LMFDB - Embedded newform 289.2.c.a.38.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(38,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("289.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.c (of order $4$, degree $2$, not 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	289.38
Dual form			289.2.c.a.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{4} +(1.41421 - 1.41421i) q^{5} +(-2.82843 - 2.82843i) q^{7} -3.00000i q^{8} +3.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{4} +(1.41421 - 1.41421i) q^{5} +(-2.82843 - 2.82843i) q^{7} -3.00000i q^{8} +3.00000i q^{9} +(-1.41421 - 1.41421i) q^{10} +2.00000 q^{13} +(-2.82843 + 2.82843i) q^{14} -1.00000 q^{16} +3.00000 q^{18} -4.00000i q^{19} +(1.41421 - 1.41421i) q^{20} +(2.82843 + 2.82843i) q^{23} +1.00000i q^{25} -2.00000i q^{26} +(-2.82843 - 2.82843i) q^{28} +(-4.24264 + 4.24264i) q^{29} +(2.82843 - 2.82843i) q^{31} -5.00000i q^{32} -8.00000 q^{35} +3.00000i q^{36} +(-1.41421 + 1.41421i) q^{37} -4.00000 q^{38} +(-4.24264 - 4.24264i) q^{40} +(4.24264 + 4.24264i) q^{41} -4.00000i q^{43} +(4.24264 + 4.24264i) q^{45} +(2.82843 - 2.82843i) q^{46} +9.00000i q^{49} +1.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(-8.48528 + 8.48528i) q^{56} +(4.24264 + 4.24264i) q^{58} +12.0000i q^{59} +(7.07107 + 7.07107i) q^{61} +(-2.82843 - 2.82843i) q^{62} +(8.48528 - 8.48528i) q^{63} -7.00000 q^{64} +(2.82843 - 2.82843i) q^{65} +4.00000 q^{67} +8.00000i q^{70} +(-2.82843 + 2.82843i) q^{71} +9.00000 q^{72} +(4.24264 - 4.24264i) q^{73} +(1.41421 + 1.41421i) q^{74} -4.00000i q^{76} +(8.48528 + 8.48528i) q^{79} +(-1.41421 + 1.41421i) q^{80} -9.00000 q^{81} +(4.24264 - 4.24264i) q^{82} -4.00000i q^{83} -4.00000 q^{86} -10.0000 q^{89} +(4.24264 - 4.24264i) q^{90} +(-5.65685 - 5.65685i) q^{91} +(2.82843 + 2.82843i) q^{92} +(-5.65685 - 5.65685i) q^{95} +(-1.41421 + 1.41421i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4}+O(q^{10}) $ 4 * q + 4 * q^4	$ 4 q + 4 q^{4} + 8 q^{13} - 4 q^{16} + 12 q^{18} - 32 q^{35} - 16 q^{38} + 4 q^{50} + 8 q^{52} - 28 q^{64} + 16 q^{67} + 36 q^{72} - 36 q^{81} - 16 q^{86} - 40 q^{89} + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^4 + 8 * q^13 - 4 * q^16 + 12 * q^18 - 32 * q^35 - 16 * q^38 + 4 * q^50 + 8 * q^52 - 28 * q^64 + 16 * q^67 + 36 * q^72 - 36 * q^81 - 16 * q^86 - 40 * q^89 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$	1.00000			0.500000
$5$	1.41421	−	1.41421i	0.632456	−	0.632456i	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	1.41421	−	1.41421i	0.632456	−	0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$6$		0			0
$7$	−2.82843	−	2.82843i	−1.06904	−	1.06904i	−0.997433	−	0.0716124i	$-0.977186\pi$
$7$	−2.82843	−	2.82843i	−1.06904	−	1.06904i	−0.0716124	−	0.997433i	$-0.522814\pi$
$8$		−	3.00000i		−	1.06066i
$9$			3.00000i			1.00000i
$10$	−1.41421	−	1.41421i	−0.447214	−	0.447214i
$11$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$11$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.82843	+	2.82843i	−0.755929	+	0.755929i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	3.00000			0.707107
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	1.41421	−	1.41421i	0.316228	−	0.316228i
$21$		0			0
$22$		0			0
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	0.937568	−	0.347801i	$-0.113071\pi$
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	−0.347801	+	0.937568i	$0.613071\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		−	2.00000i		−	0.392232i
$27$		0			0
$28$	−2.82843	−	2.82843i	−0.534522	−	0.534522i
$29$	−4.24264	+	4.24264i	−0.787839	+	0.787839i	−0.981140	−	0.193301i	$-0.938081\pi$
$29$	−4.24264	+	4.24264i	−0.787839	+	0.787839i	0.193301	+	0.981140i	$0.438081\pi$
$30$		0			0
$31$	2.82843	−	2.82843i	0.508001	−	0.508001i	−0.405912	−	0.913912i	$-0.633046\pi$
$31$	2.82843	−	2.82843i	0.508001	−	0.508001i	0.913912	+	0.405912i	$0.133046\pi$
$32$		−	5.00000i		−	0.883883i
$33$		0			0
$34$		0			0
$35$	−8.00000			−1.35225
$36$			3.00000i			0.500000i
$37$	−1.41421	+	1.41421i	−0.232495	+	0.232495i	−0.813733	−	0.581238i	$-0.802568\pi$
$37$	−1.41421	+	1.41421i	−0.232495	+	0.232495i	0.581238	+	0.813733i	$0.302568\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	−4.24264	−	4.24264i	−0.670820	−	0.670820i
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	−0.293400	+	0.955990i	$0.594787\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	4.24264	+	4.24264i	0.632456	+	0.632456i
$46$	2.82843	−	2.82843i	0.417029	−	0.417029i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$			9.00000i			1.28571i
$50$	1.00000			0.141421
$51$		0			0
$52$	2.00000			0.277350
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$	−8.48528	+	8.48528i	−1.13389	+	1.13389i
$57$		0			0
$58$	4.24264	+	4.24264i	0.557086	+	0.557086i
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$		0			0
$61$	7.07107	+	7.07107i	0.905357	+	0.905357i	0.995893	−	0.0905357i	$-0.0288579\pi$
$61$	7.07107	+	7.07107i	0.905357	+	0.905357i	−0.0905357	+	0.995893i	$0.528858\pi$
$62$	−2.82843	−	2.82843i	−0.359211	−	0.359211i
$63$	8.48528	−	8.48528i	1.06904	−	1.06904i
$64$	−7.00000			−0.875000
$65$	2.82843	−	2.82843i	0.350823	−	0.350823i
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$		0			0
$70$			8.00000i			0.956183i
$71$	−2.82843	+	2.82843i	−0.335673	+	0.335673i	−0.854736	−	0.519063i	$-0.826281\pi$
$71$	−2.82843	+	2.82843i	−0.335673	+	0.335673i	0.519063	+	0.854736i	$0.326281\pi$
$72$	9.00000			1.06066
$73$	4.24264	−	4.24264i	0.496564	−	0.496564i	−0.413803	−	0.910366i	$-0.635800\pi$
$73$	4.24264	−	4.24264i	0.496564	−	0.496564i	0.910366	+	0.413803i	$0.135800\pi$
$74$	1.41421	+	1.41421i	0.164399	+	0.164399i
$75$		0			0
$76$		−	4.00000i		−	0.458831i
$77$		0			0
$78$		0			0
$79$	8.48528	+	8.48528i	0.954669	+	0.954669i	0.999016	−	0.0443474i	$-0.0141209\pi$
$79$	8.48528	+	8.48528i	0.954669	+	0.954669i	−0.0443474	+	0.999016i	$0.514121\pi$
$80$	−1.41421	+	1.41421i	−0.158114	+	0.158114i
$81$	−9.00000			−1.00000
$82$	4.24264	−	4.24264i	0.468521	−	0.468521i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000			−0.431331
$87$		0			0
