LMFDB - Embedded newform 510.2.l.a.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, 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:	$4.07237050309$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	510.137
Dual form			510.2.l.a.443.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} +1.41421i q^{11} +(-0.292893 - 1.70711i) q^{12} +(-2.00000 + 2.00000i) q^{13} +4.24264 q^{14} +(0.585786 - 3.82843i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.29289 + 2.70711i) q^{18} -8.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(-6.00000 - 4.24264i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} -2.82843i q^{26} +(4.53553 - 2.53553i) q^{27} +(-3.00000 + 3.00000i) q^{28} -4.24264 q^{29} +(2.29289 + 3.12132i) q^{30} +10.0000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.414214 + 2.41421i) q^{33} +1.00000i q^{34} +(-8.48528 + 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(5.65685 + 5.65685i) q^{38} +(-2.82843 + 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} +8.48528i q^{41} +(7.24264 - 1.24264i) q^{42} +1.41421 q^{44} +(-0.121320 - 6.70711i) q^{45} +(2.82843 - 2.82843i) q^{47} +(-1.70711 + 0.292893i) q^{48} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(1.00000 - 1.41421i) q^{51} +(2.00000 + 2.00000i) q^{52} +(-5.65685 - 5.65685i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} -4.24264i q^{56} +(-2.34315 - 13.6569i) q^{57} +(3.00000 - 3.00000i) q^{58} +9.89949 q^{59} +(-3.82843 - 0.585786i) q^{60} +10.0000 q^{61} +(-7.07107 + 7.07107i) q^{62} +(-11.4853 - 5.48528i) q^{63} +1.00000i q^{64} +(2.82843 + 5.65685i) q^{65} +(-2.00000 - 1.41421i) q^{66} +(10.0000 + 10.0000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(3.00000 - 9.00000i) q^{70} +11.3137i q^{71} +(2.70711 + 1.29289i) q^{72} +(-3.00000 + 3.00000i) q^{73} +2.82843 q^{74} +(-7.70711 - 3.94975i) q^{75} -8.00000 q^{76} +(4.24264 - 4.24264i) q^{77} +(-0.828427 - 4.82843i) q^{78} -14.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-6.00000 - 6.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(-4.24264 + 6.00000i) q^{84} +(-1.00000 - 2.00000i) q^{85} +(-7.24264 + 1.24264i) q^{87} +(-1.00000 + 1.00000i) q^{88} +2.82843 q^{89} +(4.82843 + 4.65685i) q^{90} +12.0000 q^{91} +(17.0711 - 2.92893i) q^{93} +4.00000i q^{94} +(-16.9706 - 5.65685i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +(1.41421 + 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} - 12 q^{7}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^6 - 12 * q^7	$ 4 q + 4 q^{3} - 4 q^{6} - 12 q^{7} + 4 q^{10} - 4 q^{12} - 8 q^{13} + 8 q^{15} - 4 q^{16} - 8 q^{18} - 24 q^{21} - 4 q^{22} - 16 q^{25} + 4 q^{27} - 12 q^{28} + 12 q^{30} + 40 q^{31} - 4 q^{33} - 4 q^{36} - 8 q^{37} + 8 q^{40} + 12 q^{42} + 8 q^{45} - 4 q^{48} + 4 q^{51} + 8 q^{52} + 12 q^{55} - 32 q^{57} + 12 q^{58} - 4 q^{60} + 40 q^{61} - 12 q^{63} - 8 q^{66} + 40 q^{67} + 12 q^{70} + 8 q^{72} - 12 q^{73} - 28 q^{75} - 32 q^{76} + 8 q^{78} + 28 q^{81} - 24 q^{82} - 4 q^{85} - 12 q^{87} - 4 q^{88} + 8 q^{90} + 48 q^{91} + 40 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 - 12 * q^7 + 4 * q^10 - 4 * q^12 - 8 * q^13 + 8 * q^15 - 4 * q^16 - 8 * q^18 - 24 * q^21 - 4 * q^22 - 16 * q^25 + 4 * q^27 - 12 * q^28 + 12 * q^30 + 40 * q^31 - 4 * q^33 - 4 * q^36 - 8 * q^37 + 8 * q^40 + 12 * q^42 + 8 * q^45 - 4 * q^48 + 4 * q^51 + 8 * q^52 + 12 * q^55 - 32 * q^57 + 12 * q^58 - 4 * q^60 + 40 * q^61 - 12 * q^63 - 8 * q^66 + 40 * q^67 + 12 * q^70 + 8 * q^72 - 12 * q^73 - 28 * q^75 - 32 * q^76 + 8 * q^78 + 28 * q^81 - 24 * q^82 - 4 * q^85 - 12 * q^87 - 4 * q^88 + 8 * q^90 + 48 * q^91 + 40 * q^93 + 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$	−0.292893	−	1.70711i	−0.0845510	−	0.492799i
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$	4.24264			1.13389
$15$	0.585786	−	3.82843i	0.151249	−	0.988496i
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		−	8.00000i		−	1.83533i	−0.397360	−	0.917663i	$-0.630073\pi$
$19$		−	8.00000i		−	1.83533i	0.397360	−	0.917663i	$-0.369927\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$	−6.00000	−	4.24264i	−1.30931	−	0.925820i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$23$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$24$	1.41421	+	1.00000i	0.288675	+	0.204124i
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		−	2.82843i		−	0.554700i
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$	−3.00000	+	3.00000i	−0.566947	+	0.566947i
$29$	−4.24264			−0.787839			−0.393919	−	0.919145i	$-0.628881\pi$
$29$	−4.24264			−0.787839			−0.393919	+	0.919145i	$0.628881\pi$
$30$	2.29289	+	3.12132i	0.418623	+	0.569873i
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.414214	+	2.41421i	0.0721053	+	0.420261i
$34$			1.00000i			0.171499i
$35$	−8.48528	+	4.24264i	−1.43427	+	0.717137i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	5.65685	+	5.65685i	0.917663	+	0.917663i
$39$	−2.82843	+	4.00000i	−0.452911	+	0.640513i
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	7.24264	−	1.24264i	1.11756	−	0.191744i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$	1.41421			0.213201
$45$	−0.121320	−	6.70711i	−0.0180854	−	0.999836i
$46$		0			0
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	−0.470064	−	0.882632i	$-0.655769\pi$
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	0.882632	+	0.470064i	$0.155769\pi$
$48$	−1.70711	+	0.292893i	−0.246400	+	0.0422755i
$49$			11.0000i			1.57143i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	1.00000	−	1.41421i	0.140028	−	0.198030i
$52$	2.00000	+	2.00000i	0.277350	+	0.277350i
$53$	−5.65685	−	5.65685i	−0.777029	−	0.777029i	0.202296	−	0.979324i	$-0.435160\pi$
$53$	−5.65685	−	5.65685i	−0.777029	−	0.777029i	−0.979324	+	0.202296i	$0.935160\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$		−	4.24264i		−	0.566947i
$57$	−2.34315	−	13.6569i	−0.310357	−	1.80889i
$58$	3.00000	−	3.00000i	0.393919	−	0.393919i
$59$	9.89949			1.28880			0.644402	−	0.764687i	$-0.277106\pi$
$59$	9.89949			1.28880			0.644402	+	0.764687i	$0.277106\pi$
$60$	−3.82843	−	0.585786i	−0.494248	−	0.0756247i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	−7.07107	+	7.07107i	−0.898027	+	0.898027i
$63$	−11.4853	−	5.48528i	−1.44701	−	0.691080i
$64$			1.00000i			0.125000i
$65$	2.82843	+	5.65685i	0.350823	+	0.701646i
$66$	−2.00000	−	1.41421i	−0.246183	−	0.174078i
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.967029	+	0.254665i	$0.0819652\pi$
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.254665	+	0.967029i	$0.418035\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	3.00000	−	9.00000i	0.358569	−	1.07571i
$71$			11.3137i			1.34269i	0.741145	+	0.671345i	$0.234283\pi$
$71$			11.3137i			1.34269i	−0.741145	+	0.671345i	$0.765717\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$	2.82843			0.328798
$75$	−7.70711	−	3.94975i	−0.889940	−	0.456078i
$76$	−8.00000			−0.917663
$77$	4.24264	−	4.24264i	0.483494	−	0.483494i
$78$	−0.828427	−	4.82843i	−0.0938009	−	0.546712i
$79$		−	14.0000i		−	1.57512i	−0.616236	−	0.787562i	$-0.711343\pi$
$79$		−	14.0000i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	−6.00000	−	6.00000i	−0.662589	−	0.662589i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$	−4.24264	+	6.00000i	−0.462910	+	0.654654i
$85$	−1.00000	−	2.00000i	−0.108465	−	0.216930i
$86$		0			0
$87$	−7.24264	+	1.24264i	−0.776493	+	0.133225i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	2.82843			0.299813			0.149906	−	0.988700i	$-0.452103\pi$
$89$	2.82843			0.299813			0.149906	+	0.988700i	$0.452103\pi$
$90$	4.82843	+	4.65685i	0.508961	+	0.490876i
$91$	12.0000			1.25794
$92$		0			0
$93$	17.0711	−	2.92893i	1.77019	−	0.303716i
$94$			4.00000i			0.412568i
