LMFDB - Embedded newform 578.2.c.e.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [578,2,Mod(251,578)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(578, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("578.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.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:	$4.61535323683$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	578.251
Dual form			578.2.c.e.327.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(4.24264 - 4.24264i) q^{11} +(1.41421 + 1.41421i) q^{12} -2.00000 q^{13} +(-2.82843 - 2.82843i) q^{14} +1.00000 q^{16} +1.00000 q^{18} +4.00000i q^{19} -8.00000 q^{21} +(-4.24264 - 4.24264i) q^{22} +(1.41421 - 1.41421i) q^{24} -5.00000i q^{25} +2.00000i q^{26} +(-2.82843 + 2.82843i) q^{27} +(-2.82843 + 2.82843i) q^{28} +(-2.82843 - 2.82843i) q^{31} -1.00000i q^{32} -12.0000 q^{33} -1.00000i q^{36} +(-2.82843 - 2.82843i) q^{37} +4.00000 q^{38} +(2.82843 + 2.82843i) q^{39} +(-4.24264 + 4.24264i) q^{41} +8.00000i q^{42} +8.00000i q^{43} +(-4.24264 + 4.24264i) q^{44} +(-1.41421 - 1.41421i) q^{48} -9.00000i q^{49} -5.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(2.82843 + 2.82843i) q^{54} +(2.82843 + 2.82843i) q^{56} +(5.65685 - 5.65685i) q^{57} +(2.82843 - 2.82843i) q^{61} +(-2.82843 + 2.82843i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +12.0000i q^{66} +8.00000 q^{67} -1.00000 q^{72} +(-1.41421 - 1.41421i) q^{73} +(-2.82843 + 2.82843i) q^{74} +(-7.07107 + 7.07107i) q^{75} -4.00000i q^{76} -24.0000i q^{77} +(2.82843 - 2.82843i) q^{78} +(5.65685 - 5.65685i) q^{79} +11.0000 q^{81} +(4.24264 + 4.24264i) q^{82} +8.00000 q^{84} +8.00000 q^{86} +(4.24264 + 4.24264i) q^{88} +6.00000 q^{89} +(-5.65685 + 5.65685i) q^{91} +8.00000i q^{93} +(-1.41421 + 1.41421i) q^{96} +(-9.89949 - 9.89949i) q^{97} -9.00000 q^{98} +(4.24264 + 4.24264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} - 8 q^{13} + 4 q^{16} + 4 q^{18} - 32 q^{21} - 48 q^{33} + 16 q^{38} - 20 q^{50} + 8 q^{52} - 4 q^{64} + 32 q^{67} - 4 q^{72} + 44 q^{81} + 32 q^{84} + 32 q^{86} + 24 q^{89} - 36 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 8 * q^13 + 4 * q^16 + 4 * q^18 - 32 * q^21 - 48 * q^33 + 16 * q^38 - 20 * q^50 + 8 * q^52 - 4 * q^64 + 32 * q^67 - 4 * q^72 + 44 * q^81 + 32 * q^84 + 32 * q^86 + 24 * q^89 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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
$2$		−	1.00000i		−	0.707107i
$3$	−1.41421	−	1.41421i	−0.816497	−	0.816497i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	−1.41421	−	1.41421i	−0.816497	−	0.816497i	−0.985599	+	0.169102i	$0.945913\pi$
$4$	−1.00000			−0.500000
$5$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$5$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$6$	−1.41421	+	1.41421i	−0.577350	+	0.577350i
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.997433	−	0.0716124i	$-0.0228145\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	4.24264	−	4.24264i	1.27920	−	1.27920i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	4.24264	−	4.24264i	1.27920	−	1.27920i	0.941113	−	0.338091i	$-0.109781\pi$
$12$	1.41421	+	1.41421i	0.408248	+	0.408248i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	−2.82843	−	2.82843i	−0.755929	−	0.755929i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	1.00000			0.235702
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$	−8.00000			−1.74574
$22$	−4.24264	−	4.24264i	−0.904534	−	0.904534i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	1.41421	−	1.41421i	0.288675	−	0.288675i
$25$		−	5.00000i		−	1.00000i
$26$			2.00000i			0.392232i
$27$	−2.82843	+	2.82843i	−0.544331	+	0.544331i
$28$	−2.82843	+	2.82843i	−0.534522	+	0.534522i
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$		0			0
$31$	−2.82843	−	2.82843i	−0.508001	−	0.508001i	0.405912	−	0.913912i	$-0.366954\pi$
$31$	−2.82843	−	2.82843i	−0.508001	−	0.508001i	−0.913912	+	0.405912i	$0.866954\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−12.0000			−2.08893
$34$		0			0
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$	−2.82843	−	2.82843i	−0.464991	−	0.464991i	0.435297	−	0.900287i	$-0.356644\pi$
$37$	−2.82843	−	2.82843i	−0.464991	−	0.464991i	−0.900287	+	0.435297i	$0.856644\pi$
$38$	4.00000			0.648886
$39$	2.82843	+	2.82843i	0.452911	+	0.452911i
$40$		0			0
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	−0.955990	−	0.293400i	$-0.905213\pi$
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	0.293400	+	0.955990i	$0.405213\pi$
$42$			8.00000i			1.23443i
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	−4.24264	+	4.24264i	−0.639602	+	0.639602i
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.41421	−	1.41421i	−0.204124	−	0.204124i
$49$		−	9.00000i		−	1.28571i
$50$	−5.00000			−0.707107
$51$		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	$0.864802\pi$
$54$	2.82843	+	2.82843i	0.384900	+	0.384900i
$55$		0			0
$56$	2.82843	+	2.82843i	0.377964	+	0.377964i
$57$	5.65685	−	5.65685i	0.749269	−	0.749269i
$58$		0			0
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	2.82843	−	2.82843i	0.362143	−	0.362143i	−0.502458	−	0.864601i	$-0.667571\pi$
$61$	2.82843	−	2.82843i	0.362143	−	0.362143i	0.864601	+	0.502458i	$0.167571\pi$
$62$	−2.82843	+	2.82843i	−0.359211	+	0.359211i
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$	−1.00000			−0.125000
$65$		0			0
$66$			12.0000i			1.47710i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	−1.00000			−0.117851
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	0.619486	−	0.785007i	$-0.287341\pi$
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	−0.785007	+	0.619486i	$0.787341\pi$
$74$	−2.82843	+	2.82843i	−0.328798	+	0.328798i
$75$	−7.07107	+	7.07107i	−0.816497	+	0.816497i
$76$		−	4.00000i		−	0.458831i
$77$		−	24.0000i		−	2.73505i
$78$	2.82843	−	2.82843i	0.320256	−	0.320256i
$79$	5.65685	−	5.65685i	0.636446	−	0.636446i	−0.313231	−	0.949677i	$-0.601411\pi$
$79$	5.65685	−	5.65685i	0.636446	−	0.636446i	0.949677	+	0.313231i	$0.101411\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$	4.24264	+	4.24264i	0.468521	+	0.468521i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	8.00000			0.872872
