LMFDB - Embedded newform 1734.2.f.g.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (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:	$13.8460597105$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1734.829
Dual form			1734.2.f.g.1483.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.82843 - 2.82843i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.82843 - 2.82843i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.82843 - 2.82843i) q^{10} +(-0.707107 - 0.707107i) q^{12} +6.00000 q^{13} +(-1.41421 - 1.41421i) q^{14} -4.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} +(2.82843 + 2.82843i) q^{20} -2.00000 q^{21} +(-4.24264 + 4.24264i) q^{23} +(0.707107 - 0.707107i) q^{24} +11.0000i q^{25} +6.00000i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.41421 - 1.41421i) q^{28} +(-2.82843 - 2.82843i) q^{29} +4.00000 q^{30} +(4.24264 + 4.24264i) q^{31} +1.00000i q^{32} +8.00000 q^{35} -1.00000i q^{36} +(2.82843 + 2.82843i) q^{37} +4.00000 q^{38} +(4.24264 + 4.24264i) q^{39} +(-2.82843 + 2.82843i) q^{40} +(-7.07107 + 7.07107i) q^{41} -2.00000i q^{42} -4.00000i q^{43} +(2.82843 - 2.82843i) q^{45} +(-4.24264 - 4.24264i) q^{46} -4.00000 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} -11.0000 q^{50} -6.00000 q^{52} +2.00000i q^{53} +(-0.707107 - 0.707107i) q^{54} +(1.41421 + 1.41421i) q^{56} +(2.82843 - 2.82843i) q^{57} +(2.82843 - 2.82843i) q^{58} +12.0000i q^{59} +4.00000i q^{60} +(-2.82843 + 2.82843i) q^{61} +(-4.24264 + 4.24264i) q^{62} +(-1.41421 - 1.41421i) q^{63} -1.00000 q^{64} +(-16.9706 - 16.9706i) q^{65} -12.0000 q^{67} -6.00000 q^{69} +8.00000i q^{70} +(4.24264 + 4.24264i) q^{71} +1.00000 q^{72} +(1.41421 + 1.41421i) q^{73} +(-2.82843 + 2.82843i) q^{74} +(-7.77817 + 7.77817i) q^{75} +4.00000i q^{76} +(-4.24264 + 4.24264i) q^{78} +(-7.07107 + 7.07107i) q^{79} +(-2.82843 - 2.82843i) q^{80} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} -4.00000i q^{87} +2.00000 q^{89} +(2.82843 + 2.82843i) q^{90} +(-8.48528 + 8.48528i) q^{91} +(4.24264 - 4.24264i) q^{92} +6.00000i q^{93} -4.00000i q^{94} +(-11.3137 + 11.3137i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.24264 + 4.24264i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} + 24 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} + 16 q^{30} + 32 q^{35} + 16 q^{38} - 16 q^{47} - 44 q^{50} - 24 q^{52} - 4 q^{64} - 48 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 8 q^{89} - 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 24 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 + 16 * q^30 + 32 * q^35 + 16 * q^38 - 16 * q^47 - 44 * q^50 - 24 * q^52 - 4 * q^64 - 48 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 8 * q^89 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.82843	−	2.82843i	−1.26491	−	1.26491i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$	−2.82843	−	2.82843i	−1.26491	−	1.26491i	−0.316228	−	0.948683i	$-0.602416\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.41421	+	1.41421i	−0.534522	+	0.534522i	−0.921915	−	0.387392i	$-0.873376\pi$
$7$	−1.41421	+	1.41421i	−0.534522	+	0.534522i	0.387392	+	0.921915i	$0.373376\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	2.82843	−	2.82843i	0.894427	−	0.894427i
$11$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$11$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		−	4.00000i		−	1.03280i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	2.82843	+	2.82843i	0.632456	+	0.632456i
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	−0.994003	−	0.109351i	$-0.965123\pi$
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	0.109351	+	0.994003i	$0.465123\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$			11.0000i			2.20000i
$26$			6.00000i			1.17670i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.41421	−	1.41421i	0.267261	−	0.267261i
$29$	−2.82843	−	2.82843i	−0.525226	−	0.525226i	0.393919	−	0.919145i	$-0.371119\pi$
$29$	−2.82843	−	2.82843i	−0.525226	−	0.525226i	−0.919145	+	0.393919i	$0.871119\pi$
$30$	4.00000			0.730297
$31$	4.24264	+	4.24264i	0.762001	+	0.762001i	0.976684	−	0.214683i	$-0.0688718\pi$
$31$	4.24264	+	4.24264i	0.762001	+	0.762001i	−0.214683	+	0.976684i	$0.568872\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		0			0
$35$	8.00000			1.35225
$36$		−	1.00000i		−	0.166667i
$37$	2.82843	+	2.82843i	0.464991	+	0.464991i	0.900287	−	0.435297i	$-0.143356\pi$
$37$	2.82843	+	2.82843i	0.464991	+	0.464991i	−0.435297	+	0.900287i	$0.643356\pi$
$38$	4.00000			0.648886
$39$	4.24264	+	4.24264i	0.679366	+	0.679366i
$40$	−2.82843	+	2.82843i	−0.447214	+	0.447214i
$41$	−7.07107	+	7.07107i	−1.10432	+	1.10432i	−0.110432	+	0.993884i	$0.535223\pi$
$41$	−7.07107	+	7.07107i	−1.10432	+	1.10432i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	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
$45$	2.82843	−	2.82843i	0.421637	−	0.421637i
$46$	−4.24264	−	4.24264i	−0.625543	−	0.625543i
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			3.00000i			0.428571i
$50$	−11.0000			−1.55563
$51$		0			0
$52$	−6.00000			−0.832050
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$		0			0
$56$	1.41421	+	1.41421i	0.188982	+	0.188982i
$57$	2.82843	−	2.82843i	0.374634	−	0.374634i
$58$	2.82843	−	2.82843i	0.371391	−	0.371391i
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$			4.00000i			0.516398i
$61$	−2.82843	+	2.82843i	−0.362143	+	0.362143i	−0.864601	−	0.502458i	$-0.832429\pi$
$61$	−2.82843	+	2.82843i	−0.362143	+	0.362143i	0.502458	+	0.864601i	$0.332429\pi$
$62$	−4.24264	+	4.24264i	−0.538816	+	0.538816i
$63$	−1.41421	−	1.41421i	−0.178174	−	0.178174i
$64$	−1.00000			−0.125000
$65$	−16.9706	−	16.9706i	−2.10494	−	2.10494i
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$			8.00000i			0.956183i
$71$	4.24264	+	4.24264i	0.503509	+	0.503509i	0.912526	−	0.409018i	$-0.134129\pi$
$71$	4.24264	+	4.24264i	0.503509	+	0.503509i	−0.409018	+	0.912526i	$0.634129\pi$
$72$	1.00000			0.117851
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	0.785007	−	0.619486i	$-0.212659\pi$
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	−0.619486	+	0.785007i	$0.712659\pi$
$74$	−2.82843	+	2.82843i	−0.328798	+	0.328798i
$75$	−7.77817	+	7.77817i	−0.898146	+	0.898146i
$76$			4.00000i			0.458831i
$77$		0			0
$78$	−4.24264	+	4.24264i	−0.480384	+	0.480384i
$79$	−7.07107	+	7.07107i	−0.795557	+	0.795557i	−0.982391	−	0.186834i	$-0.940177\pi$
$79$	−7.07107	+	7.07107i	−0.795557	+	0.795557i	0.186834	+	0.982391i	$0.440177\pi$
$80$	−2.82843	−	2.82843i	−0.316228	−	0.316228i
$81$	−1.00000			−0.111111
$82$	−7.07107	−	7.07107i	−0.780869	−	0.780869i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	4.00000			0.431331