$95$	−16.9706	−	5.65685i	−1.74114	−	0.580381i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$	−7.77817	−	7.77817i	−0.785714	−	0.785714i
$99$	1.41421	+	4.00000i	0.142134	+	0.402015i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$			4.24264i			0.422159i	0.977469	+	0.211079i	$0.0676978\pi$
$101$			4.24264i			0.422159i	−0.977469	+	0.211079i	$0.932302\pi$
$102$	0.292893	+	1.70711i	0.0290008	+	0.169029i
$103$	−3.00000	+	3.00000i	−0.295599	+	0.295599i	−0.839287	−	0.543688i	$-0.817027\pi$
$103$	−3.00000	+	3.00000i	−0.295599	+	0.295599i	0.543688	+	0.839287i	$0.317027\pi$
$104$	−2.82843			−0.277350
$105$	−13.2426	+	9.72792i	−1.29235	+	0.949348i
$106$	8.00000			0.777029
$107$	−14.1421	+	14.1421i	−1.36717	+	1.36717i	−0.502726	+	0.864446i	$0.667670\pi$
$107$	−14.1421	+	14.1421i	−1.36717	+	1.36717i	−0.864446	+	0.502726i	$0.832330\pi$
$108$	−2.53553	−	4.53553i	−0.243982	−	0.436432i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	−2.82843	+	1.41421i	−0.269680	+	0.134840i
$111$	−4.00000	−	2.82843i	−0.379663	−	0.268462i
$112$	3.00000	+	3.00000i	0.283473	+	0.283473i
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$	11.3137	+	8.00000i	1.05963	+	0.749269i
$115$		0			0
$116$			4.24264i			0.393919i
$117$	−3.65685	+	7.65685i	−0.338076	+	0.707876i
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−4.24264			−0.388922
$120$	3.12132	−	2.29289i	0.284936	−	0.209312i
$121$	9.00000			0.818182
$122$	−7.07107	+	7.07107i	−0.640184	+	0.640184i
$123$	2.48528	+	14.4853i	0.224090	+	1.30609i
$124$		−	10.0000i		−	0.898027i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	12.0000	−	4.24264i	1.06904	−	0.377964i
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	0.561363	−	0.827570i	$-0.310277\pi$
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	−0.827570	+	0.561363i	$0.810277\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−6.00000	−	2.00000i	−0.526235	−	0.175412i
$131$		−	9.89949i		−	0.864923i	−0.901652	−	0.432461i	$-0.857645\pi$
$131$		−	9.89949i		−	0.864923i	0.901652	−	0.432461i	$-0.142355\pi$
$132$	2.41421	−	0.414214i	0.210130	−	0.0360527i
$133$	−24.0000	+	24.0000i	−2.08106	+	2.08106i
$134$	−14.1421			−1.22169
$135$	−2.17157	−	11.4142i	−0.186899	−	0.982379i
$136$	1.00000			0.0857493
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	−0.864723	−	0.502249i	$-0.832506\pi$
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	0.502249	+	0.864723i	$0.332506\pi$
$138$		0			0
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$	4.24264	+	8.48528i	0.358569	+	0.717137i
$141$	4.00000	−	5.65685i	0.336861	−	0.476393i
$142$	−8.00000	−	8.00000i	−0.671345	−	0.671345i
$143$	−2.82843	−	2.82843i	−0.236525	−	0.236525i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	−3.00000	+	9.00000i	−0.249136	+	0.747409i
$146$		−	4.24264i		−	0.351123i
$147$	3.22183	+	18.7782i	0.265732	+	1.54880i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$	8.24264	−	2.65685i	0.673009	−	0.216931i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	5.65685	−	5.65685i	0.458831	−	0.458831i
$153$	1.29289	−	2.70711i	0.104524	−	0.218857i
$154$			6.00000i			0.483494i
$155$	7.07107	−	21.2132i	0.567962	−	1.70389i
$156$	4.00000	+	2.82843i	0.320256	+	0.226455i
$157$	−10.0000	−	10.0000i	−0.798087	−	0.798087i	0.184707	−	0.982794i	$-0.440866\pi$
$157$	−10.0000	−	10.0000i	−0.798087	−	0.798087i	−0.982794	+	0.184707i	$0.940866\pi$
$158$	9.89949	+	9.89949i	0.787562	+	0.787562i
$159$	−11.3137	−	8.00000i	−0.897235	−	0.634441i
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		0			0
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	4.00000	−	4.00000i	0.313304	−	0.313304i	−0.532884	−	0.846188i	$-0.678892\pi$
$163$	4.00000	−	4.00000i	0.313304	−	0.313304i	0.846188	+	0.532884i	$0.178892\pi$
$164$	8.48528			0.662589
$165$	5.41421	+	0.828427i	0.421496	+	0.0644930i
$166$	−12.0000			−0.931381
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	−0.117582	−	0.993063i	$-0.537514\pi$
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	0.993063	+	0.117582i	$0.0375143\pi$
$168$	−1.24264	−	7.24264i	−0.0958718	−	0.558782i
$169$			5.00000i			0.384615i
$170$	2.12132	+	0.707107i	0.162698	+	0.0542326i
$171$	−8.00000	−	22.6274i	−0.611775	−	1.73036i
$172$		0			0
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	0.222327	−	0.974972i	$-0.428635\pi$
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	−0.974972	+	0.222327i	$0.928635\pi$
$174$	4.24264	−	6.00000i	0.321634	−	0.454859i
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$		−	1.41421i		−	0.106600i
$177$	16.8995	−	2.89949i	1.27024	−	0.217939i
$178$	−2.00000	+	2.00000i	−0.149906	+	0.149906i
$179$	21.2132			1.58555			0.792775	−	0.609515i	$-0.208636\pi$
$179$	21.2132			1.58555			0.792775	+	0.609515i	$0.208636\pi$
$180$	−6.70711	+	0.121320i	−0.499918	+	0.00904268i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−8.48528	+	8.48528i	−0.628971	+	0.628971i
$183$	17.0711	−	2.92893i	1.26193	−	0.216513i
$184$		0			0
$185$	−5.65685	+	2.82843i	−0.415900	+	0.207950i
$186$	−10.0000	+	14.1421i	−0.733236	+	1.03695i
$187$	1.00000	+	1.00000i	0.0731272	+	0.0731272i
$188$	−2.82843	−	2.82843i	−0.206284	−	0.206284i
$189$	−21.2132	−	6.00000i	−1.54303	−	0.436436i
$190$	16.0000	−	8.00000i	1.16076	−	0.580381i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	0.292893	+	1.70711i	0.0211377	+	0.123200i
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	−0.590842	−	0.806787i	$-0.701204\pi$
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	0.806787	+	0.590842i	$0.201204\pi$
$194$	4.24264			0.304604
$195$	6.48528	+	8.82843i	0.464421	+	0.632217i
$196$	11.0000			0.785714
$197$	−11.3137	+	11.3137i	−0.806068	+	0.806068i	−0.984036	−	0.177968i	$-0.943048\pi$
$197$	−11.3137	+	11.3137i	−0.806068	+	0.806068i	0.177968	+	0.984036i	$0.443048\pi$
$198$	−3.82843	−	1.82843i	−0.272074	−	0.129941i
$199$			16.0000i			1.13421i	0.823646	+	0.567105i	$0.191937\pi$
$199$			16.0000i			1.13421i	−0.823646	+	0.567105i	$0.808063\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$	20.0000	+	14.1421i	1.41069	+	0.997509i
$202$	−3.00000	−	3.00000i	−0.211079	−	0.211079i
$203$	12.7279	+	12.7279i	0.893325	+	0.893325i
$204$	−1.41421	−	1.00000i	−0.0990148	−	0.0700140i
$205$	18.0000	+	6.00000i	1.25717	+	0.419058i
$206$		−	4.24264i		−	0.295599i
$207$		0			0
$208$	2.00000	−	2.00000i	0.138675	−	0.138675i
$209$	11.3137			0.782586
$210$	2.48528	−	16.2426i	0.171501	−	1.12085i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−5.65685	+	5.65685i	−0.388514	+	0.388514i
$213$	3.31371	+	19.3137i	0.227052	+	1.32335i
$214$		−	20.0000i		−	1.36717i
$215$		0			0
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	−30.0000	−	30.0000i	−2.03653	−	2.03653i
$218$	−1.41421	−	1.41421i	−0.0957826	−	0.0957826i
$219$	−4.24264	+	6.00000i	−0.286691	+	0.405442i
$220$	1.00000	−	3.00000i	0.0674200	−	0.202260i
$221$			2.82843i			0.190261i
$222$	4.82843	−	0.828427i	0.324063	−	0.0556004i
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	−0.599489	−	0.800383i	$-0.704629\pi$
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	0.800383	+	0.599489i	$0.204629\pi$
$224$	−4.24264			−0.283473
$225$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$226$	−2.00000			−0.133038
$227$	1.41421	−	1.41421i	0.0938647	−	0.0938647i	−0.658615	−	0.752480i	$-0.728857\pi$
$227$	1.41421	−	1.41421i	0.0938647	−	0.0938647i	0.752480	+	0.658615i	$0.228857\pi$
$228$	−13.6569	+	2.34315i	−0.904447	+	0.155179i
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$		0			0
$231$	6.00000	−	8.48528i	0.394771	−	0.558291i
$232$	−3.00000	−	3.00000i	−0.196960	−	0.196960i
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	0.899716	−	0.436475i	$-0.143773\pi$
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	−0.436475	+	0.899716i	$0.643773\pi$
