LMFDB - Embedded newform 690.2.i.b.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, 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("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
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			47.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.b.323.1

$q$-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} +4.24264i 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} +(-4.24264 + 4.24264i) q^{17} +(-1.29289 + 2.70711i) q^{18} -4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(6.00000 + 4.24264i) q^{21} +(-3.00000 - 3.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(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} -7.07107 q^{29} +(2.29289 + 3.12132i) q^{30} +2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.24264 + 7.24264i) q^{33} -6.00000i q^{34} +(8.48528 - 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(2.82843 - 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} -5.65685i q^{41} +(-7.24264 + 1.24264i) q^{42} +4.24264 q^{44} +(-0.121320 - 6.70711i) q^{45} -1.00000 q^{46} +(8.48528 - 8.48528i) q^{47} +(-1.70711 + 0.292893i) q^{48} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-6.00000 + 8.48528i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(-2.82843 - 2.82843i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(9.00000 + 3.00000i) q^{55} +4.24264i q^{56} +(-1.17157 - 6.82843i) q^{57} +(5.00000 - 5.00000i) q^{58} +1.41421 q^{59} +(-3.82843 - 0.585786i) q^{60} -10.0000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(11.4853 + 5.48528i) q^{63} +1.00000i q^{64} +(-2.82843 - 5.65685i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-10.0000 - 10.0000i) q^{67} +(4.24264 + 4.24264i) q^{68} +(1.41421 + 1.00000i) q^{69} +(-3.00000 + 9.00000i) q^{70} +5.65685i q^{71} +(2.70711 + 1.29289i) q^{72} +(-1.00000 + 1.00000i) q^{73} -8.48528 q^{74} +(-7.70711 - 3.94975i) q^{75} -4.00000 q^{76} +(-12.7279 + 12.7279i) q^{77} +(0.828427 + 4.82843i) q^{78} +14.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} +(4.24264 - 6.00000i) q^{84} +(6.00000 + 12.0000i) q^{85} +(-12.0711 + 2.07107i) q^{87} +(-3.00000 + 3.00000i) q^{88} +11.3137 q^{89} +(4.82843 + 4.65685i) q^{90} +12.0000 q^{91} +(0.707107 - 0.707107i) q^{92} +(3.41421 - 0.585786i) q^{93} +12.0000i q^{94} +(-8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +(4.24264 + 12.0000i) 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} - 12 q^{22} - 16 q^{25} + 4 q^{27} + 12 q^{28} + 12 q^{30} + 8 q^{31} - 12 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} - 12 q^{42} + 8 q^{45} - 4 q^{46} - 4 q^{48} - 24 q^{51} - 8 q^{52} + 36 q^{55} - 16 q^{57} + 20 q^{58} - 4 q^{60} - 40 q^{61} + 12 q^{63} - 24 q^{66} - 40 q^{67} - 12 q^{70} + 8 q^{72} - 4 q^{73} - 28 q^{75} - 16 q^{76} - 8 q^{78} + 28 q^{81} + 16 q^{82} + 24 q^{85} - 20 q^{87} - 12 q^{88} + 8 q^{90} + 48 q^{91} + 8 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 - 12 * q^22 - 16 * q^25 + 4 * q^27 + 12 * q^28 + 12 * q^30 + 8 * q^31 - 12 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 - 12 * q^42 + 8 * q^45 - 4 * q^46 - 4 * q^48 - 24 * q^51 - 8 * q^52 + 36 * q^55 - 16 * q^57 + 20 * q^58 - 4 * q^60 - 40 * q^61 + 12 * q^63 - 24 * q^66 - 40 * q^67 - 12 * q^70 + 8 * q^72 - 4 * q^73 - 28 * q^75 - 16 * q^76 - 8 * q^78 + 28 * q^81 + 16 * q^82 + 24 * q^85 - 20 * q^87 - 12 * q^88 + 8 * q^90 + 48 * q^91 + 8 * q^93 + 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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	$0.0461154\pi$
$7$	3.00000	+	3.00000i	1.13389	+	1.13389i	0.144370	+	0.989524i	$0.453885\pi$
$8$	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
$11$			4.24264i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$11$			4.24264i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$12$	−0.292893	−	1.70711i	−0.0845510	−	0.492799i