$87$		−	4.00000i		−	0.428845i
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	2.82843	+	2.82843i	0.298142	+	0.298142i
$91$	−8.48528	+	8.48528i	−0.889499	+	0.889499i
$92$	4.24264	−	4.24264i	0.442326	−	0.442326i
$93$			6.00000i			0.622171i
$94$		−	4.00000i		−	0.412568i
$95$	−11.3137	+	11.3137i	−1.16076	+	1.16076i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	4.24264	+	4.24264i	0.430775	+	0.430775i	0.888892	−	0.458117i	$-0.151476\pi$
$97$	4.24264	+	4.24264i	0.430775	+	0.430775i	−0.458117	+	0.888892i	$0.651476\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$		−	11.0000i		−	1.10000i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		−	6.00000i		−	0.588348i
$105$	5.65685	+	5.65685i	0.552052	+	0.552052i
$106$	−2.00000			−0.194257
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	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
$111$			4.00000i			0.379663i
$112$	−1.41421	+	1.41421i	−0.133631	+	0.133631i
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$	2.82843	+	2.82843i	0.264906	+	0.264906i
$115$	24.0000			2.23801
$116$	2.82843	+	2.82843i	0.262613	+	0.262613i
$117$			6.00000i			0.554700i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−4.00000			−0.365148
$121$			11.0000i			1.00000i
$122$	−2.82843	−	2.82843i	−0.256074	−	0.256074i
$123$	−10.0000			−0.901670
$124$	−4.24264	−	4.24264i	−0.381000	−	0.381000i
$125$	16.9706	−	16.9706i	1.51789	−	1.51789i
$126$	1.41421	−	1.41421i	0.125988	−	0.125988i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.82843	−	2.82843i	0.249029	−	0.249029i
$130$	16.9706	−	16.9706i	1.48842	−	1.48842i
$131$	−11.3137	−	11.3137i	−0.988483	−	0.988483i	0.0114511	−	0.999934i	$-0.496355\pi$
$131$	−11.3137	−	11.3137i	−0.988483	−	0.988483i	−0.999934	+	0.0114511i	$0.996355\pi$
$132$		0			0
$133$	5.65685	+	5.65685i	0.490511	+	0.490511i
$134$		−	12.0000i		−	1.03664i
$135$	4.00000			0.344265
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−5.65685	−	5.65685i	−0.479808	−	0.479808i	0.425262	−	0.905070i	$-0.360182\pi$
$139$	−5.65685	−	5.65685i	−0.479808	−	0.479808i	−0.905070	+	0.425262i	$0.860182\pi$
$140$	−8.00000			−0.676123
$141$	−2.82843	−	2.82843i	−0.238197	−	0.238197i
$142$	−4.24264	+	4.24264i	−0.356034	+	0.356034i
$143$		0			0
$144$			1.00000i			0.0833333i
$145$			16.0000i			1.32873i
$146$	−1.41421	+	1.41421i	−0.117041	+	0.117041i
$147$	−2.12132	+	2.12132i	−0.174964	+	0.174964i
$148$	−2.82843	−	2.82843i	−0.232495	−	0.232495i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−7.77817	−	7.77817i	−0.635085	−	0.635085i
$151$			24.0000i			1.95309i	0.215308	+	0.976546i	$0.430924\pi$
$151$			24.0000i			1.95309i	−0.215308	+	0.976546i	$0.569076\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$		0			0
$155$		−	24.0000i		−	1.92773i
$156$	−4.24264	−	4.24264i	−0.339683	−	0.339683i
$157$	−6.00000			−0.478852			−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000			−0.478852			−0.239426	+	0.970915i	$0.576959\pi$
$158$	−7.07107	−	7.07107i	−0.562544	−	0.562544i
$159$	−1.41421	+	1.41421i	−0.112154	+	0.112154i
$160$	2.82843	−	2.82843i	0.223607	−	0.223607i
$161$		−	12.0000i		−	0.945732i
$162$		−	1.00000i		−	0.0785674i
$163$	8.48528	−	8.48528i	0.664619	−	0.664619i	−0.291847	−	0.956465i	$-0.594270\pi$
$163$	8.48528	−	8.48528i	0.664619	−	0.664619i	0.956465	+	0.291847i	$0.0942697\pi$
$164$	7.07107	−	7.07107i	0.552158	−	0.552158i
$165$		0			0
$166$	−12.0000			−0.931381
$167$	1.41421	+	1.41421i	0.109435	+	0.109435i	0.759704	−	0.650269i	$-0.225344\pi$
$167$	1.41421	+	1.41421i	0.109435	+	0.109435i	−0.650269	+	0.759704i	$0.725344\pi$
$168$			2.00000i			0.154303i
$169$	23.0000			1.76923
$170$		0			0
$171$	4.00000			0.305888
$172$			4.00000i			0.304997i
$173$	2.82843	+	2.82843i	0.215041	+	0.215041i	0.806405	−	0.591364i	$-0.201410\pi$
$173$	2.82843	+	2.82843i	0.215041	+	0.215041i	−0.591364	+	0.806405i	$0.701410\pi$
$174$	4.00000			0.303239
$175$	−15.5563	−	15.5563i	−1.17595	−	1.17595i
$176$		0			0
$177$	−8.48528	+	8.48528i	−0.637793	+	0.637793i
$178$			2.00000i			0.149906i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	−2.82843	+	2.82843i	−0.210819	+	0.210819i
$181$	14.1421	−	14.1421i	1.05118	−	1.05118i	0.0525588	−	0.998618i	$-0.483262\pi$
$181$	14.1421	−	14.1421i	1.05118	−	1.05118i	0.998618	−	0.0525588i	$-0.0167377\pi$
$182$	−8.48528	−	8.48528i	−0.628971	−	0.628971i
$183$	−4.00000			−0.295689
$184$	4.24264	+	4.24264i	0.312772	+	0.312772i
$185$		−	16.0000i		−	1.17634i
$186$	−6.00000			−0.439941
$187$		0			0
$188$	4.00000			0.291730
$189$		−	2.00000i		−	0.145479i
$190$	−11.3137	−	11.3137i	−0.820783	−	0.820783i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−4.24264	+	4.24264i	−0.305392	+	0.305392i	−0.843119	−	0.537727i	$-0.819283\pi$
$193$	−4.24264	+	4.24264i	−0.305392	+	0.305392i	0.537727	+	0.843119i	$0.319283\pi$
$194$	−4.24264	+	4.24264i	−0.304604	+	0.304604i
$195$		−	24.0000i		−	1.71868i
$196$		−	3.00000i		−	0.214286i
$197$	5.65685	−	5.65685i	0.403034	−	0.403034i	−0.476267	−	0.879301i	$-0.658010\pi$
$197$	5.65685	−	5.65685i	0.403034	−	0.403034i	0.879301	+	0.476267i	$0.158010\pi$
$198$		0			0
$199$	9.89949	+	9.89949i	0.701757	+	0.701757i	0.964787	−	0.263031i	$-0.0847221\pi$
$199$	9.89949	+	9.89949i	0.701757	+	0.701757i	−0.263031	+	0.964787i	$0.584722\pi$
$200$	11.0000			0.777817
$201$	−8.48528	−	8.48528i	−0.598506	−	0.598506i
$202$			14.0000i			0.985037i
$203$	8.00000			0.561490
$204$		0			0
$205$	40.0000			2.79372
$206$			4.00000i			0.278693i
$207$	−4.24264	−	4.24264i	−0.294884	−	0.294884i
$208$	6.00000			0.416025
$209$		0			0
$210$	−5.65685	+	5.65685i	−0.390360	+	0.390360i
$211$	5.65685	−	5.65685i	0.389434	−	0.389434i	−0.485052	−	0.874486i	$-0.661199\pi$
$211$	5.65685	−	5.65685i	0.389434	−	0.389434i	0.874486	+	0.485052i	$0.161199\pi$
$212$		−	2.00000i		−	0.137361i
$213$			6.00000i			0.411113i
$214$		0			0
$215$	−11.3137	+	11.3137i	−0.771589	+	0.771589i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−12.0000			−0.814613
$218$	11.3137	+	11.3137i	0.766261	+	0.766261i
$219$			2.00000i			0.135147i
$220$		0			0
$221$		0			0
$222$	−4.00000			−0.268462
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	−1.41421	−	1.41421i	−0.0944911	−	0.0944911i
$225$	−11.0000			−0.733333
$226$	−1.41421	−	1.41421i	−0.0940721	−	0.0940721i
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	−0.794714	−	0.606984i	$-0.792379\pi$
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	0.606984	+	0.794714i	$0.292379\pi$
$228$	−2.82843	+	2.82843i	−0.187317	+	0.187317i
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$			24.0000i			1.58251i
$231$		0			0
$232$	−2.82843	+	2.82843i	−0.185695	+	0.185695i