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$	4.24264	−	4.24264i	0.447214	−	0.447214i
$91$	−5.65685	−	5.65685i	−0.592999	−	0.592999i
$92$	2.82843	+	2.82843i	0.294884	+	0.294884i
$93$		0			0
$94$		0			0
$95$	−5.65685	−	5.65685i	−0.580381	−	0.580381i
$96$		0			0
$97$	−1.41421	+	1.41421i	−0.143592	+	0.143592i	−0.775248	−	0.631657i	$-0.782375\pi$
$97$	−1.41421	+	1.41421i	−0.143592	+	0.143592i	0.631657	+	0.775248i	$0.282375\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$			1.00000i			0.100000i
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		−	6.00000i		−	0.588348i
$105$		0			0
$106$	6.00000			0.582772
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$108$		0			0
$109$	−4.24264	−	4.24264i	−0.406371	−	0.406371i	0.474100	−	0.880471i	$-0.342774\pi$
$109$	−4.24264	−	4.24264i	−0.406371	−	0.406371i	−0.880471	+	0.474100i	$0.842774\pi$
$110$		0			0
$111$		0			0
$112$	2.82843	+	2.82843i	0.267261	+	0.267261i
$113$	−9.89949	−	9.89949i	−0.931266	−	0.931266i	0.0665190	−	0.997785i	$-0.478811\pi$
$113$	−9.89949	−	9.89949i	−0.931266	−	0.931266i	−0.997785	+	0.0665190i	$0.978811\pi$
$114$		0			0
$115$	8.00000			0.746004
$116$	−4.24264	+	4.24264i	−0.393919	+	0.393919i
$117$			6.00000i			0.554700i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$		−	11.0000i		−	1.00000i
$122$	7.07107	−	7.07107i	0.640184	−	0.640184i
$123$		0			0
$124$	2.82843	−	2.82843i	0.254000	−	0.254000i
$125$	8.48528	+	8.48528i	0.758947	+	0.758947i
$126$	−8.48528	−	8.48528i	−0.755929	−	0.755929i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		−	3.00000i		−	0.265165i
$129$		0			0
$130$	−2.82843	−	2.82843i	−0.248069	−	0.248069i
$131$	−11.3137	+	11.3137i	−0.988483	+	0.988483i	−0.999934	−	0.0114511i	$-0.996355\pi$
$131$	−11.3137	+	11.3137i	−0.988483	+	0.988483i	0.0114511	+	0.999934i	$0.496355\pi$
$132$		0			0
$133$	−11.3137	+	11.3137i	−0.981023	+	0.981023i
$134$		−	4.00000i		−	0.345547i
$135$		0			0
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	−0.905070	−	0.425262i	$-0.860182\pi$
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	0.425262	+	0.905070i	$0.360182\pi$
$140$	−8.00000			−0.676123
$141$		0			0
$142$	2.82843	+	2.82843i	0.237356	+	0.237356i
$143$		0			0
$144$		−	3.00000i		−	0.250000i
$145$			12.0000i			0.996546i
$146$	−4.24264	−	4.24264i	−0.351123	−	0.351123i
$147$		0			0
$148$	−1.41421	+	1.41421i	−0.116248	+	0.116248i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		−	16.0000i		−	1.30206i	−0.759051	−	0.651031i	$-0.774337\pi$
$151$		−	16.0000i		−	1.30206i	0.759051	−	0.651031i	$-0.225663\pi$
$152$	−12.0000			−0.973329
$153$		0			0
$154$		0			0
$155$		−	8.00000i		−	0.642575i
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	8.48528	−	8.48528i	0.675053	−	0.675053i
$159$		0			0
$160$	−7.07107	−	7.07107i	−0.559017	−	0.559017i
$161$		−	16.0000i		−	1.26098i
$162$			9.00000i			0.707107i
$163$	−16.9706	−	16.9706i	−1.32924	−	1.32924i	−0.906036	−	0.423201i	$-0.860906\pi$
$163$	−16.9706	−	16.9706i	−1.32924	−	1.32924i	−0.423201	−	0.906036i	$-0.639094\pi$
$164$	4.24264	+	4.24264i	0.331295	+	0.331295i
$165$		0			0
$166$	−4.00000			−0.310460
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	−0.808022	−	0.589152i	$-0.799462\pi$
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	0.589152	+	0.808022i	$0.299462\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	12.0000			0.917663
$172$		−	4.00000i		−	0.304997i
$173$	15.5563	−	15.5563i	1.18273	−	1.18273i	0.203692	−	0.979035i	$-0.434706\pi$
$173$	15.5563	−	15.5563i	1.18273	−	1.18273i	0.979035	−	0.203692i	$-0.0652942\pi$
$174$		0			0
$175$	2.82843	−	2.82843i	0.213809	−	0.213809i
$176$		0			0
$177$		0			0
$178$			10.0000i			0.749532i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	4.24264	+	4.24264i	0.316228	+	0.316228i
$181$	−1.41421	−	1.41421i	−0.105118	−	0.105118i	0.652592	−	0.757710i	$-0.273682\pi$
$181$	−1.41421	−	1.41421i	−0.105118	−	0.105118i	−0.757710	+	0.652592i	$0.773682\pi$
$182$	−5.65685	+	5.65685i	−0.419314	+	0.419314i
$183$		0			0
$184$	8.48528	−	8.48528i	0.625543	−	0.625543i
$185$			4.00000i			0.294086i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−5.65685	+	5.65685i	−0.410391	+	0.410391i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$	1.41421	+	1.41421i	0.101797	+	0.101797i	0.756171	−	0.654374i	$-0.227068\pi$
$193$	1.41421	+	1.41421i	0.101797	+	0.101797i	−0.654374	+	0.756171i	$0.727068\pi$
$194$	1.41421	+	1.41421i	0.101535	+	0.101535i
$195$		0			0
$196$			9.00000i			0.642857i
$197$	12.7279	+	12.7279i	0.906827	+	0.906827i	0.996015	−	0.0891879i	$-0.0284272\pi$
$197$	12.7279	+	12.7279i	0.906827	+	0.906827i	−0.0891879	+	0.996015i	$0.528427\pi$
$198$		0			0
$199$	14.1421	−	14.1421i	1.00251	−	1.00251i	0.00251257	−	0.999997i	$-0.499200\pi$
$199$	14.1421	−	14.1421i	1.00251	−	1.00251i	0.999997	−	0.00251257i	$-0.000799777\pi$
$200$	3.00000			0.212132
$201$		0			0
$202$			10.0000i			0.703598i
$203$	24.0000			1.68447
$204$		0			0
$205$	12.0000			0.838116
$206$		−	8.00000i		−	0.557386i
$207$	−8.48528	+	8.48528i	−0.589768	+	0.589768i
$208$	−2.00000			−0.138675
$209$		0			0
$210$		0			0
$211$	−5.65685	−	5.65685i	−0.389434	−	0.389434i	0.485052	−	0.874486i	$-0.338801\pi$
$211$	−5.65685	−	5.65685i	−0.389434	−	0.389434i	−0.874486	+	0.485052i	$0.838801\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	5.65685	+	5.65685i	0.386695	+	0.386695i
$215$	−5.65685	−	5.65685i	−0.385794	−	0.385794i
$216$		0			0
$217$	−16.0000			−1.08615
$218$	−4.24264	+	4.24264i	−0.287348	+	0.287348i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$	−14.1421	+	14.1421i	−0.944911	+	0.944911i
$225$	−3.00000			−0.200000
$226$	−9.89949	+	9.89949i	−0.658505	+	0.658505i
$227$	−16.9706	−	16.9706i	−1.12638	−	1.12638i	−0.990762	−	0.135614i	$-0.956699\pi$
$227$	−16.9706	−	16.9706i	−1.12638	−	1.12638i	−0.135614	−	0.990762i	$-0.543301\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		−	8.00000i		−	0.527504i
$231$		0			0
$232$	12.7279	+	12.7279i	0.835629	+	0.835629i
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	−0.554343	−	0.832288i	$-0.687031\pi$
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	0.832288	+	0.554343i	$0.187031\pi$
$234$	6.00000			0.392232
