			1.70561
$89$		−	8.48528i		−	0.899438i	−0.893170	−	0.449719i	$-0.851524\pi$
$89$		−	8.48528i		−	0.899438i	0.893170	−	0.449719i	$-0.148476\pi$
$90$	16.0000	−	5.65685i	1.68655	−	0.596285i
$91$	16.0000			1.67726
$92$	2.00000			0.208514
$93$	−8.00000	−	5.65685i	−0.829561	−	0.586588i
$94$		0			0
$95$	−8.00000			−0.820783
$96$	−8.00000	−	5.65685i	−0.816497	−	0.577350i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		−	1.41421i		−	0.142857i
$99$	16.0000	−	5.65685i	1.60806	−	0.568535i
$100$	−22.0000			−2.20000
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$	4.00000	−	5.65685i	0.396059	−	0.560112i
$103$		−	2.82843i		−	0.278693i	−0.990244	−	0.139347i	$-0.955500\pi$
$103$		−	2.82843i		−	0.278693i	0.990244	−	0.139347i	$-0.0445002\pi$
$104$	16.0000			1.56893
$105$	16.0000	+	11.3137i	1.56144	+	1.10410i
$106$			16.9706i			1.64833i
$107$		−	11.3137i		−	1.09374i	−0.837218	−	0.546869i	$-0.815820\pi$
$107$		−	11.3137i		−	1.09374i	0.837218	−	0.546869i	$-0.184180\pi$
$108$	−10.0000	−	2.82843i	−0.962250	−	0.272166i
$109$			8.48528i			0.812743i	0.913708	+	0.406371i	$0.133206\pi$
$109$			8.48528i			0.812743i	−0.913708	+	0.406371i	$0.866794\pi$
$110$	−32.0000			−3.05108
$111$	4.00000	+	2.82843i	0.379663	+	0.268462i
$112$		−	11.3137i		−	1.06904i
$113$		−	2.82843i		−	0.266076i	−0.991111	−	0.133038i	$-0.957527\pi$
$113$		−	2.82843i		−	0.266076i	0.991111	−	0.133038i	$-0.0424732\pi$
$114$	4.00000	+	2.82843i	0.374634	+	0.264906i
$115$	−4.00000			−0.373002
$116$		0			0
$117$	16.0000	−	5.65685i	1.47920	−	0.522976i
$118$	4.00000			0.368230
$119$	8.00000			0.733359
$120$	16.0000	+	11.3137i	1.46059	+	1.03280i
$121$	−21.0000			−1.90909
$122$	−4.00000			−0.362143
$123$	8.00000	+	5.65685i	0.721336	+	0.510061i
$124$		−	11.3137i		−	1.01600i
$125$	24.0000			2.14663
$126$	−4.00000	−	11.3137i	−0.356348	−	1.00791i
$127$		−	16.9706i		−	1.50589i	−0.658081	−	0.752947i	$-0.728632\pi$
$127$		−	16.9706i		−	1.50589i	0.658081	−	0.752947i	$-0.271368\pi$
$128$		−	11.3137i		−	1.00000i
$129$	6.00000	−	8.48528i	0.528271	−	0.747087i
$130$	−32.0000			−2.80659
$131$		−	2.82843i		−	0.247121i	−0.992337	−	0.123560i	$-0.960569\pi$
$131$		−	2.82843i		−	0.247121i	0.992337	−	0.123560i	$-0.0394313\pi$
$132$	16.0000	+	11.3137i	1.39262	+	0.984732i
$133$			5.65685i			0.490511i
$134$			2.82843i			0.244339i
$135$	20.0000	+	5.65685i	1.72133	+	0.486864i
$136$	8.00000			0.685994
$137$			2.82843i			0.241649i	0.992674	+	0.120824i	$0.0385538\pi$
$137$			2.82843i			0.241649i	−0.992674	+	0.120824i	$0.961446\pi$
$138$	2.00000	+	1.41421i	0.170251	+	0.120386i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$			22.6274i			1.91237i
$141$		0			0
$142$			11.3137i			0.949425i
$143$	−32.0000			−2.67597
$144$	−4.00000	−	11.3137i	−0.333333	−	0.942809i
$145$		0			0
$146$		−	8.48528i		−	0.702247i
$147$	1.00000	−	1.41421i	0.0824786	−	0.116642i
$148$			5.65685i			0.464991i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	−22.0000	−	15.5563i	−1.79629	−	1.27017i
$151$			11.3137i			0.920697i	0.887738	+	0.460348i	$0.152275\pi$
$151$			11.3137i			0.920697i	−0.887738	+	0.460348i	$0.847725\pi$
$152$			5.65685i			0.458831i
$153$	8.00000	−	2.82843i	0.646762	−	0.228665i
$154$			22.6274i			1.82337i
$155$			22.6274i			1.81748i
$156$	16.0000	+	11.3137i	1.28103	+	0.905822i
$157$		−	19.7990i		−	1.58013i	−0.613022	−	0.790066i	$-0.710046\pi$
$157$		−	19.7990i		−	1.58013i	0.613022	−	0.790066i	$-0.289954\pi$
$158$	4.00000			0.318223
$159$	−12.0000	+	16.9706i	−0.951662	+	1.34585i
$160$			22.6274i			1.78885i
$161$			2.82843i			0.222911i
$162$	−8.00000	−	9.89949i	−0.628539	−	0.777778i
$163$	−6.00000			−0.469956			−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000			−0.469956			−0.234978	+	0.972001i	$0.575502\pi$
$164$			11.3137i			0.883452i
$165$	−32.0000	−	22.6274i	−2.49120	−	1.76154i
$166$	8.00000			0.620920
$167$	24.0000			1.85718			0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000			1.85718			0.928588	+	0.371113i	$0.121024\pi$
$168$	8.00000	−	11.3137i	0.617213	−	0.872872i
$169$	−19.0000			−1.46154
$170$	−16.0000			−1.22714
$171$	2.00000	+	5.65685i	0.152944	+	0.432590i
$172$	12.0000			0.914991
$173$	−16.0000			−1.21646			−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000			−1.21646			−0.608229	+	0.793762i	$0.708120\pi$
$174$		0			0
$175$		−	31.1127i		−	2.35190i
$176$			22.6274i			1.70561i
$177$	4.00000	+	2.82843i	0.300658	+	0.212598i
$178$	12.0000			0.899438
$179$			14.1421i			1.05703i	0.848923	+	0.528516i	$0.177252\pi$
$179$			14.1421i			1.05703i	−0.848923	+	0.528516i	$0.822748\pi$
$180$	8.00000	+	22.6274i	0.596285	+	1.68655i
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$			22.6274i			1.67726i
$183$	−4.00000	−	2.82843i	−0.295689	−	0.209083i
$184$			2.82843i			0.208514i
$185$		−	11.3137i		−	0.831800i
$186$	8.00000	−	11.3137i	0.586588	−	0.829561i
$187$	−16.0000			−1.17004
$188$		0			0
$189$	4.00000	−	14.1421i	0.290957	−	1.02869i
$190$		−	11.3137i		−	0.820783i
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	8.00000	−	11.3137i	0.577350	−	0.816497i
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$		−	2.82843i		−	0.203069i
$195$	−32.0000	−	22.6274i	−2.29157	−	1.62038i
$196$	2.00000			0.142857
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$	8.00000	+	22.6274i	0.568535	+	1.60806i
$199$			8.48528i			0.601506i	0.953702	+	0.300753i	$0.0972379\pi$
$199$			8.48528i			0.601506i	−0.953702	+	0.300753i	$0.902762\pi$
$200$		−	31.1127i		−	2.20000i
$201$	−2.00000	+	2.82843i	−0.141069	+	0.199502i
$202$		−	11.3137i		−	0.796030i
$203$		0			0
$204$	8.00000	+	5.65685i	0.560112	+	0.396059i
$205$		−	22.6274i		−	1.58037i