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	0.554343	−	0.832288i	$-0.312969\pi$
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	−0.832288	+	0.554343i	$0.812969\pi$
$234$	−6.00000			−0.392232
$235$	11.3137	+	11.3137i	0.738025	+	0.738025i
$236$		−	12.0000i		−	0.781133i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		−	4.00000i		−	0.258199i
$241$	12.7279	+	12.7279i	0.819878	+	0.819878i	0.986090	−	0.166212i	$-0.0531537\pi$
$241$	12.7279	+	12.7279i	0.819878	+	0.819878i	−0.166212	+	0.986090i	$0.553154\pi$
$242$	−11.0000			−0.707107
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	2.82843	−	2.82843i	0.181071	−	0.181071i
$245$	8.48528	−	8.48528i	0.542105	−	0.542105i
$246$		−	10.0000i		−	0.637577i
$247$		−	24.0000i		−	1.52708i
$248$	4.24264	−	4.24264i	0.269408	−	0.269408i
$249$	−8.48528	+	8.48528i	−0.537733	+	0.537733i
$250$	16.9706	+	16.9706i	1.07331	+	1.07331i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	1.41421	+	1.41421i	0.0890871	+	0.0890871i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	2.82843	+	2.82843i	0.176090	+	0.176090i
$259$	−8.00000			−0.497096
$260$	16.9706	+	16.9706i	1.05247	+	1.05247i
$261$	2.82843	−	2.82843i	0.175075	−	0.175075i
$262$	11.3137	−	11.3137i	0.698963	−	0.698963i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$	5.65685	−	5.65685i	0.347498	−	0.347498i
$266$	−5.65685	+	5.65685i	−0.346844	+	0.346844i
$267$	1.41421	+	1.41421i	0.0865485	+	0.0865485i
$268$	12.0000			0.733017
$269$	8.48528	+	8.48528i	0.517357	+	0.517357i	0.916771	−	0.399414i	$-0.130786\pi$
$269$	8.48528	+	8.48528i	0.517357	+	0.517357i	−0.399414	+	0.916771i	$0.630786\pi$
$270$			4.00000i			0.243432i
$271$	−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
$273$	−12.0000			−0.726273
$274$		−	6.00000i		−	0.362473i
$275$		0			0
$276$	6.00000			0.361158
$277$	−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	$0.827258\pi$
$278$	5.65685	−	5.65685i	0.339276	−	0.339276i
$279$	−4.24264	+	4.24264i	−0.254000	+	0.254000i
$280$		−	8.00000i		−	0.478091i
$281$		−	18.0000i		−	1.07379i	−0.843649	−	0.536895i	$-0.819597\pi$
$281$		−	18.0000i		−	1.07379i	0.843649	−	0.536895i	$-0.180403\pi$
$282$	2.82843	−	2.82843i	0.168430	−	0.168430i
$283$	−22.6274	+	22.6274i	−1.34506	+	1.34506i	−0.454120	+	0.890941i	$0.650046\pi$
$283$	−22.6274	+	22.6274i	−1.34506	+	1.34506i	−0.890941	+	0.454120i	$0.849954\pi$
$284$	−4.24264	−	4.24264i	−0.251754	−	0.251754i
$285$	−16.0000			−0.947758
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$	−16.0000			−0.939552
$291$			6.00000i			0.351726i
$292$	−1.41421	−	1.41421i	−0.0827606	−	0.0827606i
$293$	−2.00000			−0.116841			−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000			−0.116841			−0.0584206	+	0.998292i	$0.518606\pi$
$294$	−2.12132	−	2.12132i	−0.123718	−	0.123718i
$295$	33.9411	−	33.9411i	1.97613	−	1.97613i
$296$	2.82843	−	2.82843i	0.164399	−	0.164399i
$297$		0			0
$298$			6.00000i			0.347571i
$299$	−25.4558	+	25.4558i	−1.47215	+	1.47215i
$300$	7.77817	−	7.77817i	0.449073	−	0.449073i
$301$	5.65685	+	5.65685i	0.326056	+	0.326056i
$302$	−24.0000			−1.38104
$303$	9.89949	+	9.89949i	0.568711	+	0.568711i
$304$		−	4.00000i		−	0.229416i
$305$	16.0000			0.916157
$306$		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
$309$	2.82843	+	2.82843i	0.160904	+	0.160904i
$310$	24.0000			1.36311
$311$	21.2132	+	21.2132i	1.20289	+	1.20289i	0.973283	+	0.229607i	$0.0737441\pi$
$311$	21.2132	+	21.2132i	1.20289	+	1.20289i	0.229607	+	0.973283i	$0.426256\pi$
$312$	4.24264	−	4.24264i	0.240192	−	0.240192i
$313$	−18.3848	+	18.3848i	−1.03917	+	1.03917i	−0.0399680	+	0.999201i	$0.512726\pi$
$313$	−18.3848	+	18.3848i	−1.03917	+	1.03917i	−0.999201	+	0.0399680i	$0.987274\pi$
$314$		−	6.00000i		−	0.338600i
$315$			8.00000i			0.450749i
$316$	7.07107	−	7.07107i	0.397779	−	0.397779i
$317$	11.3137	−	11.3137i	0.635441	−	0.635441i	−0.313986	−	0.949428i	$-0.601665\pi$
$317$	11.3137	−	11.3137i	0.635441	−	0.635441i	0.949428	+	0.313986i	$0.101665\pi$
$318$	−1.41421	−	1.41421i	−0.0793052	−	0.0793052i
$319$		0			0
$320$	2.82843	+	2.82843i	0.158114	+	0.158114i
$321$		0			0
$322$	12.0000			0.668734
$323$		0			0
$324$	1.00000			0.0555556
$325$			66.0000i			3.66102i
$326$	8.48528	+	8.48528i	0.469956	+	0.469956i
$327$	16.0000			0.884802
$328$	7.07107	+	7.07107i	0.390434	+	0.390434i
$329$	5.65685	−	5.65685i	0.311872	−	0.311872i
$330$		0			0
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$		−	12.0000i		−	0.658586i
$333$	−2.82843	+	2.82843i	−0.154997	+	0.154997i
$334$	−1.41421	+	1.41421i	−0.0773823	+	0.0773823i
$335$	33.9411	+	33.9411i	1.85440	+	1.85440i
$336$	−2.00000			−0.109109
$337$	4.24264	+	4.24264i	0.231111	+	0.231111i	0.813156	−	0.582045i	$-0.197747\pi$
$337$	4.24264	+	4.24264i	0.231111	+	0.231111i	−0.582045	+	0.813156i	$0.697747\pi$
$338$			23.0000i			1.25104i
$339$	−2.00000			−0.108625
$340$		0			0
$341$		0			0
$342$			4.00000i			0.216295i
$343$	−14.1421	−	14.1421i	−0.763604	−	0.763604i
$344$	−4.00000			−0.215666
$345$	16.9706	+	16.9706i	0.913664	+	0.913664i
$346$	−2.82843	+	2.82843i	−0.152057	+	0.152057i
$347$	−2.82843	+	2.82843i	−0.151838	+	0.151838i	−0.778938	−	0.627100i	$-0.784242\pi$
$347$	−2.82843	+	2.82843i	−0.151838	+	0.151838i	0.627100	+	0.778938i	$0.284242\pi$
$348$			4.00000i			0.214423i
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$	15.5563	−	15.5563i	0.831522	−	0.831522i
$351$	−4.24264	+	4.24264i	−0.226455	+	0.226455i
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$	−8.48528	−	8.48528i	−0.450988	−	0.450988i
$355$		−	24.0000i		−	1.27379i
$356$	−2.00000			−0.106000
$357$		0			0
$358$	12.0000			0.634220
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−2.82843	−	2.82843i	−0.149071	−	0.149071i
$361$	3.00000			0.157895
$362$	14.1421	+	14.1421i	0.743294	+	0.743294i
$363$	−7.77817	+	7.77817i	−0.408248	+	0.408248i
$364$	8.48528	−	8.48528i	0.444750	−	0.444750i
$365$		−	8.00000i		−	0.418739i
$366$		−	4.00000i		−	0.209083i
$367$	7.07107	−	7.07107i	0.369107	−	0.369107i	−0.498045	−	0.867151i	$-0.665948\pi$
$367$	7.07107	−	7.07107i	0.369107	−	0.369107i	0.867151	+	0.498045i	$0.165948\pi$
$368$	−4.24264	+	4.24264i	−0.221163	+	0.221163i
$369$	−7.07107	−	7.07107i	−0.368105	−	0.368105i
$370$	16.0000			0.831800
$371$	−2.82843	−	2.82843i	−0.146845	−	0.146845i
$372$		−	6.00000i		−	0.311086i
$373$	−14.0000			−0.724893			−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000			−0.724893			−0.362446	+	0.932005i	$0.618058\pi$
$374$		0			0
$375$	24.0000			1.23935
$376$			4.00000i			0.206284i
$377$	−16.9706	−	16.9706i	−0.874028	−	0.874028i
$378$	2.00000			0.102869
$379$	−2.82843	−	2.82843i	−0.145287	−	0.145287i	0.630722	−	0.776009i	$-0.282759\pi$