$235$		0			0
$236$			12.0000i			0.781133i
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	12.7279	−	12.7279i	0.819878	−	0.819878i	−0.166212	−	0.986090i	$-0.553154\pi$
$241$	12.7279	−	12.7279i	0.819878	−	0.819878i	0.986090	+	0.166212i	$0.0531537\pi$
$242$	−11.0000			−0.707107
$243$		0			0
$244$	7.07107	+	7.07107i	0.452679	+	0.452679i
$245$	12.7279	+	12.7279i	0.813157	+	0.813157i
$246$		0			0
$247$		−	8.00000i		−	0.509028i
$248$	−8.48528	−	8.48528i	−0.538816	−	0.538816i
$249$		0			0
$250$	8.48528	−	8.48528i	0.536656	−	0.536656i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	8.48528	−	8.48528i	0.534522	−	0.534522i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		0			0
$256$	−17.0000			−1.06250
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$		0			0
$259$	8.00000			0.497096
$260$	2.82843	−	2.82843i	0.175412	−	0.175412i
$261$	−12.7279	−	12.7279i	−0.787839	−	0.787839i
$262$	11.3137	+	11.3137i	0.698963	+	0.698963i
$263$			16.0000i			0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$			16.0000i			0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$		0			0
$265$	8.48528	+	8.48528i	0.521247	+	0.521247i
$266$	11.3137	+	11.3137i	0.693688	+	0.693688i
$267$		0			0
$268$	4.00000			0.244339
$269$	15.5563	−	15.5563i	0.948487	−	0.948487i	−0.0502494	−	0.998737i	$-0.516002\pi$
$269$	15.5563	−	15.5563i	0.948487	−	0.948487i	0.998737	+	0.0502494i	$0.0160016\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$		0			0
$274$			6.00000i			0.362473i
$275$		0			0
$276$		0			0
$277$	−9.89949	+	9.89949i	−0.594803	+	0.594803i	−0.938925	−	0.344122i	$-0.888177\pi$
$277$	−9.89949	+	9.89949i	−0.594803	+	0.594803i	0.344122	+	0.938925i	$0.388177\pi$
$278$	5.65685	+	5.65685i	0.339276	+	0.339276i
$279$	8.48528	+	8.48528i	0.508001	+	0.508001i
$280$			24.0000i			1.43427i
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$		0			0
$283$	−11.3137	−	11.3137i	−0.672530	−	0.672530i	0.285769	−	0.958299i	$-0.407751\pi$
$283$	−11.3137	−	11.3137i	−0.672530	−	0.672530i	−0.958299	+	0.285769i	$0.907751\pi$
$284$	−2.82843	+	2.82843i	−0.167836	+	0.167836i
$285$		0			0
$286$		0			0
$287$		−	24.0000i		−	1.41668i
$288$	15.0000			0.883883
$289$		0			0
$290$	12.0000			0.704664
$291$		0			0
$292$	4.24264	−	4.24264i	0.248282	−	0.248282i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	16.9706	+	16.9706i	0.988064	+	0.988064i
$296$	4.24264	+	4.24264i	0.246598	+	0.246598i
$297$		0			0
$298$		−	10.0000i		−	0.579284i
$299$	5.65685	+	5.65685i	0.327144	+	0.327144i
$300$		0			0
$301$	−11.3137	+	11.3137i	−0.652111	+	0.652111i
$302$	−16.0000			−0.920697
$303$		0			0
$304$			4.00000i			0.229416i
$305$	20.0000			1.14520
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$	−8.00000			−0.454369
$311$	−19.7990	+	19.7990i	−1.12270	+	1.12270i	−0.131363	+	0.991334i	$0.541935\pi$
$311$	−19.7990	+	19.7990i	−1.12270	+	1.12270i	−0.991334	+	0.131363i	$0.958065\pi$
$312$		0			0
$313$	15.5563	+	15.5563i	0.879297	+	0.879297i	0.993462	−	0.114165i	$-0.0364192\pi$
$313$	15.5563	+	15.5563i	0.879297	+	0.879297i	−0.114165	+	0.993462i	$0.536419\pi$
$314$		−	2.00000i		−	0.112867i
$315$		−	24.0000i		−	1.35225i
$316$	8.48528	+	8.48528i	0.477334	+	0.477334i
$317$	−7.07107	−	7.07107i	−0.397151	−	0.397151i	0.480076	−	0.877227i	$-0.340609\pi$
$317$	−7.07107	−	7.07107i	−0.397151	−	0.397151i	−0.877227	+	0.480076i	$0.840609\pi$
$318$		0			0
$319$		0			0
$320$	−9.89949	+	9.89949i	−0.553399	+	0.553399i
$321$		0			0
$322$	−16.0000			−0.891645
$323$		0			0
$324$	−9.00000			−0.500000
$325$			2.00000i			0.110940i
$326$	−16.9706	+	16.9706i	−0.939913	+	0.939913i
$327$		0			0
$328$	12.7279	−	12.7279i	0.702782	−	0.702782i
$329$		0			0
$330$		0			0
$331$		−	4.00000i		−	0.219860i	−0.993939	−	0.109930i	$-0.964937\pi$
$331$		−	4.00000i		−	0.219860i	0.993939	−	0.109930i	$-0.0350627\pi$
$332$		−	4.00000i		−	0.219529i
$333$	−4.24264	−	4.24264i	−0.232495	−	0.232495i
$334$	2.82843	+	2.82843i	0.154765	+	0.154765i
$335$	5.65685	−	5.65685i	0.309067	−	0.309067i
$336$		0			0
$337$	−9.89949	+	9.89949i	−0.539260	+	0.539260i	−0.923312	−	0.384052i	$-0.874528\pi$
$337$	−9.89949	+	9.89949i	−0.539260	+	0.539260i	0.384052	+	0.923312i	$0.374528\pi$
$338$			9.00000i			0.489535i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		−	12.0000i		−	0.648886i
$343$	5.65685	−	5.65685i	0.305441	−	0.305441i
$344$	−12.0000			−0.646997
$345$		0			0
$346$	−15.5563	−	15.5563i	−0.836315	−	0.836315i
$347$	−22.6274	−	22.6274i	−1.21470	−	1.21470i	−0.969462	−	0.245241i	$-0.921133\pi$
$347$	−22.6274	−	22.6274i	−1.21470	−	1.21470i	−0.245241	−	0.969462i	$-0.578867\pi$
$348$		0			0
$349$			18.0000i			0.963518i	0.876304	+	0.481759i	$0.160002\pi$
$349$			18.0000i			0.963518i	−0.876304	+	0.481759i	$0.839998\pi$
$350$	−2.82843	−	2.82843i	−0.151186	−	0.151186i
$351$		0			0
$352$		0			0
$353$	30.0000			1.59674			0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000			1.59674			0.798369	+	0.602168i	$0.205696\pi$
$354$		0			0
$355$			8.00000i			0.424596i
$356$	−10.0000			−0.529999
$357$		0			0
$358$	−12.0000			−0.634220
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	12.7279	−	12.7279i	0.670820	−	0.670820i
$361$	3.00000			0.157895
$362$	−1.41421	+	1.41421i	−0.0743294	+	0.0743294i
$363$		0			0
$364$	−5.65685	−	5.65685i	−0.296500	−	0.296500i
$365$		−	12.0000i		−	0.628109i
$366$		0			0
$367$	−19.7990	−	19.7990i	−1.03350	−	1.03350i	−0.999419	−	0.0340797i	$-0.989150\pi$
$367$	−19.7990	−	19.7990i	−1.03350	−	1.03350i	−0.0340797	−	0.999419i	$-0.510850\pi$
$368$	−2.82843	−	2.82843i	−0.147442	−	0.147442i
$369$	−12.7279	+	12.7279i	−0.662589	+	0.662589i
$370$	4.00000			0.207950
$371$	16.9706	−	16.9706i	0.881068	−	0.881068i
$372$		0			0
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.48528	+	8.48528i	−0.437014	+	0.437014i
$378$		0			0
$379$	5.65685	−	5.65685i	0.290573	−	0.290573i	−0.546734	−	0.837307i	$-0.684129\pi$
$379$	5.65685	−	5.65685i	0.290573	−	0.290573i	0.837307	+	0.546734i	$0.184129\pi$
$380$	−5.65685	−	5.65685i	−0.290191	−	0.290191i
$381$		0			0
$382$		−	16.0000i		−	0.818631i
$383$			24.0000i			1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$			24.0000i			1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$		0			0