$85$		0			0
$86$	8.00000			0.862662
$87$		0			0
$88$	4.24264	+	4.24264i	0.452267	+	0.452267i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−5.65685	+	5.65685i	−0.592999	+	0.592999i
$92$		0			0
$93$			8.00000i			0.829561i
$94$		0			0
$95$		0			0
$96$	−1.41421	+	1.41421i	−0.144338	+	0.144338i
$97$	−9.89949	−	9.89949i	−1.00514	−	1.00514i	−0.999987	−	0.00515471i	$-0.998359\pi$
$97$	−9.89949	−	9.89949i	−1.00514	−	1.00514i	−0.00515471	−	0.999987i	$-0.501641\pi$
$98$	−9.00000			−0.909137
$99$	4.24264	+	4.24264i	0.426401	+	0.426401i
$100$			5.00000i			0.500000i
$101$	18.0000			1.79107			0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000			1.79107			0.895533	+	0.444994i	$0.146794\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		−	2.00000i		−	0.196116i
$105$		0			0
$106$	6.00000			0.582772
$107$	4.24264	+	4.24264i	0.410152	+	0.410152i	0.881791	−	0.471640i	$-0.156338\pi$
$107$	4.24264	+	4.24264i	0.410152	+	0.410152i	−0.471640	+	0.881791i	$0.656338\pi$
$108$	2.82843	−	2.82843i	0.272166	−	0.272166i
$109$	11.3137	−	11.3137i	1.08366	−	1.08366i	0.0874915	−	0.996165i	$-0.472115\pi$
$109$	11.3137	−	11.3137i	1.08366	−	1.08366i	0.996165	−	0.0874915i	$-0.0278851\pi$
$110$		0			0
$111$			8.00000i			0.759326i
$112$	2.82843	−	2.82843i	0.267261	−	0.267261i
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	−0.877920	−	0.478806i	$-0.841070\pi$
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	0.478806	+	0.877920i	$0.341070\pi$
$114$	−5.65685	−	5.65685i	−0.529813	−	0.529813i
$115$		0			0
$116$		0			0
$117$		−	2.00000i		−	0.184900i
$118$		0			0
$119$		0			0
$120$		0			0
$121$		−	25.0000i		−	2.27273i
$122$	−2.82843	−	2.82843i	−0.256074	−	0.256074i
$123$	12.0000			1.08200
$124$	2.82843	+	2.82843i	0.254000	+	0.254000i
$125$		0			0
$126$	2.82843	−	2.82843i	0.251976	−	0.251976i
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$			1.00000i			0.0883883i
$129$	11.3137	−	11.3137i	0.996116	−	0.996116i
$130$		0			0
$131$	4.24264	+	4.24264i	0.370681	+	0.370681i	0.867725	−	0.497044i	$-0.165581\pi$
$131$	4.24264	+	4.24264i	0.370681	+	0.370681i	−0.497044	+	0.867725i	$0.665581\pi$
$132$	12.0000			1.04447
$133$	11.3137	+	11.3137i	0.981023	+	0.981023i
$134$		−	8.00000i		−	0.691095i
$135$		0			0
$136$		0			0
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	1.41421	+	1.41421i	0.119952	+	0.119952i	0.764535	−	0.644583i	$-0.222969\pi$
$139$	1.41421	+	1.41421i	0.119952	+	0.119952i	−0.644583	+	0.764535i	$0.722969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.48528	+	8.48528i	−0.709575	+	0.709575i
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	−1.41421	+	1.41421i	−0.117041	+	0.117041i
$147$	−12.7279	+	12.7279i	−1.04978	+	1.04978i
$148$	2.82843	+	2.82843i	0.232495	+	0.232495i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	7.07107	+	7.07107i	0.577350	+	0.577350i
$151$			16.0000i			1.30206i	0.759051	+	0.651031i	$0.225663\pi$
$151$			16.0000i			1.30206i	−0.759051	+	0.651031i	$0.774337\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$	−24.0000			−1.93398
$155$		0			0
$156$	−2.82843	−	2.82843i	−0.226455	−	0.226455i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−5.65685	−	5.65685i	−0.450035	−	0.450035i
$159$	8.48528	−	8.48528i	0.672927	−	0.672927i
$160$		0			0
$161$		0			0
$162$		−	11.0000i		−	0.864242i
$163$	−1.41421	+	1.41421i	−0.110770	+	0.110770i	−0.760319	−	0.649550i	$-0.774958\pi$
$163$	−1.41421	+	1.41421i	−0.110770	+	0.110770i	0.649550	+	0.760319i	$0.274958\pi$
$164$	4.24264	−	4.24264i	0.331295	−	0.331295i
$165$		0			0
$166$		0			0
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		−	8.00000i		−	0.617213i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−4.00000			−0.305888
$172$		−	8.00000i		−	0.609994i
$173$	16.9706	+	16.9706i	1.29025	+	1.29025i	0.934632	+	0.355616i	$0.115729\pi$
$173$	16.9706	+	16.9706i	1.29025	+	1.29025i	0.355616	+	0.934632i	$0.384271\pi$
$174$		0			0
$175$	−14.1421	−	14.1421i	−1.06904	−	1.06904i
$176$	4.24264	−	4.24264i	0.319801	−	0.319801i
$177$		0			0
$178$		−	6.00000i		−	0.449719i
$179$			12.0000i			0.896922i	0.893802	+	0.448461i	$0.148028\pi$
$179$			12.0000i			0.896922i	−0.893802	+	0.448461i	$0.851972\pi$
$180$		0			0
$181$	−2.82843	+	2.82843i	−0.210235	+	0.210235i	−0.804367	−	0.594132i	$-0.797496\pi$
$181$	−2.82843	+	2.82843i	−0.210235	+	0.210235i	0.594132	+	0.804367i	$0.297496\pi$
$182$	5.65685	+	5.65685i	0.419314	+	0.419314i
$183$	−8.00000			−0.591377
$184$		0			0
$185$		0			0
$186$	8.00000			0.586588
$187$		0			0
$188$		0			0
$189$			16.0000i			1.16383i
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	1.41421	+	1.41421i	0.102062	+	0.102062i
$193$	−7.07107	+	7.07107i	−0.508987	+	0.508987i	−0.914215	−	0.405229i	$-0.867192\pi$
$193$	−7.07107	+	7.07107i	−0.508987	+	0.508987i	0.405229	+	0.914215i	$0.367192\pi$
$194$	−9.89949	+	9.89949i	−0.710742	+	0.710742i
$195$		0			0
$196$			9.00000i			0.642857i
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	−0.336966	−	0.941517i	$-0.609401\pi$
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	0.941517	+	0.336966i	$0.109401\pi$
$198$	4.24264	−	4.24264i	0.301511	−	0.301511i
$199$	11.3137	+	11.3137i	0.802008	+	0.802008i	0.983409	−	0.181402i	$-0.0580634\pi$
$199$	11.3137	+	11.3137i	0.802008	+	0.802008i	−0.181402	+	0.983409i	$0.558063\pi$
$200$	5.00000			0.353553
$201$	−11.3137	−	11.3137i	−0.798007	−	0.798007i
$202$		−	18.0000i		−	1.26648i
$203$		0			0
$204$		0			0
$205$		0			0
$206$			16.0000i			1.11477i
$207$		0			0
$208$	−2.00000			−0.138675
$209$	16.9706	+	16.9706i	1.17388	+	1.17388i
$210$		0			0
$211$	7.07107	−	7.07107i	0.486792	−	0.486792i	−0.420500	−	0.907292i	$-0.638145\pi$
$211$	7.07107	−	7.07107i	0.486792	−	0.486792i	0.907292	+	0.420500i	$0.138145\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$	4.24264	−	4.24264i	0.290021	−	0.290021i
$215$		0			0
$216$	−2.82843	−	2.82843i	−0.192450	−	0.192450i
$217$	−16.0000			−1.08615
$218$	−11.3137	−	11.3137i	−0.766261	−	0.766261i
$219$			4.00000i			0.270295i
$220$		0			0
$221$		0			0
$222$	8.00000			0.536925
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	−2.82843	−	2.82843i	−0.188982	−	0.188982i
