LMFDB - Embedded newform 510.2.l.a.137.2

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			137.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	510.137
Dual form			510.2.l.a.443.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) 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} +(-1.70711 - 0.292893i) q^{12} +(-2.00000 + 2.00000i) q^{13} -4.24264 q^{14} +(3.41421 + 1.82843i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.70711 + 1.29289i) 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} +(-2.53553 + 4.53553i) q^{27} +(-3.00000 + 3.00000i) q^{28} +4.24264 q^{29} +(3.70711 - 1.12132i) q^{30} +10.0000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.41421 - 0.414214i) 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} +(-1.24264 + 7.24264i) q^{42} -1.41421 q^{44} +(4.12132 - 5.29289i) q^{45} +(-2.82843 + 2.82843i) q^{47} +(-0.292893 + 1.70711i) 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} +(-13.6569 - 2.34315i) q^{57} +(3.00000 - 3.00000i) q^{58} -9.89949 q^{59} +(1.82843 - 3.41421i) q^{60} +10.0000 q^{61} +(7.07107 - 7.07107i) q^{62} +(5.48528 + 11.4853i) 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} +(1.29289 + 2.70711i) q^{72} +(-3.00000 + 3.00000i) q^{73} -2.82843 q^{74} +(-6.29289 + 5.94975i) q^{75} -8.00000 q^{76} +(-4.24264 + 4.24264i) q^{77} +(4.82843 + 0.828427i) 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} +(1.24264 - 7.24264i) q^{87} +(-1.00000 + 1.00000i) q^{88} -2.82843 q^{89} +(-0.828427 - 6.65685i) q^{90} +12.0000 q^{91} +(2.92893 - 17.0711i) 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
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$4$		−	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	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	−1.70711	−	0.292893i	−0.492799	−	0.0845510i
$13$	−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
$15$	3.41421	+	1.82843i	0.881546	+	0.472098i
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$		−	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
$27$	−2.53553	+	4.53553i	−0.487964	+	0.872864i
$28$	−3.00000	+	3.00000i	−0.566947	+	0.566947i
$29$	4.24264			0.787839			0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264			0.787839			0.393919	+	0.919145i	$0.371119\pi$
$30$	3.70711	−	1.12132i	0.676822	−	0.204724i
$31$	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
$33$	−2.41421	−	0.414214i	−0.420261	−	0.0721053i
$34$			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	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$	−1.24264	+	7.24264i	−0.191744	+	1.11756i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$	−1.41421			−0.213201
$45$	4.12132	−	5.29289i	0.614370	−	0.789018i
$46$		0			0
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	−0.882632	−	0.470064i	$-0.844231\pi$
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	0.470064	+	0.882632i	$0.344231\pi$
$48$	−0.292893	+	1.70711i	−0.0422755	+	0.246400i
$49$			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	0.979324	−	0.202296i	$-0.0648402\pi$
$53$	5.65685	+	5.65685i	0.777029	+	0.777029i	−0.202296	+	0.979324i	$0.564840\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$			4.24264i			0.566947i
$57$	−13.6569	−	2.34315i	−1.80889	−	0.310357i
$58$	3.00000	−	3.00000i	0.393919	−	0.393919i
$59$	−9.89949			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$60$	1.82843	−	3.41421i	0.236049	−	0.440773i
$61$	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
$63$	5.48528	+	11.4853i	0.691080	+	1.44701i
$64$			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	$-0.765717\pi$
$71$		−	11.3137i		−	1.34269i	0.741145	−	0.671345i	$-0.234283\pi$
$72$	1.29289	+	2.70711i	0.152369	+	0.319036i
$73$	−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
$75$	−6.29289	+	5.94975i	−0.726641	+	0.687018i
$76$	−8.00000			−0.917663
$77$	−4.24264	+	4.24264i	−0.483494	+	0.483494i
$78$	4.82843	+	0.828427i	0.546712	+	0.0938009i
$79$		−	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	0.0664117	−	0.997792i	$-0.478845\pi$
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	−0.997792	+	0.0664117i	$0.978845\pi$
$84$	4.24264	+	6.00000i	0.462910	+	0.654654i
$85$	−1.00000	−	2.00000i	−0.108465	−	0.216930i
$86$		0			0
$87$	1.24264	−	7.24264i	0.133225	−	0.776493i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	−2.82843			−0.299813			−0.149906	−	0.988700i	$-0.547897\pi$