$206$	4.00000			0.278693
$207$	1.00000	+	2.82843i	0.0695048	+	0.196589i
$208$			22.6274i			1.56893i
$209$		−	11.3137i		−	0.782586i
$210$	−16.0000	+	22.6274i	−1.10410	+	1.56144i
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−24.0000			−1.64833
$213$	−8.00000	+	11.3137i	−0.548151	+	0.775203i
$214$	16.0000			1.09374
$215$	−24.0000			−1.63679
$216$	4.00000	−	14.1421i	0.272166	−	0.962250i
$217$	16.0000			1.08615
$218$	−12.0000			−0.812743
$219$	6.00000	−	8.48528i	0.405442	−	0.573382i
$220$		−	45.2548i		−	3.05108i
$221$	−16.0000			−1.07628
$222$	−4.00000	+	5.65685i	−0.268462	+	0.379663i
$223$		−	11.3137i		−	0.757622i	−0.925474	−	0.378811i	$-0.876333\pi$
$223$		−	11.3137i		−	0.757622i	0.925474	−	0.378811i	$-0.123667\pi$
$224$	16.0000			1.06904
$225$	−11.0000	−	31.1127i	−0.733333	−	2.07418i
$226$	4.00000			0.266076
$227$		−	11.3137i		−	0.750917i	−0.926839	−	0.375459i	$-0.877485\pi$
$227$		−	11.3137i		−	0.750917i	0.926839	−	0.375459i	$-0.122515\pi$
$228$	−4.00000	+	5.65685i	−0.264906	+	0.374634i
$229$			8.48528i			0.560723i	0.959894	+	0.280362i	$0.0904544\pi$
$229$			8.48528i			0.560723i	−0.959894	+	0.280362i	$0.909546\pi$
$230$		−	5.65685i		−	0.373002i
$231$	−16.0000	+	22.6274i	−1.05272	+	1.48877i
$232$		0			0
$233$			16.9706i			1.11178i	0.831256	+	0.555889i	$0.187622\pi$
$233$			16.9706i			1.11178i	−0.831256	+	0.555889i	$0.812378\pi$
$234$	8.00000	+	22.6274i	0.522976	+	1.47920i
$235$		0			0
$236$			5.65685i			0.368230i
$237$	4.00000	+	2.82843i	0.259828	+	0.183726i
$238$			11.3137i			0.733359i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	−16.0000	+	22.6274i	−1.03280	+	1.46059i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$		−	29.6985i		−	1.90909i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$		−	5.65685i		−	0.362143i
$245$	−4.00000			−0.255551
$246$	−8.00000	+	11.3137i	−0.510061	+	0.721336i
$247$		−	11.3137i		−	0.719874i
$248$	16.0000			1.01600
$249$	8.00000	+	5.65685i	0.506979	+	0.358489i
$250$			33.9411i			2.14663i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	16.0000	−	5.65685i	1.00791	−	0.356348i
$253$		−	5.65685i		−	0.355643i
$254$	24.0000			1.50589
$255$	−16.0000	−	11.3137i	−1.00196	−	0.708492i
$256$	16.0000			1.00000
$257$		−	28.2843i		−	1.76432i	−0.470946	−	0.882162i	$-0.656087\pi$
$257$		−	28.2843i		−	1.76432i	0.470946	−	0.882162i	$-0.343913\pi$
$258$	12.0000	+	8.48528i	0.747087	+	0.528271i
$259$	−8.00000			−0.497096
$260$		−	45.2548i		−	2.80659i
$261$		0			0
$262$	4.00000			0.247121
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$	−16.0000	+	22.6274i	−0.984732	+	1.39262i
$265$	48.0000			2.94862
$266$	−8.00000			−0.490511
$267$	12.0000	+	8.48528i	0.734388	+	0.519291i
$268$	−4.00000			−0.244339
$269$	16.0000			0.975537			0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000			0.975537			0.487769	+	0.872973i	$0.337811\pi$
$270$	−8.00000	+	28.2843i	−0.486864	+	1.72133i
$271$		−	5.65685i		−	0.343629i	−0.985129	−	0.171815i	$-0.945037\pi$
$271$		−	5.65685i		−	0.343629i	0.985129	−	0.171815i	$-0.0549630\pi$
$272$			11.3137i			0.685994i
$273$	−16.0000	+	22.6274i	−0.968364	+	1.36947i
$274$	−4.00000			−0.241649
$275$			62.2254i			3.75233i
$276$	−2.00000	+	2.82843i	−0.120386	+	0.170251i
$277$		−	5.65685i		−	0.339887i	−0.985454	−	0.169944i	$-0.945641\pi$
$277$		−	5.65685i		−	0.339887i	0.985454	−	0.169944i	$-0.0543586\pi$
$278$			14.1421i			0.848189i
$279$	16.0000	−	5.65685i	0.957895	−	0.338667i
$280$	−32.0000			−1.91237
$281$		−	19.7990i		−	1.18111i	−0.806998	−	0.590554i	$-0.798909\pi$
$281$		−	19.7990i		−	1.18111i	0.806998	−	0.590554i	$-0.201091\pi$
$282$		0			0
$283$	22.0000			1.30776			0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000			1.30776			0.653882	+	0.756596i	$0.273139\pi$
$284$	−16.0000			−0.949425
$285$	8.00000	−	11.3137i	0.473879	−	0.670166i
$286$		−	45.2548i		−	2.67597i
$287$	−16.0000			−0.944450
$288$	16.0000	−	5.65685i	0.942809	−	0.333333i
$289$	9.00000			0.529412
$290$		0			0
$291$	2.00000	−	2.82843i	0.117242	−	0.165805i
$292$	12.0000			0.702247
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$	2.00000	+	1.41421i	0.116642	+	0.0824786i
$295$		−	11.3137i		−	0.658710i
$296$	−8.00000			−0.464991
$297$	−8.00000	+	28.2843i	−0.464207	+	1.64122i
$298$			16.9706i			0.983078i
$299$		−	5.65685i		−	0.327144i
$300$	22.0000	−	31.1127i	1.27017	−	1.79629i
$301$			16.9706i			0.978167i
$302$	−16.0000			−0.920697
$303$	8.00000	−	11.3137i	0.459588	−	0.649956i
$304$	−8.00000			−0.458831
$305$			11.3137i			0.647821i
$306$	4.00000	+	11.3137i	0.228665	+	0.646762i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$	−32.0000			−1.82337
$309$	4.00000	+	2.82843i	0.227552	+	0.160904i
$310$	−32.0000			−1.81748
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$	−16.0000	+	22.6274i	−0.905822	+	1.28103i
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	28.0000			1.58013
$315$	−32.0000	+	11.3137i	−1.80300	+	0.637455i
$316$			5.65685i			0.318223i
$317$	−16.0000			−0.898650			−0.449325	−	0.893368i	$-0.648335\pi$
$317$	−16.0000			−0.898650			−0.449325	+	0.893368i	$0.648335\pi$
$318$	−24.0000	−	16.9706i	−1.34585	−	0.951662i
$319$		0			0
$320$	−32.0000			−1.78885
$321$	16.0000	+	11.3137i	0.893033	+	0.631470i
$322$	−4.00000			−0.222911
$323$		−	5.65685i		−	0.314756i
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$			62.2254i			3.45164i
$326$		−	8.48528i		−	0.469956i
$327$	−12.0000	−	8.48528i	−0.663602	−	0.469237i
$328$	−16.0000			−0.883452
$329$		0			0
$330$	32.0000	−	45.2548i	1.76154	−	2.49120i
$331$	2.00000			0.109930			0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000			0.109930			0.0549650	+	0.998488i	$0.482495\pi$