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	−4.24264			−1.13389
$15$	0.585786	−	3.82843i	0.151249	−	0.988496i
$16$	−1.00000			−0.250000
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.0294245	+	0.999567i	$0.509367\pi$
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.999567	+	0.0294245i	$0.990633\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$	6.00000	+	4.24264i	1.30931	+	0.925820i
$22$	−3.00000	−	3.00000i	−0.639602	−	0.639602i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	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
$29$	−7.07107			−1.31306			−0.656532	−	0.754298i	$-0.727977\pi$
$29$	−7.07107			−1.31306			−0.656532	+	0.754298i	$0.727977\pi$
$30$	2.29289	+	3.12132i	0.418623	+	0.569873i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.24264	+	7.24264i	0.216316	+	1.26078i
$34$		−	6.00000i		−	1.02899i
$35$	8.48528	−	4.24264i	1.43427	−	0.717137i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	2.82843	+	2.82843i	0.458831	+	0.458831i
$39$	2.82843	−	4.00000i	0.452911	−	0.640513i
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	−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	$0.250000\pi$
$44$	4.24264			0.639602
$45$	−0.121320	−	6.70711i	−0.0180854	−	0.999836i
$46$	−1.00000			−0.147442
$47$	8.48528	−	8.48528i	1.23771	−	1.23771i	0.276769	−	0.960936i	$-0.410736\pi$
$47$	8.48528	−	8.48528i	1.23771	−	1.23771i	0.960936	−	0.276769i	$-0.0892637\pi$
$48$	−1.70711	+	0.292893i	−0.246400	+	0.0422755i
$49$			11.0000i			1.57143i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	−6.00000	+	8.48528i	−0.840168	+	1.18818i
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	0.485643	−	0.874157i	$-0.338586\pi$
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	−0.874157	+	0.485643i	$0.838586\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	9.00000	+	3.00000i	1.21356	+	0.404520i
$56$			4.24264i			0.566947i
$57$	−1.17157	−	6.82843i	−0.155179	−	0.904447i
$58$	5.00000	−	5.00000i	0.656532	−	0.656532i
$59$	1.41421			0.184115			0.0920575	−	0.995754i	$-0.470656\pi$
$59$	1.41421			0.184115			0.0920575	+	0.995754i	$0.470656\pi$
$60$	−3.82843	−	0.585786i	−0.494248	−	0.0756247i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	−1.41421	+	1.41421i	−0.179605	+	0.179605i
$63$	11.4853	+	5.48528i	1.44701	+	0.691080i
$64$			1.00000i			0.125000i
$65$	−2.82843	−	5.65685i	−0.350823	−	0.701646i
$66$	−6.00000	−	4.24264i	−0.738549	−	0.522233i
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.967029	−	0.254665i	$-0.918035\pi$
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.254665	−	0.967029i	$-0.581965\pi$
$68$	4.24264	+	4.24264i	0.514496	+	0.514496i
$69$	1.41421	+	1.00000i	0.170251	+	0.120386i
$70$	−3.00000	+	9.00000i	−0.358569	+	1.07571i
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	−0.763202	−	0.646160i	$-0.776374\pi$
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	0.646160	+	0.763202i	$0.276374\pi$
$74$	−8.48528			−0.986394
$75$	−7.70711	−	3.94975i	−0.889940	−	0.456078i
$76$	−4.00000			−0.458831
$77$	−12.7279	+	12.7279i	−1.45048	+	1.45048i
$78$	0.828427	+	4.82843i	0.0938009	+	0.546712i
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$	−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
$85$	6.00000	+	12.0000i	0.650791	+	1.30158i
$86$		0			0
$87$	−12.0711	+	2.07107i	−1.29415	+	0.222042i
$88$	−3.00000	+	3.00000i	−0.319801	+	0.319801i
$89$	11.3137			1.19925			0.599625	−	0.800281i	$-0.295316\pi$
$89$	11.3137			1.19925			0.599625	+	0.800281i	$0.295316\pi$
$90$	4.82843	+	4.65685i	0.508961	+	0.490876i
$91$	12.0000			1.25794
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	3.41421	−	0.585786i	0.354037	−	0.0607432i
$94$			12.0000i			1.23771i
$95$	−8.48528	−	2.82843i	−0.870572	−	0.290191i