$385$		0			0
$386$	1.41421	−	1.41421i	0.0719816	−	0.0719816i
$387$	12.0000			0.609994
$388$	−1.41421	+	1.41421i	−0.0717958	+	0.0717958i
$389$			6.00000i			0.304212i	0.988364	+	0.152106i	$0.0486055\pi$
$389$			6.00000i			0.304212i	−0.988364	+	0.152106i	$0.951394\pi$
$390$		0			0
$391$		0			0
$392$	27.0000			1.36371
$393$		0			0
$394$	12.7279	−	12.7279i	0.641223	−	0.641223i
$395$	24.0000			1.20757
$396$		0			0
$397$	4.24264	+	4.24264i	0.212932	+	0.212932i	0.805512	−	0.592580i	$-0.201890\pi$
$397$	4.24264	+	4.24264i	0.212932	+	0.212932i	−0.592580	+	0.805512i	$0.701890\pi$
$398$	−14.1421	−	14.1421i	−0.708881	−	0.708881i
$399$		0			0
$400$		−	1.00000i		−	0.0500000i
$401$	9.89949	+	9.89949i	0.494357	+	0.494357i	0.909676	−	0.415319i	$-0.136330\pi$
$401$	9.89949	+	9.89949i	0.494357	+	0.494357i	−0.415319	+	0.909676i	$0.636330\pi$
$402$		0			0
$403$	5.65685	−	5.65685i	0.281788	−	0.281788i
$404$	−10.0000			−0.497519
$405$	−12.7279	+	12.7279i	−0.632456	+	0.632456i
$406$		−	24.0000i		−	1.19110i
$407$		0			0
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$		−	12.0000i		−	0.592638i
$411$		0			0
$412$	8.00000			0.394132
$413$	33.9411	−	33.9411i	1.67013	−	1.67013i
$414$	8.48528	+	8.48528i	0.417029	+	0.417029i
$415$	−5.65685	−	5.65685i	−0.277684	−	0.277684i
$416$		−	10.0000i		−	0.490290i
$417$		0			0
$418$		0			0
$419$	5.65685	+	5.65685i	0.276355	+	0.276355i	0.831652	−	0.555297i	$-0.187395\pi$
$419$	5.65685	+	5.65685i	0.276355	+	0.276355i	−0.555297	+	0.831652i	$0.687395\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−5.65685	+	5.65685i	−0.275371	+	0.275371i
$423$		0			0
$424$	18.0000			0.874157
$425$		0			0
$426$		0			0
$427$		−	40.0000i		−	1.93574i
$428$	−5.65685	+	5.65685i	−0.273434	+	0.273434i
$429$		0			0
$430$	−5.65685	+	5.65685i	−0.272798	+	0.272798i
$431$	8.48528	+	8.48528i	0.408722	+	0.408722i	0.881293	−	0.472571i	$-0.156674\pi$
$431$	8.48528	+	8.48528i	0.408722	+	0.408722i	−0.472571	+	0.881293i	$0.656674\pi$
$432$		0			0
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$			16.0000i			0.768025i
$435$		0			0
$436$	−4.24264	−	4.24264i	−0.203186	−	0.203186i
$437$	11.3137	−	11.3137i	0.541208	−	0.541208i
$438$		0			0
$439$	−14.1421	+	14.1421i	−0.674967	+	0.674967i	−0.958857	−	0.283890i	$-0.908375\pi$
$439$	−14.1421	+	14.1421i	−0.674967	+	0.674967i	0.283890	+	0.958857i	$0.408375\pi$
$440$		0			0
$441$	−27.0000			−1.28571
$442$		0			0
$443$	28.0000			1.33032			0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000			1.33032			0.665160	+	0.746701i	$0.268363\pi$
$444$		0			0
$445$	−14.1421	+	14.1421i	−0.670402	+	0.670402i
$446$	24.0000			1.13643
$447$		0			0
$448$	19.7990	+	19.7990i	0.935414	+	0.935414i
$449$	−24.0416	−	24.0416i	−1.13459	−	1.13459i	−0.989404	−	0.145191i	$-0.953620\pi$
$449$	−24.0416	−	24.0416i	−1.13459	−	1.13459i	−0.145191	−	0.989404i	$-0.546380\pi$
$450$			3.00000i			0.141421i
$451$		0			0
$452$	−9.89949	−	9.89949i	−0.465633	−	0.465633i
$453$		0			0
$454$	−16.9706	+	16.9706i	−0.796468	+	0.796468i
$455$	−16.0000			−0.750092
$456$		0			0
$457$		−	6.00000i		−	0.280668i	−0.990104	−	0.140334i	$-0.955182\pi$
$457$		−	6.00000i		−	0.280668i	0.990104	−	0.140334i	$-0.0448177\pi$
$458$	−6.00000			−0.280362
$459$		0			0
$460$	8.00000			0.373002
$461$		−	2.00000i		−	0.0931493i	−0.998915	−	0.0465746i	$-0.985169\pi$
$461$		−	2.00000i		−	0.0931493i	0.998915	−	0.0465746i	$-0.0148305\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	4.24264	−	4.24264i	0.196960	−	0.196960i
$465$		0			0
$466$	−4.24264	−	4.24264i	−0.196537	−	0.196537i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$			6.00000i			0.277350i
$469$	−11.3137	−	11.3137i	−0.522419	−	0.522419i
$470$		0			0
$471$		0			0
$472$	36.0000			1.65703
$473$		0			0
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−18.0000			−0.824163
$478$			16.0000i			0.731823i
$479$	25.4558	−	25.4558i	1.16311	−	1.16311i	0.179316	−	0.983792i	$-0.442612\pi$
$479$	25.4558	−	25.4558i	1.16311	−	1.16311i	0.983792	−	0.179316i	$-0.0573883\pi$
$480$		0			0
$481$	−2.82843	+	2.82843i	−0.128965	+	0.128965i
$482$	−12.7279	−	12.7279i	−0.579741	−	0.579741i
$483$		0			0
$484$		−	11.0000i		−	0.500000i
$485$			4.00000i			0.181631i
$486$		0			0
$487$	14.1421	+	14.1421i	0.640841	+	0.640841i	0.950762	−	0.309921i	$-0.100303\pi$
$487$	14.1421	+	14.1421i	0.640841	+	0.640841i	−0.309921	+	0.950762i	$0.600303\pi$
$488$	21.2132	−	21.2132i	0.960277	−	0.960277i
$489$		0			0
$490$	12.7279	−	12.7279i	0.574989	−	0.574989i
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−2.82843	+	2.82843i	−0.127000	+	0.127000i
$497$	16.0000			0.717698
$498$		0			0
$499$	−28.2843	−	28.2843i	−1.26618	−	1.26618i	−0.948047	−	0.318131i	$-0.896945\pi$
$499$	−28.2843	−	28.2843i	−1.26618	−	1.26618i	−0.318131	−	0.948047i	$-0.603055\pi$
$500$	8.48528	+	8.48528i	0.379473	+	0.379473i
$501$		0			0
$502$			12.0000i			0.535586i
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	0.870503	−	0.492163i	$-0.163794\pi$
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	−0.492163	+	0.870503i	$0.663794\pi$
$504$	−25.4558	−	25.4558i	−1.13389	−	1.13389i
$505$	−14.1421	+	14.1421i	−0.629317	+	0.629317i
$506$		0			0
$507$		0			0
$508$		−	8.00000i		−	0.354943i
$509$	−2.00000			−0.0886484			−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000			−0.0886484			−0.0443242	+	0.999017i	$0.514113\pi$
$510$		0			0
$511$	−24.0000			−1.06170
$512$			11.0000i			0.486136i
$513$		0			0
$514$	18.0000			0.793946
$515$	11.3137	−	11.3137i	0.498542	−	0.498542i
$516$		0			0
$517$		0			0
$518$		−	8.00000i		−	0.351500i
$519$		0			0
$520$	−8.48528	−	8.48528i	−0.372104	−	0.372104i
$521$	18.3848	+	18.3848i	0.805452	+	0.805452i	0.983942	−	0.178490i	$-0.0571212\pi$
$521$	18.3848	+	18.3848i	0.805452	+	0.805452i	−0.178490	+	0.983942i	$0.557121\pi$
$522$	−12.7279	+	12.7279i	−0.557086	+	0.557086i
$523$	36.0000			1.57417			0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000			1.57417			0.787085	+	0.616844i	$0.211589\pi$
$524$	−11.3137	+	11.3137i	−0.494242	+	0.494242i
$525$		0			0
$526$	16.0000			0.697633
$527$		0			0