$234$	−2.82843	−	8.00000i	−0.184900	−	0.522976i
$235$	−4.00000	−	8.00000i	−0.260931	−	0.521862i
$236$		−	9.89949i		−	0.644402i
$237$	−4.10051	−	23.8995i	−0.266356	−	1.55244i
$238$	3.00000	−	3.00000i	0.194461	−	0.194461i
$239$	2.82843			0.182956			0.0914779	−	0.995807i	$-0.470841\pi$
$239$	2.82843			0.182956			0.0914779	+	0.995807i	$0.470841\pi$
$240$	−0.585786	+	3.82843i	−0.0378124	+	0.247124i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$	10.2929	−	11.7071i	0.660289	−	0.751011i
$244$		−	10.0000i		−	0.640184i
$245$	23.3345	+	7.77817i	1.49079	+	0.496929i
$246$	−12.0000	−	8.48528i	−0.765092	−	0.541002i
$247$	16.0000	+	16.0000i	1.01806	+	1.01806i
$248$	7.07107	+	7.07107i	0.449013	+	0.449013i
$249$	16.9706	+	12.0000i	1.07547	+	0.760469i
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$		−	15.5563i		−	0.981908i	−0.871185	−	0.490954i	$-0.836648\pi$
$251$		−	15.5563i		−	0.981908i	0.871185	−	0.490954i	$-0.163352\pi$
$252$	−5.48528	+	11.4853i	−0.345540	+	0.723505i
$253$		0			0
$254$	4.24264			0.266207
$255$	−2.29289	−	3.12132i	−0.143587	−	0.195465i
$256$	1.00000			0.0625000
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	−0.562291	−	0.826940i	$-0.690080\pi$
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	0.826940	+	0.562291i	$0.190080\pi$
$258$		0			0
$259$			12.0000i			0.745644i
$260$	5.65685	−	2.82843i	0.350823	−	0.175412i
$261$	−12.0000	+	4.24264i	−0.742781	+	0.262613i
$262$	7.00000	+	7.00000i	0.432461	+	0.432461i
$263$	−11.3137	−	11.3137i	−0.697633	−	0.697633i	0.266266	−	0.963899i	$-0.414210\pi$
$263$	−11.3137	−	11.3137i	−0.697633	−	0.697633i	−0.963899	+	0.266266i	$0.914210\pi$
$264$	−1.41421	+	2.00000i	−0.0870388	+	0.123091i
$265$	−16.0000	+	8.00000i	−0.982872	+	0.491436i
$266$		−	33.9411i		−	2.08106i
$267$	4.82843	−	0.828427i	0.295495	−	0.0506989i
$268$	10.0000	−	10.0000i	0.610847	−	0.610847i
$269$	−18.3848			−1.12094			−0.560470	−	0.828175i	$-0.689379\pi$
$269$	−18.3848			−1.12094			−0.560470	+	0.828175i	$0.689379\pi$
$270$	9.60660	+	6.53553i	0.584639	+	0.397740i
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	20.4853	−	3.51472i	1.23983	−	0.212720i
$274$		−	6.00000i		−	0.362473i
$275$	4.24264	−	5.65685i	0.255841	−	0.341121i
$276$		0			0
$277$	−10.0000	−	10.0000i	−0.600842	−	0.600842i	0.339694	−	0.940536i	$-0.389676\pi$
$277$	−10.0000	−	10.0000i	−0.600842	−	0.600842i	−0.940536	+	0.339694i	$0.889676\pi$
$278$	−8.48528	−	8.48528i	−0.508913	−	0.508913i
$279$	28.2843	−	10.0000i	1.69334	−	0.598684i
$280$	−9.00000	−	3.00000i	−0.537853	−	0.179284i
$281$		−	19.7990i		−	1.18111i	−0.806998	−	0.590554i	$-0.798909\pi$
$281$		−	19.7990i		−	1.18111i	0.806998	−	0.590554i	$-0.201091\pi$
$282$	1.17157	+	6.82843i	0.0697661	+	0.406627i
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.211498	−	0.977378i	$-0.432166\pi$
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.977378	−	0.211498i	$-0.0678343\pi$
$284$	11.3137			0.671345
$285$	−30.6274	−	4.68629i	−1.81421	−	0.277592i
$286$	4.00000			0.236525
$287$	25.4558	−	25.4558i	1.50261	−	1.50261i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$		−	1.00000i		−	0.0588235i
$290$	−4.24264	−	8.48528i	−0.249136	−	0.498273i
$291$	−6.00000	−	4.24264i	−0.351726	−	0.248708i
$292$	3.00000	+	3.00000i	0.175562	+	0.175562i
$293$	2.82843	+	2.82843i	0.165238	+	0.165238i	0.784883	−	0.619644i	$-0.212723\pi$
$293$	2.82843	+	2.82843i	0.165238	+	0.165238i	−0.619644	+	0.784883i	$0.712723\pi$
$294$	−15.5563	−	11.0000i	−0.907265	−	0.641533i
$295$	7.00000	−	21.0000i	0.407556	−	1.22267i
$296$		−	2.82843i		−	0.164399i
$297$	3.58579	+	6.41421i	0.208068	+	0.372190i
$298$	−1.00000	+	1.00000i	−0.0579284	+	0.0579284i
$299$		0			0
$300$	−3.94975	+	7.70711i	−0.228039	+	0.444970i
$301$		0			0
$302$		0			0
$303$	1.24264	+	7.24264i	0.0713878	+	0.416079i
$304$			8.00000i			0.458831i
$305$	7.07107	−	21.2132i	0.404888	−	1.21466i
$306$	1.00000	+	2.82843i	0.0571662	+	0.161690i
$307$	8.00000	+	8.00000i	0.456584	+	0.456584i	0.897532	−	0.440948i	$-0.145358\pi$
$307$	8.00000	+	8.00000i	0.456584	+	0.456584i	−0.440948	+	0.897532i	$0.645358\pi$
$308$	−4.24264	−	4.24264i	−0.241747	−	0.241747i
$309$	−4.24264	+	6.00000i	−0.241355	+	0.341328i
$310$	10.0000	+	20.0000i	0.567962	+	1.13592i
$311$			5.65685i			0.320771i	0.987054	+	0.160385i	$0.0512737\pi$
$311$			5.65685i			0.320771i	−0.987054	+	0.160385i	$0.948726\pi$
$312$	−4.82843	+	0.828427i	−0.273356	+	0.0469005i
$313$	−21.0000	+	21.0000i	−1.18699	+	1.18699i	−0.209095	+	0.977895i	$0.567052\pi$
$313$	−21.0000	+	21.0000i	−1.18699	+	1.18699i	−0.977895	+	0.209095i	$0.932948\pi$
$314$	14.1421			0.798087
$315$	−19.7574	+	20.4853i	−1.11320	+	1.15421i
$316$	−14.0000			−0.787562
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	−0.666276	−	0.745706i	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$	13.6569	−	2.34315i	0.765838	−	0.131397i
$319$		−	6.00000i		−	0.335936i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$	−20.0000	+	28.2843i	−1.11629	+	1.57867i
$322$		0			0
$323$	−5.65685	−	5.65685i	−0.314756	−	0.314756i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	14.0000	−	2.00000i	0.776580	−	0.110940i
$326$			5.65685i			0.313304i
$327$	0.585786	+	3.41421i	0.0323941	+	0.188806i
$328$	−6.00000	+	6.00000i	−0.331295	+	0.331295i
$329$	−16.9706			−0.935617
$330$	−4.41421	+	3.24264i	−0.242994	+	0.178501i
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$	8.48528	−	8.48528i	0.465690	−	0.465690i
$333$	−7.65685	−	3.65685i	−0.419593	−	0.200394i
$334$			16.0000i			0.875481i
$335$	28.2843	−	14.1421i	1.54533	−	0.772667i
$336$	6.00000	+	4.24264i	0.327327	+	0.231455i
$337$	1.00000	+	1.00000i	0.0544735	+	0.0544735i	0.733819	−	0.679345i	$-0.237736\pi$
$337$	1.00000	+	1.00000i	0.0544735	+	0.0544735i	−0.679345	+	0.733819i	$0.737736\pi$
$338$	−3.53553	−	3.53553i	−0.192308	−	0.192308i
$339$	2.82843	+	2.00000i	0.153619	+	0.108625i
$340$	−2.00000	+	1.00000i	−0.108465	+	0.0542326i
$341$			14.1421i			0.765840i
$342$	21.6569	+	10.3431i	1.17107	+	0.559293i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$	14.0000			0.752645
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	−0.920999	−	0.389566i	$-0.872625\pi$
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	0.389566	+	0.920999i	$0.372625\pi$
$348$	1.24264	+	7.24264i	0.0666125	+	0.388246i
$349$			6.00000i			0.321173i	0.987022	+	0.160586i	$0.0513385\pi$
$349$			6.00000i			0.321173i	−0.987022	+	0.160586i	$0.948662\pi$
$350$	−16.9706	−	12.7279i	−0.907115	−	0.680336i
$351$	−4.00000	+	14.1421i	−0.213504	+	0.754851i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	15.5563	+	15.5563i	0.827981	+	0.827981i	0.987237	−	0.159256i	$-0.0509096\pi$
$353$	15.5563	+	15.5563i	0.827981	+	0.827981i	−0.159256	+	0.987237i	$0.550910\pi$
$354$	−9.89949	+	14.0000i	−0.526152	+	0.744092i
$355$	24.0000	+	8.00000i	1.27379	+	0.424596i
$356$		−	2.82843i		−	0.149906i
$357$	−7.24264	+	1.24264i	−0.383321	+	0.0657675i
$358$	−15.0000	+	15.0000i	−0.792775	+	0.792775i
$359$	−5.65685			−0.298557			−0.149279	−	0.988795i	$-0.547695\pi$
$359$	−5.65685			−0.298557			−0.149279	+	0.988795i	$0.547695\pi$
$360$	4.65685	−	4.82843i	0.245438	−	0.254480i
$361$	−45.0000			−2.36842
$362$	1.41421	−	1.41421i	0.0743294	−	0.0743294i
$363$	15.3640	−	2.63604i	0.806399	−	0.138356i
$364$		−	12.0000i		−	0.628971i
$365$	4.24264	+	8.48528i	0.222070	+	0.444140i
$366$	−10.0000	+	14.1421i	−0.522708	+	0.739221i
$367$	−5.00000	−	5.00000i	−0.260998	−	0.260998i	0.564462	−	0.825459i	$-0.309084\pi$
$367$	−5.00000	−	5.00000i	−0.260998	−	0.260998i	−0.825459	+	0.564462i	$0.809084\pi$
$368$		0			0
$369$	8.48528	+	24.0000i	0.441726	+	1.24939i
$370$	2.00000	−	6.00000i	0.103975	−	0.311925i
$371$			33.9411i			1.76214i
$372$	−2.92893	−	17.0711i	−0.151858	−	0.885094i