$96$	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
$99$	4.24264	+	12.0000i	0.426401	+	1.20605i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		−	12.7279i		−	1.26648i	−0.773957	−	0.633238i	$-0.781726\pi$
$101$		−	12.7279i		−	1.26648i	0.773957	−	0.633238i	$-0.218274\pi$
$102$	−1.75736	−	10.2426i	−0.174005	−	1.01417i
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	−0.416480	−	0.909145i	$-0.636736\pi$
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	0.909145	+	0.416480i	$0.136736\pi$
$104$	2.82843			0.277350
$105$	13.2426	−	9.72792i	1.29235	−	0.949348i
$106$	4.00000			0.388514
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$	−2.53553	−	4.53553i	−0.243982	−	0.436432i
$109$			6.00000i			0.574696i	0.957826	+	0.287348i	$0.0927736\pi$
$109$			6.00000i			0.574696i	−0.957826	+	0.287348i	$0.907226\pi$
$110$	−8.48528	+	4.24264i	−0.809040	+	0.404520i
$111$	12.0000	+	8.48528i	1.13899	+	0.805387i
$112$	−3.00000	−	3.00000i	−0.283473	−	0.283473i
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$	5.65685	+	4.00000i	0.529813	+	0.374634i
$115$	2.00000	−	1.00000i	0.186501	−	0.0932505i
$116$			7.07107i			0.656532i
$117$	3.65685	−	7.65685i	0.338076	−	0.707876i
$118$	−1.00000	+	1.00000i	−0.0920575	+	0.0920575i
$119$	−25.4558			−2.33353
$120$	3.12132	−	2.29289i	0.284936	−	0.209312i
$121$	−7.00000			−0.636364
$122$	7.07107	−	7.07107i	0.640184	−	0.640184i
$123$	−1.65685	−	9.65685i	−0.149394	−	0.870729i
$124$		−	2.00000i		−	0.179605i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	−12.0000	+	4.24264i	−1.06904	+	0.377964i
$127$	−9.00000	−	9.00000i	−0.798621	−	0.798621i	0.184257	−	0.982878i	$-0.441012\pi$
$127$	−9.00000	−	9.00000i	−0.798621	−	0.798621i	−0.982878	+	0.184257i	$0.941012\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	6.00000	+	2.00000i	0.526235	+	0.175412i
$131$			1.41421i			0.123560i	0.998090	+	0.0617802i	$0.0196778\pi$
$131$			1.41421i			0.123560i	−0.998090	+	0.0617802i	$0.980322\pi$
$132$	7.24264	−	1.24264i	0.630391	−	0.108158i
$133$	12.0000	−	12.0000i	1.04053	−	1.04053i
$134$	14.1421			1.22169
$135$	−2.17157	−	11.4142i	−0.186899	−	0.982379i
$136$	−6.00000			−0.514496
$137$	−1.41421	+	1.41421i	−0.120824	+	0.120824i	−0.764934	−	0.644109i	$-0.777228\pi$
$137$	−1.41421	+	1.41421i	−0.120824	+	0.120824i	0.644109	+	0.764934i	$0.277228\pi$
$138$	−1.70711	+	0.292893i	−0.145319	+	0.0249327i
$139$			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
$141$	12.0000	−	16.9706i	1.01058	−	1.42918i
$142$	−4.00000	−	4.00000i	−0.335673	−	0.335673i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	−5.00000	+	15.0000i	−0.415227	+	1.24568i
$146$		−	1.41421i		−	0.117041i
$147$	3.22183	+	18.7782i	0.265732	+	1.54880i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−1.41421			−0.115857			−0.0579284	−	0.998321i	$-0.518450\pi$
$149$	−1.41421			−0.115857			−0.0579284	+	0.998321i	$0.518450\pi$
$150$	8.24264	−	2.65685i	0.673009	−	0.216931i
$151$	−24.0000			−1.95309			−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000			−1.95309			−0.976546	+	0.215308i	$0.930924\pi$
$152$	2.82843	−	2.82843i	0.229416	−	0.229416i
$153$	−7.75736	+	16.2426i	−0.627145	+	1.31314i
$154$		−	18.0000i		−	1.45048i
$155$	1.41421	−	4.24264i	0.113592	−	0.340777i
$156$	−4.00000	−	2.82843i	−0.320256	−	0.226455i
$157$	−12.0000	−	12.0000i	−0.957704	−	0.957704i	0.0414369	−	0.999141i	$-0.486806\pi$
$157$	−12.0000	−	12.0000i	−0.957704	−	0.957704i	−0.999141	+	0.0414369i	$0.986806\pi$
$158$	−9.89949	−	9.89949i	−0.787562	−	0.787562i
$159$	−5.65685	−	4.00000i	−0.448618	−	0.317221i
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$			4.24264i			0.334367i
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.298947	−	0.954270i	$-0.403365\pi$
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.954270	−	0.298947i	$-0.0966354\pi$