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$	8.48528	−	8.48528i	0.368577	−	0.368577i
$531$	−36.0000			−1.56227
$532$	−11.3137	+	11.3137i	−0.490511	+	0.490511i
$533$	8.48528	+	8.48528i	0.367538	+	0.367538i
$534$		0			0
$535$			16.0000i			0.691740i
$536$		−	12.0000i		−	0.518321i
$537$		0			0
$538$	−15.5563	−	15.5563i	−0.670682	−	0.670682i
$539$		0			0
$540$		0			0
$541$	4.24264	−	4.24264i	0.182405	−	0.182405i	−0.609998	−	0.792403i	$-0.708830\pi$
$541$	4.24264	−	4.24264i	0.182405	−	0.182405i	0.792403	+	0.609998i	$0.208830\pi$
$542$			16.0000i			0.687259i
$543$		0			0
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−22.6274	+	22.6274i	−0.967478	+	0.967478i	−0.999488	−	0.0320091i	$-0.989809\pi$
$547$	−22.6274	+	22.6274i	−0.967478	+	0.967478i	0.0320091	+	0.999488i	$0.489809\pi$
$548$	−6.00000			−0.256307
$549$	−21.2132	+	21.2132i	−0.905357	+	0.905357i
$550$		0			0
$551$	16.9706	+	16.9706i	0.722970	+	0.722970i
$552$		0			0
$553$		−	48.0000i		−	2.04117i
$554$	9.89949	+	9.89949i	0.420589	+	0.420589i
$555$		0			0
$556$	−5.65685	+	5.65685i	−0.239904	+	0.239904i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$	8.48528	−	8.48528i	0.359211	−	0.359211i
$559$		−	8.00000i		−	0.338364i
$560$	8.00000			0.338062
$561$		0			0
$562$	6.00000			0.253095
$563$		−	4.00000i		−	0.168580i	−0.996441	−	0.0842900i	$-0.973138\pi$
$563$		−	4.00000i		−	0.168580i	0.996441	−	0.0842900i	$-0.0268622\pi$
$564$		0			0
$565$	−28.0000			−1.17797
$566$	−11.3137	+	11.3137i	−0.475551	+	0.475551i
$567$	25.4558	+	25.4558i	1.06904	+	1.06904i
$568$	8.48528	+	8.48528i	0.356034	+	0.356034i
$569$			38.0000i			1.59304i	0.604610	+	0.796521i	$0.293329\pi$
$569$			38.0000i			1.59304i	−0.604610	+	0.796521i	$0.706671\pi$
$570$		0			0
$571$	22.6274	+	22.6274i	0.946928	+	0.946928i	0.998661	−	0.0517330i	$-0.0164745\pi$
$571$	22.6274	+	22.6274i	0.946928	+	0.946928i	−0.0517330	+	0.998661i	$0.516474\pi$
$572$		0			0
$573$		0			0
$574$	−24.0000			−1.00174
$575$	−2.82843	+	2.82843i	−0.117954	+	0.117954i
$576$		−	21.0000i		−	0.875000i
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$		0			0
$579$		0			0
$580$			12.0000i			0.498273i
$581$	−11.3137	+	11.3137i	−0.469372	+	0.469372i
$582$		0			0
$583$		0			0
$584$	−12.7279	−	12.7279i	−0.526685	−	0.526685i
$585$	8.48528	+	8.48528i	0.350823	+	0.350823i
$586$			6.00000i			0.247858i
$587$		−	4.00000i		−	0.165098i	−0.996587	−	0.0825488i	$-0.973694\pi$
$587$		−	4.00000i		−	0.165098i	0.996587	−	0.0825488i	$-0.0263060\pi$
$588$		0			0
$589$	−11.3137	−	11.3137i	−0.466173	−	0.466173i
$590$	16.9706	−	16.9706i	0.698667	−	0.698667i
$591$		0			0
$592$	1.41421	−	1.41421i	0.0581238	−	0.0581238i
$593$			18.0000i			0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$			18.0000i			0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	5.65685	−	5.65685i	0.231326	−	0.231326i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	7.07107	+	7.07107i	0.288435	+	0.288435i	0.836461	−	0.548026i	$-0.184621\pi$
$601$	7.07107	+	7.07107i	0.288435	+	0.288435i	−0.548026	+	0.836461i	$0.684621\pi$
$602$	11.3137	+	11.3137i	0.461112	+	0.461112i
$603$			12.0000i			0.488678i
$604$		−	16.0000i		−	0.651031i
$605$	−15.5563	−	15.5563i	−0.632456	−	0.632456i
$606$		0			0
$607$	−14.1421	+	14.1421i	−0.574012	+	0.574012i	−0.933247	−	0.359235i	$-0.883038\pi$
$607$	−14.1421	+	14.1421i	−0.574012	+	0.574012i	0.359235	+	0.933247i	$0.383038\pi$
$608$	−20.0000			−0.811107
$609$		0			0
$610$		−	20.0000i		−	0.809776i
$611$		0			0
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$			12.0000i			0.484281i
$615$		0			0
$616$		0			0
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	−0.616530	−	0.787332i	$-0.711462\pi$
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	0.787332	+	0.616530i	$0.211462\pi$
$618$		0			0
$619$	33.9411	+	33.9411i	1.36421	+	1.36421i	0.868474	+	0.495735i	$0.165101\pi$
$619$	33.9411	+	33.9411i	1.36421	+	1.36421i	0.495735	+	0.868474i	$0.334899\pi$
$620$		−	8.00000i		−	0.321288i
$621$		0			0
$622$	19.7990	+	19.7990i	0.793867	+	0.793867i
$623$	28.2843	+	28.2843i	1.13319	+	1.13319i
$624$		0			0
$625$	19.0000			0.760000
$626$	15.5563	−	15.5563i	0.621757	−	0.621757i
$627$		0			0
$628$	2.00000			0.0798087
$629$		0			0
$630$	−24.0000			−0.956183
$631$			16.0000i			0.636950i	0.947931	+	0.318475i	$0.103171\pi$
$631$			16.0000i			0.636950i	−0.947931	+	0.318475i	$0.896829\pi$
$632$	25.4558	−	25.4558i	1.01258	−	1.01258i
$633$		0			0
$634$	−7.07107	+	7.07107i	−0.280828	+	0.280828i
$635$	−11.3137	−	11.3137i	−0.448971	−	0.448971i
$636$		0			0
$637$			18.0000i			0.713186i
$638$		0			0
$639$	−8.48528	−	8.48528i	−0.335673	−	0.335673i
$640$	−4.24264	−	4.24264i	−0.167705	−	0.167705i
$641$	21.2132	−	21.2132i	0.837871	−	0.837871i	−0.150707	−	0.988578i	$-0.548155\pi$
$641$	21.2132	−	21.2132i	0.837871	−	0.837871i	0.988578	+	0.150707i	$0.0481551\pi$
$642$		0			0
$643$	22.6274	−	22.6274i	0.892338	−	0.892338i	−0.102405	−	0.994743i	$-0.532654\pi$
$643$	22.6274	−	22.6274i	0.892338	−	0.892338i	0.994743	+	0.102405i	$0.0326536\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$			27.0000i			1.06066i
$649$		0			0
$650$	2.00000			0.0784465
$651$		0			0
$652$	−16.9706	−	16.9706i	−0.664619	−	0.664619i
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$		0			0
$655$			32.0000i			1.25034i
$656$	−4.24264	−	4.24264i	−0.165647	−	0.165647i
$657$	12.7279	+	12.7279i	0.496564	+	0.496564i
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$			38.0000i			1.47803i	0.673690	+	0.739014i	$0.264708\pi$
$661$			38.0000i			1.47803i	−0.673690	+	0.739014i	$0.735292\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	−12.0000			−0.465690
$665$			32.0000i			1.24091i
$666$	−4.24264	+	4.24264i	−0.164399	+	0.164399i
$667$	−24.0000			−0.929284
$668$	−2.82843	+	2.82843i	−0.109435	+	0.109435i
$669$		0			0
$670$	−5.65685	−	5.65685i	−0.218543	−	0.218543i
$671$		0			0
$672$		0			0
$673$	−1.41421	−	1.41421i	−0.0545139	−	0.0545139i	0.679324	−	0.733838i	$-0.262273\pi$
$673$	−1.41421	−	1.41421i	−0.0545139	−	0.0545139i	−0.733838	+	0.679324i	$0.762273\pi$
$674$	9.89949	+	9.89949i	0.381314	+	0.381314i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	21.2132	−	21.2132i	0.815290	−	0.815290i	−0.170132	−	0.985421i	$-0.554419\pi$