$89$	−2.82843			−0.299813			−0.149906	+	0.988700i	$0.547897\pi$
$90$	−0.828427	−	6.65685i	−0.0873239	−	0.701694i
$91$	12.0000			1.25794
$92$		0			0
$93$	2.92893	−	17.0711i	0.303716	−	1.77019i
$94$			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	$-0.932302\pi$
$101$		−	4.24264i		−	0.422159i	0.977469	−	0.211079i	$-0.0676978\pi$
$102$	1.70711	+	0.292893i	0.169029	+	0.0290008i
$103$	−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
$105$	−4.75736	−	15.7279i	−0.464271	−	1.53489i
$106$	8.00000			0.777029
$107$	14.1421	−	14.1421i	1.36717	−	1.36717i	0.502726	−	0.864446i	$-0.332330\pi$
$107$	14.1421	−	14.1421i	1.36717	−	1.36717i	0.864446	−	0.502726i	$-0.167670\pi$
$108$	4.53553	+	2.53553i	0.436432	+	0.243982i
$109$			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	0.637452	−	0.770490i	$-0.279988\pi$
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	−0.770490	+	0.637452i	$0.779988\pi$
$114$	−11.3137	+	8.00000i	−1.05963	+	0.749269i
$115$		0			0
$116$		−	4.24264i		−	0.393919i
$117$	7.65685	−	3.65685i	0.707876	−	0.338076i
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	4.24264			0.388922
$120$	−1.12132	−	3.70711i	−0.102362	−	0.338411i
$121$	9.00000			0.818182
$122$	7.07107	−	7.07107i	0.640184	−	0.640184i
$123$	−14.4853	−	2.48528i	−1.30609	−	0.224090i
$124$		−	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	$0.142355\pi$
$131$			9.89949i			0.864923i	−0.901652	+	0.432461i	$0.857645\pi$
$132$	−0.414214	+	2.41421i	−0.0360527	+	0.210130i
$133$	−24.0000	+	24.0000i	−2.08106	+	2.08106i
$134$	14.1421			1.22169
$135$	−7.82843	−	8.58579i	−0.673764	−	0.738947i
$136$	1.00000			0.0857493
$137$	4.24264	−	4.24264i	0.362473	−	0.362473i	−0.502249	−	0.864723i	$-0.667494\pi$
$137$	4.24264	−	4.24264i	0.362473	−	0.362473i	0.864723	+	0.502249i	$0.167494\pi$
$138$		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
$147$	18.7782	+	3.22183i	1.54880	+	0.265732i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	−1.41421			−0.115857			−0.0579284	−	0.998321i	$-0.518450\pi$
$149$	−1.41421			−0.115857			−0.0579284	+	0.998321i	$0.518450\pi$
$150$	−0.242641	+	8.65685i	−0.0198115	+	0.706829i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−5.65685	+	5.65685i	−0.458831	+	0.458831i
$153$	2.70711	−	1.29289i	0.218857	−	0.104524i
$154$			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
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	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
$165$	2.58579	−	4.82843i	0.201303	−	0.375893i
$166$	−12.0000			−0.931381
$167$	−11.3137	+	11.3137i	−0.875481	+	0.875481i	−0.993063	−	0.117582i	$-0.962486\pi$
$167$	−11.3137	+	11.3137i	−0.875481	+	0.875481i	0.117582	+	0.993063i	$0.462486\pi$
$168$	7.24264	+	1.24264i	0.558782	+	0.0958718i
$169$			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	0.974972	−	0.222327i	$-0.0713654\pi$
$173$	9.89949	+	9.89949i	0.752645	+	0.752645i	−0.222327	+	0.974972i	$0.571365\pi$
$174$	−4.24264	−	6.00000i	−0.321634	−	0.454859i
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$			1.41421i			0.106600i
$177$	−2.89949	+	16.8995i	−0.217939	+	1.27024i
$178$	−2.00000	+	2.00000i	−0.149906	+	0.149906i
$179$	−21.2132			−1.58555			−0.792775	−	0.609515i	$-0.791364\pi$
$179$	−21.2132			−1.58555			−0.792775	+	0.609515i	$0.791364\pi$
$180$	−5.29289	−	4.12132i	−0.394509	−	0.307185i
$181$	−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
$183$	2.92893	−	17.0711i	0.216513	−	1.26193i
$184$		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	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	1.70711	+	0.292893i	0.123200	+	0.0211377i
$193$	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
$195$	−10.4853	+	3.17157i	−0.750867	+	0.227121i
$196$	11.0000			0.785714
$197$	11.3137	−	11.3137i	0.806068	−	0.806068i	−0.177968	−	0.984036i	$-0.556952\pi$
$197$	11.3137	−	11.3137i	0.806068	−	0.806068i	0.984036	+	0.177968i	$0.0569523\pi$
$198$	1.82843	+	3.82843i	0.129941	+	0.272074i
$199$			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
$210$	−14.4853	−	7.75736i	−0.999579	−	0.535309i
$211$	−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
$213$	−19.3137	−	3.31371i	−1.32335	−	0.227052i
$214$		−	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
$222$	−0.828427	+	4.82843i	−0.0556004	+	0.324063i
$223$	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