$332$			11.3137i			0.620920i
$333$	−8.00000	+	2.82843i	−0.438397	+	0.154997i
$334$			33.9411i			1.85718i
$335$	8.00000			0.437087
$336$	16.0000	+	11.3137i	0.872872	+	0.617213i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		−	26.8701i		−	1.46154i
$339$	4.00000	+	2.82843i	0.217250	+	0.153619i
$340$		−	22.6274i		−	1.22714i
$341$	−32.0000			−1.73290
$342$	−8.00000	+	2.82843i	−0.432590	+	0.152944i
$343$		−	16.9706i		−	0.916324i
$344$			16.9706i			0.914991i
$345$	4.00000	−	5.65685i	0.215353	−	0.304555i
$346$		−	22.6274i		−	1.21646i
$347$		−	14.1421i		−	0.759190i	−0.925153	−	0.379595i	$-0.876063\pi$
$347$		−	14.1421i		−	0.759190i	0.925153	−	0.379595i	$-0.123937\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	44.0000			2.35190
$351$	−8.00000	+	28.2843i	−0.427008	+	1.50970i
$352$	−32.0000			−1.70561
$353$			28.2843i			1.50542i	0.658352	+	0.752710i	$0.271254\pi$
$353$			28.2843i			1.50542i	−0.658352	+	0.752710i	$0.728746\pi$
$354$	−4.00000	+	5.65685i	−0.212598	+	0.300658i
$355$	32.0000			1.69838
$356$			16.9706i			0.899438i
$357$	−8.00000	+	11.3137i	−0.423405	+	0.598785i
$358$	−20.0000			−1.05703
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	−32.0000	+	11.3137i	−1.68655	+	0.596285i
$361$	−15.0000			−0.789474
$362$	12.0000			0.630706
$363$	21.0000	−	29.6985i	1.10221	−	1.55877i
$364$	−32.0000			−1.67726
$365$	−24.0000			−1.25622
$366$	4.00000	−	5.65685i	0.209083	−	0.295689i
$367$		−	14.1421i		−	0.738213i	−0.929387	−	0.369107i	$-0.879664\pi$
$367$		−	14.1421i		−	0.738213i	0.929387	−	0.369107i	$-0.120336\pi$
$368$	−4.00000			−0.208514
$369$	−16.0000	+	5.65685i	−0.832927	+	0.294484i
$370$	16.0000			0.831800
$371$		−	33.9411i		−	1.76214i
$372$	16.0000	+	11.3137i	0.829561	+	0.586588i
$373$		−	8.48528i		−	0.439351i	−0.975573	−	0.219676i	$-0.929500\pi$
$373$		−	8.48528i		−	0.439351i	0.975573	−	0.219676i	$-0.0704999\pi$
$374$		−	22.6274i		−	1.17004i
$375$	−24.0000	+	33.9411i	−1.23935	+	1.75271i
$376$		0			0
$377$		0			0
$378$	20.0000	+	5.65685i	1.02869	+	0.290957i
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$	16.0000			0.820783
$381$	24.0000	+	16.9706i	1.22956	+	0.869428i
$382$			33.9411i			1.73658i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	16.0000	+	11.3137i	0.816497	+	0.577350i
$385$	64.0000			3.26174
$386$			25.4558i			1.29567i
$387$	6.00000	+	16.9706i	0.304997	+	0.862662i
$388$	4.00000			0.203069
$389$	36.0000			1.82527			0.912636	−	0.408773i	$-0.134043\pi$
$389$	36.0000			1.82527			0.912636	+	0.408773i	$0.134043\pi$
$390$	32.0000	−	45.2548i	1.62038	−	2.29157i
$391$		−	2.82843i		−	0.143040i
$392$			2.82843i			0.142857i
$393$	4.00000	+	2.82843i	0.201773	+	0.142675i
$394$		−	22.6274i		−	1.13995i
$395$		−	11.3137i		−	0.569254i
$396$	−32.0000	+	11.3137i	−1.60806	+	0.568535i
$397$			22.6274i			1.13564i	0.823154	+	0.567819i	$0.192213\pi$
$397$			22.6274i			1.13564i	−0.823154	+	0.567819i	$0.807787\pi$
$398$	−12.0000			−0.601506
$399$	−8.00000	−	5.65685i	−0.400501	−	0.283197i
$400$	44.0000			2.20000
$401$		−	36.7696i		−	1.83618i	−0.396368	−	0.918092i	$-0.629729\pi$
$401$		−	36.7696i		−	1.83618i	0.396368	−	0.918092i	$-0.370271\pi$
$402$	−4.00000	−	2.82843i	−0.199502	−	0.141069i
$403$	−32.0000			−1.59403
$404$	16.0000			0.796030
$405$	−28.0000	+	22.6274i	−1.39133	+	1.12437i
$406$		0			0
$407$	16.0000			0.793091
$408$	−8.00000	+	11.3137i	−0.396059	+	0.560112i
$409$	−30.0000			−1.48340			−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000			−1.48340			−0.741702	+	0.670729i	$0.765981\pi$
$410$	32.0000			1.58037
$411$	−4.00000	−	2.82843i	−0.197305	−	0.139516i
$412$			5.65685i			0.278693i
$413$	−8.00000			−0.393654
$414$	−4.00000	+	1.41421i	−0.196589	+	0.0695048i
$415$		−	22.6274i		−	1.11074i
$416$	−32.0000			−1.56893
$417$	−10.0000	+	14.1421i	−0.489702	+	0.692543i
$418$	16.0000			0.782586
$419$		−	5.65685i		−	0.276355i	−0.990407	−	0.138178i	$-0.955875\pi$
$419$		−	5.65685i		−	0.276355i	0.990407	−	0.138178i	$-0.0441245\pi$
$420$	−32.0000	−	22.6274i	−1.56144	−	1.10410i
$421$			36.7696i			1.79204i	0.444015	+	0.896019i	$0.353554\pi$
$421$			36.7696i			1.79204i	−0.444015	+	0.896019i	$0.646446\pi$
$422$		−	14.1421i		−	0.688428i
$423$		0			0
$424$		−	33.9411i		−	1.64833i
$425$			31.1127i			1.50919i
$426$	−16.0000	−	11.3137i	−0.775203	−	0.548151i
$427$	8.00000			0.387147
$428$			22.6274i			1.09374i
$429$	32.0000	−	45.2548i	1.54497	−	2.18492i
$430$		−	33.9411i		−	1.63679i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$	20.0000	+	5.65685i	0.962250	+	0.272166i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$			22.6274i			1.08615i
$435$		0			0
$436$		−	16.9706i		−	0.812743i
$437$	2.00000			0.0956730
$438$	12.0000	+	8.48528i	0.573382	+	0.405442i
$439$			22.6274i			1.07995i	0.841682	+	0.539974i	$0.181566\pi$
$439$			22.6274i			1.07995i	−0.841682	+	0.539974i	$0.818434\pi$
$440$	64.0000			3.05108
$441$	1.00000	+	2.82843i	0.0476190	+	0.134687i
$442$		−	22.6274i		−	1.07628i
$443$			8.48528i			0.403148i	0.979473	+	0.201574i	$0.0646056\pi$
$443$			8.48528i			0.403148i	−0.979473	+	0.201574i	$0.935394\pi$
$444$	−8.00000	−	5.65685i	−0.379663	−	0.268462i
$445$		−	33.9411i		−	1.60896i
$446$	16.0000			0.757622
$447$	−12.0000	+	16.9706i	−0.567581	+	0.802680i
$448$			22.6274i			1.06904i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	44.0000	−	15.5563i	2.07418	−	0.733333i
$451$	32.0000			1.50682
$452$			5.65685i			0.266076i
$453$	−16.0000	−	11.3137i	−0.751746	−	0.531564i
$454$	16.0000			0.750917
$455$	64.0000			3.00037
$456$	−8.00000	−	5.65685i	−0.374634	−	0.264906i
$457$	−38.0000			−1.77757			−0.888783	−	0.458329i	$-0.848448\pi$