$225$	5.00000			0.333333
$226$	4.24264	+	4.24264i	0.282216	+	0.282216i
$227$	−4.24264	+	4.24264i	−0.281594	+	0.281594i	−0.833744	−	0.552151i	$-0.813807\pi$
$227$	−4.24264	+	4.24264i	−0.281594	+	0.281594i	0.552151	+	0.833744i	$0.313807\pi$
$228$	−5.65685	+	5.65685i	−0.374634	+	0.374634i
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$		0			0
$231$	−33.9411	+	33.9411i	−2.23316	+	2.23316i
$232$		0			0
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	0.154205	−	0.988039i	$-0.450718\pi$
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	−0.988039	+	0.154205i	$0.950718\pi$
$234$	−2.00000			−0.130744
$235$		0			0
$236$		0			0
$237$	−16.0000			−1.03931
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−7.07107	−	7.07107i	−0.455488	−	0.455488i	0.441683	−	0.897171i	$-0.354381\pi$
$241$	−7.07107	−	7.07107i	−0.455488	−	0.455488i	−0.897171	+	0.441683i	$0.854381\pi$
$242$	−25.0000			−1.60706
$243$	−7.07107	−	7.07107i	−0.453609	−	0.453609i
$244$	−2.82843	+	2.82843i	−0.181071	+	0.181071i
$245$		0			0
$246$		−	12.0000i		−	0.765092i
$247$		−	8.00000i		−	0.509028i
$248$	2.82843	−	2.82843i	0.179605	−	0.179605i
$249$		0			0
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−2.82843	−	2.82843i	−0.178174	−	0.178174i
$253$		0			0
$254$	−16.0000			−1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	6.00000i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$		−	6.00000i		−	0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	−11.3137	−	11.3137i	−0.704361	−	0.704361i
$259$	−16.0000			−0.994192
$260$		0			0
$261$		0			0
$262$	4.24264	−	4.24264i	0.262111	−	0.262111i
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		−	12.0000i		−	0.738549i
$265$		0			0
$266$	11.3137	−	11.3137i	0.693688	−	0.693688i
$267$	−8.48528	−	8.48528i	−0.519291	−	0.519291i
$268$	−8.00000			−0.488678
$269$	−16.9706	−	16.9706i	−1.03471	−	1.03471i	−0.999375	−	0.0353381i	$-0.988749\pi$
$269$	−16.9706	−	16.9706i	−1.03471	−	1.03471i	−0.0353381	−	0.999375i	$-0.511251\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$	16.0000			0.968364
$274$		−	6.00000i		−	0.362473i
$275$	−21.2132	−	21.2132i	−1.27920	−	1.27920i
$276$		0			0
$277$	−5.65685	−	5.65685i	−0.339887	−	0.339887i	0.516437	−	0.856325i	$-0.327258\pi$
$277$	−5.65685	−	5.65685i	−0.339887	−	0.339887i	−0.856325	+	0.516437i	$0.827258\pi$
$278$	1.41421	−	1.41421i	0.0848189	−	0.0848189i
$279$	2.82843	−	2.82843i	0.169334	−	0.169334i
$280$		0			0
$281$			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
$283$	9.89949	−	9.89949i	0.588464	−	0.588464i	−0.348751	−	0.937215i	$-0.613394\pi$
$283$	9.89949	−	9.89949i	0.588464	−	0.588464i	0.937215	+	0.348751i	$0.113394\pi$
$284$		0			0
$285$		0			0
$286$	8.48528	+	8.48528i	0.501745	+	0.501745i
$287$			24.0000i			1.41668i
$288$	1.00000			0.0589256
$289$		0			0
$290$		0			0
$291$			28.0000i			1.64139i
$292$	1.41421	+	1.41421i	0.0827606	+	0.0827606i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	12.7279	+	12.7279i	0.742307	+	0.742307i
$295$		0			0
$296$	2.82843	−	2.82843i	0.164399	−	0.164399i
$297$			24.0000i			1.39262i
$298$			6.00000i			0.347571i
$299$		0			0
$300$	7.07107	−	7.07107i	0.408248	−	0.408248i
$301$	22.6274	+	22.6274i	1.30422	+	1.30422i
$302$	16.0000			0.920697
$303$	−25.4558	−	25.4558i	−1.46240	−	1.46240i
$304$			4.00000i			0.229416i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$			24.0000i			1.36753i
$309$	22.6274	+	22.6274i	1.28723	+	1.28723i
$310$		0			0
$311$	−8.48528	−	8.48528i	−0.481156	−	0.481156i	0.424345	−	0.905501i	$-0.360505\pi$
$311$	−8.48528	−	8.48528i	−0.481156	−	0.481156i	−0.905501	+	0.424345i	$0.860505\pi$
$312$	−2.82843	+	2.82843i	−0.160128	+	0.160128i
$313$	24.0416	−	24.0416i	1.35891	−	1.35891i	0.483654	−	0.875259i	$-0.339309\pi$
$313$	24.0416	−	24.0416i	1.35891	−	1.35891i	0.875259	−	0.483654i	$-0.160691\pi$
$314$			14.0000i			0.790066i
$315$		0			0
$316$	−5.65685	+	5.65685i	−0.318223	+	0.318223i
$317$	−8.48528	+	8.48528i	−0.476581	+	0.476581i	−0.904036	−	0.427456i	$-0.859410\pi$
$317$	−8.48528	+	8.48528i	−0.476581	+	0.476581i	0.427456	+	0.904036i	$0.359410\pi$
$318$	−8.48528	−	8.48528i	−0.475831	−	0.475831i
$319$		0			0
$320$		0			0
$321$		−	12.0000i		−	0.669775i
$322$		0			0
$323$		0			0
$324$	−11.0000			−0.611111
$325$			10.0000i			0.554700i
$326$	1.41421	+	1.41421i	0.0783260	+	0.0783260i
$327$	−32.0000			−1.76960
$328$	−4.24264	−	4.24264i	−0.234261	−	0.234261i
$329$		0			0
$330$		0			0
$331$		−	16.0000i		−	0.879440i	−0.898135	−	0.439720i	$-0.855078\pi$
$331$		−	16.0000i		−	0.879440i	0.898135	−	0.439720i	$-0.144922\pi$
$332$		0			0
$333$	2.82843	−	2.82843i	0.154997	−	0.154997i
$334$	8.48528	−	8.48528i	0.464294	−	0.464294i
$335$		0			0
$336$	−8.00000			−0.436436
$337$	−15.5563	−	15.5563i	−0.847408	−	0.847408i	0.142401	−	0.989809i	$-0.454518\pi$
$337$	−15.5563	−	15.5563i	−0.847408	−	0.847408i	−0.989809	+	0.142401i	$0.954518\pi$
$338$			9.00000i			0.489535i
$339$	12.0000			0.651751
$340$		0			0
$341$	−24.0000			−1.29967
$342$			4.00000i			0.216295i
$343$	−5.65685	−	5.65685i	−0.305441	−	0.305441i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	16.9706	−	16.9706i	0.912343	−	0.912343i
$347$	−12.7279	+	12.7279i	−0.683271	+	0.683271i	−0.960736	−	0.277465i	$-0.910506\pi$
$347$	−12.7279	+	12.7279i	−0.683271	+	0.683271i	0.277465	+	0.960736i	$0.410506\pi$
$348$		0			0
$349$			26.0000i			1.39175i	0.718164	+	0.695874i	$0.244983\pi$
$349$			26.0000i			1.39175i	−0.718164	+	0.695874i	$0.755017\pi$
$350$	−14.1421	+	14.1421i	−0.755929	+	0.755929i
$351$	5.65685	−	5.65685i	0.301941	−	0.301941i
$352$	−4.24264	−	4.24264i	−0.226134	−	0.226134i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	2.82843	+	2.82843i	0.148659	+	0.148659i
$363$	−35.3553	+	35.3553i	−1.85567	+	1.85567i
$364$	5.65685	−	5.65685i	0.296500	−	0.296500i
$365$		0			0
$366$			8.00000i			0.418167i
$367$	11.3137	−	11.3137i	0.590571	−	0.590571i	−0.347215	−	0.937786i	$-0.612873\pi$
$367$	11.3137	−	11.3137i	0.590571	−	0.590571i	0.937786	+	0.347215i	$0.112873\pi$
$368$		0			0
$369$	−4.24264	−	4.24264i	−0.220863	−	0.220863i
$370$		0			0
$371$	16.9706	+	16.9706i	0.881068	+	0.881068i