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	−0.534500	−	0.845168i	$-0.679500\pi$
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	0.845168	+	0.534500i	$0.179500\pi$
$374$	−1.41421			−0.0731272
$375$	−13.8284	+	13.5563i	−0.714097	+	0.700047i
$376$	4.00000			0.206284
$377$	8.48528	−	8.48528i	0.437014	−	0.437014i
$378$	19.2426	−	10.7574i	0.989735	−	0.553299i
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$	−5.65685	+	16.9706i	−0.290191	+	0.870572i
$381$	−6.00000	−	4.24264i	−0.307389	−	0.217357i
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	−11.3137	−	11.3137i	−0.578103	−	0.578103i	0.356277	−	0.934380i	$-0.384046\pi$
$383$	−11.3137	−	11.3137i	−0.578103	−	0.578103i	−0.934380	+	0.356277i	$0.884046\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	−6.00000	−	12.0000i	−0.305788	−	0.611577i
$386$			4.24264i			0.215945i
$387$		0			0
$388$	−3.00000	+	3.00000i	−0.152302	+	0.152302i
$389$	15.5563			0.788738			0.394369	−	0.918952i	$-0.370963\pi$
$389$	15.5563			0.788738			0.394369	+	0.918952i	$0.370963\pi$
$390$	−10.8284	−	1.65685i	−0.548319	−	0.0838981i
$391$		0			0
$392$	−7.77817	+	7.77817i	−0.392857	+	0.392857i
$393$	−2.89949	−	16.8995i	−0.146260	−	0.852467i
$394$		−	16.0000i		−	0.806068i
$395$	−29.6985	−	9.89949i	−1.49429	−	0.498098i
$396$	4.00000	−	1.41421i	0.201008	−	0.0710669i
$397$	18.0000	+	18.0000i	0.903394	+	0.903394i	0.995728	−	0.0923340i	$-0.0294327\pi$
$397$	18.0000	+	18.0000i	0.903394	+	0.903394i	−0.0923340	+	0.995728i	$0.529433\pi$
$398$	−11.3137	−	11.3137i	−0.567105	−	0.567105i
$399$	−33.9411	+	48.0000i	−1.69918	+	2.40301i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$			28.2843i			1.41245i	0.707988	+	0.706225i	$0.249603\pi$
$401$			28.2843i			1.41245i	−0.707988	+	0.706225i	$0.750397\pi$
$402$	−24.1421	+	4.14214i	−1.20410	+	0.206591i
$403$	−20.0000	+	20.0000i	−0.996271	+	0.996271i
$404$	4.24264			0.211079
$405$	−7.05025	−	18.8492i	−0.350330	−	0.936626i
$406$	−18.0000			−0.893325
$407$	2.82843	−	2.82843i	0.140200	−	0.140200i
$408$	1.70711	−	0.292893i	0.0845144	−	0.0145004i
$409$			16.0000i			0.791149i	0.918434	+	0.395575i	$0.129455\pi$
$409$			16.0000i			0.791149i	−0.918434	+	0.395575i	$0.870545\pi$
$410$	−16.9706	+	8.48528i	−0.838116	+	0.419058i
$411$	−6.00000	+	8.48528i	−0.295958	+	0.418548i
$412$	3.00000	+	3.00000i	0.147799	+	0.147799i
$413$	−29.6985	−	29.6985i	−1.46137	−	1.46137i
$414$		0			0
$415$	24.0000	−	12.0000i	1.17811	−	0.589057i
$416$			2.82843i			0.138675i
$417$	3.51472	+	20.4853i	0.172117	+	1.00317i
$418$	−8.00000	+	8.00000i	−0.391293	+	0.391293i
$419$	−38.1838			−1.86540			−0.932700	−	0.360654i	$-0.882553\pi$
$419$	−38.1838			−1.86540			−0.932700	+	0.360654i	$0.882553\pi$
$420$	9.72792	+	13.2426i	0.474674	+	0.646175i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	5.65685	−	5.65685i	0.275371	−	0.275371i
$423$	5.17157	−	10.8284i	0.251450	−	0.526496i
$424$		−	8.00000i		−	0.388514i
$425$	−4.94975	+	0.707107i	−0.240098	+	0.0342997i
$426$	−16.0000	−	11.3137i	−0.775203	−	0.548151i
$427$	−30.0000	−	30.0000i	−1.45180	−	1.45180i
$428$	14.1421	+	14.1421i	0.683586	+	0.683586i
$429$	−5.65685	−	4.00000i	−0.273115	−	0.193122i
$430$		0			0
$431$		−	31.1127i		−	1.49865i	−0.662205	−	0.749323i	$-0.730379\pi$
$431$		−	31.1127i		−	1.49865i	0.662205	−	0.749323i	$-0.269621\pi$
$432$	−4.53553	+	2.53553i	−0.218216	+	0.121991i
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	−0.631337	−	0.775508i	$-0.717494\pi$
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	0.775508	+	0.631337i	$0.217494\pi$
$434$	42.4264			2.03653
$435$	−2.48528	+	16.2426i	−0.119160	+	0.778775i
$436$	2.00000			0.0957826
$437$		0			0
$438$	−1.24264	−	7.24264i	−0.0593757	−	0.346067i
$439$			32.0000i			1.52728i	0.645644	+	0.763638i	$0.276589\pi$
$439$			32.0000i			1.52728i	−0.645644	+	0.763638i	$0.723411\pi$
$440$	1.41421	+	2.82843i	0.0674200	+	0.134840i
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$	−2.00000	−	2.00000i	−0.0951303	−	0.0951303i
$443$	29.6985	+	29.6985i	1.41102	+	1.41102i	0.753020	+	0.657997i	$0.228596\pi$
$443$	29.6985	+	29.6985i	1.41102	+	1.41102i	0.657997	+	0.753020i	$0.271404\pi$
$444$	−2.82843	+	4.00000i	−0.134231	+	0.189832i
$445$	2.00000	−	6.00000i	0.0948091	−	0.284427i
$446$			4.24264i			0.200895i
$447$	2.41421	−	0.414214i	0.114188	−	0.0195916i
$448$	3.00000	−	3.00000i	0.141737	−	0.141737i
$449$	−16.9706			−0.800890			−0.400445	−	0.916321i	$-0.631145\pi$
$449$	−16.9706			−0.800890			−0.400445	+	0.916321i	$0.631145\pi$
$450$	13.2929	−	6.94975i	0.626633	−	0.327614i
$451$	−12.0000			−0.565058
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$		0			0
$454$			2.00000i			0.0938647i
$455$	8.48528	−	25.4558i	0.397796	−	1.19339i
$456$	8.00000	−	11.3137i	0.374634	−	0.529813i
$457$	13.0000	+	13.0000i	0.608114	+	0.608114i	0.942453	−	0.334339i	$-0.108513\pi$
$457$	13.0000	+	13.0000i	0.608114	+	0.608114i	−0.334339	+	0.942453i	$0.608513\pi$
$458$	1.41421	+	1.41421i	0.0660819	+	0.0660819i
$459$	1.41421	−	5.00000i	0.0660098	−	0.233380i
$460$		0			0
$461$			35.3553i			1.64666i	0.567561	+	0.823331i	$0.307887\pi$
$461$			35.3553i			1.64666i	−0.567561	+	0.823331i	$0.692113\pi$
$462$	1.75736	+	10.2426i	0.0817598	+	0.476531i
$463$	9.00000	−	9.00000i	0.418265	−	0.418265i	−0.466340	−	0.884606i	$-0.654428\pi$
$463$	9.00000	−	9.00000i	0.418265	−	0.418265i	0.884606	+	0.466340i	$0.154428\pi$
$464$	4.24264			0.196960
$465$	5.85786	−	38.2843i	0.271652	−	1.77539i
$466$	−10.0000			−0.463241
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$	7.65685	+	3.65685i	0.353938	+	0.169038i
$469$		−	60.0000i		−	2.77054i
$470$	8.48528	+	2.82843i	0.391397	+	0.130466i
$471$	−20.0000	−	14.1421i	−0.921551	−	0.651635i
$472$	7.00000	+	7.00000i	0.322201	+	0.322201i
$473$		0			0
$474$	19.7990	+	14.0000i	0.909398	+	0.643041i
$475$	−24.0000	+	32.0000i	−1.10120	+	1.46826i
$476$			4.24264i			0.194461i
$477$	−21.6569	−	10.3431i	−0.991599	−	0.473580i
$478$	−2.00000	+	2.00000i	−0.0914779	+	0.0914779i
$479$	−28.2843			−1.29234			−0.646171	−	0.763193i	$-0.723631\pi$
$479$	−28.2843			−1.29234			−0.646171	+	0.763193i	$0.723631\pi$
$480$	−2.29289	−	3.12132i	−0.104656	−	0.142468i
$481$	8.00000			0.364769
$482$		0			0
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$	−8.48528	+	4.24264i	−0.385297	+	0.192648i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	23.0000	+	23.0000i	1.04223	+	1.04223i	0.999068	+	0.0431614i	$0.0137430\pi$
$487$	23.0000	+	23.0000i	1.04223	+	1.04223i	0.0431614	+	0.999068i	$0.486257\pi$
$488$	7.07107	+	7.07107i	0.320092	+	0.320092i
$489$	5.65685	−	8.00000i	0.255812	−	0.361773i
$490$	−22.0000	+	11.0000i	−0.993859	+	0.496929i
$491$			26.8701i			1.21263i	0.795225	+	0.606314i	$0.207353\pi$
$491$			26.8701i			1.21263i	−0.795225	+	0.606314i	$0.792647\pi$
$492$	14.4853	−	2.48528i	0.653047	−	0.112045i
$493$	−3.00000	+	3.00000i	−0.135113	+	0.135113i
$494$	−22.6274			−1.01806
$495$	9.48528	−	0.171573i	0.426332	−	0.00771163i
$496$	−10.0000			−0.449013
$497$	33.9411	−	33.9411i	1.52247	−	1.52247i
$498$	−20.4853	+	3.51472i	−0.917967	+	0.157498i
$499$		−	28.0000i		−	1.25345i	−0.779240	−	0.626726i	$-0.784395\pi$
$499$		−	28.0000i		−	1.25345i	0.779240	−	0.626726i	$-0.215605\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$	16.0000	−	22.6274i	0.714827	−	1.01092i
$502$	11.0000	+	11.0000i	0.490954	+	0.490954i
$503$	14.1421	+	14.1421i	0.630567	+	0.630567i	0.948210	−	0.317644i	$-0.102892\pi$
$503$	14.1421	+	14.1421i	0.630567	+	0.630567i	−0.317644	+	0.948210i	$0.602892\pi$
$504$	−4.24264	−	12.0000i	−0.188982	−	0.534522i
$505$	9.00000	+	3.00000i	0.400495	+	0.133498i
$506$		0			0
$507$	1.46447	+	8.53553i	0.0650392	+	0.379076i
$508$	−3.00000	+	3.00000i	−0.133103	+	0.133103i
$509$	−18.3848			−0.814891			−0.407445	−	0.913230i	$-0.633580\pi$