$457$	−38.0000			−1.77757			−0.888783	+	0.458329i	$0.848448\pi$
$458$	−12.0000			−0.560723
$459$	−4.00000	+	14.1421i	−0.186704	+	0.660098i
$460$	8.00000			0.373002
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$	−32.0000	−	22.6274i	−1.48877	−	1.05272i
$463$		−	33.9411i		−	1.57738i	−0.614792	−	0.788689i	$-0.710760\pi$
$463$		−	33.9411i		−	1.57738i	0.614792	−	0.788689i	$-0.289240\pi$
$464$		0			0
$465$	−32.0000	−	22.6274i	−1.48396	−	1.04932i
$466$	−24.0000			−1.11178
$467$		−	5.65685i		−	0.261768i	−0.991398	−	0.130884i	$-0.958218\pi$
$467$		−	5.65685i		−	0.261768i	0.991398	−	0.130884i	$-0.0417815\pi$
$468$	−32.0000	+	11.3137i	−1.47920	+	0.522976i
$469$		−	5.65685i		−	0.261209i
$470$		0			0
$471$	28.0000	+	19.7990i	1.29017	+	0.912289i
$472$	−8.00000			−0.368230
$473$		−	33.9411i		−	1.56061i
$474$	−4.00000	+	5.65685i	−0.183726	+	0.259828i
$475$	−22.0000			−1.00943
$476$	−16.0000			−0.733359
$477$	−12.0000	−	33.9411i	−0.549442	−	1.55406i
$478$			33.9411i			1.55243i
$479$	−16.0000			−0.731059			−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000			−0.731059			−0.365529	+	0.930800i	$0.619112\pi$
$480$	−32.0000	−	22.6274i	−1.46059	−	1.03280i
$481$	16.0000			0.729537
$482$		−	19.7990i		−	0.901819i
$483$	−4.00000	−	2.82843i	−0.182006	−	0.128698i
$484$	42.0000			1.90909
$485$	−8.00000			−0.363261
$486$	22.0000	−	1.41421i	0.997940	−	0.0641500i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	8.00000			0.362143
$489$	6.00000	−	8.48528i	0.271329	−	0.383718i
$490$		−	5.65685i		−	0.255551i
$491$			36.7696i			1.65939i	0.558219	+	0.829693i	$0.311485\pi$
$491$			36.7696i			1.65939i	−0.558219	+	0.829693i	$0.688515\pi$
$492$	−16.0000	−	11.3137i	−0.721336	−	0.510061i
$493$		0			0
$494$	16.0000			0.719874
$495$	64.0000	−	22.6274i	2.87659	−	1.01703i
$496$			22.6274i			1.01600i
$497$		−	22.6274i		−	1.01498i
$498$	−8.00000	+	11.3137i	−0.358489	+	0.506979i
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$	−48.0000			−2.14663
$501$	−24.0000	+	33.9411i	−1.07224	+	1.51638i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	8.00000	+	22.6274i	0.356348	+	1.00791i
$505$	−32.0000			−1.42398
$506$	8.00000			0.355643
$507$	19.0000	−	26.8701i	0.843820	−	1.19334i
$508$			33.9411i			1.50589i
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$	16.0000	−	22.6274i	0.708492	−	1.00196i
$511$			16.9706i			0.750733i
$512$			22.6274i			1.00000i
$513$	−10.0000	−	2.82843i	−0.441511	−	0.124878i
$514$	40.0000			1.76432
$515$		−	11.3137i		−	0.498542i
$516$	−12.0000	+	16.9706i	−0.528271	+	0.747087i
$517$		0			0
$518$		−	11.3137i		−	0.497096i
$519$	16.0000	−	22.6274i	0.702322	−	0.993233i
$520$	64.0000			2.80659
$521$			31.1127i			1.36307i	0.731785	+	0.681536i	$0.238688\pi$
$521$			31.1127i			1.36307i	−0.731785	+	0.681536i	$0.761312\pi$
$522$		0			0
$523$	−30.0000			−1.31181			−0.655904	−	0.754844i	$-0.727712\pi$
$523$	−30.0000			−1.31181			−0.655904	+	0.754844i	$0.727712\pi$
$524$			5.65685i			0.247121i
$525$	44.0000	+	31.1127i	1.92032	+	1.35787i
$526$		−	33.9411i		−	1.47990i
$527$	−16.0000			−0.696971
$528$	−32.0000	−	22.6274i	−1.39262	−	0.984732i
$529$	1.00000			0.0434783
$530$			67.8823i			2.94862i
$531$	−8.00000	+	2.82843i	−0.347170	+	0.122743i
$532$		−	11.3137i		−	0.490511i
$533$	32.0000			1.38607
$534$	−12.0000	+	16.9706i	−0.519291	+	0.734388i
$535$		−	45.2548i		−	1.95654i
$536$		−	5.65685i		−	0.244339i
$537$	−20.0000	−	14.1421i	−0.863064	−	0.610278i
$538$			22.6274i			0.975537i
$539$		−	5.65685i		−	0.243658i
$540$	−40.0000	−	11.3137i	−1.72133	−	0.486864i
$541$			22.6274i			0.972829i	0.873728	+	0.486414i	$0.161695\pi$
$541$			22.6274i			0.972829i	−0.873728	+	0.486414i	$0.838305\pi$
$542$	8.00000			0.343629
$543$	12.0000	+	8.48528i	0.514969	+	0.364138i
$544$	−16.0000			−0.685994
$545$			33.9411i			1.45388i
$546$	−32.0000	−	22.6274i	−1.36947	−	0.968364i
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$		−	5.65685i		−	0.241649i
$549$	8.00000	−	2.82843i	0.341432	−	0.120714i
$550$	−88.0000			−3.75233
$551$		0			0
$552$	−4.00000	−	2.82843i	−0.170251	−	0.120386i
$553$	−8.00000			−0.340195
$554$	8.00000			0.339887
$555$	16.0000	+	11.3137i	0.679162	+	0.480240i
$556$	−20.0000			−0.848189
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$	8.00000	+	22.6274i	0.338667	+	0.957895i
$559$		−	33.9411i		−	1.43556i
$560$		−	45.2548i		−	1.91237i
$561$	16.0000	−	22.6274i	0.675521	−	0.955330i
$562$	28.0000			1.18111
$563$			33.9411i			1.43045i	0.698895	+	0.715224i	$0.253675\pi$
$563$			33.9411i			1.43045i	−0.698895	+	0.715224i	$0.746325\pi$
$564$		0			0
$565$		−	11.3137i		−	0.475971i
$566$			31.1127i			1.30776i
$567$	16.0000	+	19.7990i	0.671937	+	0.831479i
$568$		−	22.6274i		−	0.949425i
$569$		−	8.48528i		−	0.355722i	−0.984056	−	0.177861i	$-0.943082\pi$
$569$		−	8.48528i		−	0.355722i	0.984056	−	0.177861i	$-0.0569177\pi$
$570$	16.0000	+	11.3137i	0.670166	+	0.473879i
$571$	30.0000			1.25546			0.627730	−	0.778431i	$-0.283984\pi$
$571$	30.0000			1.25546			0.627730	+	0.778431i	$0.283984\pi$
$572$	64.0000			2.67597
$573$	−24.0000	+	33.9411i	−1.00261	+	1.41791i
$574$		−	22.6274i		−	0.944450i
$575$	−11.0000			−0.458732
$576$	8.00000	+	22.6274i	0.333333	+	0.942809i
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$			12.7279i			0.529412i
$579$	−18.0000	+	25.4558i	−0.748054	+	1.05791i
$580$		0			0
$581$	−16.0000			−0.663792
$582$	4.00000	+	2.82843i	0.165805	+	0.117242i
$583$			67.8823i			2.81140i
$584$			16.9706i			0.702247i
$585$	64.0000	−	22.6274i	2.64607	−	0.935529i
$586$			5.65685i			0.233682i
$587$			8.48528i			0.350225i	0.984548	+	0.175113i	$0.0560289\pi$