$372$		−	8.00000i		−	0.414781i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	16.0000			0.822951
$379$	−9.89949	−	9.89949i	−0.508503	−	0.508503i	0.405564	−	0.914067i	$-0.367075\pi$
$379$	−9.89949	−	9.89949i	−0.508503	−	0.508503i	−0.914067	+	0.405564i	$0.867075\pi$
$380$		0			0
$381$	−22.6274	+	22.6274i	−1.15924	+	1.15924i
$382$		−	24.0000i		−	1.22795i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$	1.41421	−	1.41421i	0.0721688	−	0.0721688i
$385$		0			0
$386$	7.07107	+	7.07107i	0.359908	+	0.359908i
$387$	−8.00000			−0.406663
$388$	9.89949	+	9.89949i	0.502571	+	0.502571i
$389$		−	30.0000i		−	1.52106i	−0.649303	−	0.760530i	$-0.724939\pi$
$389$		−	30.0000i		−	1.52106i	0.649303	−	0.760530i	$-0.275061\pi$
$390$		0			0
$391$		0			0
$392$	9.00000			0.454569
$393$		−	12.0000i		−	0.605320i
$394$	−8.48528	−	8.48528i	−0.427482	−	0.427482i
$395$		0			0
$396$	−4.24264	−	4.24264i	−0.213201	−	0.213201i
$397$	14.1421	−	14.1421i	0.709773	−	0.709773i	−0.256714	−	0.966487i	$-0.582640\pi$
$397$	14.1421	−	14.1421i	0.709773	−	0.709773i	0.966487	+	0.256714i	$0.0826398\pi$
$398$	11.3137	−	11.3137i	0.567105	−	0.567105i
$399$		−	32.0000i		−	1.60200i
$400$		−	5.00000i		−	0.250000i
$401$	−21.2132	+	21.2132i	−1.05934	+	1.05934i	−0.0612120	+	0.998125i	$0.519497\pi$
$401$	−21.2132	+	21.2132i	−1.05934	+	1.05934i	−0.998125	+	0.0612120i	$0.980503\pi$
$402$	−11.3137	+	11.3137i	−0.564276	+	0.564276i
$403$	5.65685	+	5.65685i	0.281788	+	0.281788i
$404$	−18.0000			−0.895533
$405$		0			0
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$		0			0
$411$	−8.48528	−	8.48528i	−0.418548	−	0.418548i
$412$	16.0000			0.788263
$413$		0			0
$414$		0			0
$415$		0			0
$416$			2.00000i			0.0980581i
$417$		−	4.00000i		−	0.195881i
$418$	16.9706	−	16.9706i	0.830057	−	0.830057i
$419$	−21.2132	+	21.2132i	−1.03633	+	1.03633i	−0.0370182	+	0.999315i	$0.511786\pi$
$419$	−21.2132	+	21.2132i	−1.03633	+	1.03633i	−0.999315	+	0.0370182i	$0.988214\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−7.07107	−	7.07107i	−0.344214	−	0.344214i
$423$		0			0
$424$	−6.00000			−0.291386
$425$		0			0
$426$		0			0
$427$		−	16.0000i		−	0.774294i
$428$	−4.24264	−	4.24264i	−0.205076	−	0.205076i
$429$	24.0000			1.15873
$430$		0			0
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	−0.168294	−	0.985737i	$-0.553826\pi$
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	0.985737	+	0.168294i	$0.0538257\pi$
$432$	−2.82843	+	2.82843i	−0.136083	+	0.136083i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$			16.0000i			0.768025i
$435$		0			0
$436$	−11.3137	+	11.3137i	−0.541828	+	0.541828i
$437$		0			0
$438$	4.00000			0.191127
$439$	5.65685	+	5.65685i	0.269987	+	0.269987i	0.829095	−	0.559108i	$-0.188856\pi$
$439$	5.65685	+	5.65685i	0.269987	+	0.269987i	−0.559108	+	0.829095i	$0.688856\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		−	8.00000i		−	0.379663i
$445$		0			0
$446$	−8.00000			−0.378811
$447$	8.48528	+	8.48528i	0.401340	+	0.401340i
$448$	−2.82843	+	2.82843i	−0.133631	+	0.133631i
$449$	12.7279	−	12.7279i	0.600668	−	0.600668i	−0.339822	−	0.940490i	$-0.610367\pi$
$449$	12.7279	−	12.7279i	0.600668	−	0.600668i	0.940490	+	0.339822i	$0.110367\pi$
$450$		−	5.00000i		−	0.235702i
$451$			36.0000i			1.69517i
$452$	4.24264	−	4.24264i	0.199557	−	0.199557i
$453$	22.6274	−	22.6274i	1.06313	−	1.06313i
$454$	4.24264	+	4.24264i	0.199117	+	0.199117i
$455$		0			0
$456$	5.65685	+	5.65685i	0.264906	+	0.264906i
$457$		−	26.0000i		−	1.21623i	−0.793849	−	0.608114i	$-0.791926\pi$
$457$		−	26.0000i		−	1.21623i	0.793849	−	0.608114i	$-0.208074\pi$
$458$	14.0000			0.654177
$459$		0			0
$460$		0			0
$461$			6.00000i			0.279448i	0.990190	+	0.139724i	$0.0446215\pi$
$461$			6.00000i			0.279448i	−0.990190	+	0.139724i	$0.955378\pi$
$462$	33.9411	+	33.9411i	1.57908	+	1.57908i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$		0			0
$466$	−12.7279	+	12.7279i	−0.589610	+	0.589610i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$			2.00000i			0.0924500i
$469$	22.6274	−	22.6274i	1.04484	−	1.04484i
$470$		0			0
$471$	19.7990	+	19.7990i	0.912289	+	0.912289i
$472$		0			0
$473$	33.9411	+	33.9411i	1.56061	+	1.56061i
$474$			16.0000i			0.734904i
$475$	20.0000			0.917663
$476$		0			0
$477$	−6.00000			−0.274721
$478$		−	24.0000i		−	1.09773i
$479$	16.9706	+	16.9706i	0.775405	+	0.775405i	0.979046	−	0.203641i	$-0.0652775\pi$
$479$	16.9706	+	16.9706i	0.775405	+	0.775405i	−0.203641	+	0.979046i	$0.565277\pi$
$480$		0			0
$481$	5.65685	+	5.65685i	0.257930	+	0.257930i
$482$	−7.07107	+	7.07107i	−0.322078	+	0.322078i
$483$		0			0
$484$			25.0000i			1.13636i
$485$		0			0
$486$	−7.07107	+	7.07107i	−0.320750	+	0.320750i
$487$	5.65685	−	5.65685i	0.256337	−	0.256337i	−0.567226	−	0.823562i	$-0.691983\pi$
$487$	5.65685	−	5.65685i	0.256337	−	0.256337i	0.823562	+	0.567226i	$0.191983\pi$
$488$	2.82843	+	2.82843i	0.128037	+	0.128037i
$489$	4.00000			0.180886
$490$		0			0
$491$			12.0000i			0.541552i	0.962642	+	0.270776i	$0.0872803\pi$
$491$			12.0000i			0.541552i	−0.962642	+	0.270776i	$0.912720\pi$
$492$	−12.0000			−0.541002
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−2.82843	−	2.82843i	−0.127000	−	0.127000i
$497$		0			0
$498$		0			0
$499$	9.89949	−	9.89949i	0.443162	−	0.443162i	−0.449911	−	0.893073i	$-0.648544\pi$
$499$	9.89949	−	9.89949i	0.443162	−	0.443162i	0.893073	+	0.449911i	$0.148544\pi$
$500$		0			0
$501$		−	24.0000i		−	1.07224i
$502$		−	24.0000i		−	1.07117i
$503$	16.9706	−	16.9706i	0.756680	−	0.756680i	−0.219037	−	0.975717i	$-0.570291\pi$
$503$	16.9706	−	16.9706i	0.756680	−	0.756680i	0.975717	+	0.219037i	$0.0702914\pi$
$504$	−2.82843	+	2.82843i	−0.125988	+	0.125988i
$505$		0			0
$506$		0			0
$507$	12.7279	+	12.7279i	0.565267	+	0.565267i
$508$			16.0000i			0.709885i
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$		−	1.00000i		−	0.0441942i
$513$	−11.3137	−	11.3137i	−0.499512	−	0.499512i
$514$	−6.00000			−0.264649
$515$		0			0
$516$	−11.3137	+	11.3137i	−0.498058	+	0.498058i
$517$		0			0
$518$			16.0000i			0.703000i
$519$		−	48.0000i		−	2.10697i
$520$		0			0
$521$	−12.7279	+	12.7279i	−0.557620	+	0.557620i	−0.928629	−	0.371009i	$-0.879012\pi$
$521$	−12.7279	+	12.7279i	−0.557620	+	0.557620i	0.371009	+	0.928629i	$0.379012\pi$