$509$	−18.3848			−0.814891			−0.407445	+	0.913230i	$0.633580\pi$
$510$	3.82843	+	0.585786i	0.169526	+	0.0259391i
$511$	18.0000			0.796273
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−20.2843	−	36.2843i	−0.895572	−	1.60199i
$514$			6.00000i			0.264649i
$515$	4.24264	+	8.48528i	0.186953	+	0.373906i
$516$		0			0
$517$	4.00000	+	4.00000i	0.175920	+	0.175920i
$518$	−8.48528	−	8.48528i	−0.372822	−	0.372822i
$519$	−19.7990	−	14.0000i	−0.869079	−	0.614532i
$520$	−2.00000	+	6.00000i	−0.0877058	+	0.263117i
$521$		−	22.6274i		−	0.991325i	−0.868515	−	0.495663i	$-0.834925\pi$
$521$		−	22.6274i		−	0.991325i	0.868515	−	0.495663i	$-0.165075\pi$
$522$	5.48528	−	11.4853i	0.240084	−	0.502697i
$523$	6.00000	−	6.00000i	0.262362	−	0.262362i	−0.563651	−	0.826013i	$-0.690604\pi$
$523$	6.00000	−	6.00000i	0.262362	−	0.262362i	0.826013	+	0.563651i	$0.190604\pi$
$524$	−9.89949			−0.432461
$525$	11.2721	+	34.9706i	0.491954	+	1.52624i
$526$	16.0000			0.697633
$527$	7.07107	−	7.07107i	0.308021	−	0.308021i
$528$	−0.414214	−	2.41421i	−0.0180263	−	0.105065i
$529$		−	23.0000i		−	1.00000i
$530$	5.65685	−	16.9706i	0.245718	−	0.737154i
$531$	28.0000	−	9.89949i	1.21510	−	0.429601i
$532$	24.0000	+	24.0000i	1.04053	+	1.04053i
$533$	−16.9706	−	16.9706i	−0.735077	−	0.735077i
$534$	−2.82843	+	4.00000i	−0.122398	+	0.173097i
$535$	20.0000	+	40.0000i	0.864675	+	1.72935i
$536$			14.1421i			0.610847i
$537$	36.2132	−	6.21320i	1.56272	−	0.268120i
$538$	13.0000	−	13.0000i	0.560470	−	0.560470i
$539$	−15.5563			−0.670059
$540$	−11.4142	+	2.17157i	−0.491190	+	0.0934496i
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	−5.65685	+	5.65685i	−0.242983	+	0.242983i
$543$	−3.41421	+	0.585786i	−0.146518	+	0.0251385i
$544$		−	1.00000i		−	0.0428746i
$545$	4.24264	+	1.41421i	0.181735	+	0.0605783i
$546$	−12.0000	+	16.9706i	−0.513553	+	0.726273i
$547$	−26.0000	−	26.0000i	−1.11168	−	1.11168i	−0.992923	−	0.118756i	$-0.962109\pi$
$547$	−26.0000	−	26.0000i	−1.11168	−	1.11168i	−0.118756	−	0.992923i	$-0.537891\pi$
$548$	4.24264	+	4.24264i	0.181237	+	0.181237i
$549$	28.2843	−	10.0000i	1.20714	−	0.426790i
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$			33.9411i			1.44594i
$552$		0			0
$553$	−42.0000	+	42.0000i	−1.78602	+	1.78602i
$554$	14.1421			0.600842
$555$	−8.82843	+	6.48528i	−0.374746	+	0.275285i
$556$	12.0000			0.508913
$557$	−8.48528	+	8.48528i	−0.359533	+	0.359533i	−0.863641	−	0.504108i	$-0.831821\pi$
$557$	−8.48528	+	8.48528i	−0.359533	+	0.359533i	0.504108	+	0.863641i	$0.331821\pi$
$558$	−12.9289	+	27.0711i	−0.547325	+	1.14601i
$559$		0			0
$560$	8.48528	−	4.24264i	0.358569	−	0.179284i
$561$	2.00000	+	1.41421i	0.0844401	+	0.0597081i
$562$	14.0000	+	14.0000i	0.590554	+	0.590554i
$563$	−7.07107	−	7.07107i	−0.298010	−	0.298010i	0.542224	−	0.840234i	$-0.317582\pi$
$563$	−7.07107	−	7.07107i	−0.298010	−	0.298010i	−0.840234	+	0.542224i	$0.817582\pi$
$564$	−5.65685	−	4.00000i	−0.238197	−	0.168430i
$565$	4.00000	−	2.00000i	0.168281	−	0.0841406i
$566$			28.2843i			1.18888i
$567$	−37.9706	−	4.02944i	−1.59461	−	0.169220i
$568$	−8.00000	+	8.00000i	−0.335673	+	0.335673i
$569$	−2.82843			−0.118574			−0.0592869	−	0.998241i	$-0.518883\pi$
$569$	−2.82843			−0.118574			−0.0592869	+	0.998241i	$0.518883\pi$
$570$	24.9706	−	18.3431i	1.04590	−	0.768310i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	−2.82843	+	2.82843i	−0.118262	+	0.118262i
$573$	−0.828427	−	4.82843i	−0.0346080	−	0.201710i
$574$			36.0000i			1.50261i
$575$		0			0
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	0.869177	−	0.494502i	$-0.164649\pi$
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	−0.494502	+	0.869177i	$0.664649\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	4.24264	−	6.00000i	0.176318	−	0.249351i
$580$	9.00000	+	3.00000i	0.373705	+	0.124568i
$581$		−	50.9117i		−	2.11217i
$582$	7.24264	−	1.24264i	0.300217	−	0.0515091i
$583$	8.00000	−	8.00000i	0.331326	−	0.331326i
$584$	−4.24264			−0.175562
$585$	13.6569	+	13.1716i	0.564641	+	0.544578i
$586$	−4.00000			−0.165238
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	−0.860193	−	0.509968i	$-0.829657\pi$
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	0.509968	+	0.860193i	$0.329657\pi$
$588$	18.7782	−	3.22183i	0.774399	−	0.132866i
$589$		−	80.0000i		−	3.29634i
$590$	9.89949	+	19.7990i	0.407556	+	0.815112i
$591$	−16.0000	+	22.6274i	−0.658152	+	0.930768i
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$	−4.24264	−	4.24264i	−0.174224	−	0.174224i	0.614608	−	0.788833i	$-0.289314\pi$
$593$	−4.24264	−	4.24264i	−0.174224	−	0.174224i	−0.788833	+	0.614608i	$0.789314\pi$
$594$	−7.07107	−	2.00000i	−0.290129	−	0.0820610i
$595$	−3.00000	+	9.00000i	−0.122988	+	0.368964i
$596$		−	1.41421i		−	0.0579284i
$597$	4.68629	+	27.3137i	0.191797	+	1.11788i
$598$		0			0
$599$	−11.3137			−0.462266			−0.231133	−	0.972922i	$-0.574243\pi$
$599$	−11.3137			−0.462266			−0.231133	+	0.972922i	$0.574243\pi$
$600$	−2.65685	−	8.24264i	−0.108466	−	0.336504i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	38.2843	+	18.2843i	1.55906	+	0.744593i
$604$		0			0
$605$	6.36396	−	19.0919i	0.258732	−	0.776195i
$606$	−6.00000	−	4.24264i	−0.243733	−	0.172345i
$607$	−19.0000	−	19.0000i	−0.771186	−	0.771186i	0.207128	−	0.978314i	$-0.433588\pi$
$607$	−19.0000	−	19.0000i	−0.771186	−	0.771186i	−0.978314	+	0.207128i	$0.933588\pi$
$608$	−5.65685	−	5.65685i	−0.229416	−	0.229416i
$609$	25.4558	+	18.0000i	1.03152	+	0.729397i
$610$	10.0000	+	20.0000i	0.404888	+	0.809776i
$611$			11.3137i			0.457704i
$612$	−2.70711	−	1.29289i	−0.109428	−	0.0522621i
$613$	16.0000	−	16.0000i	0.646234	−	0.646234i	−0.305847	−	0.952081i	$-0.598940\pi$
$613$	16.0000	−	16.0000i	0.646234	−	0.646234i	0.952081	+	0.305847i	$0.0989395\pi$
$614$	−11.3137			−0.456584
$615$	32.4853	+	4.97056i	1.30993	+	0.200432i
$616$	6.00000			0.241747
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	−0.787332	−	0.616530i	$-0.788538\pi$
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	0.616530	+	0.787332i	$0.288538\pi$
$618$	−1.24264	−	7.24264i	−0.0499863	−	0.291342i
$619$		−	40.0000i		−	1.60774i	−0.594808	−	0.803868i	$-0.702772\pi$
$619$		−	40.0000i		−	1.60774i	0.594808	−	0.803868i	$-0.297228\pi$
$620$	−21.2132	−	7.07107i	−0.851943	−	0.283981i
$621$		0			0
$622$	−4.00000	−	4.00000i	−0.160385	−	0.160385i
$623$	−8.48528	−	8.48528i	−0.339956	−	0.339956i
$624$	2.82843	−	4.00000i	0.113228	−	0.160128i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		−	29.6985i		−	1.18699i
$627$	19.3137	−	3.31371i	0.771315	−	0.132337i
$628$	−10.0000	+	10.0000i	−0.399043	+	0.399043i
$629$	−2.82843			−0.112777
$630$	−0.514719	−	28.4558i	−0.0205069	−	1.13371i
$631$	−30.0000			−1.19428			−0.597141	−	0.802137i	$-0.703697\pi$
$631$	−30.0000			−1.19428			−0.597141	+	0.802137i	$0.703697\pi$
$632$	9.89949	−	9.89949i	0.393781	−	0.393781i
$633$	−13.6569	+	2.34315i	−0.542811	+	0.0931317i
$634$			2.00000i			0.0794301i
$635$	−8.48528	+	4.24264i	−0.336728	+	0.168364i
$636$	−8.00000	+	11.3137i	−0.317221	+	0.448618i
$637$	−22.0000	−	22.0000i	−0.871672	−	0.871672i
$638$	4.24264	+	4.24264i	0.167968	+	0.167968i
$639$	11.3137	+	32.0000i	0.447563	+	1.26590i
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$		−	19.7990i		−	0.782013i	−0.920388	−	0.391007i	$-0.872127\pi$
$641$		−	19.7990i		−	0.782013i	0.920388	−	0.391007i	$-0.127873\pi$
$642$	−5.85786	−	34.1421i	−0.231191	−	1.34748i
$643$	28.0000	−	28.0000i	1.10421	−	1.10421i	0.110316	−	0.993897i	$-0.464814\pi$
$643$	28.0000	−	28.0000i	1.10421	−	1.10421i	0.993897	−	0.110316i	$-0.0351862\pi$
$644$		0			0
$645$		0			0
$646$	8.00000			0.314756
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	−0.853948	−	0.520358i	$-0.825799\pi$
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	0.520358	+	0.853948i	$0.325799\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$			14.0000i			0.549548i