$587$			8.48528i			0.350225i	−0.984548	+	0.175113i	$0.943971\pi$
$588$	−2.00000	+	2.82843i	−0.0824786	+	0.116642i
$589$		−	11.3137i		−	0.466173i
$590$	16.0000			0.658710
$591$	16.0000	−	22.6274i	0.658152	−	0.930768i
$592$		−	11.3137i		−	0.464991i
$593$			5.65685i			0.232299i	0.993232	+	0.116150i	$0.0370552\pi$
$593$			5.65685i			0.232299i	−0.993232	+	0.116150i	$0.962945\pi$
$594$	−40.0000	−	11.3137i	−1.64122	−	0.464207i
$595$	32.0000			1.31187
$596$	−24.0000			−0.983078
$597$	−12.0000	−	8.48528i	−0.491127	−	0.347279i
$598$	8.00000			0.327144
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	44.0000	+	31.1127i	1.79629	+	1.27017i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	−24.0000			−0.978167
$603$	−2.00000	−	5.65685i	−0.0814463	−	0.230365i
$604$		−	22.6274i		−	0.920697i
$605$	−84.0000			−3.41509
$606$	16.0000	+	11.3137i	0.649956	+	0.459588i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		−	11.3137i		−	0.458831i
$609$		0			0
$610$	−16.0000			−0.647821
$611$		0			0
$612$	−16.0000	+	5.65685i	−0.646762	+	0.228665i
$613$			8.48528i			0.342717i	0.985209	+	0.171359i	$0.0548157\pi$
$613$			8.48528i			0.342717i	−0.985209	+	0.171359i	$0.945184\pi$
$614$		−	14.1421i		−	0.570730i
$615$	32.0000	+	22.6274i	1.29036	+	0.912426i
$616$		−	45.2548i		−	1.82337i
$617$			8.48528i			0.341605i	0.985305	+	0.170802i	$0.0546359\pi$
$617$			8.48528i			0.341605i	−0.985305	+	0.170802i	$0.945364\pi$
$618$	−4.00000	+	5.65685i	−0.160904	+	0.227552i
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$		−	45.2548i		−	1.81748i
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$		−	22.6274i		−	0.907277i
$623$	−24.0000			−0.961540
$624$	−32.0000	−	22.6274i	−1.28103	−	0.905822i
$625$	41.0000			1.64000
$626$		−	36.7696i		−	1.46961i
$627$	16.0000	+	11.3137i	0.638978	+	0.451826i
$628$			39.5980i			1.58013i
$629$	8.00000			0.318981
$630$	−16.0000	−	45.2548i	−0.637455	−	1.80300i
$631$			2.82843i			0.112598i	0.998414	+	0.0562990i	$0.0179300\pi$
$631$			2.82843i			0.112598i	−0.998414	+	0.0562990i	$0.982070\pi$
$632$	−8.00000			−0.318223
$633$	10.0000	−	14.1421i	0.397464	−	0.562099i
$634$		−	22.6274i		−	0.898650i
$635$		−	67.8823i		−	2.69382i
$636$	24.0000	−	33.9411i	0.951662	−	1.34585i
$637$		−	5.65685i		−	0.224133i
$638$		0			0
$639$	−8.00000	−	22.6274i	−0.316475	−	0.895127i
$640$		−	45.2548i		−	1.78885i
$641$		−	14.1421i		−	0.558581i	−0.960207	−	0.279290i	$-0.909901\pi$
$641$		−	14.1421i		−	0.558581i	0.960207	−	0.279290i	$-0.0900992\pi$
$642$	−16.0000	+	22.6274i	−0.631470	+	0.893033i
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		−	5.65685i		−	0.222911i
$645$	24.0000	−	33.9411i	0.944999	−	1.33643i
$646$	8.00000			0.314756
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	16.0000	+	19.7990i	0.628539	+	0.777778i
$649$	16.0000			0.628055
$650$	−88.0000			−3.45164
$651$	−16.0000	+	22.6274i	−0.627089	+	0.886838i
$652$	12.0000			0.469956
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$	12.0000	−	16.9706i	0.469237	−	0.663602i
$655$		−	11.3137i		−	0.442063i
$656$		−	22.6274i		−	0.883452i
$657$	6.00000	+	16.9706i	0.234082	+	0.662085i
$658$		0			0
$659$		−	5.65685i		−	0.220360i	−0.993912	−	0.110180i	$-0.964857\pi$
$659$		−	5.65685i		−	0.220360i	0.993912	−	0.110180i	$-0.0351427\pi$
$660$	64.0000	+	45.2548i	2.49120	+	1.76154i
$661$			8.48528i			0.330039i	0.986290	+	0.165020i	$0.0527687\pi$
$661$			8.48528i			0.330039i	−0.986290	+	0.165020i	$0.947231\pi$
$662$			2.82843i			0.109930i
$663$	16.0000	−	22.6274i	0.621389	−	0.878776i
$664$	−16.0000			−0.620920
$665$			22.6274i			0.877454i
$666$	−4.00000	−	11.3137i	−0.154997	−	0.438397i
$667$		0			0
$668$	−48.0000			−1.85718
$669$	16.0000	+	11.3137i	0.618596	+	0.437413i
$670$			11.3137i			0.437087i
$671$	−16.0000			−0.617673
$672$	−16.0000	+	22.6274i	−0.617213	+	0.872872i
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$		−	25.4558i		−	0.980522i
$675$	55.0000	+	15.5563i	2.11695	+	0.598764i
$676$	38.0000			1.46154
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$	−4.00000	+	5.65685i	−0.153619	+	0.217250i
$679$			5.65685i			0.217090i
$680$	32.0000			1.22714
$681$	16.0000	+	11.3137i	0.613121	+	0.433542i
$682$		−	45.2548i		−	1.73290i
$683$		−	31.1127i		−	1.19049i	−0.803543	−	0.595247i	$-0.797054\pi$
$683$		−	31.1127i		−	1.19049i	0.803543	−	0.595247i	$-0.202946\pi$
$684$	−4.00000	−	11.3137i	−0.152944	−	0.432590i
$685$			11.3137i			0.432275i
$686$	24.0000			0.916324
$687$	−12.0000	−	8.48528i	−0.457829	−	0.323734i
$688$	−24.0000			−0.914991
$689$			67.8823i			2.58611i
$690$	8.00000	+	5.65685i	0.304555	+	0.215353i
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	32.0000			1.21646
$693$	−16.0000	−	45.2548i	−0.607790	−	1.71909i
$694$	20.0000			0.759190
$695$	40.0000			1.51729
$696$		0			0
$697$	16.0000			0.606043
$698$		0			0
$699$	−24.0000	−	16.9706i	−0.907763	−	0.641886i
$700$			62.2254i			2.35190i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$	−40.0000	−	11.3137i	−1.50970	−	0.427008i
$703$			5.65685i			0.213352i
$704$		−	45.2548i		−	1.70561i
$705$		0			0
$706$	−40.0000			−1.50542
$707$			22.6274i			0.850992i
$708$	−8.00000	−	5.65685i	−0.300658	−	0.212598i
$709$			2.82843i			0.106224i	0.998589	+	0.0531119i	$0.0169140\pi$
$709$			2.82843i			0.106224i	−0.998589	+	0.0531119i	$0.983086\pi$
$710$			45.2548i			1.69838i
$711$	−8.00000	+	2.82843i	−0.300023	+	0.106074i
$712$	−24.0000			−0.899438
$713$		−	5.65685i		−	0.211851i
$714$	−16.0000	−	11.3137i	−0.598785	−	0.423405i
$715$	−128.000			−4.78693
$716$		−	28.2843i		−	1.05703i
$717$	−24.0000	+	33.9411i	−0.896296	+	1.26755i
$718$			22.6274i			0.844448i