$225$	8.31371	+	12.4853i	0.554247	+	0.832352i
$226$	−2.00000			−0.133038
$227$	−1.41421	+	1.41421i	−0.0938647	+	0.0938647i	−0.752480	−	0.658615i	$-0.771143\pi$
$227$	−1.41421	+	1.41421i	−0.0938647	+	0.0938647i	0.658615	+	0.752480i	$0.271143\pi$
$228$	−2.34315	+	13.6569i	−0.155179	+	0.904447i
$229$		−	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	0.436475	−	0.899716i	$-0.356227\pi$
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	−0.899716	+	0.436475i	$0.856227\pi$
$234$	2.82843	−	8.00000i	0.184900	−	0.522976i
$235$	−4.00000	−	8.00000i	−0.260931	−	0.521862i
$236$			9.89949i			0.644402i
$237$	−23.8995	−	4.10051i	−1.55244	−	0.266356i
$238$	3.00000	−	3.00000i	0.194461	−	0.194461i
$239$	−2.82843			−0.182956			−0.0914779	−	0.995807i	$-0.529159\pi$
$239$	−2.82843			−0.182956			−0.0914779	+	0.995807i	$0.529159\pi$
$240$	−3.41421	−	1.82843i	−0.220387	−	0.118024i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$	11.7071	−	10.2929i	0.751011	−	0.660289i
$244$		−	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	$0.163352\pi$
$251$			15.5563i			0.981908i	−0.871185	+	0.490954i	$0.836648\pi$
$252$	11.4853	−	5.48528i	0.723505	−	0.345540i
$253$		0			0
$254$	−4.24264			−0.266207
$255$	−3.70711	+	1.12132i	−0.232148	+	0.0702198i
$256$	1.00000			0.0625000
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	−0.826940	−	0.562291i	$-0.809920\pi$
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	0.562291	+	0.826940i	$0.309920\pi$
$258$		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	0.963899	−	0.266266i	$-0.0857901\pi$
$263$	11.3137	+	11.3137i	0.697633	+	0.697633i	−0.266266	+	0.963899i	$0.585790\pi$
$264$	1.41421	+	2.00000i	0.0870388	+	0.123091i
$265$	−16.0000	+	8.00000i	−0.982872	+	0.491436i
$266$			33.9411i			2.08106i
$267$	−0.828427	+	4.82843i	−0.0506989	+	0.295495i
$268$	10.0000	−	10.0000i	0.610847	−	0.610847i
$269$	18.3848			1.12094			0.560470	−	0.828175i	$-0.310621\pi$
$269$	18.3848			1.12094			0.560470	+	0.828175i	$0.310621\pi$
$270$	−11.6066	−	0.535534i	−0.706355	−	0.0325916i
$271$	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
$273$	3.51472	−	20.4853i	0.212720	−	1.23983i
$274$		−	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	$0.201091\pi$
$281$			19.7990i			1.18111i	−0.806998	+	0.590554i	$0.798909\pi$
$282$	6.82843	+	1.17157i	0.406627	+	0.0697661i
$283$	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
$285$	14.6274	−	27.3137i	0.866453	−	1.61792i
$286$	4.00000			0.236525
$287$	−25.4558	+	25.4558i	−1.50261	+	1.50261i
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$		−	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	0.619644	−	0.784883i	$-0.287277\pi$
$293$	−2.82843	−	2.82843i	−0.165238	−	0.165238i	−0.784883	+	0.619644i	$0.787277\pi$
$294$	15.5563	−	11.0000i	0.907265	−	0.641533i
$295$	7.00000	−	21.0000i	0.407556	−	1.22267i
$296$			2.82843i			0.164399i
$297$	6.41421	+	3.58579i	0.372190	+	0.208068i
$298$	−1.00000	+	1.00000i	−0.0579284	+	0.0579284i
$299$		0			0
$300$	5.94975	+	6.29289i	0.343509	+	0.363320i
$301$		0			0
$302$		0			0
$303$	−7.24264	−	1.24264i	−0.416079	−	0.0713878i
$304$			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	$-0.948726\pi$
$311$		−	5.65685i		−	0.320771i	0.987054	−	0.160385i	$-0.0512737\pi$
$312$	0.828427	−	4.82843i	0.0469005	−	0.273356i
$313$	−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
$315$	−28.2426	+	3.51472i	−1.59129	+	0.198032i
$316$	−14.0000			−0.787562
$317$	−1.41421	+	1.41421i	−0.0794301	+	0.0794301i	−0.745706	−	0.666276i	$-0.767887\pi$
$317$	−1.41421	+	1.41421i	−0.0794301	+	0.0794301i	0.666276	+	0.745706i	$0.267887\pi$
$318$	2.34315	−	13.6569i	0.131397	−	0.765838i
$319$		−	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
$327$	3.41421	+	0.585786i	0.188806	+	0.0323941i
$328$	−6.00000	+	6.00000i	−0.331295	+	0.331295i
$329$	16.9706			0.935617
$330$	−1.58579	−	5.24264i	−0.0872947	−	0.288598i
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	3.65685	+	7.65685i	0.200394	+	0.419593i
$334$			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
$342$	10.3431	+	21.6569i	0.559293	+	1.17107i
$343$	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	−0.389566	−	0.920999i	$-0.627375\pi$
$347$	9.89949	−	9.89949i	0.531433	−	0.531433i	0.920999	+	0.389566i	$0.127375\pi$
$348$	−7.24264	−	1.24264i	−0.388246	−	0.0666125i