$379$	−2.82843	−	2.82843i	−0.145287	−	0.145287i	−0.776009	+	0.630722i	$0.782759\pi$
$380$	11.3137	−	11.3137i	0.580381	−	0.580381i
$381$	−5.65685	+	5.65685i	−0.289809	+	0.289809i
$382$			4.00000i			0.204658i
$383$			28.0000i			1.43073i	0.698749	+	0.715367i	$0.253740\pi$
$383$			28.0000i			1.43073i	−0.698749	+	0.715367i	$0.746260\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$		0			0
$386$	−4.24264	−	4.24264i	−0.215945	−	0.215945i
$387$	4.00000			0.203331
$388$	−4.24264	−	4.24264i	−0.215387	−	0.215387i
$389$			14.0000i			0.709828i	0.934899	+	0.354914i	$0.115490\pi$
$389$			14.0000i			0.709828i	−0.934899	+	0.354914i	$0.884510\pi$
$390$	24.0000			1.21529
$391$		0			0
$392$	3.00000			0.151523
$393$		−	16.0000i		−	0.807093i
$394$	5.65685	+	5.65685i	0.284988	+	0.284988i
$395$	40.0000			2.01262
$396$		0			0
$397$	−14.1421	+	14.1421i	−0.709773	+	0.709773i	−0.966487	−	0.256714i	$-0.917360\pi$
$397$	−14.1421	+	14.1421i	−0.709773	+	0.709773i	0.256714	+	0.966487i	$0.417360\pi$
$398$	−9.89949	+	9.89949i	−0.496217	+	0.496217i
$399$			8.00000i			0.400501i
$400$			11.0000i			0.550000i
$401$	21.2132	−	21.2132i	1.05934	−	1.05934i	0.0612120	−	0.998125i	$-0.480503\pi$
$401$	21.2132	−	21.2132i	1.05934	−	1.05934i	0.998125	−	0.0612120i	$-0.0194966\pi$
$402$	8.48528	−	8.48528i	0.423207	−	0.423207i
$403$	25.4558	+	25.4558i	1.26805	+	1.26805i
$404$	−14.0000			−0.696526
$405$	2.82843	+	2.82843i	0.140546	+	0.140546i
$406$			8.00000i			0.397033i
$407$		0			0
$408$		0			0
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$			40.0000i			1.97546i
$411$	−4.24264	−	4.24264i	−0.209274	−	0.209274i
$412$	−4.00000			−0.197066
$413$	−16.9706	−	16.9706i	−0.835067	−	0.835067i
$414$	4.24264	−	4.24264i	0.208514	−	0.208514i
$415$	33.9411	−	33.9411i	1.66610	−	1.66610i
$416$			6.00000i			0.294174i
$417$		−	8.00000i		−	0.391762i
$418$		0			0
$419$	8.48528	−	8.48528i	0.414533	−	0.414533i	−0.468781	−	0.883314i	$-0.655307\pi$
$419$	8.48528	−	8.48528i	0.414533	−	0.414533i	0.883314	+	0.468781i	$0.155307\pi$
$420$	−5.65685	−	5.65685i	−0.276026	−	0.276026i
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	5.65685	+	5.65685i	0.275371	+	0.275371i
$423$		−	4.00000i		−	0.194487i
$424$	2.00000			0.0971286
$425$		0			0
$426$	−6.00000			−0.290701
$427$		−	8.00000i		−	0.387147i
$428$		0			0
$429$		0			0
$430$	−11.3137	−	11.3137i	−0.545595	−	0.545595i
$431$	−9.89949	+	9.89949i	−0.476842	+	0.476842i	−0.904120	−	0.427278i	$-0.859472\pi$
$431$	−9.89949	+	9.89949i	−0.476842	+	0.476842i	0.427278	+	0.904120i	$0.359472\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	18.0000i		−	0.865025i	−0.901628	−	0.432512i	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$		−	12.0000i		−	0.576018i
$435$	−11.3137	+	11.3137i	−0.542451	+	0.542451i
$436$	−11.3137	+	11.3137i	−0.541828	+	0.541828i
$437$	16.9706	+	16.9706i	0.811812	+	0.811812i
$438$	−2.00000			−0.0955637
$439$	7.07107	+	7.07107i	0.337484	+	0.337484i	0.855419	−	0.517936i	$-0.173299\pi$
$439$	7.07107	+	7.07107i	0.337484	+	0.337484i	−0.517936	+	0.855419i	$0.673299\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		−	4.00000i		−	0.189832i
$445$	−5.65685	−	5.65685i	−0.268161	−	0.268161i
$446$	−4.00000			−0.189405
$447$	4.24264	+	4.24264i	0.200670	+	0.200670i
$448$	1.41421	−	1.41421i	0.0668153	−	0.0668153i
$449$	−18.3848	+	18.3848i	−0.867631	+	0.867631i	−0.992210	−	0.124579i	$-0.960242\pi$
$449$	−18.3848	+	18.3848i	−0.867631	+	0.867631i	0.124579	+	0.992210i	$0.460242\pi$
$450$		−	11.0000i		−	0.518545i
$451$		0			0
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$	−16.9706	+	16.9706i	−0.797347	+	0.797347i
$454$	−2.82843	−	2.82843i	−0.132745	−	0.132745i
$455$	48.0000			2.25027
$456$	−2.82843	−	2.82843i	−0.132453	−	0.132453i
$457$		−	22.0000i		−	1.02912i	−0.857455	−	0.514558i	$-0.827956\pi$
$457$		−	22.0000i		−	1.02912i	0.857455	−	0.514558i	$-0.172044\pi$
$458$	2.00000			0.0934539
$459$		0			0
$460$	−24.0000			−1.11901
$461$			10.0000i			0.465746i	0.972507	+	0.232873i	$0.0748127\pi$
$461$			10.0000i			0.465746i	−0.972507	+	0.232873i	$0.925187\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−2.82843	−	2.82843i	−0.131306	−	0.131306i
$465$	16.9706	−	16.9706i	0.786991	−	0.786991i
$466$	4.24264	−	4.24264i	0.196537	−	0.196537i
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		−	6.00000i		−	0.277350i
$469$	16.9706	−	16.9706i	0.783628	−	0.783628i
$470$	−11.3137	+	11.3137i	−0.521862	+	0.521862i
$471$	−4.24264	−	4.24264i	−0.195491	−	0.195491i
$472$	12.0000			0.552345
$473$		0			0
$474$		−	10.0000i		−	0.459315i
$475$	44.0000			2.01886
$476$		0			0
$477$	−2.00000			−0.0915737
$478$		−	20.0000i		−	0.914779i
$479$	−7.07107	−	7.07107i	−0.323085	−	0.323085i	0.526864	−	0.849949i	$-0.323368\pi$
$479$	−7.07107	−	7.07107i	−0.323085	−	0.323085i	−0.849949	+	0.526864i	$0.823368\pi$
$480$	4.00000			0.182574
$481$	16.9706	+	16.9706i	0.773791	+	0.773791i
$482$	−12.7279	+	12.7279i	−0.579741	+	0.579741i
$483$	8.48528	−	8.48528i	0.386094	−	0.386094i
$484$		−	11.0000i		−	0.500000i
$485$		−	24.0000i		−	1.08978i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	26.8701	−	26.8701i	1.21760	−	1.21760i	0.249128	−	0.968471i	$-0.419856\pi$
$487$	26.8701	−	26.8701i	1.21760	−	1.21760i	0.968471	−	0.249128i	$-0.0801440\pi$
$488$	2.82843	+	2.82843i	0.128037	+	0.128037i
$489$	12.0000			0.542659
$490$	8.48528	+	8.48528i	0.383326	+	0.383326i
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$	10.0000			0.450835
$493$		0			0
$494$	24.0000			1.07981
$495$		0			0
$496$	4.24264	+	4.24264i	0.190500	+	0.190500i
$497$	−12.0000			−0.538274
$498$	−8.48528	−	8.48528i	−0.380235	−	0.380235i
$499$	−22.6274	+	22.6274i	−1.01294	+	1.01294i	−0.0130272	+	0.999915i	$0.504147\pi$
$499$	−22.6274	+	22.6274i	−1.01294	+	1.01294i	−0.999915	+	0.0130272i	$0.995853\pi$
$500$	−16.9706	+	16.9706i	−0.758947	+	0.758947i
$501$			2.00000i			0.0893534i
$502$		−	12.0000i		−	0.535586i
$503$	−18.3848	+	18.3848i	−0.819737	+	0.819737i	−0.986070	−	0.166333i	$-0.946807\pi$
$503$	−18.3848	+	18.3848i	−0.819737	+	0.819737i	0.166333	+	0.986070i	$0.446807\pi$
$504$	−1.41421	+	1.41421i	−0.0629941	+	0.0629941i
$505$	−39.5980	−	39.5980i	−1.76209	−	1.76209i
$506$		0			0
$507$	16.2635	+	16.2635i	0.722285	+	0.722285i
$508$		−	8.00000i		−	0.354943i
$509$	26.0000			1.15243			0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000			1.15243			0.576215	+	0.817298i	$0.304529\pi$
$510$		0			0
$511$	−4.00000			−0.176950
$512$			1.00000i			0.0441942i
$513$	2.82843	+	2.82843i	0.124878	+	0.124878i
$514$	18.0000			0.793946
$515$	−11.3137	−	11.3137i	−0.498542	−	0.498542i
$516$	−2.82843	+	2.82843i	−0.124515	+	0.124515i
$517$		0			0
$518$		−	8.00000i		−	0.351500i