$650$	−8.48528	+	11.3137i	−0.332820	+	0.443760i
$651$	−60.0000	−	42.4264i	−2.35159	−	1.66282i
$652$	−4.00000	−	4.00000i	−0.156652	−	0.156652i
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$	−2.82843	−	2.00000i	−0.110600	−	0.0782062i
$655$	−21.0000	−	7.00000i	−0.820538	−	0.273513i
$656$		−	8.48528i		−	0.331295i
$657$	−5.48528	+	11.4853i	−0.214001	+	0.448084i
$658$	12.0000	−	12.0000i	0.467809	−	0.467809i
$659$	−24.0416			−0.936529			−0.468264	−	0.883588i	$-0.655121\pi$
$659$	−24.0416			−0.936529			−0.468264	+	0.883588i	$0.655121\pi$
$660$	0.828427	−	5.41421i	0.0322465	−	0.210748i
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$		0			0
$663$	0.828427	+	4.82843i	0.0321734	+	0.187521i
$664$			12.0000i			0.465690i
$665$	33.9411	+	67.8823i	1.31618	+	2.63236i
$666$	8.00000	−	2.82843i	0.309994	−	0.109599i
$667$		0			0
$668$	−11.3137	−	11.3137i	−0.437741	−	0.437741i
$669$	4.24264	−	6.00000i	0.164030	−	0.231973i
$670$	−10.0000	+	30.0000i	−0.386334	+	1.15900i
$671$			14.1421i			0.545951i
$672$	−7.24264	+	1.24264i	−0.279391	+	0.0479359i
$673$	−17.0000	+	17.0000i	−0.655302	+	0.655302i	−0.954265	−	0.298963i	$-0.903359\pi$
$673$	−17.0000	+	17.0000i	−0.655302	+	0.655302i	0.298963	+	0.954265i	$0.403359\pi$
$674$	−1.41421			−0.0544735
$675$	−25.7487	−	3.46447i	−0.991069	−	0.133347i
$676$	5.00000			0.192308
$677$	9.89949	−	9.89949i	0.380468	−	0.380468i	−0.490802	−	0.871271i	$-0.663296\pi$
$677$	9.89949	−	9.89949i	0.380468	−	0.380468i	0.871271	+	0.490802i	$0.163296\pi$
$678$	−3.41421	+	0.585786i	−0.131122	+	0.0224970i
$679$			18.0000i			0.690777i
$680$	0.707107	−	2.12132i	0.0271163	−	0.0813489i
$681$	2.00000	−	2.82843i	0.0766402	−	0.108386i
$682$	−10.0000	−	10.0000i	−0.382920	−	0.382920i
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	0.0256307	−	0.999671i	$-0.491841\pi$
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	−0.999671	+	0.0256307i	$0.991841\pi$
$684$	−22.6274	+	8.00000i	−0.865181	+	0.305888i
$685$	6.00000	+	12.0000i	0.229248	+	0.458496i
$686$			16.9706i			0.647939i
$687$	−0.585786	−	3.41421i	−0.0223491	−	0.130260i
$688$		0			0
$689$	22.6274			0.862036
$690$		0			0
$691$	−36.0000			−1.36950			−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000			−1.36950			−0.684752	+	0.728776i	$0.740090\pi$
$692$	−9.89949	+	9.89949i	−0.376322	+	0.376322i
$693$	7.75736	−	16.2426i	0.294678	−	0.617007i
$694$		−	14.0000i		−	0.531433i
$695$	25.4558	+	8.48528i	0.965595	+	0.321865i
$696$	−6.00000	−	4.24264i	−0.227429	−	0.160817i
$697$	6.00000	+	6.00000i	0.227266	+	0.227266i
$698$	−4.24264	−	4.24264i	−0.160586	−	0.160586i
$699$	14.1421	+	10.0000i	0.534905	+	0.378235i
$700$	21.0000	−	3.00000i	0.793725	−	0.113389i
$701$			7.07107i			0.267071i	0.991044	+	0.133535i	$0.0426329\pi$
$701$			7.07107i			0.267071i	−0.991044	+	0.133535i	$0.957367\pi$
$702$	−7.17157	−	12.8284i	−0.270674	−	0.484178i
$703$	−16.0000	+	16.0000i	−0.603451	+	0.603451i
$704$	−1.41421			−0.0533002
$705$	−9.17157	−	12.4853i	−0.345421	−	0.470223i
$706$	−22.0000			−0.827981
$707$	12.7279	−	12.7279i	0.478683	−	0.478683i
$708$	−2.89949	−	16.8995i	−0.108970	−	0.635122i
$709$			34.0000i			1.27690i	0.769665	+	0.638448i	$0.220423\pi$
$709$			34.0000i			1.27690i	−0.769665	+	0.638448i	$0.779577\pi$
$710$	−22.6274	+	11.3137i	−0.849192	+	0.424596i
$711$	−14.0000	−	39.5980i	−0.525041	−	1.48504i
$712$	2.00000	+	2.00000i	0.0749532	+	0.0749532i
$713$		0			0
$714$	4.24264	−	6.00000i	0.158777	−	0.224544i
$715$	−8.00000	+	4.00000i	−0.299183	+	0.149592i
$716$		−	21.2132i		−	0.792775i
$717$	4.82843	−	0.828427i	0.180321	−	0.0309382i
$718$	4.00000	−	4.00000i	0.149279	−	0.149279i
$719$	−19.7990			−0.738378			−0.369189	−	0.929354i	$-0.620364\pi$
$719$	−19.7990			−0.738378			−0.369189	+	0.929354i	$0.620364\pi$
$720$	0.121320	+	6.70711i	0.00452134	+	0.249959i
$721$	18.0000			0.670355
$722$	31.8198	−	31.8198i	1.18421	−	1.18421i
$723$		0			0
$724$			2.00000i			0.0743294i
$725$	16.9706	+	12.7279i	0.630271	+	0.472703i
$726$	−9.00000	+	12.7279i	−0.334021	+	0.472377i
$727$	17.0000	+	17.0000i	0.630495	+	0.630495i	0.948192	−	0.317697i	$-0.102910\pi$
$727$	17.0000	+	17.0000i	0.630495	+	0.630495i	−0.317697	+	0.948192i	$0.602910\pi$
$728$	8.48528	+	8.48528i	0.314485	+	0.314485i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−9.00000	−	3.00000i	−0.333105	−	0.111035i
$731$		0			0
$732$	−2.92893	−	17.0711i	−0.108256	−	0.630965i
$733$	16.0000	−	16.0000i	0.590973	−	0.590973i	−0.346921	−	0.937894i	$-0.612773\pi$
$733$	16.0000	−	16.0000i	0.590973	−	0.590973i	0.937894	+	0.346921i	$0.112773\pi$
$734$	7.07107			0.260998
$735$	42.1127	+	6.44365i	1.55335	+	0.237678i
$736$		0			0
$737$	−14.1421	+	14.1421i	−0.520932	+	0.520932i
$738$	−22.9706	−	10.9706i	−0.845558	−	0.403832i
$739$		−	40.0000i		−	1.47142i	−0.677295	−	0.735712i	$-0.736848\pi$
$739$		−	40.0000i		−	1.47142i	0.677295	−	0.735712i	$-0.263152\pi$
$740$	2.82843	+	5.65685i	0.103975	+	0.207950i
$741$	32.0000	+	22.6274i	1.17555	+	0.831239i
$742$	−24.0000	−	24.0000i	−0.881068	−	0.881068i
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.957824	+	0.287355i	$0.0927759\pi$
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.287355	+	0.957824i	$0.407224\pi$
$744$	14.1421	+	10.0000i	0.518476	+	0.366618i
$745$	1.00000	−	3.00000i	0.0366372	−	0.109911i
$746$			8.48528i			0.310668i
$747$	32.4853	+	15.5147i	1.18857	+	0.567654i
$748$	1.00000	−	1.00000i	0.0365636	−	0.0365636i
$749$	84.8528			3.10045
$750$	0.192388	−	19.3640i	0.00702502	−	0.707072i
$751$	6.00000			0.218943			0.109472	−	0.993990i	$-0.465084\pi$
$751$	6.00000			0.218943			0.109472	+	0.993990i	$0.465084\pi$
$752$	−2.82843	+	2.82843i	−0.103142	+	0.103142i
$753$	−4.55635	−	26.5563i	−0.166043	−	0.967767i
$754$			12.0000i			0.437014i
$755$		0			0
$756$	−6.00000	+	21.2132i	−0.218218	+	0.771517i
$757$	12.0000	+	12.0000i	0.436147	+	0.436147i	0.890713	−	0.454566i	$-0.150206\pi$
$757$	12.0000	+	12.0000i	0.436147	+	0.436147i	−0.454566	+	0.890713i	$0.650206\pi$
$758$	19.7990	+	19.7990i	0.719132	+	0.719132i
$759$		0			0
$760$	−8.00000	−	16.0000i	−0.290191	−	0.580381i
$761$			19.7990i			0.717713i	0.933393	+	0.358856i	$0.116833\pi$
$761$			19.7990i			0.717713i	−0.933393	+	0.358856i	$0.883167\pi$
$762$	7.24264	−	1.24264i	0.262373	−	0.0450161i
$763$	6.00000	−	6.00000i	0.217215	−	0.217215i
$764$	−2.82843			−0.102329
$765$	−4.82843	−	4.65685i	−0.174572	−	0.168369i
$766$	16.0000			0.578103
$767$	−19.7990	+	19.7990i	−0.714900	+	0.714900i
$768$	1.70711	−	0.292893i	0.0615999	−	0.0105689i
$769$			2.00000i			0.0721218i	0.999350	+	0.0360609i	$0.0114810\pi$
$769$			2.00000i			0.0721218i	−0.999350	+	0.0360609i	$0.988519\pi$
$770$	12.7279	+	4.24264i	0.458682	+	0.152894i
$771$	6.00000	−	8.48528i	0.216085	−	0.305590i
$772$	−3.00000	−	3.00000i	−0.107972	−	0.107972i
$773$	−18.3848	−	18.3848i	−0.661254	−	0.661254i	0.294421	−	0.955676i	$-0.404873\pi$
$773$	−18.3848	−	18.3848i	−0.661254	−	0.661254i	−0.955676	+	0.294421i	$0.904873\pi$
$774$		0			0
$775$	−40.0000	−	30.0000i	−1.43684	−	1.07763i
$776$		−	4.24264i		−	0.152302i
$777$	3.51472	+	20.4853i	0.126090	+	0.734905i
$778$	−11.0000	+	11.0000i	−0.394369	+	0.394369i
$779$	67.8823			2.43213
$780$	8.82843	−	6.48528i	0.316108	−	0.232210i
$781$	−16.0000			−0.572525
$782$		0			0
$783$	−19.2426	+	10.7574i	−0.687676	+	0.384437i
$784$		−	11.0000i		−	0.392857i
$785$	−28.2843	+	14.1421i	−1.00951	+	0.504754i
$786$	14.0000	+	9.89949i	0.499363	+	0.353103i
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	0.999998	−	0.00190598i	$-0.000606691\pi$
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	−0.00190598	+	0.999998i	$0.500607\pi$
$788$	11.3137	+	11.3137i	0.403034	+	0.403034i
$789$	−22.6274	−	16.0000i	−0.805557	−	0.569615i