$349$			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	0.159256	−	0.987237i	$-0.449090\pi$
$353$	−15.5563	−	15.5563i	−0.827981	−	0.827981i	−0.987237	+	0.159256i	$0.949090\pi$
$354$	9.89949	+	14.0000i	0.526152	+	0.744092i
$355$	24.0000	+	8.00000i	1.27379	+	0.424596i
$356$			2.82843i			0.149906i
$357$	1.24264	−	7.24264i	0.0657675	−	0.383321i
$358$	−15.0000	+	15.0000i	−0.792775	+	0.792775i
$359$	5.65685			0.298557			0.149279	−	0.988795i	$-0.452305\pi$
$359$	5.65685			0.298557			0.149279	+	0.988795i	$0.452305\pi$
$360$	−6.65685	+	0.828427i	−0.350847	+	0.0436619i
$361$	−45.0000			−2.36842
$362$	−1.41421	+	1.41421i	−0.0743294	+	0.0743294i
$363$	2.63604	−	15.3640i	0.138356	−	0.806399i
$364$		−	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
$372$	−17.0711	−	2.92893i	−0.885094	−	0.151858i
$373$	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
$375$	−8.17157	−	17.5563i	−0.421978	−	0.906606i
$376$	4.00000			0.206284
$377$	−8.48528	+	8.48528i	−0.437014	+	0.437014i
$378$	10.7574	−	19.2426i	0.553299	−	0.989735i
$379$		−	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	0.934380	−	0.356277i	$-0.115954\pi$
$383$	11.3137	+	11.3137i	0.578103	+	0.578103i	−0.356277	+	0.934380i	$0.615954\pi$
$384$	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	$-0.629037\pi$
$389$	−15.5563			−0.788738			−0.394369	+	0.918952i	$0.629037\pi$
$390$	−5.17157	+	9.65685i	−0.261873	+	0.488994i
$391$		0			0
$392$	7.77817	−	7.77817i	0.392857	−	0.392857i
$393$	16.8995	+	2.89949i	0.852467	+	0.146260i
$394$		−	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	$-0.750397\pi$
$401$		−	28.2843i		−	1.41245i	0.707988	−	0.706225i	$-0.249603\pi$
$402$	4.14214	−	24.1421i	0.206591	−	1.20410i
$403$	−20.0000	+	20.0000i	−0.996271	+	0.996271i
$404$	−4.24264			−0.211079
$405$	−16.9497	+	10.8492i	−0.842240	+	0.539103i
$406$	−18.0000			−0.893325
$407$	−2.82843	+	2.82843i	−0.140200	+	0.140200i
$408$	0.292893	−	1.70711i	0.0145004	−	0.0845144i
$409$			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
$417$	20.4853	+	3.51472i	1.00317	+	0.172117i
$418$	−8.00000	+	8.00000i	−0.391293	+	0.391293i
$419$	38.1838			1.86540			0.932700	−	0.360654i	$-0.117447\pi$
$419$	38.1838			1.86540			0.932700	+	0.360654i	$0.117447\pi$
$420$	−15.7279	+	4.75736i	−0.767444	+	0.232135i
$421$	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
$423$	10.8284	−	5.17157i	0.526496	−	0.251450i
$424$		−	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	$0.269621\pi$
$431$			31.1127i			1.49865i	−0.662205	+	0.749323i	$0.730379\pi$
$432$	2.53553	−	4.53553i	0.121991	−	0.218216i
$433$	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
$435$	14.4853	+	7.75736i	0.694516	+	0.371937i
$436$	2.00000			0.0957826
$437$		0			0
$438$	7.24264	+	1.24264i	0.346067	+	0.0593757i
$439$			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	$-0.771404\pi$
$443$	−29.6985	−	29.6985i	−1.41102	−	1.41102i	−0.657997	−	0.753020i	$-0.728596\pi$
$444$	2.82843	+	4.00000i	0.134231	+	0.189832i
$445$	2.00000	−	6.00000i	0.0948091	−	0.284427i
$446$		−	4.24264i		−	0.200895i
$447$	−0.414214	+	2.41421i	−0.0195916	+	0.114188i
$448$	3.00000	−	3.00000i	0.141737	−	0.141737i
$449$	16.9706			0.800890			0.400445	−	0.916321i	$-0.368855\pi$
$449$	16.9706			0.800890			0.400445	+	0.916321i	$0.368855\pi$
$450$	14.7071	+	2.94975i	0.693300	+	0.139052i
$451$	−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	$-0.692113\pi$
$461$		−	35.3553i		−	1.64666i	0.567561	−	0.823331i	$-0.307887\pi$
$462$	10.2426	+	1.75736i	0.476531	+	0.0817598i
$463$	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
$465$	34.1421	+	18.2843i	1.58330	+	0.847913i
$466$	−10.0000			−0.463241
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	−0.769514	−	0.638630i	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$	−3.65685	−	7.65685i	−0.169038	−	0.353938i
$469$		−	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
$477$	−10.3431	−	21.6569i	−0.473580	−	0.991599i
$478$	−2.00000	+	2.00000i	−0.0914779	+	0.0914779i
$479$	28.2843			1.29234			0.646171	−	0.763193i	$-0.276369\pi$
$479$	28.2843			1.29234			0.646171	+	0.763193i	$0.276369\pi$
$480$	−3.70711	+	1.12132i	−0.169206	+	0.0511810i
$481$	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	$-0.792647\pi$
$491$		−	26.8701i		−	1.21263i	0.795225	−	0.606314i	$-0.207353\pi$
$492$	−2.48528	+	14.4853i	−0.112045	+	0.653047i
$493$	−3.00000	+	3.00000i	−0.135113	+	0.135113i