$519$			4.00000i			0.175581i
$520$	−16.9706	+	16.9706i	−0.744208	+	0.744208i
$521$	7.07107	−	7.07107i	0.309789	−	0.309789i	−0.535039	−	0.844828i	$-0.679703\pi$
$521$	7.07107	−	7.07107i	0.309789	−	0.309789i	0.844828	+	0.535039i	$0.179703\pi$
$522$	2.82843	+	2.82843i	0.123797	+	0.123797i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	11.3137	+	11.3137i	0.494242	+	0.494242i
$525$		−	22.0000i		−	0.960159i
$526$	12.0000			0.523225
$527$		0			0
$528$		0			0
$529$		−	13.0000i		−	0.565217i
$530$	5.65685	+	5.65685i	0.245718	+	0.245718i
$531$	−12.0000			−0.520756
$532$	−5.65685	−	5.65685i	−0.245256	−	0.245256i
$533$	−42.4264	+	42.4264i	−1.83769	+	1.83769i
$534$	−1.41421	+	1.41421i	−0.0611990	+	0.0611990i
$535$		0			0
$536$			12.0000i			0.518321i
$537$	8.48528	−	8.48528i	0.366167	−	0.366167i
$538$	−8.48528	+	8.48528i	−0.365826	+	0.365826i
$539$		0			0
$540$	−4.00000			−0.172133
$541$	8.48528	+	8.48528i	0.364811	+	0.364811i	0.865581	−	0.500770i	$-0.166950\pi$
$541$	8.48528	+	8.48528i	0.364811	+	0.364811i	−0.500770	+	0.865581i	$0.666950\pi$
$542$		−	16.0000i		−	0.687259i
$543$	20.0000			0.858282
$544$		0			0
$545$	−64.0000			−2.74146
$546$		−	12.0000i		−	0.513553i
$547$	5.65685	+	5.65685i	0.241870	+	0.241870i	0.817623	−	0.575754i	$-0.195291\pi$
$547$	5.65685	+	5.65685i	0.241870	+	0.241870i	−0.575754	+	0.817623i	$0.695291\pi$
$548$	6.00000			0.256307
$549$	−2.82843	−	2.82843i	−0.120714	−	0.120714i
$550$		0			0
$551$	−11.3137	+	11.3137i	−0.481980	+	0.481980i
$552$			6.00000i			0.255377i
$553$		−	20.0000i		−	0.850487i
$554$	5.65685	−	5.65685i	0.240337	−	0.240337i
$555$	11.3137	−	11.3137i	0.480240	−	0.480240i
$556$	5.65685	+	5.65685i	0.239904	+	0.239904i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$	−4.24264	−	4.24264i	−0.179605	−	0.179605i
$559$		−	24.0000i		−	1.01509i
$560$	8.00000			0.338062
$561$		0			0
$562$	18.0000			0.759284
$563$			4.00000i			0.168580i	0.996441	+	0.0842900i	$0.0268622\pi$
$563$			4.00000i			0.168580i	−0.996441	+	0.0842900i	$0.973138\pi$
$564$	2.82843	+	2.82843i	0.119098	+	0.119098i
$565$	8.00000			0.336563
$566$	−22.6274	−	22.6274i	−0.951101	−	0.951101i
$567$	1.41421	−	1.41421i	0.0593914	−	0.0593914i
$568$	4.24264	−	4.24264i	0.178017	−	0.178017i
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		−	16.0000i		−	0.670166i
$571$	31.1127	−	31.1127i	1.30203	−	1.30203i	0.375002	−	0.927024i	$-0.377642\pi$
$571$	31.1127	−	31.1127i	1.30203	−	1.30203i	0.927024	−	0.375002i	$-0.122358\pi$
$572$		0			0
$573$	2.82843	+	2.82843i	0.118159	+	0.118159i
$574$	20.0000			0.834784
$575$	−46.6690	−	46.6690i	−1.94623	−	1.94623i
$576$		−	1.00000i		−	0.0416667i
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$		0			0
$579$	−6.00000			−0.249351
$580$		−	16.0000i		−	0.664364i
$581$	−16.9706	−	16.9706i	−0.704058	−	0.704058i
$582$	−6.00000			−0.248708
$583$		0			0
$584$	1.41421	−	1.41421i	0.0585206	−	0.0585206i
$585$	16.9706	−	16.9706i	0.701646	−	0.701646i
$586$		−	2.00000i		−	0.0826192i
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$	2.12132	−	2.12132i	0.0874818	−	0.0874818i
$589$	16.9706	−	16.9706i	0.699260	−	0.699260i
$590$	33.9411	+	33.9411i	1.39733	+	1.39733i
$591$	8.00000			0.329076
$592$	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	$0.788762\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$			14.0000i			0.572982i
$598$	−25.4558	−	25.4558i	−1.04097	−	1.04097i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$	7.77817	+	7.77817i	0.317543	+	0.317543i
$601$	26.8701	−	26.8701i	1.09605	−	1.09605i	0.101185	−	0.994868i	$-0.467737\pi$
$601$	26.8701	−	26.8701i	1.09605	−	1.09605i	0.994868	−	0.101185i	$-0.0322634\pi$
$602$	−5.65685	+	5.65685i	−0.230556	+	0.230556i
$603$		−	12.0000i		−	0.488678i
$604$		−	24.0000i		−	0.976546i
$605$	31.1127	−	31.1127i	1.26491	−	1.26491i
$606$	−9.89949	+	9.89949i	−0.402139	+	0.402139i
$607$	−26.8701	−	26.8701i	−1.09062	−	1.09062i	−0.995462	−	0.0951600i	$-0.969664\pi$
$607$	−26.8701	−	26.8701i	−1.09062	−	1.09062i	−0.0951600	−	0.995462i	$-0.530336\pi$
$608$	4.00000			0.162221
$609$	5.65685	+	5.65685i	0.229227	+	0.229227i
$610$			16.0000i			0.647821i
$611$	−24.0000			−0.970936
$612$		0			0
$613$	30.0000			1.21169			0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000			1.21169			0.605844	+	0.795583i	$0.292835\pi$
$614$		−	12.0000i		−	0.484281i
$615$	28.2843	+	28.2843i	1.14053	+	1.14053i
$616$		0			0
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	0.616530	−	0.787332i	$-0.288538\pi$
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	−0.787332	+	0.616530i	$0.788538\pi$
$618$	−2.82843	+	2.82843i	−0.113776	+	0.113776i
$619$	−14.1421	+	14.1421i	−0.568420	+	0.568420i	−0.931686	−	0.363265i	$-0.881662\pi$
$619$	−14.1421	+	14.1421i	−0.568420	+	0.568420i	0.363265	+	0.931686i	$0.381662\pi$
$620$			24.0000i			0.963863i
$621$		−	6.00000i		−	0.240772i
$622$	−21.2132	+	21.2132i	−0.850572	+	0.850572i
$623$	−2.82843	+	2.82843i	−0.113319	+	0.113319i
$624$	4.24264	+	4.24264i	0.169842	+	0.169842i
$625$	−41.0000			−1.64000
$626$	−18.3848	−	18.3848i	−0.734803	−	0.734803i
$627$		0			0
$628$	6.00000			0.239426
$629$		0			0
$630$	−8.00000			−0.318728
$631$		−	20.0000i		−	0.796187i	−0.917345	−	0.398094i	$-0.869672\pi$
$631$		−	20.0000i		−	0.796187i	0.917345	−	0.398094i	$-0.130328\pi$
$632$	7.07107	+	7.07107i	0.281272	+	0.281272i
$633$	8.00000			0.317971
$634$	11.3137	+	11.3137i	0.449325	+	0.449325i
$635$	22.6274	−	22.6274i	0.897942	−	0.897942i
$636$	1.41421	−	1.41421i	0.0560772	−	0.0560772i
$637$			18.0000i			0.713186i
$638$		0			0
$639$	−4.24264	+	4.24264i	−0.167836	+	0.167836i
$640$	−2.82843	+	2.82843i	−0.111803	+	0.111803i
$641$	−1.41421	−	1.41421i	−0.0558581	−	0.0558581i	0.678626	−	0.734484i	$-0.262576\pi$
$641$	−1.41421	−	1.41421i	−0.0558581	−	0.0558581i	−0.734484	+	0.678626i	$0.762576\pi$
$642$		0			0
$643$	−2.82843	−	2.82843i	−0.111542	−	0.111542i	0.649133	−	0.760675i	$-0.275132\pi$
$643$	−2.82843	−	2.82843i	−0.111542	−	0.111542i	−0.760675	+	0.649133i	$0.775132\pi$
$644$			12.0000i			0.472866i
$645$	−16.0000			−0.629999
$646$		0			0
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$			1.00000i			0.0392837i
$649$		0			0
$650$	−66.0000			−2.58873
$651$	−8.48528	−	8.48528i	−0.332564	−	0.332564i
$652$	−8.48528	+	8.48528i	−0.332309	+	0.332309i
$653$	14.1421	−	14.1421i	0.553425	−	0.553425i	−0.374003	−	0.927428i	$-0.622015\pi$
$653$	14.1421	−	14.1421i	0.553425	−	0.553425i	0.927428	+	0.374003i	$0.122015\pi$
$654$			16.0000i			0.625650i
$655$			64.0000i			2.50069i
$656$	−7.07107	+	7.07107i	−0.276079	+	0.276079i
$657$	−1.41421	+	1.41421i	−0.0551737	+	0.0551737i