$790$	28.0000	−	14.0000i	0.996195	−	0.498098i
$791$		−	8.48528i		−	0.301702i
$792$	−1.82843	+	3.82843i	−0.0649703	+	0.136037i
$793$	−20.0000	+	20.0000i	−0.710221	+	0.710221i
$794$	−25.4558			−0.903394
$795$	−24.9706	+	18.3431i	−0.885615	+	0.650564i
$796$	16.0000			0.567105
$797$	26.8701	−	26.8701i	0.951786	−	0.951786i	−0.0471037	−	0.998890i	$-0.514999\pi$
$797$	26.8701	−	26.8701i	0.951786	−	0.951786i	0.998890	+	0.0471037i	$0.0149991\pi$
$798$	−9.94113	−	57.9411i	−0.351912	−	2.05109i
$799$		−	4.00000i		−	0.141510i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$	8.00000	−	2.82843i	0.282666	−	0.0999376i
$802$	−20.0000	−	20.0000i	−0.706225	−	0.706225i
$803$	−4.24264	−	4.24264i	−0.149720	−	0.149720i
$804$	14.1421	−	20.0000i	0.498755	−	0.705346i
$805$		0			0
$806$		−	28.2843i		−	0.996271i
$807$	−31.3848	+	5.38478i	−1.10480	+	0.189553i
$808$	−3.00000	+	3.00000i	−0.105540	+	0.105540i
$809$	−25.4558			−0.894980			−0.447490	−	0.894289i	$-0.647682\pi$
$809$	−25.4558			−0.894980			−0.447490	+	0.894289i	$0.647682\pi$
$810$	18.3137	+	8.34315i	0.643478	+	0.293148i
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	12.7279	−	12.7279i	0.446663	−	0.446663i
$813$	13.6569	−	2.34315i	0.478967	−	0.0821777i
$814$			4.00000i			0.140200i
$815$	−5.65685	−	11.3137i	−0.198151	−	0.396302i
$816$	−1.00000	+	1.41421i	−0.0350070	+	0.0495074i
$817$		0			0
$818$	−11.3137	−	11.3137i	−0.395575	−	0.395575i
$819$	33.9411	−	12.0000i	1.18600	−	0.419314i
$820$	6.00000	−	18.0000i	0.209529	−	0.628587i
$821$			26.8701i			0.937771i	0.883259	+	0.468886i	$0.155344\pi$
$821$			26.8701i			0.937771i	−0.883259	+	0.468886i	$0.844656\pi$
$822$	−1.75736	−	10.2426i	−0.0612949	−	0.357253i
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	−0.239004	−	0.971018i	$-0.576821\pi$
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	0.971018	+	0.239004i	$0.0768211\pi$
$824$	−4.24264			−0.147799
$825$	5.58579	−	10.8995i	0.194472	−	0.379472i
$826$	42.0000			1.46137
$827$	−26.8701	+	26.8701i	−0.934363	+	0.934363i	−0.997975	−	0.0636113i	$-0.979738\pi$
$827$	−26.8701	+	26.8701i	−0.934363	+	0.934363i	0.0636113	+	0.997975i	$0.479738\pi$
$828$		0			0
$829$			26.0000i			0.903017i	0.892267	+	0.451509i	$0.149114\pi$
$829$			26.0000i			0.903017i	−0.892267	+	0.451509i	$0.850886\pi$
$830$	−8.48528	+	25.4558i	−0.294528	+	0.883585i
$831$	−20.0000	−	14.1421i	−0.693792	−	0.490585i
$832$	−2.00000	−	2.00000i	−0.0693375	−	0.0693375i
$833$	7.77817	+	7.77817i	0.269498	+	0.269498i
$834$	−16.9706	−	12.0000i	−0.587643	−	0.415526i
$835$	−16.0000	−	32.0000i	−0.553703	−	1.10741i
$836$		−	11.3137i		−	0.391293i
$837$	45.3553	−	25.3553i	1.56771	−	0.876409i
$838$	27.0000	−	27.0000i	0.932700	−	0.932700i
$839$	−8.48528			−0.292944			−0.146472	−	0.989215i	$-0.546792\pi$
$839$	−8.48528			−0.292944			−0.146472	+	0.989215i	$0.546792\pi$
$840$	−16.2426	−	2.48528i	−0.560424	−	0.0857504i
$841$	−11.0000			−0.379310
$842$	−18.3848	+	18.3848i	−0.633581	+	0.633581i
$843$	−5.79899	−	33.7990i	−0.199728	−	1.16410i
$844$			8.00000i			0.275371i
$845$	10.6066	+	3.53553i	0.364878	+	0.121626i
$846$	4.00000	+	11.3137i	0.137523	+	0.388973i
$847$	−27.0000	−	27.0000i	−0.927731	−	0.927731i
$848$	5.65685	+	5.65685i	0.194257	+	0.194257i
$849$	28.2843	−	40.0000i	0.970714	−	1.37280i
$850$	3.00000	−	4.00000i	0.102899	−	0.137199i
$851$		0			0
$852$	19.3137	−	3.31371i	0.661677	−	0.113526i
$853$	−18.0000	+	18.0000i	−0.616308	+	0.616308i	−0.944582	−	0.328274i	$-0.893533\pi$
$853$	−18.0000	+	18.0000i	−0.616308	+	0.616308i	0.328274	+	0.944582i	$0.393533\pi$
$854$	42.4264			1.45180
$855$	−53.6569	+	0.970563i	−1.83503	+	0.0331925i
$856$	−20.0000			−0.683586
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	−0.890250	−	0.455472i	$-0.849470\pi$
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	0.455472	+	0.890250i	$0.349470\pi$
$858$	6.82843	−	1.17157i	0.233119	−	0.0399968i
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$		0			0
$861$	36.0000	−	50.9117i	1.22688	−	1.73507i
$862$	22.0000	+	22.0000i	0.749323	+	0.749323i
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	0.934265	−	0.356580i	$-0.116057\pi$
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	−0.356580	+	0.934265i	$0.616057\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	−28.0000	+	14.0000i	−0.952029	+	0.476014i
$866$			4.24264i			0.144171i
$867$	−0.292893	−	1.70711i	−0.00994718	−	0.0579764i
$868$	−30.0000	+	30.0000i	−1.01827	+	1.01827i
$869$	19.7990			0.671635
$870$	−9.72792	−	13.2426i	−0.329807	−	0.448968i
$871$	−40.0000			−1.35535
$872$	−1.41421	+	1.41421i	−0.0478913	+	0.0478913i
$873$	−11.4853	−	5.48528i	−0.388718	−	0.185649i
$874$		0			0
$875$	46.6690	+	8.48528i	1.57770	+	0.286855i
$876$	6.00000	+	4.24264i	0.202721	+	0.143346i
$877$	−40.0000	−	40.0000i	−1.35070	−	1.35070i	−0.884874	−	0.465830i	$-0.845756\pi$
$877$	−40.0000	−	40.0000i	−1.35070	−	1.35070i	−0.465830	−	0.884874i	$-0.654244\pi$
$878$	−22.6274	−	22.6274i	−0.763638	−	0.763638i
$879$	5.65685	+	4.00000i	0.190801	+	0.134917i
$880$	−3.00000	−	1.00000i	−0.101130	−	0.0337100i
$881$			39.5980i			1.33409i	0.745018	+	0.667045i	$0.232441\pi$
$881$			39.5980i			1.33409i	−0.745018	+	0.667045i	$0.767559\pi$
$882$	−29.7782	−	14.2218i	−1.00268	−	0.478874i
$883$	−10.0000	+	10.0000i	−0.336527	+	0.336527i	−0.855058	−	0.518532i	$-0.826479\pi$
$883$	−10.0000	+	10.0000i	−0.336527	+	0.336527i	0.518532	+	0.855058i	$0.326479\pi$
$884$	2.82843			0.0951303
$885$	5.79899	−	37.8995i	0.194931	−	1.27398i
$886$	−42.0000			−1.41102
$887$	11.3137	−	11.3137i	0.379877	−	0.379877i	−0.491181	−	0.871058i	$-0.663434\pi$
$887$	11.3137	−	11.3137i	0.379877	−	0.379877i	0.871058	+	0.491181i	$0.163434\pi$
$888$	−0.828427	−	4.82843i	−0.0278002	−	0.162031i
$889$			18.0000i			0.603701i
$890$	2.82843	+	5.65685i	0.0948091	+	0.189618i
$891$	8.00000	+	9.89949i	0.268010	+	0.331646i
$892$	−3.00000	−	3.00000i	−0.100447	−	0.100447i
$893$	−22.6274	−	22.6274i	−0.757198	−	0.757198i
$894$	−1.41421	+	2.00000i	−0.0472984	+	0.0668900i
$895$	15.0000	−	45.0000i	0.501395	−	1.50418i
$896$			4.24264i			0.141737i
$897$		0			0
$898$	12.0000	−	12.0000i	0.400445	−	0.400445i
$899$	−42.4264			−1.41500
$900$	−4.48528	+	14.3137i	−0.149509	+	0.477124i
$901$	−8.00000			−0.266519
$902$	8.48528	−	8.48528i	0.282529	−	0.282529i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$	−1.41421	+	4.24264i	−0.0470100	+	0.141030i
$906$		0			0
$907$	6.00000	+	6.00000i	0.199227	+	0.199227i	0.799668	−	0.600442i	$-0.205009\pi$
$907$	6.00000	+	6.00000i	0.199227	+	0.199227i	−0.600442	+	0.799668i	$0.705009\pi$
$908$	−1.41421	−	1.41421i	−0.0469323	−	0.0469323i
$909$	4.24264	+	12.0000i	0.140720	+	0.398015i
$910$	12.0000	+	24.0000i	0.397796	+	0.795592i
$911$			2.82843i			0.0937100i	0.998902	+	0.0468550i	$0.0149199\pi$
$911$			2.82843i			0.0937100i	−0.998902	+	0.0468550i	$0.985080\pi$
$912$	2.34315	+	13.6569i	0.0775893	+	0.452224i
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	−18.3848			−0.608114
$915$	5.85786	−	38.2843i	0.193655	−	1.26564i
$916$	−2.00000			−0.0660819
$917$	−29.6985	+	29.6985i	−0.980730	+	0.980730i
$918$	2.53553	+	4.53553i	0.0836851	+	0.149695i
$919$			38.0000i			1.25350i	0.779219	+	0.626752i	$0.215616\pi$
$919$			38.0000i			1.25350i	−0.779219	+	0.626752i	$0.784384\pi$
$920$		0			0
$921$	16.0000	+	11.3137i	0.527218	+	0.372799i
$922$	−25.0000	−	25.0000i	−0.823331	−	0.823331i
$923$	−22.6274	−	22.6274i	−0.744791	−	0.744791i
$924$	−8.48528	−	6.00000i	−0.279145	−	0.197386i
$925$	2.00000	+	14.0000i	0.0657596	+	0.460317i
$926$			12.7279i			0.418265i
$927$	−5.48528	+	11.4853i	−0.180160	+	0.377226i
$928$	−3.00000	+	3.00000i	−0.0984798	+	0.0984798i
$929$	56.5685			1.85595			0.927977	−	0.372638i	$-0.121547\pi$
$929$	56.5685			1.85595			0.927977	+	0.372638i	$0.121547\pi$