$494$	22.6274			1.01806
$495$	−7.48528	−	5.82843i	−0.336438	−	0.261968i
$496$	−10.0000			−0.449013
$497$	−33.9411	+	33.9411i	−1.52247	+	1.52247i
$498$	−3.51472	+	20.4853i	−0.157498	+	0.917967i
$499$		−	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	0.317644	−	0.948210i	$-0.397108\pi$
$503$	−14.1421	−	14.1421i	−0.630567	−	0.630567i	−0.948210	+	0.317644i	$0.897108\pi$
$504$	4.24264	−	12.0000i	0.188982	−	0.534522i
$505$	9.00000	+	3.00000i	0.400495	+	0.133498i
$506$		0			0
$507$	8.53553	+	1.46447i	0.379076	+	0.0650392i
$508$	−3.00000	+	3.00000i	−0.133103	+	0.133103i
$509$	18.3848			0.814891			0.407445	−	0.913230i	$-0.366420\pi$
$509$	18.3848			0.814891			0.407445	+	0.913230i	$0.366420\pi$
$510$	−1.82843	+	3.41421i	−0.0809641	+	0.151184i
$511$	18.0000			0.796273
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	36.2843	+	20.2843i	1.60199	+	0.895572i
$514$			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	$0.165075\pi$
$521$			22.6274i			0.991325i	−0.868515	+	0.495663i	$0.834925\pi$
$522$	−11.4853	+	5.48528i	−0.502697	+	0.240084i
$523$	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
$525$	36.7279	+	1.02944i	1.60294	+	0.0449283i
$526$	16.0000			0.697633
$527$	−7.07107	+	7.07107i	−0.308021	+	0.308021i
$528$	2.41421	+	0.414214i	0.105065	+	0.0180263i
$529$		−	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
$537$	−6.21320	+	36.2132i	−0.268120	+	1.56272i
$538$	13.0000	−	13.0000i	0.560470	−	0.560470i
$539$	15.5563			0.670059
$540$	−8.58579	+	7.82843i	−0.369473	+	0.336882i
$541$	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
$543$	−0.585786	+	3.41421i	−0.0251385	+	0.146518i
$544$		−	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
$555$	−3.17157	−	10.4853i	−0.134626	−	0.445075i
$556$	12.0000			0.508913
$557$	8.48528	−	8.48528i	0.359533	−	0.359533i	−0.504108	−	0.863641i	$-0.668179\pi$
$557$	8.48528	−	8.48528i	0.359533	−	0.359533i	0.863641	+	0.504108i	$0.168179\pi$
$558$	−27.0711	+	12.9289i	−1.14601	+	0.547325i
$559$		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	0.840234	−	0.542224i	$-0.182418\pi$
$563$	7.07107	+	7.07107i	0.298010	+	0.298010i	−0.542224	+	0.840234i	$0.682418\pi$
$564$	5.65685	−	4.00000i	0.238197	−	0.168430i
$565$	4.00000	−	2.00000i	0.168281	−	0.0841406i
$566$		−	28.2843i		−	1.18888i
$567$	−4.02944	−	37.9706i	−0.169220	−	1.59461i
$568$	−8.00000	+	8.00000i	−0.335673	+	0.335673i
$569$	2.82843			0.118574			0.0592869	−	0.998241i	$-0.481117\pi$
$569$	2.82843			0.118574			0.0592869	+	0.998241i	$0.481117\pi$
$570$	−8.97056	−	29.6569i	−0.375736	−	1.24219i
$571$	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
$573$	4.82843	+	0.828427i	0.201710	+	0.0346080i
$574$			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
$582$	−1.24264	+	7.24264i	−0.0515091	+	0.300217i
$583$	8.00000	−	8.00000i	0.331326	−	0.331326i
$584$	4.24264			0.175562
$585$	2.34315	+	18.8284i	0.0968772	+	0.778460i
$586$	−4.00000			−0.165238
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	−0.509968	−	0.860193i	$-0.670343\pi$
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	0.860193	+	0.509968i	$0.170343\pi$
$588$	3.22183	−	18.7782i	0.132866	−	0.774399i
$589$		−	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	0.788833	−	0.614608i	$-0.210686\pi$
$593$	4.24264	+	4.24264i	0.174224	+	0.174224i	−0.614608	+	0.788833i	$0.710686\pi$
$594$	7.07107	−	2.00000i	0.290129	−	0.0820610i
$595$	−3.00000	+	9.00000i	−0.122988	+	0.368964i
$596$			1.41421i			0.0579284i
$597$	27.3137	+	4.68629i	1.11788	+	0.191797i
$598$		0			0
$599$	11.3137			0.462266			0.231133	−	0.972922i	$-0.425757\pi$
$599$	11.3137			0.462266			0.231133	+	0.972922i	$0.425757\pi$
$600$	8.65685	+	0.242641i	0.353415	+	0.00990576i
$601$	−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
$603$	−18.2843	−	38.2843i	−0.744593	−	1.55906i
$604$		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
$612$	−1.29289	−	2.70711i	−0.0522621	−	0.109428i
$613$	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
$615$	15.5147	−	28.9706i	0.625614	−	1.16821i
$616$	6.00000			0.241747
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	−0.616530	−	0.787332i	$-0.711462\pi$
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	0.787332	+	0.616530i	$0.211462\pi$
$618$	7.24264	+	1.24264i	0.291342	+	0.0499863i
$619$		−	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