$677$	21.2132	−	21.2132i	0.815290	−	0.815290i	0.985421	+	0.170132i	$0.0544193\pi$
$678$		0			0
$679$	8.00000			0.307012
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−28.2843	+	28.2843i	−1.08227	+	1.08227i	−0.0859698	+	0.996298i	$0.527399\pi$
$683$	−28.2843	+	28.2843i	−1.08227	+	1.08227i	−0.996298	+	0.0859698i	$0.972601\pi$
$684$	12.0000			0.458831
$685$	−8.48528	+	8.48528i	−0.324206	+	0.324206i
$686$	−5.65685	−	5.65685i	−0.215980	−	0.215980i
$687$		0			0
$688$			4.00000i			0.152499i
$689$			12.0000i			0.457164i
$690$		0			0
$691$	−5.65685	−	5.65685i	−0.215197	−	0.215197i	0.591274	−	0.806471i	$-0.298625\pi$
$691$	−5.65685	−	5.65685i	−0.215197	−	0.215197i	−0.806471	+	0.591274i	$0.798625\pi$
$692$	15.5563	−	15.5563i	0.591364	−	0.591364i
$693$		0			0
$694$	−22.6274	+	22.6274i	−0.858925	+	0.858925i
$695$			16.0000i			0.606915i
$696$		0			0
$697$		0			0
$698$	18.0000			0.681310
$699$		0			0
$700$	2.82843	−	2.82843i	0.106904	−	0.106904i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	5.65685	+	5.65685i	0.213352	+	0.213352i
$704$		0			0
$705$		0			0
$706$		−	30.0000i		−	1.12906i
$707$	28.2843	+	28.2843i	1.06374	+	1.06374i
$708$		0			0
$709$	24.0416	−	24.0416i	0.902902	−	0.902902i	−0.0927839	−	0.995686i	$-0.529577\pi$
$709$	24.0416	−	24.0416i	0.902902	−	0.902902i	0.995686	+	0.0927839i	$0.0295766\pi$
$710$	8.00000			0.300235
$711$	−25.4558	+	25.4558i	−0.954669	+	0.954669i
$712$			30.0000i			1.12430i
$713$	16.0000			0.599205
$714$		0			0
$715$		0			0
$716$		−	12.0000i		−	0.448461i
$717$		0			0
$718$		0			0
$719$	−2.82843	+	2.82843i	−0.105483	+	0.105483i	−0.757878	−	0.652396i	$-0.773764\pi$
$719$	−2.82843	+	2.82843i	−0.105483	+	0.105483i	0.652396	+	0.757878i	$0.273764\pi$
$720$	−4.24264	−	4.24264i	−0.158114	−	0.158114i
$721$	−22.6274	−	22.6274i	−0.842689	−	0.842689i
$722$		−	3.00000i		−	0.111648i
$723$		0			0
$724$	−1.41421	−	1.41421i	−0.0525588	−	0.0525588i
$725$	−4.24264	−	4.24264i	−0.157568	−	0.157568i
$726$		0			0
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$	−16.9706	+	16.9706i	−0.628971	+	0.628971i
$729$		−	27.0000i		−	1.00000i
$730$	−12.0000			−0.444140
$731$		0			0
$732$		0			0
$733$		−	50.0000i		−	1.84679i	−0.383849	−	0.923396i	$-0.625402\pi$
$733$		−	50.0000i		−	1.84679i	0.383849	−	0.923396i	$-0.374598\pi$
$734$	−19.7990	+	19.7990i	−0.730794	+	0.730794i
$735$		0			0
$736$	14.1421	−	14.1421i	0.521286	−	0.521286i
$737$		0			0
$738$	12.7279	+	12.7279i	0.468521	+	0.468521i
$739$		−	28.0000i		−	1.03000i	−0.857191	−	0.514998i	$-0.827793\pi$
$739$		−	28.0000i		−	1.03000i	0.857191	−	0.514998i	$-0.172207\pi$
$740$			4.00000i			0.147043i
$741$		0			0
$742$	−16.9706	−	16.9706i	−0.623009	−	0.623009i
$743$	−8.48528	+	8.48528i	−0.311295	+	0.311295i	−0.845411	−	0.534116i	$-0.820644\pi$
$743$	−8.48528	+	8.48528i	−0.311295	+	0.311295i	0.534116	+	0.845411i	$0.320644\pi$
$744$		0			0
$745$	14.1421	−	14.1421i	0.518128	−	0.518128i
$746$		−	6.00000i		−	0.219676i
$747$	12.0000			0.439057
$748$		0			0
$749$	32.0000			1.16925
$750$		0			0
$751$	14.1421	−	14.1421i	0.516054	−	0.516054i	−0.400321	−	0.916375i	$-0.631101\pi$
$751$	14.1421	−	14.1421i	0.516054	−	0.516054i	0.916375	+	0.400321i	$0.131101\pi$
$752$		0			0
$753$		0			0
$754$	8.48528	+	8.48528i	0.309016	+	0.309016i
$755$	−22.6274	−	22.6274i	−0.823496	−	0.823496i
$756$		0			0
$757$		−	22.0000i		−	0.799604i	−0.916602	−	0.399802i	$-0.869079\pi$
$757$		−	22.0000i		−	0.799604i	0.916602	−	0.399802i	$-0.130921\pi$
$758$	−5.65685	−	5.65685i	−0.205466	−	0.205466i
$759$		0			0
$760$	−16.9706	+	16.9706i	−0.615587	+	0.615587i
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$		0			0
$763$			24.0000i			0.868858i
$764$	16.0000			0.578860
$765$		0			0
$766$	24.0000			0.867155
$767$			24.0000i			0.866590i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$	1.41421	+	1.41421i	0.0508987	+	0.0508987i
$773$			26.0000i			0.935155i	0.883952	+	0.467578i	$0.154873\pi$
$773$			26.0000i			0.935155i	−0.883952	+	0.467578i	$0.845127\pi$
$774$		−	12.0000i		−	0.431331i
$775$	2.82843	+	2.82843i	0.101600	+	0.101600i
$776$	4.24264	+	4.24264i	0.152302	+	0.152302i
$777$		0			0
$778$	6.00000			0.215110
$779$	16.9706	−	16.9706i	0.608034	−	0.608034i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		−	9.00000i		−	0.321429i
$785$	2.82843	−	2.82843i	0.100951	−	0.100951i
$786$		0			0
$787$	22.6274	−	22.6274i	0.806580	−	0.806580i	−0.177534	−	0.984115i	$-0.556812\pi$
$787$	22.6274	−	22.6274i	0.806580	−	0.806580i	0.984115	+	0.177534i	$0.0568121\pi$
$788$	12.7279	+	12.7279i	0.453413	+	0.453413i
$789$		0			0
$790$		−	24.0000i		−	0.853882i
$791$			56.0000i			1.99113i
$792$		0			0
$793$	14.1421	+	14.1421i	0.502202	+	0.502202i
$794$	4.24264	−	4.24264i	0.150566	−	0.150566i
$795$		0			0
$796$	14.1421	−	14.1421i	0.501255	−	0.501255i
$797$		−	50.0000i		−	1.77109i	−0.464553	−	0.885545i	$-0.653785\pi$
$797$		−	50.0000i		−	1.77109i	0.464553	−	0.885545i	$-0.346215\pi$
$798$		0			0
$799$		0			0
$800$	5.00000			0.176777
$801$		−	30.0000i		−	1.06000i
$802$	9.89949	−	9.89949i	0.349563	−	0.349563i
$803$		0			0
$804$		0			0
$805$	−22.6274	−	22.6274i	−0.797512	−	0.797512i
$806$	−5.65685	−	5.65685i	−0.199254	−	0.199254i
$807$		0			0
$808$			30.0000i			1.05540i
$809$	−18.3848	−	18.3848i	−0.646374	−	0.646374i	0.305741	−	0.952115i	$-0.401096\pi$
$809$	−18.3848	−	18.3848i	−0.646374	−	0.646374i	−0.952115	+	0.305741i	$0.901096\pi$
$810$	12.7279	+	12.7279i	0.447214	+	0.447214i
$811$	−28.2843	+	28.2843i	−0.993195	+	0.993195i	−0.999977	−	0.00678191i	$-0.997841\pi$
$811$	−28.2843	+	28.2843i	−0.993195	+	0.993195i	0.00678191	+	0.999977i	$0.497841\pi$
$812$	24.0000			0.842235
$813$		0			0
$814$		0			0
$815$	−48.0000			−1.68137
$816$		0			0
$817$	−16.0000			−0.559769
$818$		−	26.0000i		−	0.909069i
$819$	16.9706	−	16.9706i	0.592999	−	0.592999i
$820$	12.0000			0.419058
$821$	12.7279	−	12.7279i	0.444208	−	0.444208i	−0.449216	−	0.893423i	$-0.648297\pi$
$821$	12.7279	−	12.7279i	0.444208	−	0.444208i	0.893423	+	0.449216i	$0.148297\pi$
$822$		0			0
$823$	−14.1421	−	14.1421i	−0.492964	−	0.492964i	0.416275	−	0.909239i	$-0.363335\pi$