$930$	22.9289	+	31.2132i	0.751869	+	1.02352i
$931$	88.0000			2.88408
$932$	7.07107	−	7.07107i	0.231621	−	0.231621i
$933$	1.65685	+	9.65685i	0.0542430	+	0.316151i
$934$			4.00000i			0.130884i
$935$	2.82843	−	1.41421i	0.0924995	−	0.0462497i
$936$	−8.00000	+	2.82843i	−0.261488	+	0.0924500i
$937$	23.0000	+	23.0000i	0.751377	+	0.751377i	0.974736	−	0.223359i	$-0.0717022\pi$
$937$	23.0000	+	23.0000i	0.751377	+	0.751377i	−0.223359	+	0.974736i	$0.571702\pi$
$938$	42.4264	+	42.4264i	1.38527	+	1.38527i
$939$	−29.6985	+	42.0000i	−0.969173	+	1.37062i
$940$	−8.00000	+	4.00000i	−0.260931	+	0.130466i
$941$			18.3848i			0.599327i	0.954045	+	0.299663i	$0.0968743\pi$
$941$			18.3848i			0.599327i	−0.954045	+	0.299663i	$0.903126\pi$
$942$	24.1421	−	4.14214i	0.786593	−	0.134958i
$943$		0			0
$944$	−9.89949			−0.322201
$945$	−27.7279	+	40.7574i	−0.901989	+	1.32584i
$946$		0			0
$947$	−32.5269	+	32.5269i	−1.05698	+	1.05698i	−0.0587074	+	0.998275i	$0.518698\pi$
$947$	−32.5269	+	32.5269i	−1.05698	+	1.05698i	−0.998275	+	0.0587074i	$0.981302\pi$
$948$	−23.8995	+	4.10051i	−0.776220	+	0.133178i
$949$		−	12.0000i		−	0.389536i
$950$	−5.65685	−	39.5980i	−0.183533	−	1.28473i
$951$	2.00000	−	2.82843i	0.0648544	−	0.0917180i
$952$	−3.00000	−	3.00000i	−0.0972306	−	0.0972306i
$953$	−21.2132	−	21.2132i	−0.687163	−	0.687163i	0.274441	−	0.961604i	$-0.411507\pi$
$953$	−21.2132	−	21.2132i	−0.687163	−	0.687163i	−0.961604	+	0.274441i	$0.911507\pi$
$954$	22.6274	−	8.00000i	0.732590	−	0.259010i
$955$	−6.00000	−	2.00000i	−0.194155	−	0.0647185i
$956$		−	2.82843i		−	0.0914779i
$957$	−1.75736	−	10.2426i	−0.0568074	−	0.331098i
$958$	20.0000	−	20.0000i	0.646171	−	0.646171i
$959$	25.4558			0.822012
$960$	3.82843	+	0.585786i	0.123562	+	0.0189062i
$961$	69.0000			2.22581
$962$	−5.65685	+	5.65685i	−0.182384	+	0.182384i
$963$	−25.8579	+	54.1421i	−0.833258	+	1.74471i
$964$		0			0
$965$	−4.24264	−	8.48528i	−0.136575	−	0.273151i
$966$		0			0
$967$	−29.0000	−	29.0000i	−0.932577	−	0.932577i	0.0652893	−	0.997866i	$-0.479203\pi$
$967$	−29.0000	−	29.0000i	−0.932577	−	0.932577i	−0.997866	+	0.0652893i	$0.979203\pi$
$968$	6.36396	+	6.36396i	0.204545	+	0.204545i
$969$	−11.3137	−	8.00000i	−0.363449	−	0.256997i
$970$	3.00000	−	9.00000i	0.0963242	−	0.288973i
$971$		−	52.3259i		−	1.67922i	−0.543191	−	0.839609i	$-0.682784\pi$
$971$		−	52.3259i		−	1.67922i	0.543191	−	0.839609i	$-0.317216\pi$
$972$	−11.7071	−	10.2929i	−0.375506	−	0.330145i
$973$	36.0000	−	36.0000i	1.15411	−	1.15411i
$974$	−32.5269			−1.04223
$975$	23.3137	−	7.51472i	0.746636	−	0.240664i
$976$	−10.0000			−0.320092
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	−0.0486759	−	0.998815i	$-0.515500\pi$
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	0.998815	+	0.0486759i	$0.0155002\pi$
$978$	1.65685	+	9.65685i	0.0529804	+	0.308792i
$979$			4.00000i			0.127841i
$980$	7.77817	−	23.3345i	0.248465	−	0.745394i
$981$	2.00000	+	5.65685i	0.0638551	+	0.180609i
$982$	−19.0000	−	19.0000i	−0.606314	−	0.606314i
$983$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$983$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$984$	−8.48528	+	12.0000i	−0.270501	+	0.382546i
$985$	16.0000	+	32.0000i	0.509802	+	1.01960i
$986$		−	4.24264i		−	0.135113i
$987$	−28.9706	+	4.97056i	−0.922143	+	0.158215i
$988$	16.0000	−	16.0000i	0.509028	−	0.509028i
$989$		0			0
$990$	−6.58579	+	6.82843i	−0.209310	+	0.217022i
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	7.07107	−	7.07107i	0.224507	−	0.224507i
$993$		0			0
$994$			48.0000i			1.52247i
$995$	33.9411	+	11.3137i	1.07601	+	0.358669i
$996$	12.0000	−	16.9706i	0.380235	−	0.537733i
$997$	24.0000	+	24.0000i	0.760088	+	0.760088i	0.976338	−	0.216250i	$-0.0693827\pi$
$997$	24.0000	+	24.0000i	0.760088	+	0.760088i	−0.216250	+	0.976338i	$0.569383\pi$
$998$	19.7990	+	19.7990i	0.626726	+	0.626726i
$999$	−14.1421	−	4.00000i	−0.447437	−	0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.a.137.1	✓	4
3.2	odd	2	inner	510.2.l.a.137.2	yes	4
5.3	odd	4	inner	510.2.l.a.443.2	yes	4
15.8	even	4	inner	510.2.l.a.443.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.a.137.1	✓	4	1.1	even	1	trivial
510.2.l.a.137.2	yes	4	3.2	odd	2	inner
510.2.l.a.443.1	yes	4	15.8	even	4	inner
510.2.l.a.443.2	yes	4	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} +1.41421i q^{11} +(-0.292893 - 1.70711i) q^{12} +(-2.00000 + 2.00000i) q^{13} +4.24264 q^{14} +(0.585786 - 3.82843i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.29289 + 2.70711i) q^{18} -8.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(-6.00000 - 4.24264i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} -2.82843i q^{26} +(4.53553 - 2.53553i) q^{27} +(-3.00000 + 3.00000i) q^{28} -4.24264 q^{29} +(2.29289 + 3.12132i) q^{30} +10.0000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.414214 + 2.41421i) q^{33} +1.00000i q^{34} +(-8.48528 + 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(5.65685 + 5.65685i) q^{38} +(-2.82843 + 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} +8.48528i q^{41} +(7.24264 - 1.24264i) q^{42} +1.41421 q^{44} +(-0.121320 - 6.70711i) q^{45} +(2.82843 - 2.82843i) q^{47} +(-1.70711 + 0.292893i) q^{48} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(1.00000 - 1.41421i) q^{51} +(2.00000 + 2.00000i) q^{52} +(-5.65685 - 5.65685i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} -4.24264i q^{56} +(-2.34315 - 13.6569i) q^{57} +(3.00000 - 3.00000i) q^{58} +9.89949 q^{59} +(-3.82843 - 0.585786i) q^{60} +10.0000 q^{61} +(-7.07107 + 7.07107i) q^{62} +(-11.4853 - 5.48528i) q^{63} +1.00000i q^{64} +(2.82843 + 5.65685i) q^{65} +(-2.00000 - 1.41421i) q^{66} +(10.0000 + 10.0000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(3.00000 - 9.00000i) q^{70} +11.3137i q^{71} +(2.70711 + 1.29289i) q^{72} +(-3.00000 + 3.00000i) q^{73} +2.82843 q^{74} +(-7.70711 - 3.94975i) q^{75} -8.00000 q^{76} +(4.24264 - 4.24264i) q^{77} +(-0.828427 - 4.82843i) q^{78} -14.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-6.00000 - 6.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(-4.24264 + 6.00000i) q^{84} +(-1.00000 - 2.00000i) q^{85} +(-7.24264 + 1.24264i) q^{87} +(-1.00000 + 1.00000i) q^{88} +2.82843 q^{89} +(4.82843 + 4.65685i) q^{90} +12.0000 q^{91} +(17.0711 - 2.92893i) q^{93} +4.00000i q^{94} +(-16.9706 - 5.65685i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +(1.41421 + 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} - 12 q^{7}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^6 - 12 * q^7	\( 4 q + 4 q^{3} - 4 q^{6} - 12 q^{7} + 4 q^{10} - 4 q^{12} - 8 q^{13} + 8 q^{15} - 4 q^{16} - 8 q^{18} - 24 q^{21} - 4 q^{22} - 16 q^{25} + 4 q^{27} - 12 q^{28} + 12 q^{30} + 40 q^{31} - 4 q^{33} - 4 q^{36} - 8 q^{37} + 8 q^{40} + 12 q^{42} + 8 q^{45} - 4 q^{48} + 4 q^{51} + 8 q^{52} + 12 q^{55} - 32 q^{57} + 12 q^{58} - 4 q^{60} + 40 q^{61} - 12 q^{63} - 8 q^{66} + 40 q^{67} + 12 q^{70} + 8 q^{72} - 12 q^{73} - 28 q^{75} - 32 q^{76} + 8 q^{78} + 28 q^{81} - 24 q^{82} - 4 q^{85} - 12 q^{87} - 4 q^{88} + 8 q^{90} + 48 q^{91} + 40 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 - 12 * q^7 + 4 * q^10 - 4 * q^12 - 8 * q^13 + 8 * q^15 - 4 * q^16 - 8 * q^18 - 24 * q^21 - 4 * q^22 - 16 * q^25 + 4 * q^27 - 12 * q^28 + 12 * q^30 + 40 * q^31 - 4 * q^33 - 4 * q^36 - 8 * q^37 + 8 * q^40 + 12 * q^42 + 8 * q^45 - 4 * q^48 + 4 * q^51 + 8 * q^52 + 12 * q^55 - 32 * q^57 + 12 * q^58 - 4 * q^60 + 40 * q^61 - 12 * q^63 - 8 * q^66 + 40 * q^67 + 12 * q^70 + 8 * q^72 - 12 * q^73 - 28 * q^75 - 32 * q^76 + 8 * q^78 + 28 * q^81 - 24 * q^82 - 4 * q^85 - 12 * q^87 - 4 * q^88 + 8 * q^90 + 48 * q^91 + 40 * q^93 + 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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