$627$	−3.31371	+	19.3137i	−0.132337	+	0.771315i
$628$	−10.0000	+	10.0000i	−0.399043	+	0.399043i
$629$	2.82843			0.112777
$630$	−17.4853	+	22.4558i	−0.696630	+	0.894662i
$631$	−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
$633$	−2.34315	+	13.6569i	−0.0931317	+	0.542811i
$634$			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	$0.127873\pi$
$641$			19.7990i			0.782013i	−0.920388	+	0.391007i	$0.872127\pi$
$642$	−34.1421	−	5.85786i	−1.34748	−	0.231191i
$643$	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	−0.520358	−	0.853948i	$-0.674201\pi$
$647$	8.48528	−	8.48528i	0.333591	−	0.333591i	0.853948	+	0.520358i	$0.174201\pi$
$648$	−0.949747	−	8.94975i	−0.0373096	−	0.351579i
$649$			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	0.785231	−	0.619203i	$-0.212544\pi$
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	−0.619203	+	0.785231i	$0.712544\pi$
$654$	2.82843	−	2.00000i	0.110600	−	0.0782062i
$655$	−21.0000	−	7.00000i	−0.820538	−	0.273513i
$656$			8.48528i			0.331295i
$657$	11.4853	−	5.48528i	0.448084	−	0.214001i
$658$	12.0000	−	12.0000i	0.467809	−	0.467809i
$659$	24.0416			0.936529			0.468264	−	0.883588i	$-0.344879\pi$
$659$	24.0416			0.936529			0.468264	+	0.883588i	$0.344879\pi$
$660$	−4.82843	−	2.58579i	−0.187946	−	0.100652i
$661$	−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
$663$	−4.82843	−	0.828427i	−0.187521	−	0.0321734i
$664$			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
$672$	1.24264	−	7.24264i	0.0479359	−	0.279391i
$673$	−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
$675$	23.7487	−	10.5355i	0.914089	−	0.405513i
$676$	5.00000			0.192308
$677$	−9.89949	+	9.89949i	−0.380468	+	0.380468i	−0.871271	−	0.490802i	$-0.836704\pi$
$677$	−9.89949	+	9.89949i	−0.380468	+	0.380468i	0.490802	+	0.871271i	$0.336704\pi$
$678$	−0.585786	+	3.41421i	−0.0224970	+	0.131122i
$679$			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	0.999671	−	0.0256307i	$-0.00815939\pi$
$683$	25.4558	+	25.4558i	0.974041	+	0.974041i	−0.0256307	+	0.999671i	$0.508159\pi$
$684$	22.6274	+	8.00000i	0.865181	+	0.305888i
$685$	6.00000	+	12.0000i	0.229248	+	0.458496i
$686$		−	16.9706i		−	0.647939i
$687$	−3.41421	−	0.585786i	−0.130260	−	0.0223491i
$688$		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
$693$	16.2426	−	7.75736i	0.617007	−	0.294678i
$694$		−	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	$-0.957367\pi$
$701$		−	7.07107i		−	0.267071i	0.991044	−	0.133535i	$-0.0426329\pi$
$702$	−12.8284	−	7.17157i	−0.484178	−	0.270674i
$703$	−16.0000	+	16.0000i	−0.603451	+	0.603451i
$704$	1.41421			0.0533002
$705$	−14.8284	+	4.48528i	−0.558471	+	0.168925i
$706$	−22.0000			−0.827981
$707$	−12.7279	+	12.7279i	−0.478683	+	0.478683i
$708$	16.8995	+	2.89949i	0.635122	+	0.108970i
$709$			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
$717$	−0.828427	+	4.82843i	−0.0309382	+	0.180321i
$718$	4.00000	−	4.00000i	0.149279	−	0.149279i
$719$	19.7990			0.738378			0.369189	−	0.929354i	$-0.379636\pi$
$719$	19.7990			0.738378			0.369189	+	0.929354i	$0.379636\pi$
$720$	−4.12132	+	5.29289i	−0.153593	+	0.197254i
$721$	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
$732$	−17.0711	−	2.92893i	−0.630965	−	0.108256i
$733$	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
$735$	−20.1127	+	37.5563i	−0.741868	+	1.38529i
$736$		0			0
$737$	14.1421	−	14.1421i	0.520932	−	0.520932i
$738$	10.9706	+	22.9706i	0.403832	+	0.845558i
$739$		−	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	$-0.907224\pi$
$743$	−33.9411	−	33.9411i	−1.24518	−	1.24518i	−0.287355	−	0.957824i	$-0.592776\pi$
$744$	−14.1421	+	10.0000i	−0.518476	+	0.366618i
$745$	1.00000	−	3.00000i	0.0366372	−	0.109911i
$746$		−	8.48528i		−	0.310668i
$747$	15.5147	+	32.4853i	0.567654	+	1.18857i
$748$	1.00000	−	1.00000i	0.0365636	−	0.0365636i
$749$	−84.8528			−3.10045
$750$	−18.1924	−	6.63604i	−0.664292	−	0.242314i
$751$	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
$753$	26.5563	+	4.55635i	0.967767	+	0.166043i
$754$			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	$-0.883167\pi$
$761$		−	19.7990i		−	0.717713i	0.933393	−	0.358856i	$-0.116833\pi$
$762$	−1.24264	+	7.24264i	−0.0450161	+	0.262373i
$763$	6.00000	−	6.00000i	0.217215	−	0.217215i
$764$	2.82843			0.102329
$765$	0.828427	+	6.65685i	0.0299518	+	0.240679i
$766$	16.0000			0.578103