$823$	−14.1421	−	14.1421i	−0.492964	−	0.492964i	−0.909239	+	0.416275i	$0.863335\pi$
$824$		−	24.0000i		−	0.836080i
$825$		0			0
$826$	−33.9411	−	33.9411i	−1.18096	−	1.18096i
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.979680	−	0.200569i	$-0.935721\pi$
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.200569	−	0.979680i	$-0.564279\pi$
$828$	−8.48528	+	8.48528i	−0.294884	+	0.294884i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−5.65685	+	5.65685i	−0.196352	+	0.196352i
$831$		0			0
$832$	−14.0000			−0.485363
$833$		0			0
$834$		0			0
$835$			8.00000i			0.276851i
$836$		0			0
$837$		0			0
$838$	5.65685	−	5.65685i	0.195413	−	0.195413i
$839$	14.1421	+	14.1421i	0.488241	+	0.488241i	0.907751	−	0.419510i	$-0.137798\pi$
$839$	14.1421	+	14.1421i	0.488241	+	0.488241i	−0.419510	+	0.907751i	$0.637798\pi$
$840$		0			0
$841$		−	7.00000i		−	0.241379i
$842$			22.0000i			0.758170i
$843$		0			0
$844$	−5.65685	−	5.65685i	−0.194717	−	0.194717i
$845$	−12.7279	+	12.7279i	−0.437854	+	0.437854i
$846$		0			0
$847$	−31.1127	+	31.1127i	−1.06904	+	1.06904i
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$		0			0
$851$	−8.00000			−0.274236
$852$		0			0
$853$	9.89949	−	9.89949i	0.338952	−	0.338952i	−0.517021	−	0.855973i	$-0.672959\pi$
$853$	9.89949	−	9.89949i	0.338952	−	0.338952i	0.855973	+	0.517021i	$0.172959\pi$
$854$	−40.0000			−1.36877
$855$	16.9706	−	16.9706i	0.580381	−	0.580381i
$856$	16.9706	+	16.9706i	0.580042	+	0.580042i
$857$	−7.07107	−	7.07107i	−0.241543	−	0.241543i	0.575945	−	0.817488i	$-0.304634\pi$
$857$	−7.07107	−	7.07107i	−0.241543	−	0.241543i	−0.817488	+	0.575945i	$0.804634\pi$
$858$		0			0
$859$		−	52.0000i		−	1.77422i	−0.461561	−	0.887109i	$-0.652710\pi$
$859$		−	52.0000i		−	1.77422i	0.461561	−	0.887109i	$-0.347290\pi$
$860$	−5.65685	−	5.65685i	−0.192897	−	0.192897i
$861$		0			0
$862$	8.48528	−	8.48528i	0.289010	−	0.289010i
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$		−	44.0000i		−	1.49604i
$866$	−2.00000			−0.0679628
$867$		0			0
$868$	−16.0000			−0.543075
$869$		0			0
$870$		0			0
$871$	8.00000			0.271070
$872$	−12.7279	+	12.7279i	−0.431022	+	0.431022i
$873$	−4.24264	−	4.24264i	−0.143592	−	0.143592i
$874$	−11.3137	−	11.3137i	−0.382692	−	0.382692i
$875$		−	48.0000i		−	1.62270i
$876$		0			0
$877$	−4.24264	−	4.24264i	−0.143264	−	0.143264i	0.631837	−	0.775101i	$-0.282301\pi$
$877$	−4.24264	−	4.24264i	−0.143264	−	0.143264i	−0.775101	+	0.631837i	$0.782301\pi$
$878$	14.1421	+	14.1421i	0.477274	+	0.477274i
$879$		0			0
$880$		0			0
$881$	−32.5269	+	32.5269i	−1.09586	+	1.09586i	−0.100970	+	0.994889i	$0.532195\pi$
$881$	−32.5269	+	32.5269i	−1.09586	+	1.09586i	−0.994889	+	0.100970i	$0.967805\pi$
$882$			27.0000i			0.909137i
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		0			0
$885$		0			0
$886$		−	28.0000i		−	0.940678i
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	−0.550155	−	0.835063i	$-0.685431\pi$
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	0.835063	+	0.550155i	$0.185431\pi$
$888$		0			0
$889$	−22.6274	+	22.6274i	−0.758899	+	0.758899i
$890$	14.1421	+	14.1421i	0.474045	+	0.474045i
$891$		0			0
$892$			24.0000i			0.803579i
$893$		0			0
$894$		0			0
$895$	−16.9706	−	16.9706i	−0.567263	−	0.567263i
$896$	−8.48528	+	8.48528i	−0.283473	+	0.283473i
$897$		0			0
$898$	−24.0416	+	24.0416i	−0.802280	+	0.802280i
$899$			24.0000i			0.800445i
$900$	−3.00000			−0.100000
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−29.6985	+	29.6985i	−0.987757	+	0.987757i
$905$	−4.00000			−0.132964
$906$		0			0
$907$	22.6274	+	22.6274i	0.751331	+	0.751331i	0.974728	−	0.223397i	$-0.0717145\pi$
$907$	22.6274	+	22.6274i	0.751331	+	0.751331i	−0.223397	+	0.974728i	$0.571714\pi$
$908$	−16.9706	−	16.9706i	−0.563188	−	0.563188i
$909$		−	30.0000i		−	0.995037i
$910$			16.0000i			0.530395i
$911$	2.82843	+	2.82843i	0.0937100	+	0.0937100i	0.752408	−	0.658698i	$-0.228892\pi$
$911$	2.82843	+	2.82843i	0.0937100	+	0.0937100i	−0.658698	+	0.752408i	$0.728892\pi$
$912$		0			0
$913$		0			0
$914$	−6.00000			−0.198462
$915$		0			0
$916$		−	6.00000i		−	0.198246i
$917$	64.0000			2.11347
$918$		0			0
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$		−	24.0000i		−	0.791257i
$921$		0			0
$922$	−2.00000			−0.0658665
$923$	−5.65685	+	5.65685i	−0.186198	+	0.186198i
$924$		0			0
$925$	−1.41421	−	1.41421i	−0.0464991	−	0.0464991i
$926$			32.0000i			1.05159i
$927$			24.0000i			0.788263i
$928$	21.2132	+	21.2132i	0.696358	+	0.696358i
$929$	−21.2132	−	21.2132i	−0.695983	−	0.695983i	0.267559	−	0.963542i	$-0.413783\pi$
$929$	−21.2132	−	21.2132i	−0.695983	−	0.695983i	−0.963542	+	0.267559i	$0.913783\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$	4.24264	−	4.24264i	0.138972	−	0.138972i
$933$		0			0
$934$	−12.0000			−0.392652
$935$		0			0
$936$	18.0000			0.588348
$937$			10.0000i			0.326686i	0.986569	+	0.163343i	$0.0522277\pi$
$937$			10.0000i			0.326686i	−0.986569	+	0.163343i	$0.947772\pi$
$938$	−11.3137	+	11.3137i	−0.369406	+	0.369406i
$939$		0			0
$940$		0			0
$941$	4.24264	+	4.24264i	0.138306	+	0.138306i	0.772870	−	0.634564i	$-0.218820\pi$
$941$	4.24264	+	4.24264i	0.138306	+	0.138306i	−0.634564	+	0.772870i	$0.718820\pi$
$942$		0			0
$943$			24.0000i			0.781548i
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$		0			0
$947$	−22.6274	+	22.6274i	−0.735292	+	0.735292i	−0.971663	−	0.236371i	$-0.924042\pi$
$947$	−22.6274	+	22.6274i	−0.735292	+	0.735292i	0.236371	+	0.971663i	$0.424042\pi$
$948$		0			0
$949$	8.48528	−	8.48528i	0.275444	−	0.275444i
$950$		−	4.00000i		−	0.129777i
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$			18.0000i			0.582772i
$955$	22.6274	−	22.6274i	0.732206	−	0.732206i
$956$	−16.0000			−0.517477
$957$		0			0
$958$	−25.4558	−	25.4558i	−0.822441	−	0.822441i
$959$	16.9706	+	16.9706i	0.548008	+	0.548008i
$960$		0			0
$961$			15.0000i			0.483871i
$962$	2.82843	+	2.82843i	0.0911922	+	0.0911922i
$963$	−16.9706	−	16.9706i	−0.546869	−	0.546869i
$964$	12.7279	−	12.7279i	0.409939	−	0.409939i
$965$	4.00000			0.128765
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−33.0000			−1.06066
$969$		0			0
$970$	4.00000			0.128432