$522$		0			0
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$	−4.24264	−	4.24264i	−0.185341	−	0.185341i
$525$			40.0000i			1.74574i
$526$	24.0000			1.04645
$527$		0			0
$528$	−12.0000			−0.522233
$529$			23.0000i			1.00000i
$530$		0			0
$531$		0			0
$532$	−11.3137	−	11.3137i	−0.490511	−	0.490511i
$533$	8.48528	−	8.48528i	0.367538	−	0.367538i
$534$	−8.48528	+	8.48528i	−0.367194	+	0.367194i
$535$		0			0
$536$			8.00000i			0.345547i
$537$	16.9706	−	16.9706i	0.732334	−	0.732334i
$538$	−16.9706	+	16.9706i	−0.731653	+	0.731653i
$539$	−38.1838	−	38.1838i	−1.64469	−	1.64469i
$540$		0			0
$541$	14.1421	+	14.1421i	0.608018	+	0.608018i	0.942428	−	0.334410i	$-0.108537\pi$
$541$	14.1421	+	14.1421i	0.608018	+	0.608018i	−0.334410	+	0.942428i	$0.608537\pi$
$542$		−	8.00000i		−	0.343629i
$543$	8.00000			0.343313
$544$		0			0
$545$		0			0
$546$		−	16.0000i		−	0.684737i
$547$	1.41421	+	1.41421i	0.0604674	+	0.0604674i	0.736694	−	0.676226i	$-0.236386\pi$
$547$	1.41421	+	1.41421i	0.0604674	+	0.0604674i	−0.676226	+	0.736694i	$0.736386\pi$
$548$	−6.00000			−0.256307
$549$	2.82843	+	2.82843i	0.120714	+	0.120714i
$550$	−21.2132	+	21.2132i	−0.904534	+	0.904534i
$551$		0			0
$552$		0			0
$553$		−	32.0000i		−	1.36078i
$554$	−5.65685	+	5.65685i	−0.240337	+	0.240337i
$555$		0			0
$556$	−1.41421	−	1.41421i	−0.0599760	−	0.0599760i
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$	−2.82843	−	2.82843i	−0.119737	−	0.119737i
$559$		−	16.0000i		−	0.676728i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$		0			0
$565$		0			0
$566$	−9.89949	−	9.89949i	−0.416107	−	0.416107i
$567$	31.1127	−	31.1127i	1.30661	−	1.30661i
$568$		0			0
$569$		−	30.0000i		−	1.25767i	−0.777541	−	0.628833i	$-0.783533\pi$
$569$		−	30.0000i		−	1.25767i	0.777541	−	0.628833i	$-0.216467\pi$
$570$		0			0
$571$	−18.3848	+	18.3848i	−0.769379	+	0.769379i	−0.977997	−	0.208618i	$-0.933103\pi$
$571$	−18.3848	+	18.3848i	−0.769379	+	0.769379i	0.208618	+	0.977997i	$0.433103\pi$
$572$	8.48528	−	8.48528i	0.354787	−	0.354787i
$573$	−33.9411	−	33.9411i	−1.41791	−	1.41791i
$574$	24.0000			1.00174
$575$		0			0
$576$		−	1.00000i		−	0.0416667i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$	20.0000			0.831172
$580$		0			0
$581$		0			0
$582$	28.0000			1.16064
$583$	25.4558	+	25.4558i	1.05427	+	1.05427i
$584$	1.41421	−	1.41421i	0.0585206	−	0.0585206i
$585$		0			0
$586$			6.00000i			0.247858i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	12.7279	−	12.7279i	0.524891	−	0.524891i
$589$	11.3137	−	11.3137i	0.466173	−	0.466173i
$590$		0			0
$591$	−24.0000			−0.987228
$592$	−2.82843	−	2.82843i	−0.116248	−	0.116248i
$593$			30.0000i			1.23195i	0.787765	+	0.615976i	$0.211238\pi$
$593$			30.0000i			1.23195i	−0.787765	+	0.615976i	$0.788762\pi$
$594$	24.0000			0.984732
$595$		0			0
$596$	6.00000			0.245770
$597$		−	32.0000i		−	1.30967i
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	−7.07107	−	7.07107i	−0.288675	−	0.288675i
$601$	−32.5269	+	32.5269i	−1.32680	+	1.32680i	−0.418655	+	0.908145i	$0.637498\pi$
$601$	−32.5269	+	32.5269i	−1.32680	+	1.32680i	−0.908145	+	0.418655i	$0.862502\pi$
$602$	22.6274	−	22.6274i	0.922225	−	0.922225i
$603$			8.00000i			0.325785i
$604$		−	16.0000i		−	0.651031i
$605$		0			0
$606$	−25.4558	+	25.4558i	−1.03407	+	1.03407i
$607$	−14.1421	−	14.1421i	−0.574012	−	0.574012i	0.359235	−	0.933247i	$-0.383038\pi$
$607$	−14.1421	−	14.1421i	−0.574012	−	0.574012i	−0.933247	+	0.359235i	$0.883038\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$		−	20.0000i		−	0.807134i
$615$		0			0
$616$	24.0000			0.966988
$617$	21.2132	+	21.2132i	0.854011	+	0.854011i	0.990624	−	0.136613i	$-0.0436217\pi$
$617$	21.2132	+	21.2132i	0.854011	+	0.854011i	−0.136613	+	0.990624i	$0.543622\pi$
$618$	22.6274	−	22.6274i	0.910208	−	0.910208i
$619$	−18.3848	+	18.3848i	−0.738947	+	0.738947i	−0.972374	−	0.233428i	$-0.925006\pi$
$619$	−18.3848	+	18.3848i	−0.738947	+	0.738947i	0.233428	+	0.972374i	$0.425006\pi$
$620$		0			0
$621$		0			0
$622$	−8.48528	+	8.48528i	−0.340229	+	0.340229i
$623$	16.9706	−	16.9706i	0.679911	−	0.679911i
$624$	2.82843	+	2.82843i	0.113228	+	0.113228i
$625$	−25.0000			−1.00000
$626$	−24.0416	−	24.0416i	−0.960897	−	0.960897i
$627$		−	48.0000i		−	1.91694i
$628$	14.0000			0.558661
$629$		0			0
$630$		0			0
$631$		−	8.00000i		−	0.318475i	−0.987240	−	0.159237i	$-0.949096\pi$
$631$		−	8.00000i		−	0.318475i	0.987240	−	0.159237i	$-0.0509036\pi$
$632$	5.65685	+	5.65685i	0.225018	+	0.225018i
$633$	−20.0000			−0.794929
$634$	8.48528	+	8.48528i	0.336994	+	0.336994i
$635$		0			0
$636$	−8.48528	+	8.48528i	−0.336463	+	0.336463i
$637$			18.0000i			0.713186i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.7279	+	12.7279i	0.502723	+	0.502723i	0.912283	−	0.409560i	$-0.134318\pi$
$641$	12.7279	+	12.7279i	0.502723	+	0.502723i	−0.409560	+	0.912283i	$0.634318\pi$
$642$	−12.0000			−0.473602
$643$	9.89949	+	9.89949i	0.390398	+	0.390398i	0.874829	−	0.484431i	$-0.160973\pi$
$643$	9.89949	+	9.89949i	0.390398	+	0.390398i	−0.484431	+	0.874829i	$0.660973\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.0000			−1.88707			−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000			−1.88707			−0.943537	+	0.331266i	$0.892524\pi$
$648$			11.0000i			0.432121i
$649$		0			0
$650$	10.0000			0.392232
$651$	22.6274	+	22.6274i	0.886838	+	0.886838i
$652$	1.41421	−	1.41421i	0.0553849	−	0.0553849i
$653$	−16.9706	+	16.9706i	−0.664109	+	0.664109i	−0.956346	−	0.292237i	$-0.905601\pi$
$653$	−16.9706	+	16.9706i	−0.664109	+	0.664109i	0.292237	+	0.956346i	$0.405601\pi$
$654$			32.0000i			1.25130i
$655$		0			0
$656$	−4.24264	+	4.24264i	−0.165647	+	0.165647i
$657$	1.41421	−	1.41421i	0.0551737	−	0.0551737i
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$			46.0000i			1.78919i	0.446875	+	0.894596i	$0.352537\pi$
$661$			46.0000i			1.78919i	−0.446875	+	0.894596i	$0.647463\pi$
$662$	−16.0000			−0.621858
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.82843	−	2.82843i	−0.109599	−	0.109599i
$667$		0			0
$668$	−8.48528	−	8.48528i	−0.328305	−	0.328305i
$669$	−11.3137	+	11.3137i	−0.437413	+	0.437413i
$670$		0			0
$671$		−	24.0000i		−	0.926510i