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$	−16.0000	−	45.2548i	−0.596285	−	1.68655i
$721$	−8.00000			−0.297936
$722$		−	21.2132i		−	0.789474i
$723$	14.0000	−	19.7990i	0.520666	−	0.736332i
$724$			16.9706i			0.630706i
$725$		0			0
$726$	42.0000	+	29.6985i	1.55877	+	1.10221i
$727$			42.4264i			1.57351i	0.617266	+	0.786754i	$0.288240\pi$
$727$			42.4264i			1.57351i	−0.617266	+	0.786754i	$0.711760\pi$
$728$		−	45.2548i		−	1.67726i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		−	33.9411i		−	1.25622i
$731$		−	16.9706i		−	0.627679i
$732$	8.00000	+	5.65685i	0.295689	+	0.209083i
$733$			42.4264i			1.56706i	0.621357	+	0.783528i	$0.286582\pi$
$733$			42.4264i			1.56706i	−0.621357	+	0.783528i	$0.713418\pi$
$734$	20.0000			0.738213
$735$	4.00000	−	5.65685i	0.147542	−	0.208656i
$736$		−	5.65685i		−	0.208514i
$737$			11.3137i			0.416746i
$738$	−8.00000	−	22.6274i	−0.294484	−	0.832927i
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$			22.6274i			0.831800i
$741$	16.0000	+	11.3137i	0.587775	+	0.415619i
$742$	48.0000			1.76214
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	−16.0000	+	22.6274i	−0.586588	+	0.829561i
$745$	48.0000			1.75858
$746$	12.0000			0.439351
$747$	−16.0000	+	5.65685i	−0.585409	+	0.206973i
$748$	32.0000			1.17004
$749$	−32.0000			−1.16925
$750$	−48.0000	−	33.9411i	−1.75271	−	1.23935i
$751$		−	19.7990i		−	0.722475i	−0.932474	−	0.361238i	$-0.882354\pi$
$751$		−	19.7990i		−	0.722475i	0.932474	−	0.361238i	$-0.117646\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			45.2548i			1.64699i
$756$	−8.00000	+	28.2843i	−0.290957	+	1.02869i
$757$		−	25.4558i		−	0.925208i	−0.886565	−	0.462604i	$-0.846915\pi$
$757$		−	25.4558i		−	0.925208i	0.886565	−	0.462604i	$-0.153085\pi$
$758$			25.4558i			0.924598i
$759$	8.00000	+	5.65685i	0.290382	+	0.205331i
$760$			22.6274i			0.820783i
$761$		−	28.2843i		−	1.02530i	−0.858596	−	0.512652i	$-0.828663\pi$
$761$		−	28.2843i		−	1.02530i	0.858596	−	0.512652i	$-0.171337\pi$
$762$	−24.0000	+	33.9411i	−0.869428	+	1.22956i
$763$	24.0000			0.868858
$764$	−48.0000			−1.73658
$765$	32.0000	−	11.3137i	1.15696	−	0.409048i
$766$		0			0
$767$	16.0000			0.577727
$768$	−16.0000	+	22.6274i	−0.577350	+	0.816497i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$			90.5097i			3.26174i
$771$	40.0000	+	28.2843i	1.44056	+	1.01863i
$772$	−36.0000			−1.29567
$773$	−20.0000			−0.719350			−0.359675	−	0.933078i	$-0.617112\pi$
$773$	−20.0000			−0.719350			−0.359675	+	0.933078i	$0.617112\pi$
$774$	−24.0000	+	8.48528i	−0.862662	+	0.304997i
$775$			62.2254i			2.23520i
$776$			5.65685i			0.203069i
$777$	8.00000	−	11.3137i	0.286998	−	0.405877i
$778$			50.9117i			1.82527i
$779$			11.3137i			0.405356i
$780$	64.0000	+	45.2548i	2.29157	+	1.62038i
$781$			45.2548i			1.61935i
$782$	4.00000			0.143040
$783$		0			0
$784$	−4.00000			−0.142857
$785$		−	79.1960i		−	2.82663i
$786$	−4.00000	+	5.65685i	−0.142675	+	0.201773i
$787$	−10.0000			−0.356462			−0.178231	−	0.983989i	$-0.557037\pi$
$787$	−10.0000			−0.356462			−0.178231	+	0.983989i	$0.557037\pi$
$788$	32.0000			1.13995
$789$	24.0000	−	33.9411i	0.854423	−	1.20834i
$790$	16.0000			0.569254
$791$	−8.00000			−0.284447
$792$	−16.0000	−	45.2548i	−0.568535	−	1.60806i
$793$	−16.0000			−0.568177
$794$	−32.0000			−1.13564
$795$	−48.0000	+	67.8823i	−1.70238	+	2.40754i
$796$		−	16.9706i		−	0.601506i
$797$	−28.0000			−0.991811			−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000			−0.991811			−0.495905	+	0.868377i	$0.665164\pi$
$798$	8.00000	−	11.3137i	0.283197	−	0.400501i
$799$		0			0
$800$			62.2254i			2.20000i
$801$	−24.0000	+	8.48528i	−0.847998	+	0.299813i
$802$	52.0000			1.83618
$803$		−	33.9411i		−	1.19776i
$804$	4.00000	−	5.65685i	0.141069	−	0.199502i
$805$			11.3137i			0.398756i
$806$		−	45.2548i		−	1.59403i
$807$	−16.0000	+	22.6274i	−0.563227	+	0.796523i
$808$			22.6274i			0.796030i
$809$			16.9706i			0.596653i	0.954464	+	0.298327i	$0.0964285\pi$
$809$			16.9706i			0.596653i	−0.954464	+	0.298327i	$0.903572\pi$
$810$	−32.0000	−	39.5980i	−1.12437	−	1.39133i
$811$	−50.0000			−1.75574			−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000			−1.75574			−0.877869	+	0.478901i	$0.841035\pi$
$812$		0			0
$813$	8.00000	+	5.65685i	0.280572	+	0.198395i
$814$			22.6274i			0.793091i
$815$	−24.0000			−0.840683
$816$	−16.0000	−	11.3137i	−0.560112	−	0.396059i
$817$	12.0000			0.419827
$818$		−	42.4264i		−	1.48340i
$819$	−16.0000	−	45.2548i	−0.559085	−	1.58133i
$820$			45.2548i			1.58037i
$821$	−24.0000			−0.837606			−0.418803	−	0.908077i	$-0.637550\pi$
$821$	−24.0000			−0.837606			−0.418803	+	0.908077i	$0.637550\pi$
$822$	4.00000	−	5.65685i	0.139516	−	0.197305i
$823$		−	39.5980i		−	1.38030i	−0.723667	−	0.690149i	$-0.757545\pi$
$823$		−	39.5980i		−	1.38030i	0.723667	−	0.690149i	$-0.242455\pi$
$824$	−8.00000			−0.278693
$825$	−88.0000	−	62.2254i	−3.06377	−	2.16641i
$826$		−	11.3137i		−	0.393654i
$827$		−	11.3137i		−	0.393416i	−0.980462	−	0.196708i	$-0.936975\pi$
$827$		−	11.3137i		−	0.393416i	0.980462	−	0.196708i	$-0.0630251\pi$
$828$	−2.00000	−	5.65685i	−0.0695048	−	0.196589i
$829$			45.2548i			1.57177i	0.618376	+	0.785883i	$0.287791\pi$
$829$			45.2548i			1.57177i	−0.618376	+	0.785883i	$0.712209\pi$
$830$	32.0000			1.11074
$831$	8.00000	+	5.65685i	0.277517	+	0.196234i
$832$		−	45.2548i		−	1.56893i
$833$		−	2.82843i		−	0.0979992i
$834$	−20.0000	−	14.1421i	−0.692543	−	0.489702i
$835$	96.0000			3.32222
$836$			22.6274i			0.782586i
$837$	−8.00000	+	28.2843i	−0.276520	+	0.977647i
$838$	8.00000			0.276355
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	32.0000	−	45.2548i	1.10410	−	1.56144i
$841$	−29.0000			−1.00000