$658$	5.65685	+	5.65685i	0.220527	+	0.220527i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$			14.0000i			0.544537i	0.962221	+	0.272268i	$0.0877739\pi$
$661$			14.0000i			0.544537i	−0.962221	+	0.272268i	$0.912226\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	12.0000			0.465690
$665$		−	32.0000i		−	1.24091i
$666$	−2.82843	−	2.82843i	−0.109599	−	0.109599i
$667$	24.0000			0.929284
$668$	−1.41421	−	1.41421i	−0.0547176	−	0.0547176i
$669$	−2.82843	+	2.82843i	−0.109353	+	0.109353i
$670$	−33.9411	+	33.9411i	−1.31126	+	1.31126i
$671$		0			0
$672$		−	2.00000i		−	0.0771517i
$673$	−18.3848	+	18.3848i	−0.708681	+	0.708681i	−0.966258	−	0.257577i	$-0.917076\pi$
$673$	−18.3848	+	18.3848i	−0.708681	+	0.708681i	0.257577	+	0.966258i	$0.417076\pi$
$674$	−4.24264	+	4.24264i	−0.163420	+	0.163420i
$675$	−7.77817	−	7.77817i	−0.299382	−	0.299382i
$676$	−23.0000			−0.884615
$677$	−5.65685	−	5.65685i	−0.217411	−	0.217411i	0.589996	−	0.807406i	$-0.299129\pi$
$677$	−5.65685	−	5.65685i	−0.217411	−	0.217411i	−0.807406	+	0.589996i	$0.799129\pi$
$678$		−	2.00000i		−	0.0768095i
$679$	−12.0000			−0.460518
$680$		0			0
$681$	−4.00000			−0.153280
$682$		0			0
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$	−4.00000			−0.152944
$685$	16.9706	+	16.9706i	0.648412	+	0.648412i
$686$	14.1421	−	14.1421i	0.539949	−	0.539949i
$687$	1.41421	−	1.41421i	0.0539556	−	0.0539556i
$688$		−	4.00000i		−	0.152499i
$689$			12.0000i			0.457164i
$690$	−16.9706	+	16.9706i	−0.646058	+	0.646058i
$691$	−11.3137	+	11.3137i	−0.430394	+	0.430394i	−0.888762	−	0.458368i	$-0.848434\pi$
$691$	−11.3137	+	11.3137i	−0.430394	+	0.430394i	0.458368	+	0.888762i	$0.348434\pi$
$692$	−2.82843	−	2.82843i	−0.107521	−	0.107521i
$693$		0			0
$694$	−2.82843	−	2.82843i	−0.107366	−	0.107366i
$695$			32.0000i			1.21383i
$696$	−4.00000			−0.151620
$697$		0			0
$698$	30.0000			1.13552
$699$		−	6.00000i		−	0.226941i
$700$	15.5563	+	15.5563i	0.587975	+	0.587975i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−4.24264	−	4.24264i	−0.160128	−	0.160128i
$703$	11.3137	−	11.3137i	0.426705	−	0.426705i
$704$		0			0
$705$			16.0000i			0.602595i
$706$		−	14.0000i		−	0.526897i
$707$	−19.7990	+	19.7990i	−0.744618	+	0.744618i
$708$	8.48528	−	8.48528i	0.318896	−	0.318896i
$709$	−11.3137	−	11.3137i	−0.424895	−	0.424895i	0.461990	−	0.886885i	$-0.347136\pi$
$709$	−11.3137	−	11.3137i	−0.424895	−	0.424895i	−0.886885	+	0.461990i	$0.847136\pi$
$710$	24.0000			0.900704
$711$	−7.07107	−	7.07107i	−0.265186	−	0.265186i
$712$		−	2.00000i		−	0.0749532i
$713$	−36.0000			−1.34821
$714$		0			0
$715$		0			0
$716$			12.0000i			0.448461i
$717$	−14.1421	−	14.1421i	−0.528148	−	0.528148i
$718$		0			0
$719$	29.6985	+	29.6985i	1.10757	+	1.10757i	0.993470	+	0.114097i	$0.0363975\pi$
$719$	29.6985	+	29.6985i	1.10757	+	1.10757i	0.114097	+	0.993470i	$0.463603\pi$
$720$	2.82843	−	2.82843i	0.105409	−	0.105409i
$721$	−5.65685	+	5.65685i	−0.210672	+	0.210672i
$722$			3.00000i			0.111648i
$723$			18.0000i			0.669427i
$724$	−14.1421	+	14.1421i	−0.525588	+	0.525588i
$725$	31.1127	−	31.1127i	1.15550	−	1.15550i
$726$	−7.77817	−	7.77817i	−0.288675	−	0.288675i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$	8.48528	+	8.48528i	0.314485	+	0.314485i
$729$		−	1.00000i		−	0.0370370i
$730$	8.00000			0.296093
$731$		0			0
$732$	4.00000			0.147844
$733$		−	18.0000i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$		−	18.0000i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$	7.07107	+	7.07107i	0.260998	+	0.260998i
$735$	12.0000			0.442627
$736$	−4.24264	−	4.24264i	−0.156386	−	0.156386i
$737$		0			0
$738$	7.07107	−	7.07107i	0.260290	−	0.260290i
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$			16.0000i			0.588172i
$741$	16.9706	−	16.9706i	0.623429	−	0.623429i
$742$	2.82843	−	2.82843i	0.103835	−	0.103835i
$743$	26.8701	+	26.8701i	0.985767	+	0.985767i	0.999900	−	0.0141333i	$-0.00449892\pi$
$743$	26.8701	+	26.8701i	0.985767	+	0.985767i	−0.0141333	+	0.999900i	$0.504499\pi$
$744$	6.00000			0.219971
$745$	−16.9706	−	16.9706i	−0.621753	−	0.621753i
$746$		−	14.0000i		−	0.512576i
$747$	−12.0000			−0.439057
$748$		0			0
$749$		0			0
$750$			24.0000i			0.876356i
$751$	24.0416	+	24.0416i	0.877292	+	0.877292i	0.993254	−	0.115962i	$-0.0369951\pi$
$751$	24.0416	+	24.0416i	0.877292	+	0.877292i	−0.115962	+	0.993254i	$0.536995\pi$
$752$	−4.00000			−0.145865
$753$	−8.48528	−	8.48528i	−0.309221	−	0.309221i
$754$	16.9706	−	16.9706i	0.618031	−	0.618031i
$755$	67.8823	−	67.8823i	2.47049	−	2.47049i
$756$			2.00000i			0.0727393i
$757$			14.0000i			0.508839i	0.967094	+	0.254419i	$0.0818843\pi$
$757$			14.0000i			0.508839i	−0.967094	+	0.254419i	$0.918116\pi$
$758$	2.82843	−	2.82843i	0.102733	−	0.102733i
$759$		0			0
$760$	11.3137	+	11.3137i	0.410391	+	0.410391i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$	−5.65685	−	5.65685i	−0.204926	−	0.204926i
$763$			32.0000i			1.15848i
$764$	−4.00000			−0.144715
$765$		0			0
$766$	−28.0000			−1.01168
$767$			72.0000i			2.59977i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	12.7279	−	12.7279i	0.458385	−	0.458385i
$772$	4.24264	−	4.24264i	0.152696	−	0.152696i
$773$			42.0000i			1.51064i	0.655359	+	0.755318i	$0.272517\pi$
$773$			42.0000i			1.51064i	−0.655359	+	0.755318i	$0.727483\pi$
$774$			4.00000i			0.143777i
$775$	−46.6690	+	46.6690i	−1.67640	+	1.67640i
$776$	4.24264	−	4.24264i	0.152302	−	0.152302i
$777$	−5.65685	−	5.65685i	−0.202939	−	0.202939i
$778$	−14.0000			−0.501924
$779$	28.2843	+	28.2843i	1.01339	+	1.01339i
$780$			24.0000i			0.859338i
$781$		0			0
$782$		0			0
$783$	4.00000			0.142948
$784$			3.00000i			0.107143i
$785$	16.9706	+	16.9706i	0.605705	+	0.605705i
$786$	16.0000			0.570701
$787$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$787$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$788$	−5.65685	+	5.65685i	−0.201517	+	0.201517i
$789$	8.48528	−	8.48528i	0.302084	−	0.302084i
$790$			40.0000i			1.42314i
$791$		−	4.00000i		−	0.142224i
$792$		0			0
$793$	−16.9706	+	16.9706i	−0.602642	+	0.602642i
$794$	−14.1421	−	14.1421i	−0.501886	−	0.501886i
$795$	8.00000			0.283731
$796$	−9.89949	−	9.89949i	−0.350878	−	0.350878i
$797$		−	46.0000i		−	1.62940i	−0.579880	−	0.814702i	$-0.696901\pi$
$797$		−	46.0000i		−	1.62940i	0.579880	−	0.814702i	$-0.303099\pi$
$798$	−8.00000			−0.283197
$799$		0			0
$800$	−11.0000			−0.388909
$801$			2.00000i			0.0706665i
$802$	21.2132	+	21.2132i	0.749064	+	0.749064i
$803$		0			0
$804$	8.48528	+	8.48528i	0.299253	+	0.299253i
$805$	−33.9411	+	33.9411i	−1.19627	+	1.19627i
$806$	−25.4558	+	25.4558i	−0.896644	+	0.896644i
$807$			12.0000i			0.422420i
$808$		−	14.0000i		−	0.492518i
$809$	−18.3848	+	18.3848i	−0.646374	+	0.646374i	−0.952115	−	0.305741i	$-0.901096\pi$