$672$			8.00000i			0.308607i
$673$	−26.8701	+	26.8701i	−1.03576	+	1.03576i	−0.0364283	+	0.999336i	$0.511598\pi$
$673$	−26.8701	+	26.8701i	−1.03576	+	1.03576i	−0.999336	+	0.0364283i	$0.988402\pi$
$674$	−15.5563	+	15.5563i	−0.599208	+	0.599208i
$675$	14.1421	+	14.1421i	0.544331	+	0.544331i
$676$	9.00000			0.346154
$677$	−8.48528	−	8.48528i	−0.326116	−	0.326116i	0.524992	−	0.851107i	$-0.324068\pi$
$677$	−8.48528	−	8.48528i	−0.326116	−	0.326116i	−0.851107	+	0.524992i	$0.824068\pi$
$678$		−	12.0000i		−	0.460857i
$679$	−56.0000			−2.14908
$680$		0			0
$681$	12.0000			0.459841
$682$			24.0000i			0.919007i
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	0.984889	−	0.173188i	$-0.0554069\pi$
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	−0.173188	+	0.984889i	$0.555407\pi$
$684$	4.00000			0.152944
$685$		0			0
$686$	−5.65685	+	5.65685i	−0.215980	+	0.215980i
$687$	19.7990	−	19.7990i	0.755379	−	0.755379i
$688$			8.00000i			0.304997i
$689$		−	12.0000i		−	0.457164i
$690$		0			0
$691$	−7.07107	+	7.07107i	−0.268996	+	0.268996i	−0.828696	−	0.559700i	$-0.810917\pi$
$691$	−7.07107	+	7.07107i	−0.268996	+	0.268996i	0.559700	+	0.828696i	$0.310917\pi$
$692$	−16.9706	−	16.9706i	−0.645124	−	0.645124i
$693$	24.0000			0.911685
$694$	12.7279	+	12.7279i	0.483145	+	0.483145i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	26.0000			0.984115
$699$			36.0000i			1.36165i
$700$	14.1421	+	14.1421i	0.534522	+	0.534522i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−5.65685	−	5.65685i	−0.213504	−	0.213504i
$703$	11.3137	−	11.3137i	0.426705	−	0.426705i
$704$	−4.24264	+	4.24264i	−0.159901	+	0.159901i
$705$		0			0
$706$			6.00000i			0.225813i
$707$	50.9117	−	50.9117i	1.91473	−	1.91473i
$708$		0			0
$709$	11.3137	+	11.3137i	0.424895	+	0.424895i	0.886885	−	0.461990i	$-0.152864\pi$
$709$	11.3137	+	11.3137i	0.424895	+	0.424895i	−0.461990	+	0.886885i	$0.652864\pi$
$710$		0			0
$711$	5.65685	+	5.65685i	0.212149	+	0.212149i
$712$			6.00000i			0.224860i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		−	12.0000i		−	0.448461i
$717$	−33.9411	−	33.9411i	−1.26755	−	1.26755i
$718$	−24.0000			−0.895672
$719$	−33.9411	−	33.9411i	−1.26579	−	1.26579i	−0.948242	−	0.317548i	$-0.897140\pi$
$719$	−33.9411	−	33.9411i	−1.26579	−	1.26579i	−0.317548	−	0.948242i	$-0.602860\pi$
$720$		0			0
$721$	−45.2548	+	45.2548i	−1.68538	+	1.68538i
$722$		−	3.00000i		−	0.111648i
$723$			20.0000i			0.743808i
$724$	2.82843	−	2.82843i	0.105118	−	0.105118i
$725$		0			0
$726$	35.3553	+	35.3553i	1.31216	+	1.31216i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−5.65685	−	5.65685i	−0.209657	−	0.209657i
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$		0			0
$732$	8.00000			0.295689
$733$			22.0000i			0.812589i	0.913742	+	0.406294i	$0.133179\pi$
$733$			22.0000i			0.812589i	−0.913742	+	0.406294i	$0.866821\pi$
$734$	−11.3137	−	11.3137i	−0.417597	−	0.417597i
$735$		0			0
$736$		0			0
$737$	33.9411	−	33.9411i	1.25024	−	1.25024i
$738$	−4.24264	+	4.24264i	−0.156174	+	0.156174i
$739$			20.0000i			0.735712i	0.929883	+	0.367856i	$0.119908\pi$
$739$			20.0000i			0.735712i	−0.929883	+	0.367856i	$0.880092\pi$
$740$		0			0
$741$	−11.3137	+	11.3137i	−0.415619	+	0.415619i
$742$	16.9706	−	16.9706i	0.623009	−	0.623009i
$743$	25.4558	+	25.4558i	0.933884	+	0.933884i	0.997946	−	0.0640616i	$-0.0204054\pi$
$743$	25.4558	+	25.4558i	0.933884	+	0.933884i	−0.0640616	+	0.997946i	$0.520405\pi$
$744$	−8.00000			−0.293294
$745$		0			0
$746$			22.0000i			0.805477i
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	5.65685	+	5.65685i	0.206422	+	0.206422i	0.802745	−	0.596323i	$-0.203372\pi$
$751$	5.65685	+	5.65685i	0.206422	+	0.206422i	−0.596323	+	0.802745i	$0.703372\pi$
$752$		0			0
$753$	−33.9411	−	33.9411i	−1.23688	−	1.23688i
$754$		0			0
$755$		0			0
$756$		−	16.0000i		−	0.581914i
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−9.89949	+	9.89949i	−0.359566	+	0.359566i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$	22.6274	+	22.6274i	0.819705	+	0.819705i
$763$		−	64.0000i		−	2.31696i
$764$	−24.0000			−0.868290
$765$		0			0
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−1.41421	−	1.41421i	−0.0510310	−	0.0510310i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−8.48528	+	8.48528i	−0.305590	+	0.305590i
$772$	7.07107	−	7.07107i	0.254493	−	0.254493i
$773$		−	42.0000i		−	1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$773$		−	42.0000i		−	1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$774$			8.00000i			0.287554i
$775$	−14.1421	+	14.1421i	−0.508001	+	0.508001i
$776$	9.89949	−	9.89949i	0.355371	−	0.355371i
$777$	22.6274	+	22.6274i	0.811754	+	0.811754i
$778$	−30.0000			−1.07555
$779$	−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
$785$		0			0
$786$	−12.0000			−0.428026
$787$	32.5269	+	32.5269i	1.15946	+	1.15946i	0.984592	+	0.174867i	$0.0559496\pi$
$787$	32.5269	+	32.5269i	1.15946	+	1.15946i	0.174867	+	0.984592i	$0.444050\pi$
$788$	−8.48528	+	8.48528i	−0.302276	+	0.302276i
$789$	33.9411	−	33.9411i	1.20834	−	1.20834i
$790$		0			0
$791$			24.0000i			0.853342i
$792$	−4.24264	+	4.24264i	−0.150756	+	0.150756i
$793$	−5.65685	+	5.65685i	−0.200881	+	0.200881i
$794$	−14.1421	−	14.1421i	−0.501886	−	0.501886i
$795$		0			0
$796$	−11.3137	−	11.3137i	−0.401004	−	0.401004i
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$	−32.0000			−1.13279
$799$		0			0
$800$	−5.00000			−0.176777
$801$			6.00000i			0.212000i
$802$	21.2132	+	21.2132i	0.749064	+	0.749064i
$803$	−12.0000			−0.423471
$804$	11.3137	+	11.3137i	0.399004	+	0.399004i
$805$		0			0
$806$	5.65685	−	5.65685i	0.199254	−	0.199254i
$807$			48.0000i			1.68968i
$808$			18.0000i			0.633238i
$809$	−21.2132	+	21.2132i	−0.745817	+	0.745817i	−0.973691	−	0.227874i	$-0.926823\pi$
$809$	−21.2132	+	21.2132i	−0.745817	+	0.745817i	0.227874	+	0.973691i	$0.426823\pi$
$810$		0			0
$811$	−26.8701	−	26.8701i	−0.943535	−	0.943535i	0.0549536	−	0.998489i	$-0.482499\pi$
$811$	−26.8701	−	26.8701i	−0.943535	−	0.943535i	−0.998489	+	0.0549536i	$0.982499\pi$
$812$		0			0
$813$	−11.3137	−	11.3137i	−0.396789	−	0.396789i
$814$			24.0000i			0.841200i
$815$		0			0
$816$		0			0
$817$	−32.0000			−1.11954