$767$	19.7990	−	19.7990i	0.714900	−	0.714900i
$768$	0.292893	−	1.70711i	0.0105689	−	0.0615999i
$769$			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	0.955676	−	0.294421i	$-0.0951269\pi$
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	−0.294421	+	0.955676i	$0.595127\pi$
$774$		0			0
$775$	−40.0000	−	30.0000i	−1.43684	−	1.07763i
$776$			4.24264i			0.152302i
$777$	20.4853	+	3.51472i	0.734905	+	0.126090i
$778$	−11.0000	+	11.0000i	−0.394369	+	0.394369i
$779$	−67.8823			−2.43213
$780$	3.17157	+	10.4853i	0.113561	+	0.375433i
$781$	−16.0000			−0.572525
$782$		0			0
$783$	−10.7574	+	19.2426i	−0.384437	+	0.687676i
$784$		−	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
$792$	3.82843	−	1.82843i	0.136037	−	0.0649703i
$793$	−20.0000	+	20.0000i	−0.710221	+	0.710221i
$794$	25.4558			0.903394
$795$	8.97056	+	29.6569i	0.318153	+	1.05182i
$796$	16.0000			0.567105
$797$	−26.8701	+	26.8701i	−0.951786	+	0.951786i	−0.998890	−	0.0471037i	$-0.985001\pi$
$797$	−26.8701	+	26.8701i	−0.951786	+	0.951786i	0.0471037	+	0.998890i	$0.485001\pi$
$798$	57.9411	+	9.94113i	2.05109	+	0.351912i
$799$		−	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
$807$	5.38478	−	31.3848i	0.189553	−	1.10480i
$808$	−3.00000	+	3.00000i	−0.105540	+	0.105540i
$809$	25.4558			0.894980			0.447490	−	0.894289i	$-0.352318\pi$
$809$	25.4558			0.894980			0.447490	+	0.894289i	$0.352318\pi$
$810$	−4.31371	+	19.6569i	−0.151568	+	0.690671i
$811$	−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
$813$	2.34315	−	13.6569i	0.0821777	−	0.478967i
$814$			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	$-0.844656\pi$
$821$		−	26.8701i		−	0.937771i	0.883259	−	0.468886i	$-0.155344\pi$
$822$	−10.2426	−	1.75736i	−0.357253	−	0.0612949i
$823$	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
$825$	8.41421	+	8.89949i	0.292945	+	0.309841i
$826$	42.0000			1.46137
$827$	26.8701	−	26.8701i	0.934363	−	0.934363i	−0.0636113	−	0.997975i	$-0.520262\pi$
$827$	26.8701	−	26.8701i	0.934363	−	0.934363i	0.997975	+	0.0636113i	$0.0202618\pi$
$828$		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
$837$	−25.3553	+	45.3553i	−0.876409	+	1.56771i
$838$	27.0000	−	27.0000i	0.932700	−	0.932700i
$839$	8.48528			0.292944			0.146472	−	0.989215i	$-0.453208\pi$
$839$	8.48528			0.292944			0.146472	+	0.989215i	$0.453208\pi$
$840$	−7.75736	+	14.4853i	−0.267654	+	0.499790i
$841$	−11.0000			−0.379310
$842$	18.3848	−	18.3848i	0.633581	−	0.633581i
$843$	33.7990	+	5.79899i	1.16410	+	0.199728i
$844$			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
$852$	−3.31371	+	19.3137i	−0.113526	+	0.661677i
$853$	−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
$855$	−42.3431	−	32.9706i	−1.44811	−	1.12757i
$856$	−20.0000			−0.683586
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	−0.455472	−	0.890250i	$-0.650530\pi$
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	0.890250	+	0.455472i	$0.150530\pi$
$858$	1.17157	−	6.82843i	0.0399968	−	0.233119i
$859$		−	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	0.356580	−	0.934265i	$-0.383943\pi$
$863$	−16.9706	−	16.9706i	−0.577685	−	0.577685i	−0.934265	+	0.356580i	$0.883943\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	−28.0000	+	14.0000i	−0.952029	+	0.476014i
$866$		−	4.24264i		−	0.144171i
$867$	−1.70711	−	0.292893i	−0.0579764	−	0.00994718i
$868$	−30.0000	+	30.0000i	−1.01827	+	1.01827i
$869$	−19.7990			−0.671635
$870$	15.7279	−	4.75736i	0.533226	−	0.161290i
$871$	−40.0000			−1.35535
$872$	1.41421	−	1.41421i	0.0478913	−	0.0478913i
$873$	5.48528	+	11.4853i	0.185649	+	0.388718i
$874$		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	$-0.767559\pi$
$881$		−	39.5980i		−	1.33409i	0.745018	−	0.667045i	$-0.232441\pi$
$882$	−14.2218	−	29.7782i	−0.478874	−	1.00268i
$883$	−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
$885$	−33.7990	−	18.1005i	−1.13614	−	0.608442i
$886$	−42.0000			−1.41102
$887$	−11.3137	+	11.3137i	−0.379877	+	0.379877i	−0.871058	−	0.491181i	$-0.836566\pi$
$887$	−11.3137	+	11.3137i	−0.379877	+	0.379877i	0.491181	+	0.871058i	$0.336566\pi$
$888$	4.82843	+	0.828427i	0.162031	+	0.0278002i
$889$			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
$900$	12.4853	−	8.31371i	0.416176	−	0.277124i
$901$	−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	$-0.985080\pi$
$911$		−	2.82843i		−	0.0937100i	0.998902	−	0.0468550i	$-0.0149199\pi$