$809$	−18.3848	+	18.3848i	−0.646374	+	0.646374i	0.305741	+	0.952115i	$0.401096\pi$
$810$	−2.82843	+	2.82843i	−0.0993808	+	0.0993808i
$811$	−8.48528	−	8.48528i	−0.297959	−	0.297959i	0.542255	−	0.840214i	$-0.317571\pi$
$811$	−8.48528	−	8.48528i	−0.297959	−	0.297959i	−0.840214	+	0.542255i	$0.817571\pi$
$812$	−8.00000			−0.280745
$813$	−11.3137	−	11.3137i	−0.396789	−	0.396789i
$814$		0			0
$815$	−48.0000			−1.68137
$816$		0			0
$817$	−16.0000			−0.559769
$818$		−	26.0000i		−	0.909069i
$819$	−8.48528	−	8.48528i	−0.296500	−	0.296500i
$820$	−40.0000			−1.39686
$821$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$821$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$822$	4.24264	−	4.24264i	0.147979	−	0.147979i
$823$	12.7279	−	12.7279i	0.443667	−	0.443667i	−0.449575	−	0.893243i	$-0.648425\pi$
$823$	12.7279	−	12.7279i	0.443667	−	0.443667i	0.893243	+	0.449575i	$0.148425\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$	16.9706	−	16.9706i	0.590481	−	0.590481i
$827$	−11.3137	+	11.3137i	−0.393416	+	0.393416i	−0.875903	−	0.482487i	$-0.839734\pi$
$827$	−11.3137	+	11.3137i	−0.393416	+	0.393416i	0.482487	+	0.875903i	$0.339734\pi$
$828$	4.24264	+	4.24264i	0.147442	+	0.147442i
$829$	−6.00000			−0.208389			−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000			−0.208389			−0.104194	+	0.994557i	$0.533226\pi$
$830$	33.9411	+	33.9411i	1.17811	+	1.17811i
$831$		−	8.00000i		−	0.277517i
$832$	−6.00000			−0.208013
$833$		0			0
$834$	8.00000			0.277017
$835$		−	8.00000i		−	0.276851i
$836$		0			0
$837$	−6.00000			−0.207390
$838$	8.48528	+	8.48528i	0.293119	+	0.293119i
$839$	21.2132	−	21.2132i	0.732361	−	0.732361i	−0.238726	−	0.971087i	$-0.576730\pi$
$839$	21.2132	−	21.2132i	0.732361	−	0.732361i	0.971087	+	0.238726i	$0.0767297\pi$
$840$	5.65685	−	5.65685i	0.195180	−	0.195180i
$841$		−	13.0000i		−	0.448276i
$842$		−	34.0000i		−	1.17172i
$843$	12.7279	−	12.7279i	0.438373	−	0.438373i
$844$	−5.65685	+	5.65685i	−0.194717	+	0.194717i
$845$	−65.0538	−	65.0538i	−2.23792	−	2.23792i
$846$	4.00000			0.137523
$847$	−15.5563	−	15.5563i	−0.534522	−	0.534522i
$848$			2.00000i			0.0686803i
$849$	−32.0000			−1.09824
$850$		0			0
$851$	−24.0000			−0.822709
$852$		−	6.00000i		−	0.205557i
$853$	11.3137	+	11.3137i	0.387374	+	0.387374i	0.873750	−	0.486376i	$-0.161681\pi$
$853$	11.3137	+	11.3137i	0.387374	+	0.387374i	−0.486376	+	0.873750i	$0.661681\pi$
$854$	8.00000			0.273754
$855$	−11.3137	−	11.3137i	−0.386921	−	0.386921i
$856$		0			0
$857$	−7.07107	+	7.07107i	−0.241543	+	0.241543i	−0.817488	−	0.575945i	$-0.804634\pi$
$857$	−7.07107	+	7.07107i	−0.241543	+	0.241543i	0.575945	+	0.817488i	$0.304634\pi$
$858$		0			0
$859$			20.0000i			0.682391i	0.939992	+	0.341196i	$0.110832\pi$
$859$			20.0000i			0.682391i	−0.939992	+	0.341196i	$0.889168\pi$
$860$	11.3137	−	11.3137i	0.385794	−	0.385794i
$861$	14.1421	−	14.1421i	0.481963	−	0.481963i
$862$	−9.89949	−	9.89949i	−0.337178	−	0.337178i
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$		−	16.0000i		−	0.544016i
$866$	18.0000			0.611665
$867$		0			0
$868$	12.0000			0.407307
$869$		0			0
$870$	−11.3137	−	11.3137i	−0.383571	−	0.383571i
$871$	−72.0000			−2.43963
$872$	−11.3137	−	11.3137i	−0.383131	−	0.383131i
$873$	−4.24264	+	4.24264i	−0.143592	+	0.143592i
$874$	−16.9706	+	16.9706i	−0.574038	+	0.574038i
$875$			48.0000i			1.62270i
$876$		−	2.00000i		−	0.0675737i
$877$	−16.9706	+	16.9706i	−0.573055	+	0.573055i	−0.932981	−	0.359926i	$-0.882802\pi$
$877$	−16.9706	+	16.9706i	−0.573055	+	0.573055i	0.359926	+	0.932981i	$0.382802\pi$
$878$	−7.07107	+	7.07107i	−0.238637	+	0.238637i
$879$	−1.41421	−	1.41421i	−0.0477002	−	0.0477002i
$880$		0			0
$881$	−35.3553	−	35.3553i	−1.19115	−	1.19115i	−0.976744	−	0.214407i	$-0.931218\pi$
$881$	−35.3553	−	35.3553i	−1.19115	−	1.19115i	−0.214407	−	0.976744i	$-0.568782\pi$
$882$		−	3.00000i		−	0.101015i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	48.0000			1.61350
$886$			12.0000i			0.403148i
$887$	−12.7279	−	12.7279i	−0.427362	−	0.427362i	0.460367	−	0.887729i	$-0.347718\pi$
$887$	−12.7279	−	12.7279i	−0.427362	−	0.427362i	−0.887729	+	0.460367i	$0.847718\pi$
$888$	4.00000			0.134231
$889$	−11.3137	−	11.3137i	−0.379450	−	0.379450i
$890$	5.65685	−	5.65685i	0.189618	−	0.189618i
$891$		0			0
$892$		−	4.00000i		−	0.133930i
$893$			16.0000i			0.535420i
$894$	−4.24264	+	4.24264i	−0.141895	+	0.141895i
$895$	−33.9411	+	33.9411i	−1.13453	+	1.13453i
$896$	1.41421	+	1.41421i	0.0472456	+	0.0472456i
$897$	−36.0000			−1.20201
$898$	−18.3848	−	18.3848i	−0.613508	−	0.613508i
$899$		−	24.0000i		−	0.800445i
$900$	11.0000			0.366667
$901$		0			0
$902$		0			0
$903$			8.00000i			0.266223i
$904$	1.41421	+	1.41421i	0.0470360	+	0.0470360i
$905$	−80.0000			−2.65929
$906$	−16.9706	−	16.9706i	−0.563809	−	0.563809i
$907$	−16.9706	+	16.9706i	−0.563498	+	0.563498i	−0.930299	−	0.366801i	$-0.880453\pi$
$907$	−16.9706	+	16.9706i	−0.563498	+	0.563498i	0.366801	+	0.930299i	$0.380453\pi$
$908$	2.82843	−	2.82843i	0.0938647	−	0.0938647i
$909$			14.0000i			0.464351i
$910$			48.0000i			1.59118i
$911$	18.3848	−	18.3848i	0.609115	−	0.609115i	−0.333600	−	0.942715i	$-0.608263\pi$
$911$	18.3848	−	18.3848i	0.609115	−	0.609115i	0.942715	+	0.333600i	$0.108263\pi$
$912$	2.82843	−	2.82843i	0.0936586	−	0.0936586i
$913$		0			0
$914$	22.0000			0.727695
$915$	11.3137	+	11.3137i	0.374020	+	0.374020i
$916$			2.00000i			0.0660819i
$917$	32.0000			1.05673
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		−	24.0000i		−	0.791257i
$921$	−8.48528	−	8.48528i	−0.279600	−	0.279600i
$922$	−10.0000			−0.329332
$923$	25.4558	+	25.4558i	0.837889	+	0.837889i
$924$		0			0
$925$	−31.1127	+	31.1127i	−1.02298	+	1.02298i
$926$			4.00000i			0.131448i
$927$			4.00000i			0.131377i
$928$	2.82843	−	2.82843i	0.0928477	−	0.0928477i
$929$	24.0416	−	24.0416i	0.788780	−	0.788780i	−0.192514	−	0.981294i	$-0.561664\pi$
$929$	24.0416	−	24.0416i	0.788780	−	0.788780i	0.981294	+	0.192514i	$0.0616641\pi$
$930$	16.9706	+	16.9706i	0.556487	+	0.556487i
$931$	12.0000			0.393284
$932$	4.24264	+	4.24264i	0.138972	+	0.138972i
$933$			30.0000i			0.982156i
$934$	36.0000			1.17796
$935$		0			0
$936$	6.00000			0.196116
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$	16.9706	+	16.9706i	0.554109	+	0.554109i
$939$	−26.0000			−0.848478
$940$	−11.3137	−	11.3137i	−0.369012	−	0.369012i
$941$	−33.9411	+	33.9411i	−1.10645	+	1.10645i	−0.112835	+	0.993614i	$0.535993\pi$
$941$	−33.9411	+	33.9411i	−1.10645	+	1.10645i	−0.993614	+	0.112835i	$0.964007\pi$
$942$	4.24264	−	4.24264i	0.138233	−	0.138233i
$943$		−	60.0000i		−	1.95387i
$944$			12.0000i			0.390567i
$945$	−5.65685	+	5.65685i	−0.184017	+	0.184017i
$946$		0			0