$818$			10.0000i			0.349642i
$819$	−5.65685	−	5.65685i	−0.197666	−	0.197666i
$820$		0			0
$821$	−25.4558	−	25.4558i	−0.888415	−	0.888415i	0.105956	−	0.994371i	$-0.466210\pi$
$821$	−25.4558	−	25.4558i	−0.888415	−	0.888415i	−0.994371	+	0.105956i	$0.966210\pi$
$822$	−8.48528	+	8.48528i	−0.295958	+	0.295958i
$823$	11.3137	−	11.3137i	0.394371	−	0.394371i	−0.481871	−	0.876242i	$-0.660043\pi$
$823$	11.3137	−	11.3137i	0.394371	−	0.394371i	0.876242	+	0.481871i	$0.160043\pi$
$824$		−	16.0000i		−	0.557386i
$825$			60.0000i			2.08893i
$826$		0			0
$827$	4.24264	−	4.24264i	0.147531	−	0.147531i	−0.629483	−	0.777014i	$-0.716733\pi$
$827$	4.24264	−	4.24264i	0.147531	−	0.147531i	0.777014	+	0.629483i	$0.216733\pi$
$828$		0			0
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$		0			0
$831$			16.0000i			0.555034i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	−16.9706	−	16.9706i	−0.586939	−	0.586939i
$837$	16.0000			0.553041
$838$	21.2132	+	21.2132i	0.732798	+	0.732798i
$839$	−25.4558	+	25.4558i	−0.878833	+	0.878833i	−0.993414	−	0.114581i	$-0.963448\pi$
$839$	−25.4558	+	25.4558i	−0.878833	+	0.878833i	0.114581	+	0.993414i	$0.463448\pi$
$840$		0			0
$841$		−	29.0000i		−	1.00000i
$842$			2.00000i			0.0689246i
$843$	8.48528	−	8.48528i	0.292249	−	0.292249i
$844$	−7.07107	+	7.07107i	−0.243396	+	0.243396i
$845$		0			0
$846$		0			0
$847$	−70.7107	−	70.7107i	−2.42965	−	2.42965i
$848$			6.00000i			0.206041i
$849$	−28.0000			−0.960958
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−28.2843	−	28.2843i	−0.968435	−	0.968435i	0.0310818	−	0.999517i	$-0.490105\pi$
$853$	−28.2843	−	28.2843i	−0.968435	−	0.968435i	−0.999517	+	0.0310818i	$0.990105\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$	−4.24264	+	4.24264i	−0.145010	+	0.145010i
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	−0.455472	−	0.890250i	$-0.650530\pi$
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	0.890250	+	0.455472i	$0.150530\pi$
$858$		−	24.0000i		−	0.819346i
$859$		−	16.0000i		−	0.545913i	−0.962026	−	0.272956i	$-0.911998\pi$
$859$		−	16.0000i		−	0.545913i	0.962026	−	0.272956i	$-0.0880015\pi$
$860$		0			0
$861$	33.9411	−	33.9411i	1.15671	−	1.15671i
$862$	−16.9706	−	16.9706i	−0.578020	−	0.578020i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$	2.82843	+	2.82843i	0.0962250	+	0.0962250i
$865$		0			0
$866$	2.00000			0.0679628
$867$		0			0
$868$	16.0000			0.543075
$869$		−	48.0000i		−	1.62829i
$870$		0			0
$871$	−16.0000			−0.542139
$872$	11.3137	+	11.3137i	0.383131	+	0.383131i
$873$	9.89949	−	9.89949i	0.335047	−	0.335047i
$874$		0			0
$875$		0			0
$876$		−	4.00000i		−	0.135147i
$877$	−22.6274	+	22.6274i	−0.764074	+	0.764074i	−0.977056	−	0.212982i	$-0.931682\pi$
$877$	−22.6274	+	22.6274i	−0.764074	+	0.764074i	0.212982	+	0.977056i	$0.431682\pi$
$878$	5.65685	−	5.65685i	0.190910	−	0.190910i
$879$	8.48528	+	8.48528i	0.286201	+	0.286201i
$880$		0			0
$881$	12.7279	+	12.7279i	0.428815	+	0.428815i	0.888224	−	0.459410i	$-0.151939\pi$
$881$	12.7279	+	12.7279i	0.428815	+	0.428815i	−0.459410	+	0.888224i	$0.651939\pi$
$882$		−	9.00000i		−	0.303046i
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$		0			0
$885$		0			0
$886$			24.0000i			0.806296i
$887$	16.9706	+	16.9706i	0.569816	+	0.569816i	0.932077	−	0.362261i	$-0.117995\pi$
$887$	16.9706	+	16.9706i	0.569816	+	0.569816i	−0.362261	+	0.932077i	$0.617995\pi$
$888$	−8.00000			−0.268462
$889$	−45.2548	−	45.2548i	−1.51780	−	1.51780i
$890$		0			0
$891$	46.6690	−	46.6690i	1.56347	−	1.56347i
$892$			8.00000i			0.267860i
$893$		0			0
$894$	8.48528	−	8.48528i	0.283790	−	0.283790i
$895$		0			0
$896$	2.82843	+	2.82843i	0.0944911	+	0.0944911i
$897$		0			0
$898$	−12.7279	−	12.7279i	−0.424736	−	0.424736i
$899$		0			0
$900$	−5.00000			−0.166667
$901$		0			0
$902$	36.0000			1.19867
$903$		−	64.0000i		−	2.12979i
$904$	−4.24264	−	4.24264i	−0.141108	−	0.141108i
$905$		0			0
$906$	−22.6274	−	22.6274i	−0.751746	−	0.751746i
$907$	−41.0122	+	41.0122i	−1.36179	+	1.36179i	−0.490149	+	0.871639i	$0.663058\pi$
$907$	−41.0122	+	41.0122i	−1.36179	+	1.36179i	−0.871639	+	0.490149i	$0.836942\pi$
$908$	4.24264	−	4.24264i	0.140797	−	0.140797i
$909$			18.0000i			0.597022i
$910$		0			0
$911$	−8.48528	+	8.48528i	−0.281130	+	0.281130i	−0.833560	−	0.552430i	$-0.813701\pi$
$911$	−8.48528	+	8.48528i	−0.281130	+	0.281130i	0.552430	+	0.833560i	$0.313701\pi$
$912$	5.65685	−	5.65685i	0.187317	−	0.187317i
$913$		0			0
$914$	−26.0000			−0.860004
$915$		0			0
$916$		−	14.0000i		−	0.462573i
$917$	24.0000			0.792550
$918$		0			0
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$		0			0
$921$	−28.2843	−	28.2843i	−0.931998	−	0.931998i
$922$	6.00000			0.197599
$923$		0			0
$924$	33.9411	−	33.9411i	1.11658	−	1.11658i
$925$	−14.1421	+	14.1421i	−0.464991	+	0.464991i
$926$		−	16.0000i		−	0.525793i
$927$		−	16.0000i		−	0.525509i
$928$		0			0
$929$	−12.7279	+	12.7279i	−0.417590	+	0.417590i	−0.884372	−	0.466783i	$-0.845413\pi$
$929$	−12.7279	+	12.7279i	−0.417590	+	0.417590i	0.466783	+	0.884372i	$0.345413\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$	12.7279	+	12.7279i	0.416917	+	0.416917i
$933$			24.0000i			0.785725i
$934$	12.0000			0.392652
$935$		0			0
$936$	2.00000			0.0653720
$937$			58.0000i			1.89478i	0.320085	+	0.947389i	$0.396288\pi$
$937$			58.0000i			1.89478i	−0.320085	+	0.947389i	$0.603712\pi$
$938$	−22.6274	−	22.6274i	−0.738811	−	0.738811i
$939$	−68.0000			−2.21910
$940$		0			0
$941$	−25.4558	+	25.4558i	−0.829837	+	0.829837i	−0.987494	−	0.157657i	$-0.949606\pi$
$941$	−25.4558	+	25.4558i	−0.829837	+	0.829837i	0.157657	+	0.987494i	$0.449606\pi$
$942$	19.7990	−	19.7990i	0.645086	−	0.645086i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	33.9411	−	33.9411i	1.10352	−	1.10352i
$947$	−12.7279	−	12.7279i	−0.413602	−	0.413602i	0.469389	−	0.882991i	$-0.344474\pi$
$947$	−12.7279	−	12.7279i	−0.413602	−	0.413602i	−0.882991	+	0.469389i	$0.844474\pi$
$948$	16.0000			0.519656
$949$	2.82843	+	2.82843i	0.0918146	+	0.0918146i
$950$		−	20.0000i		−	0.648886i
$951$	24.0000			0.778253
$952$		0			0
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$			6.00000i			0.194257i
$955$		0			0
$956$	−24.0000			−0.776215