$971$		−	12.0000i		−	0.385098i	−0.981287	−	0.192549i	$-0.938325\pi$
$971$		−	12.0000i		−	0.385098i	0.981287	−	0.192549i	$-0.0616755\pi$
$972$		0			0
$973$	32.0000			1.02587
$974$	14.1421	−	14.1421i	0.453143	−	0.453143i
$975$		0			0
$976$	−7.07107	−	7.07107i	−0.226339	−	0.226339i
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$		0			0
$979$		0			0
$980$	12.7279	+	12.7279i	0.406579	+	0.406579i
$981$	12.7279	−	12.7279i	0.406371	−	0.406371i
$982$	20.0000			0.638226
$983$	8.48528	−	8.48528i	0.270638	−	0.270638i	−0.558719	−	0.829357i	$-0.688707\pi$
$983$	8.48528	−	8.48528i	0.270638	−	0.270638i	0.829357	+	0.558719i	$0.188707\pi$
$984$		0			0
$985$	36.0000			1.14706
$986$		0			0
$987$		0			0
$988$		−	8.00000i		−	0.254514i
$989$	11.3137	−	11.3137i	0.359755	−	0.359755i
$990$		0			0
$991$	8.48528	−	8.48528i	0.269544	−	0.269544i	−0.559373	−	0.828916i	$-0.688958\pi$
$991$	8.48528	−	8.48528i	0.269544	−	0.269544i	0.828916	+	0.559373i	$0.188958\pi$
$992$	−14.1421	−	14.1421i	−0.449013	−	0.449013i
$993$		0			0
$994$		−	16.0000i		−	0.507489i
$995$		−	40.0000i		−	1.26809i
$996$		0			0
$997$	32.5269	+	32.5269i	1.03014	+	1.03014i	0.999532	+	0.0306061i	$0.00974375\pi$
$997$	32.5269	+	32.5269i	1.03014	+	1.03014i	0.0306061	+	0.999532i	$0.490256\pi$
$998$	−28.2843	+	28.2843i	−0.895323	+	0.895323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.a.38.2		4
17.2	even	8		289.2.b.a.288.2		2
17.3	odd	16		289.2.d.d.155.2		8
17.4	even	4	inner	289.2.c.a.251.1		4
17.5	odd	16		289.2.d.d.134.1		8
17.6	odd	16		289.2.d.d.110.1		8
17.7	odd	16		289.2.d.d.179.1		8
17.8	even	8		289.2.a.a.1.1		1
17.9	even	8		17.2.a.a.1.1	✓	1
17.10	odd	16		289.2.d.d.179.2		8
17.11	odd	16		289.2.d.d.110.2		8
17.12	odd	16		289.2.d.d.134.2		8
17.13	even	4	inner	289.2.c.a.251.2		4
17.14	odd	16		289.2.d.d.155.1		8
17.15	even	8		289.2.b.a.288.1		2
17.16	even	2	inner	289.2.c.a.38.1		4
51.8	odd	8		2601.2.a.g.1.1		1
51.26	odd	8		153.2.a.c.1.1		1
68.43	odd	8		272.2.a.b.1.1		1
68.59	odd	8		4624.2.a.d.1.1		1
85.9	even	8		425.2.a.d.1.1		1
85.43	odd	8		425.2.b.b.324.2		2
85.59	even	8		7225.2.a.g.1.1		1
85.77	odd	8		425.2.b.b.324.1		2
119.9	even	24		833.2.e.b.18.1		2
119.26	odd	24		833.2.e.a.18.1		2
119.60	even	24		833.2.e.b.324.1		2
119.94	odd	24		833.2.e.a.324.1		2
119.111	odd	8		833.2.a.a.1.1		1
136.43	odd	8		1088.2.a.h.1.1		1
136.77	even	8		1088.2.a.i.1.1		1
187.43	odd	8		2057.2.a.e.1.1		1
204.179	even	8		2448.2.a.o.1.1		1
221.77	even	8		2873.2.a.c.1.1		1
255.179	odd	8		3825.2.a.d.1.1		1
323.94	odd	8		6137.2.a.b.1.1		1
340.179	odd	8		6800.2.a.n.1.1		1
357.230	even	8		7497.2.a.l.1.1		1
391.298	odd	8		8993.2.a.a.1.1		1
408.77	odd	8		9792.2.a.n.1.1		1
408.179	even	8		9792.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.a.a.1.1	✓	1	17.9	even	8
153.2.a.c.1.1		1	51.26	odd	8
272.2.a.b.1.1		1	68.43	odd	8
289.2.a.a.1.1		1	17.8	even	8
289.2.b.a.288.1		2	17.15	even	8
289.2.b.a.288.2		2	17.2	even	8
289.2.c.a.38.1		4	17.16	even	2	inner
289.2.c.a.38.2		4	1.1	even	1	trivial
289.2.c.a.251.1		4	17.4	even	4	inner
289.2.c.a.251.2		4	17.13	even	4	inner
289.2.d.d.110.1		8	17.6	odd	16
289.2.d.d.110.2		8	17.11	odd	16
289.2.d.d.134.1		8	17.5	odd	16
289.2.d.d.134.2		8	17.12	odd	16
289.2.d.d.155.1		8	17.14	odd	16
289.2.d.d.155.2		8	17.3	odd	16
289.2.d.d.179.1		8	17.7	odd	16
289.2.d.d.179.2		8	17.10	odd	16
425.2.a.d.1.1		1	85.9	even	8
425.2.b.b.324.1		2	85.77	odd	8
425.2.b.b.324.2		2	85.43	odd	8
833.2.a.a.1.1		1	119.111	odd	8
833.2.e.a.18.1		2	119.26	odd	24
833.2.e.a.324.1		2	119.94	odd	24
833.2.e.b.18.1		2	119.9	even	24
833.2.e.b.324.1		2	119.60	even	24
1088.2.a.h.1.1		1	136.43	odd	8
1088.2.a.i.1.1		1	136.77	even	8
2057.2.a.e.1.1		1	187.43	odd	8
2448.2.a.o.1.1		1	204.179	even	8
2601.2.a.g.1.1		1	51.8	odd	8
2873.2.a.c.1.1		1	221.77	even	8
3825.2.a.d.1.1		1	255.179	odd	8
4624.2.a.d.1.1		1	68.59	odd	8
6137.2.a.b.1.1		1	323.94	odd	8
6800.2.a.n.1.1		1	340.179	odd	8
7225.2.a.g.1.1		1	85.59	even	8
7497.2.a.l.1.1		1	357.230	even	8
8993.2.a.a.1.1		1	391.298	odd	8
9792.2.a.i.1.1		1	408.179	even	8
9792.2.a.n.1.1		1	408.77	odd	8

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{4} +(1.41421 - 1.41421i) q^{5} +(-2.82843 - 2.82843i) q^{7} -3.00000i q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{4} +(1.41421 - 1.41421i) q^{5} +(-2.82843 - 2.82843i) q^{7} -3.00000i q^{8} +3.00000i q^{9} +(-1.41421 - 1.41421i) q^{10} +2.00000 q^{13} +(-2.82843 + 2.82843i) q^{14} -1.00000 q^{16} +3.00000 q^{18} -4.00000i q^{19} +(1.41421 - 1.41421i) q^{20} +(2.82843 + 2.82843i) q^{23} +1.00000i q^{25} -2.00000i q^{26} +(-2.82843 - 2.82843i) q^{28} +(-4.24264 + 4.24264i) q^{29} +(2.82843 - 2.82843i) q^{31} -5.00000i q^{32} -8.00000 q^{35} +3.00000i q^{36} +(-1.41421 + 1.41421i) q^{37} -4.00000 q^{38} +(-4.24264 - 4.24264i) q^{40} +(4.24264 + 4.24264i) q^{41} -4.00000i q^{43} +(4.24264 + 4.24264i) q^{45} +(2.82843 - 2.82843i) q^{46} +9.00000i q^{49} +1.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(-8.48528 + 8.48528i) q^{56} +(4.24264 + 4.24264i) q^{58} +12.0000i q^{59} +(7.07107 + 7.07107i) q^{61} +(-2.82843 - 2.82843i) q^{62} +(8.48528 - 8.48528i) q^{63} -7.00000 q^{64} +(2.82843 - 2.82843i) q^{65} +4.00000 q^{67} +8.00000i q^{70} +(-2.82843 + 2.82843i) q^{71} +9.00000 q^{72} +(4.24264 - 4.24264i) q^{73} +(1.41421 + 1.41421i) q^{74} -4.00000i q^{76} +(8.48528 + 8.48528i) q^{79} +(-1.41421 + 1.41421i) q^{80} -9.00000 q^{81} +(4.24264 - 4.24264i) q^{82} -4.00000i q^{83} -4.00000 q^{86} -10.0000 q^{89} +(4.24264 - 4.24264i) q^{90} +(-5.65685 - 5.65685i) q^{91} +(2.82843 + 2.82843i) q^{92} +(-5.65685 - 5.65685i) q^{95} +(-1.41421 + 1.41421i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4}+O(q^{10}) \) 4 * q + 4 * q^4	\( 4 q + 4 q^{4} + 8 q^{13} - 4 q^{16} + 12 q^{18} - 32 q^{35} - 16 q^{38} + 4 q^{50} + 8 q^{52} - 28 q^{64} + 16 q^{67} + 36 q^{72} - 36 q^{81} - 16 q^{86} - 40 q^{89} + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^4 + 8 * q^13 - 4 * q^16 + 12 * q^18 - 32 * q^35 - 16 * q^38 + 4 * q^50 + 8 * q^52 - 28 * q^64 + 16 * q^67 + 36 * q^72 - 36 * q^81 - 16 * q^86 - 40 * q^89 + 36 * q^98

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