$912$	13.6569	+	2.34315i	0.452224	+	0.0775893i
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	18.3848			0.608114
$915$	34.1421	+	18.2843i	1.12870	+	0.604459i
$916$	−2.00000			−0.0660819
$917$	29.6985	−	29.6985i	0.980730	−	0.980730i
$918$	−4.53553	−	2.53553i	−0.149695	−	0.0836851i
$919$			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
$927$	11.4853	−	5.48528i	0.377226	−	0.180160i
$928$	−3.00000	+	3.00000i	−0.0984798	+	0.0984798i
$929$	−56.5685			−1.85595			−0.927977	−	0.372638i	$-0.878453\pi$
$929$	−56.5685			−1.85595			−0.927977	+	0.372638i	$0.878453\pi$
$930$	37.0711	−	11.2132i	1.21561	−	0.367695i
$931$	88.0000			2.88408
$932$	−7.07107	+	7.07107i	−0.231621	+	0.231621i
$933$	−9.65685	−	1.65685i	−0.316151	−	0.0542430i
$934$			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	$-0.903126\pi$
$941$		−	18.3848i		−	0.599327i	0.954045	−	0.299663i	$-0.0968743\pi$
$942$	−4.14214	+	24.1421i	−0.134958	+	0.786593i
$943$		0			0
$944$	9.89949			0.322201
$945$	−2.27208	+	49.2426i	−0.0739107	+	1.60186i
$946$		0			0
$947$	32.5269	−	32.5269i	1.05698	−	1.05698i	0.0587074	−	0.998275i	$-0.481302\pi$
$947$	32.5269	−	32.5269i	1.05698	−	1.05698i	0.998275	−	0.0587074i	$-0.0186979\pi$
$948$	−4.10051	+	23.8995i	−0.133178	+	0.776220i
$949$		−	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	0.961604	−	0.274441i	$-0.0884928\pi$
$953$	21.2132	+	21.2132i	0.687163	+	0.687163i	−0.274441	+	0.961604i	$0.588493\pi$
$954$	−22.6274	−	8.00000i	−0.732590	−	0.259010i
$955$	−6.00000	−	2.00000i	−0.194155	−	0.0647185i
$956$			2.82843i			0.0914779i
$957$	−10.2426	−	1.75736i	−0.331098	−	0.0568074i
$958$	20.0000	−	20.0000i	0.646171	−	0.646171i
$959$	−25.4558			−0.822012
$960$	−1.82843	+	3.41421i	−0.0590122	+	0.110193i
$961$	69.0000			2.22581
$962$	5.65685	−	5.65685i	0.182384	−	0.182384i
$963$	−54.1421	+	25.8579i	−1.74471	+	0.833258i
$964$		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	$0.317216\pi$
$971$			52.3259i			1.67922i	−0.543191	+	0.839609i	$0.682784\pi$
$972$	−10.2929	−	11.7071i	−0.330145	−	0.375506i
$973$	36.0000	−	36.0000i	1.15411	−	1.15411i
$974$	32.5269			1.04223
$975$	0.686292	−	24.4853i	0.0219789	−	0.784157i
$976$	−10.0000			−0.320092
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	−0.998815	−	0.0486759i	$-0.984500\pi$
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	0.0486759	+	0.998815i	$0.484500\pi$
$978$	−9.65685	−	1.65685i	−0.308792	−	0.0529804i
$979$			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
$987$	4.97056	−	28.9706i	0.158215	−	0.922143i
$988$	16.0000	−	16.0000i	0.509028	−	0.509028i
$989$		0			0
$990$	−9.41421	+	1.17157i	−0.299203	+	0.0372350i
$991$	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.137.2	yes	4
3.2	odd	2	inner	510.2.l.a.137.1	✓	4
5.3	odd	4	inner	510.2.l.a.443.1	yes	4
15.8	even	4	inner	510.2.l.a.443.2	yes	4

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-3.00000 - 3.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) 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} +(-1.70711 - 0.292893i) q^{12} +(-2.00000 + 2.00000i) q^{13} -4.24264 q^{14} +(3.41421 + 1.82843i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.70711 + 1.29289i) 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} +(-2.53553 + 4.53553i) q^{27} +(-3.00000 + 3.00000i) q^{28} +4.24264 q^{29} +(3.70711 - 1.12132i) q^{30} +10.0000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.41421 - 0.414214i) 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} +(-1.24264 + 7.24264i) q^{42} -1.41421 q^{44} +(4.12132 - 5.29289i) q^{45} +(-2.82843 + 2.82843i) q^{47} +(-0.292893 + 1.70711i) 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} +(-13.6569 - 2.34315i) q^{57} +(3.00000 - 3.00000i) q^{58} -9.89949 q^{59} +(1.82843 - 3.41421i) q^{60} +10.0000 q^{61} +(7.07107 - 7.07107i) q^{62} +(5.48528 + 11.4853i) 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} +(1.29289 + 2.70711i) q^{72} +(-3.00000 + 3.00000i) q^{73} -2.82843 q^{74} +(-6.29289 + 5.94975i) q^{75} -8.00000 q^{76} +(-4.24264 + 4.24264i) q^{77} +(4.82843 + 0.828427i) 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} +(1.24264 - 7.24264i) q^{87} +(-1.00000 + 1.00000i) q^{88} -2.82843 q^{89} +(-0.828427 - 6.65685i) q^{90} +12.0000 q^{91} +(2.92893 - 17.0711i) 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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