$947$	−16.9706	−	16.9706i	−0.551469	−	0.551469i	0.375396	−	0.926865i	$-0.377507\pi$
$947$	−16.9706	−	16.9706i	−0.551469	−	0.551469i	−0.926865	+	0.375396i	$0.877507\pi$
$948$	10.0000			0.324785
$949$	8.48528	+	8.48528i	0.275444	+	0.275444i
$950$			44.0000i			1.42755i
$951$	16.0000			0.518836
$952$		0			0
$953$	22.0000			0.712650			0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000			0.712650			0.356325	+	0.934362i	$0.384030\pi$
$954$		−	2.00000i		−	0.0647524i
$955$	−11.3137	−	11.3137i	−0.366103	−	0.366103i
$956$	20.0000			0.646846
$957$		0			0
$958$	7.07107	−	7.07107i	0.228456	−	0.228456i
$959$	8.48528	−	8.48528i	0.274004	−	0.274004i
$960$			4.00000i			0.129099i
$961$			5.00000i			0.161290i
$962$	−16.9706	+	16.9706i	−0.547153	+	0.547153i
$963$		0			0
$964$	−12.7279	−	12.7279i	−0.409939	−	0.409939i
$965$	24.0000			0.772587
$966$	8.48528	+	8.48528i	0.273009	+	0.273009i
$967$			44.0000i			1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$			44.0000i			1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$	11.0000			0.353553
$969$		0			0
$970$	24.0000			0.770594
$971$		−	20.0000i		−	0.641831i	−0.947108	−	0.320915i	$-0.896010\pi$
$971$		−	20.0000i		−	0.641831i	0.947108	−	0.320915i	$-0.103990\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	16.0000			0.512936
$974$	26.8701	+	26.8701i	0.860972	+	0.860972i
$975$	−46.6690	+	46.6690i	−1.49461	+	1.49461i
$976$	−2.82843	+	2.82843i	−0.0905357	+	0.0905357i
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$			12.0000i			0.383718i
$979$		0			0
$980$	−8.48528	+	8.48528i	−0.271052	+	0.271052i
$981$	11.3137	+	11.3137i	0.361219	+	0.361219i
$982$	−20.0000			−0.638226
$983$	26.8701	+	26.8701i	0.857022	+	0.857022i	0.990986	−	0.133964i	$-0.0427708\pi$
$983$	26.8701	+	26.8701i	0.857022	+	0.857022i	−0.133964	+	0.990986i	$0.542771\pi$
$984$			10.0000i			0.318788i
$985$	−32.0000			−1.01960
$986$		0			0
$987$	8.00000			0.254643
$988$			24.0000i			0.763542i
$989$	16.9706	+	16.9706i	0.539633	+	0.539633i
$990$		0			0
$991$	−24.0416	−	24.0416i	−0.763708	−	0.763708i	0.213283	−	0.976990i	$-0.431584\pi$
$991$	−24.0416	−	24.0416i	−0.763708	−	0.763708i	−0.976990	+	0.213283i	$0.931584\pi$
$992$	−4.24264	+	4.24264i	−0.134704	+	0.134704i
$993$	−14.1421	+	14.1421i	−0.448787	+	0.448787i
$994$		−	12.0000i		−	0.380617i
$995$		−	56.0000i		−	1.77532i
$996$	8.48528	−	8.48528i	0.268866	−	0.268866i
$997$	14.1421	−	14.1421i	0.447886	−	0.447886i	−0.446765	−	0.894651i	$-0.647424\pi$
$997$	14.1421	−	14.1421i	0.447886	−	0.447886i	0.894651	+	0.446765i	$0.147424\pi$
$998$	−22.6274	−	22.6274i	−0.716258	−	0.716258i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.g.829.2		4
17.2	even	8		1734.2.a.h.1.1		1
17.4	even	4	inner	1734.2.f.g.1483.2		4
17.8	even	8		1734.2.b.d.577.1		2
17.9	even	8		1734.2.b.d.577.2		2
17.13	even	4	inner	1734.2.f.g.1483.1		4
17.15	even	8		102.2.a.a.1.1	✓	1
17.16	even	2	inner	1734.2.f.g.829.1		4
51.2	odd	8		5202.2.a.g.1.1		1
51.32	odd	8		306.2.a.d.1.1		1
68.15	odd	8		816.2.a.h.1.1		1
85.32	odd	8		2550.2.d.q.2449.1		2
85.49	even	8		2550.2.a.be.1.1		1
85.83	odd	8		2550.2.d.q.2449.2		2
119.83	odd	8		4998.2.a.x.1.1		1
136.83	odd	8		3264.2.a.p.1.1		1
136.117	even	8		3264.2.a.bf.1.1		1
204.83	even	8		2448.2.a.t.1.1		1
255.134	odd	8		7650.2.a.z.1.1		1
408.83	even	8		9792.2.a.b.1.1		1
408.389	odd	8		9792.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.a.a.1.1	✓	1	17.15	even	8
306.2.a.d.1.1		1	51.32	odd	8
816.2.a.h.1.1		1	68.15	odd	8
1734.2.a.h.1.1		1	17.2	even	8
1734.2.b.d.577.1		2	17.8	even	8
1734.2.b.d.577.2		2	17.9	even	8
1734.2.f.g.829.1		4	17.16	even	2	inner
1734.2.f.g.829.2		4	1.1	even	1	trivial
1734.2.f.g.1483.1		4	17.13	even	4	inner
1734.2.f.g.1483.2		4	17.4	even	4	inner
2448.2.a.t.1.1		1	204.83	even	8
2550.2.a.be.1.1		1	85.49	even	8
2550.2.d.q.2449.1		2	85.32	odd	8
2550.2.d.q.2449.2		2	85.83	odd	8
3264.2.a.p.1.1		1	136.83	odd	8
3264.2.a.bf.1.1		1	136.117	even	8
4998.2.a.x.1.1		1	119.83	odd	8
5202.2.a.g.1.1		1	51.2	odd	8
7650.2.a.z.1.1		1	255.134	odd	8
9792.2.a.a.1.1		1	408.389	odd	8
9792.2.a.b.1.1		1	408.83	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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.82843 - 2.82843i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.82843 - 2.82843i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.82843 - 2.82843i) q^{10} +(-0.707107 - 0.707107i) q^{12} +6.00000 q^{13} +(-1.41421 - 1.41421i) q^{14} -4.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} +(2.82843 + 2.82843i) q^{20} -2.00000 q^{21} +(-4.24264 + 4.24264i) q^{23} +(0.707107 - 0.707107i) q^{24} +11.0000i q^{25} +6.00000i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.41421 - 1.41421i) q^{28} +(-2.82843 - 2.82843i) q^{29} +4.00000 q^{30} +(4.24264 + 4.24264i) q^{31} +1.00000i q^{32} +8.00000 q^{35} -1.00000i q^{36} +(2.82843 + 2.82843i) q^{37} +4.00000 q^{38} +(4.24264 + 4.24264i) q^{39} +(-2.82843 + 2.82843i) q^{40} +(-7.07107 + 7.07107i) q^{41} -2.00000i q^{42} -4.00000i q^{43} +(2.82843 - 2.82843i) q^{45} +(-4.24264 - 4.24264i) q^{46} -4.00000 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} -11.0000 q^{50} -6.00000 q^{52} +2.00000i q^{53} +(-0.707107 - 0.707107i) q^{54} +(1.41421 + 1.41421i) q^{56} +(2.82843 - 2.82843i) q^{57} +(2.82843 - 2.82843i) q^{58} +12.0000i q^{59} +4.00000i q^{60} +(-2.82843 + 2.82843i) q^{61} +(-4.24264 + 4.24264i) q^{62} +(-1.41421 - 1.41421i) q^{63} -1.00000 q^{64} +(-16.9706 - 16.9706i) q^{65} -12.0000 q^{67} -6.00000 q^{69} +8.00000i q^{70} +(4.24264 + 4.24264i) q^{71} +1.00000 q^{72} +(1.41421 + 1.41421i) q^{73} +(-2.82843 + 2.82843i) q^{74} +(-7.77817 + 7.77817i) q^{75} +4.00000i q^{76} +(-4.24264 + 4.24264i) q^{78} +(-7.07107 + 7.07107i) q^{79} +(-2.82843 - 2.82843i) q^{80} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} -4.00000i q^{87} +2.00000 q^{89} +(2.82843 + 2.82843i) q^{90} +(-8.48528 + 8.48528i) q^{91} +(4.24264 - 4.24264i) q^{92} +6.00000i q^{93} -4.00000i q^{94} +(-11.3137 + 11.3137i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.24264 + 4.24264i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} + 24 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} + 16 q^{30} + 32 q^{35} + 16 q^{38} - 16 q^{47} - 44 q^{50} - 24 q^{52} - 4 q^{64} - 48 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 8 q^{89} - 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 24 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 + 16 * q^30 + 32 * q^35 + 16 * q^38 - 16 * q^47 - 44 * q^50 - 24 * q^52 - 4 * q^64 - 48 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 8 * q^89 - 12 * q^98

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