$842$	−52.0000			−1.79204
$843$	28.0000	+	19.7990i	0.964371	+	0.681913i
$844$	20.0000			0.688428
$845$	−76.0000			−2.61448
$846$		0			0
$847$			59.3970i			2.04090i
$848$	48.0000			1.64833
$849$	−22.0000	+	31.1127i	−0.755038	+	1.06779i
$850$	−44.0000			−1.50919
$851$			2.82843i			0.0969572i
$852$	16.0000	−	22.6274i	0.548151	−	0.775203i
$853$		−	33.9411i		−	1.16212i	−0.813860	−	0.581061i	$-0.802638\pi$
$853$		−	33.9411i		−	1.16212i	0.813860	−	0.581061i	$-0.197362\pi$
$854$			11.3137i			0.387147i
$855$	8.00000	+	22.6274i	0.273594	+	0.773841i
$856$	−32.0000			−1.09374
$857$			11.3137i			0.386469i	0.981153	+	0.193234i	$0.0618978\pi$
$857$			11.3137i			0.386469i	−0.981153	+	0.193234i	$0.938102\pi$
$858$	64.0000	+	45.2548i	2.18492	+	1.54497i
$859$	22.0000			0.750630			0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000			0.750630			0.375315	+	0.926897i	$0.377534\pi$
$860$	48.0000			1.63679
$861$	16.0000	−	22.6274i	0.545279	−	0.771140i
$862$			33.9411i			1.15604i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$	−8.00000	+	28.2843i	−0.272166	+	0.962250i
$865$	−64.0000			−2.17607
$866$			19.7990i			0.672797i
$867$	−9.00000	+	12.7279i	−0.305656	+	0.432263i
$868$	−32.0000			−1.08615
$869$	16.0000			0.542763
$870$		0			0
$871$			11.3137i			0.383350i
$872$	24.0000			0.812743
$873$	2.00000	+	5.65685i	0.0676897	+	0.191456i
$874$			2.82843i			0.0956730i
$875$		−	67.8823i		−	2.29484i
$876$	−12.0000	+	16.9706i	−0.405442	+	0.573382i
$877$		−	50.9117i		−	1.71917i	−0.510997	−	0.859583i	$-0.670724\pi$
$877$		−	50.9117i		−	1.71917i	0.510997	−	0.859583i	$-0.329276\pi$
$878$	−32.0000			−1.07995
$879$	−4.00000	+	5.65685i	−0.134917	+	0.190801i
$880$			90.5097i			3.05108i
$881$			19.7990i			0.667045i	0.942742	+	0.333522i	$0.108237\pi$
$881$			19.7990i			0.667045i	−0.942742	+	0.333522i	$0.891763\pi$
$882$	−4.00000	+	1.41421i	−0.134687	+	0.0476190i
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$	32.0000			1.07628
$885$	16.0000	+	11.3137i	0.537834	+	0.380306i
$886$	−12.0000			−0.403148
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	8.00000	−	11.3137i	0.268462	−	0.379663i
$889$	−48.0000			−1.60987
$890$	48.0000			1.60896
$891$	−32.0000	−	39.5980i	−1.07204	−	1.32658i
$892$			22.6274i			0.757622i
$893$		0			0
$894$	−24.0000	−	16.9706i	−0.802680	−	0.567581i
$895$			56.5685i			1.89088i
$896$	−32.0000			−1.06904
$897$	8.00000	+	5.65685i	0.267112	+	0.188877i
$898$		0			0
$899$		0			0
$900$	22.0000	+	62.2254i	0.733333	+	2.07418i
$901$			33.9411i			1.13074i
$902$			45.2548i			1.50682i
$903$	−24.0000	−	16.9706i	−0.798670	−	0.564745i
$904$	−8.00000			−0.266076
$905$		−	33.9411i		−	1.12824i
$906$	16.0000	−	22.6274i	0.531564	−	0.751746i
$907$	42.0000			1.39459			0.697294	−	0.716786i	$-0.254387\pi$
$907$	42.0000			1.39459			0.697294	+	0.716786i	$0.254387\pi$
$908$			22.6274i			0.750917i
$909$	8.00000	+	22.6274i	0.265343	+	0.750504i
$910$			90.5097i			3.00037i
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	8.00000	−	11.3137i	0.264906	−	0.374634i
$913$	32.0000			1.05905
$914$		−	53.7401i		−	1.77757i
$915$	−16.0000	−	11.3137i	−0.528944	−	0.374020i
$916$		−	16.9706i		−	0.560723i
$917$	−8.00000			−0.264183
$918$	−20.0000	−	5.65685i	−0.660098	−	0.186704i
$919$			2.82843i			0.0933012i	0.998911	+	0.0466506i	$0.0148547\pi$
$919$			2.82843i			0.0933012i	−0.998911	+	0.0466506i	$0.985145\pi$
$920$			11.3137i			0.373002i
$921$	10.0000	−	14.1421i	0.329511	−	0.465999i
$922$			45.2548i			1.49039i
$923$			45.2548i			1.48958i
$924$	32.0000	−	45.2548i	1.05272	−	1.48877i
$925$		−	31.1127i		−	1.02298i
$926$	48.0000			1.57738
$927$	−8.00000	+	2.82843i	−0.262754	+	0.0928977i
$928$		0			0
$929$			22.6274i			0.742381i	0.928557	+	0.371191i	$0.121050\pi$
$929$			22.6274i			0.742381i	−0.928557	+	0.371191i	$0.878950\pi$
$930$	32.0000	−	45.2548i	1.04932	−	1.48396i
$931$	2.00000			0.0655474
$932$		−	33.9411i		−	1.11178i
$933$	16.0000	−	22.6274i	0.523816	−	0.740788i
$934$	8.00000			0.261768
$935$	−64.0000			−2.09302
$936$	−16.0000	−	45.2548i	−0.522976	−	1.47920i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	8.00000			0.261209
$939$	26.0000	−	36.7696i	0.848478	−	1.19993i
$940$		0			0
$941$	28.0000			0.912774			0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000			0.912774			0.456387	+	0.889781i	$0.349143\pi$
$942$	−28.0000	+	39.5980i	−0.912289	+	1.29017i
$943$			5.65685i			0.184213i
$944$		−	11.3137i		−	0.368230i
$945$	16.0000	−	56.5685i	0.520480	−	1.84017i
$946$	48.0000			1.56061
$947$			25.4558i			0.827204i	0.910458	+	0.413602i	$0.135729\pi$
$947$			25.4558i			0.827204i	−0.910458	+	0.413602i	$0.864271\pi$
$948$	−8.00000	−	5.65685i	−0.259828	−	0.183726i
$949$		−	33.9411i		−	1.10178i
$950$		−	31.1127i		−	1.00943i
$951$	16.0000	−	22.6274i	0.518836	−	0.733744i
$952$		−	22.6274i		−	0.733359i
$953$			48.0833i			1.55757i	0.627291	+	0.778785i	$0.284164\pi$
$953$			48.0833i			1.55757i	−0.627291	+	0.778785i	$0.715836\pi$
$954$	48.0000	−	16.9706i	1.55406	−	0.549442i
$955$	96.0000			3.10649
$956$	−48.0000			−1.55243
$957$		0			0
$958$		−	22.6274i		−	0.731059i
$959$	8.00000			0.258333
$960$	32.0000	−	45.2548i	1.03280	−	1.46059i
$961$	−1.00000			−0.0322581
$962$			22.6274i			0.729537i
$963$	−32.0000	+	11.3137i	−1.03119	+	0.364579i
$964$	28.0000			0.901819
$965$	72.0000			2.31776
$966$	4.00000	−	5.65685i	0.128698	−	0.182006i
$967$		−	5.65685i		−	0.181912i	−0.995855	−	0.0909561i	$-0.971008\pi$
$967$		−	5.65685i		−	0.181912i	0.995855	−	0.0909561i	$-0.0289923\pi$
$968$			59.3970i			1.90909i
$969$	8.00000	+	5.65685i	0.256997	+	0.181724i
$970$		−	11.3137i		−	0.363261i
$971$		−	5.65685i		−	0.181537i	−0.995872	−	0.0907685i	$-0.971068\pi$