$957$		0			0
$958$	16.9706	−	16.9706i	0.548294	−	0.548294i
$959$	16.9706	−	16.9706i	0.548008	−	0.548008i
$960$		0			0
$961$		−	15.0000i		−	0.483871i
$962$	5.65685	−	5.65685i	0.182384	−	0.182384i
$963$	−4.24264	+	4.24264i	−0.136717	+	0.136717i
$964$	7.07107	+	7.07107i	0.227744	+	0.227744i
$965$		0			0
$966$		0			0
$967$			40.0000i			1.28631i	0.765735	+	0.643157i	$0.222376\pi$
$967$			40.0000i			1.28631i	−0.765735	+	0.643157i	$0.777624\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$		0			0
$971$			24.0000i			0.770197i	0.922876	+	0.385098i	$0.125832\pi$
$971$			24.0000i			0.770197i	−0.922876	+	0.385098i	$0.874168\pi$
$972$	7.07107	+	7.07107i	0.226805	+	0.226805i
$973$	8.00000			0.256468
$974$	−5.65685	−	5.65685i	−0.181257	−	0.181257i
$975$	14.1421	−	14.1421i	0.452911	−	0.452911i
$976$	2.82843	−	2.82843i	0.0905357	−	0.0905357i
$977$			42.0000i			1.34370i	0.740688	+	0.671850i	$0.234500\pi$
$977$			42.0000i			1.34370i	−0.740688	+	0.671850i	$0.765500\pi$
$978$		−	4.00000i		−	0.127906i
$979$	25.4558	−	25.4558i	0.813572	−	0.813572i
$980$		0			0
$981$	11.3137	+	11.3137i	0.361219	+	0.361219i
$982$	12.0000			0.382935
$983$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$983$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$984$			12.0000i			0.382546i
$985$		0			0
$986$		0			0
$987$		0			0
$988$			8.00000i			0.254514i
$989$		0			0
$990$		0			0
$991$	11.3137	+	11.3137i	0.359392	+	0.359392i	0.863589	−	0.504197i	$-0.168211\pi$
$991$	11.3137	+	11.3137i	0.359392	+	0.359392i	−0.504197	+	0.863589i	$0.668211\pi$
$992$	−2.82843	+	2.82843i	−0.0898027	+	0.0898027i
$993$	−22.6274	+	22.6274i	−0.718059	+	0.718059i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−19.7990	+	19.7990i	−0.627040	+	0.627040i	−0.947322	−	0.320282i	$-0.896222\pi$
$997$	−19.7990	+	19.7990i	−0.627040	+	0.627040i	0.320282	+	0.947322i	$0.396222\pi$
$998$	−9.89949	−	9.89949i	−0.313363	−	0.313363i
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.c.e.251.1		4
17.2	even	8		34.2.a.a.1.1	✓	1
17.3	odd	16		578.2.d.e.423.1		8
17.4	even	4	inner	578.2.c.e.327.1		4
17.5	odd	16		578.2.d.e.155.2		8
17.6	odd	16		578.2.d.e.179.1		8
17.7	odd	16		578.2.d.e.399.1		8
17.8	even	8		578.2.b.a.577.2		2
17.9	even	8		578.2.b.a.577.1		2
17.10	odd	16		578.2.d.e.399.2		8
17.11	odd	16		578.2.d.e.179.2		8
17.12	odd	16		578.2.d.e.155.1		8
17.13	even	4	inner	578.2.c.e.327.2		4
17.14	odd	16		578.2.d.e.423.2		8
17.15	even	8		578.2.a.a.1.1		1
17.16	even	2	inner	578.2.c.e.251.2		4
51.2	odd	8		306.2.a.a.1.1		1
51.32	odd	8		5202.2.a.d.1.1		1
68.15	odd	8		4624.2.a.a.1.1		1
68.19	odd	8		272.2.a.d.1.1		1
85.2	odd	8		850.2.c.b.749.2		2
85.19	even	8		850.2.a.e.1.1		1
85.53	odd	8		850.2.c.b.749.1		2
119.104	odd	8		1666.2.a.m.1.1		1
136.19	odd	8		1088.2.a.d.1.1		1
136.53	even	8		1088.2.a.l.1.1		1
187.87	odd	8		4114.2.a.a.1.1		1
204.155	even	8		2448.2.a.k.1.1		1
221.155	even	8		5746.2.a.b.1.1		1
255.104	odd	8		7650.2.a.ci.1.1		1
340.19	odd	8		6800.2.a.b.1.1		1
408.53	odd	8		9792.2.a.y.1.1		1
408.155	even	8		9792.2.a.bj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.a.a.1.1	✓	1	17.2	even	8
272.2.a.d.1.1		1	68.19	odd	8
306.2.a.a.1.1		1	51.2	odd	8
578.2.a.a.1.1		1	17.15	even	8
578.2.b.a.577.1		2	17.9	even	8
578.2.b.a.577.2		2	17.8	even	8
578.2.c.e.251.1		4	1.1	even	1	trivial
578.2.c.e.251.2		4	17.16	even	2	inner
578.2.c.e.327.1		4	17.4	even	4	inner
578.2.c.e.327.2		4	17.13	even	4	inner
578.2.d.e.155.1		8	17.12	odd	16
578.2.d.e.155.2		8	17.5	odd	16
578.2.d.e.179.1		8	17.6	odd	16
578.2.d.e.179.2		8	17.11	odd	16
578.2.d.e.399.1		8	17.7	odd	16
578.2.d.e.399.2		8	17.10	odd	16
578.2.d.e.423.1		8	17.3	odd	16
578.2.d.e.423.2		8	17.14	odd	16
850.2.a.e.1.1		1	85.19	even	8
850.2.c.b.749.1		2	85.53	odd	8
850.2.c.b.749.2		2	85.2	odd	8
1088.2.a.d.1.1		1	136.19	odd	8
1088.2.a.l.1.1		1	136.53	even	8
1666.2.a.m.1.1		1	119.104	odd	8
2448.2.a.k.1.1		1	204.155	even	8
4114.2.a.a.1.1		1	187.87	odd	8
4624.2.a.a.1.1		1	68.15	odd	8
5202.2.a.d.1.1		1	51.32	odd	8
5746.2.a.b.1.1		1	221.155	even	8
6800.2.a.b.1.1		1	340.19	odd	8
7650.2.a.ci.1.1		1	255.104	odd	8
9792.2.a.y.1.1		1	408.53	odd	8
9792.2.a.bj.1.1		1	408.155	even	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:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(4.24264 - 4.24264i) q^{11} +(1.41421 + 1.41421i) q^{12} -2.00000 q^{13} +(-2.82843 - 2.82843i) q^{14} +1.00000 q^{16} +1.00000 q^{18} +4.00000i q^{19} -8.00000 q^{21} +(-4.24264 - 4.24264i) q^{22} +(1.41421 - 1.41421i) q^{24} -5.00000i q^{25} +2.00000i q^{26} +(-2.82843 + 2.82843i) q^{27} +(-2.82843 + 2.82843i) q^{28} +(-2.82843 - 2.82843i) q^{31} -1.00000i q^{32} -12.0000 q^{33} -1.00000i q^{36} +(-2.82843 - 2.82843i) q^{37} +4.00000 q^{38} +(2.82843 + 2.82843i) q^{39} +(-4.24264 + 4.24264i) q^{41} +8.00000i q^{42} +8.00000i q^{43} +(-4.24264 + 4.24264i) q^{44} +(-1.41421 - 1.41421i) q^{48} -9.00000i q^{49} -5.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(2.82843 + 2.82843i) q^{54} +(2.82843 + 2.82843i) q^{56} +(5.65685 - 5.65685i) q^{57} +(2.82843 - 2.82843i) q^{61} +(-2.82843 + 2.82843i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +12.0000i q^{66} +8.00000 q^{67} -1.00000 q^{72} +(-1.41421 - 1.41421i) q^{73} +(-2.82843 + 2.82843i) q^{74} +(-7.07107 + 7.07107i) q^{75} -4.00000i q^{76} -24.0000i q^{77} +(2.82843 - 2.82843i) q^{78} +(5.65685 - 5.65685i) q^{79} +11.0000 q^{81} +(4.24264 + 4.24264i) q^{82} +8.00000 q^{84} +8.00000 q^{86} +(4.24264 + 4.24264i) q^{88} +6.00000 q^{89} +(-5.65685 + 5.65685i) q^{91} +8.00000i q^{93} +(-1.41421 + 1.41421i) q^{96} +(-9.89949 - 9.89949i) q^{97} -9.00000 q^{98} +(4.24264 + 4.24264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} - 8 q^{13} + 4 q^{16} + 4 q^{18} - 32 q^{21} - 48 q^{33} + 16 q^{38} - 20 q^{50} + 8 q^{52} - 4 q^{64} + 32 q^{67} - 4 q^{72} + 44 q^{81} + 32 q^{84} + 32 q^{86} + 24 q^{89} - 36 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 8 * q^13 + 4 * q^16 + 4 * q^18 - 32 * q^21 - 48 * q^33 + 16 * q^38 - 20 * q^50 + 8 * q^52 - 4 * q^64 + 32 * q^67 - 4 * q^72 + 44 * q^81 + 32 * q^84 + 32 * q^86 + 24 * q^89 - 36 * q^98

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