$971$		−	5.65685i		−	0.181537i	0.995872	−	0.0907685i	$-0.0289323\pi$
$972$	2.00000	+	31.1127i	0.0641500	+	0.997940i
$973$		−	28.2843i		−	0.906752i
$974$		0			0
$975$	−88.0000	−	62.2254i	−2.81826	−	1.99281i
$976$			11.3137i			0.362143i
$977$		−	31.1127i		−	0.995383i	−0.867354	−	0.497692i	$-0.834181\pi$
$977$		−	31.1127i		−	0.995383i	0.867354	−	0.497692i	$-0.165819\pi$
$978$	12.0000	+	8.48528i	0.383718	+	0.271329i
$979$	48.0000			1.53409
$980$	8.00000			0.255551
$981$	24.0000	−	8.48528i	0.766261	−	0.270914i
$982$	−52.0000			−1.65939
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	16.0000	−	22.6274i	0.510061	−	0.721336i
$985$	−64.0000			−2.03921
$986$		0			0
$987$		0			0
$988$			22.6274i			0.719874i
$989$	6.00000			0.190789
$990$	32.0000	+	90.5097i	1.01703	+	2.87659i
$991$		−	50.9117i		−	1.61726i	−0.588315	−	0.808632i	$-0.700209\pi$
$991$		−	50.9117i		−	1.61726i	0.588315	−	0.808632i	$-0.299791\pi$
$992$	−32.0000			−1.01600
$993$	−2.00000	+	2.82843i	−0.0634681	+	0.0897574i
$994$	32.0000			1.01498
$995$			33.9411i			1.07601i
$996$	−16.0000	−	11.3137i	−0.506979	−	0.358489i
$997$		−	33.9411i		−	1.07493i	−0.843287	−	0.537463i	$-0.819383\pi$
$997$		−	33.9411i		−	1.07493i	0.843287	−	0.537463i	$-0.180617\pi$
$998$			8.48528i			0.268597i
$999$	4.00000	−	14.1421i	0.126554	−	0.447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.b.323.2	yes	2
3.2	odd	2		552.2.j.a.323.1	✓	2
4.3	odd	2		2208.2.j.b.47.1		2
8.3	odd	2		552.2.j.a.323.2	yes	2
8.5	even	2		2208.2.j.a.47.1		2
12.11	even	2		2208.2.j.a.47.2		2
24.5	odd	2		2208.2.j.b.47.2		2
24.11	even	2	inner	552.2.j.b.323.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.a.323.1	✓	2	3.2	odd	2
552.2.j.a.323.2	yes	2	8.3	odd	2
552.2.j.b.323.1	yes	2	24.11	even	2	inner
552.2.j.b.323.2	yes	2	1.1	even	1	trivial
2208.2.j.a.47.1		2	8.5	even	2
2208.2.j.a.47.2		2	12.11	even	2
2208.2.j.b.47.1		2	4.3	odd	2
2208.2.j.b.47.2		2	24.5	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +4.00000 q^{5} +(-2.00000 - 1.41421i) q^{6} -2.82843i q^{7} -2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +4.00000 q^{5} +(-2.00000 - 1.41421i) q^{6} -2.82843i q^{7} -2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +5.65685i q^{10} +5.65685i q^{11} +(2.00000 - 2.82843i) q^{12} +5.65685i q^{13} +4.00000 q^{14} +(-4.00000 + 5.65685i) q^{15} +4.00000 q^{16} +2.82843i q^{17} +(4.00000 - 1.41421i) q^{18} -2.00000 q^{19} -8.00000 q^{20} +(4.00000 + 2.82843i) q^{21} -8.00000 q^{22} -1.00000 q^{23} +(4.00000 + 2.82843i) q^{24} +11.0000 q^{25} -8.00000 q^{26} +(5.00000 + 1.41421i) q^{27} +5.65685i q^{28} +(-8.00000 - 5.65685i) q^{30} +5.65685i q^{31} +5.65685i q^{32} +(-8.00000 - 5.65685i) q^{33} -4.00000 q^{34} -11.3137i q^{35} +(2.00000 + 5.65685i) q^{36} -2.82843i q^{37} -2.82843i q^{38} +(-8.00000 - 5.65685i) q^{39} -11.3137i q^{40} -5.65685i q^{41} +(-4.00000 + 5.65685i) q^{42} -6.00000 q^{43} -11.3137i q^{44} +(-4.00000 - 11.3137i) q^{45} -1.41421i q^{46} +(-4.00000 + 5.65685i) q^{48} -1.00000 q^{49} +15.5563i q^{50} +(-4.00000 - 2.82843i) q^{51} -11.3137i q^{52} +12.0000 q^{53} +(-2.00000 + 7.07107i) q^{54} +22.6274i q^{55} -8.00000 q^{56} +(2.00000 - 2.82843i) q^{57} -2.82843i q^{59} +(8.00000 - 11.3137i) q^{60} +2.82843i q^{61} -8.00000 q^{62} +(-8.00000 + 2.82843i) q^{63} -8.00000 q^{64} +22.6274i q^{65} +(8.00000 - 11.3137i) q^{66} +2.00000 q^{67} -5.65685i q^{68} +(1.00000 - 1.41421i) q^{69} +16.0000 q^{70} +8.00000 q^{71} +(-8.00000 + 2.82843i) q^{72} -6.00000 q^{73} +4.00000 q^{74} +(-11.0000 + 15.5563i) q^{75} +4.00000 q^{76} +16.0000 q^{77} +(8.00000 - 11.3137i) q^{78} -2.82843i q^{79} +16.0000 q^{80} +(-7.00000 + 5.65685i) q^{81} +8.00000 q^{82} -5.65685i q^{83} +(-8.00000 - 5.65685i) q^{84} +11.3137i q^{85} -8.48528i q^{86} +16.0000 q^{88} -8.48528i q^{89} +(16.0000 - 5.65685i) q^{90} +16.0000 q^{91} +2.00000 q^{92} +(-8.00000 - 5.65685i) q^{93} -8.00000 q^{95} +(-8.00000 - 5.65685i) q^{96} -2.00000 q^{97} -1.41421i q^{98} +(16.0000 - 5.65685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 - 2 * q^9	\( 2 q - 2 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{9} + 4 q^{12} + 8 q^{14} - 8 q^{15} + 8 q^{16} + 8 q^{18} - 4 q^{19} - 16 q^{20} + 8 q^{21} - 16 q^{22} - 2 q^{23} + 8 q^{24} + 22 q^{25} - 16 q^{26} + 10 q^{27} - 16 q^{30} - 16 q^{33} - 8 q^{34} + 4 q^{36} - 16 q^{39} - 8 q^{42} - 12 q^{43} - 8 q^{45} - 8 q^{48} - 2 q^{49} - 8 q^{51} + 24 q^{53} - 4 q^{54} - 16 q^{56} + 4 q^{57} + 16 q^{60} - 16 q^{62} - 16 q^{63} - 16 q^{64} + 16 q^{66} + 4 q^{67} + 2 q^{69} + 32 q^{70} + 16 q^{71} - 16 q^{72} - 12 q^{73} + 8 q^{74} - 22 q^{75} + 8 q^{76} + 32 q^{77} + 16 q^{78} + 32 q^{80} - 14 q^{81} + 16 q^{82} - 16 q^{84} + 32 q^{88} + 32 q^{90} + 32 q^{91} + 4 q^{92} - 16 q^{93} - 16 q^{95} - 16 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 - 2 * q^9 + 4 * q^12 + 8 * q^14 - 8 * q^15 + 8 * q^16 + 8 * q^18 - 4 * q^19 - 16 * q^20 + 8 * q^21 - 16 * q^22 - 2 * q^23 + 8 * q^24 + 22 * q^25 - 16 * q^26 + 10 * q^27 - 16 * q^30 - 16 * q^33 - 8 * q^34 + 4 * q^36 - 16 * q^39 - 8 * q^42 - 12 * q^43 - 8 * q^45 - 8 * q^48 - 2 * q^49 - 8 * q^51 + 24 * q^53 - 4 * q^54 - 16 * q^56 + 4 * q^57 + 16 * q^60 - 16 * q^62 - 16 * q^63 - 16 * q^64 + 16 * q^66 + 4 * q^67 + 2 * q^69 + 32 * q^70 + 16 * q^71 - 16 * q^72 - 12 * q^73 + 8 * q^74 - 22 * q^75 + 8 * q^76 + 32 * q^77 + 16 * q^78 + 32 * q^80 - 14 * q^81 + 16 * q^82 - 16 * q^84 + 32 * q^88 + 32 * q^90 + 32 * q^91 + 4 * q^92 - 16 * q^93 - 16 * q^95 - 16 * q^96 - 4 * q^97 + 32 * q^99

Introduction

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