$164$	−5.65685			−0.441726
$165$	16.2426	+	2.48528i	1.26449	+	0.193479i
$166$	12.0000			0.931381
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	−0.954577	−	0.297966i	$-0.903692\pi$
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	0.297966	+	0.954577i	$0.403692\pi$
$168$	1.24264	+	7.24264i	0.0958718	+	0.558782i
$169$			5.00000i			0.384615i
$170$	−12.7279	−	4.24264i	−0.976187	−	0.325396i
$171$	−4.00000	−	11.3137i	−0.305888	−	0.865181i
$172$		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	$0.928635\pi$
$174$	7.07107	−	10.0000i	0.536056	−	0.758098i
$175$	−3.00000	−	21.0000i	−0.226779	−	1.58745i
$176$		−	4.24264i		−	0.319801i
$177$	2.41421	−	0.414214i	0.181463	−	0.0311342i
$178$	−8.00000	+	8.00000i	−0.599625	+	0.599625i
$179$	−4.24264			−0.317110			−0.158555	−	0.987350i	$-0.550683\pi$
$179$	−4.24264			−0.317110			−0.158555	+	0.987350i	$0.550683\pi$
$180$	−6.70711	+	0.121320i	−0.499918	+	0.00904268i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−8.48528	+	8.48528i	−0.628971	+	0.628971i
$183$	−17.0711	+	2.92893i	−1.26193	+	0.216513i
$184$			1.00000i			0.0737210i
$185$	16.9706	−	8.48528i	1.24770	−	0.623850i
$186$	−2.00000	+	2.82843i	−0.146647	+	0.207390i
$187$	−18.0000	−	18.0000i	−1.31629	−	1.31629i
$188$	−8.48528	−	8.48528i	−0.618853	−	0.618853i
$189$	21.2132	+	6.00000i	1.54303	+	0.436436i
$190$	8.00000	−	4.00000i	0.580381	−	0.290191i
$191$		−	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
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$	4.24264			0.304604
$195$	−6.48528	−	8.82843i	−0.464421	−	0.632217i
$196$	11.0000			0.785714
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	−0.336966	−	0.941517i	$-0.609401\pi$
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	0.941517	+	0.336966i	$0.109401\pi$
$198$	−11.4853	−	5.48528i	−0.816223	−	0.389822i
$199$			8.00000i			0.567105i	0.958957	+	0.283552i	$0.0915130\pi$
$199$			8.00000i			0.567105i	−0.958957	+	0.283552i	$0.908487\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$	−20.0000	−	14.1421i	−1.41069	−	0.997509i
$202$	9.00000	+	9.00000i	0.633238	+	0.633238i
$203$	−21.2132	−	21.2132i	−1.48888	−	1.48888i
$204$	8.48528	+	6.00000i	0.594089	+	0.420084i
$205$	−12.0000	−	4.00000i	−0.838116	−	0.279372i
$206$			7.07107i			0.492665i
$207$	2.70711	+	1.29289i	0.188157	+	0.0898623i
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	16.9706			1.17388
$210$	−2.48528	+	16.2426i	−0.171501	+	1.12085i
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−2.82843	+	2.82843i	−0.194257	+	0.194257i
$213$	1.65685	+	9.65685i	0.113526	+	0.661677i
$214$		−	4.00000i		−	0.273434i
$215$		0			0
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	6.00000	+	6.00000i	0.407307	+	0.407307i
$218$	−4.24264	−	4.24264i	−0.287348	−	0.287348i
$219$	−1.41421	+	2.00000i	−0.0955637	+	0.135147i
$220$	3.00000	−	9.00000i	0.202260	−	0.606780i
$221$			16.9706i			1.14156i
$222$	−14.4853	+	2.48528i	−0.972188	+	0.166801i
$223$	−11.0000	+	11.0000i	−0.736614	+	0.736614i	−0.971921	−	0.235307i	$-0.924391\pi$
$223$	−11.0000	+	11.0000i	−0.736614	+	0.736614i	0.235307	+	0.971921i	$0.424391\pi$
$224$	4.24264			0.283473
$225$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$226$	−6.00000			−0.399114
$227$	9.89949	−	9.89949i	0.657053	−	0.657053i	−0.297629	−	0.954682i	$-0.596196\pi$
$227$	9.89949	−	9.89949i	0.657053	−	0.657053i	0.954682	+	0.297629i	$0.0961959\pi$
$228$	−6.82843	+	1.17157i	−0.452224	+	0.0775893i
$229$			10.0000i			0.660819i	0.943838	+	0.330409i	$0.107187\pi$
$229$			10.0000i			0.660819i	−0.943838	+	0.330409i	$0.892813\pi$
$230$	−0.707107	+	2.12132i	−0.0466252	+	0.139876i
$231$	−18.0000	+	25.4558i	−1.18431	+	1.67487i
$232$	−5.00000	−	5.00000i	−0.328266	−	0.328266i
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	0.832288	−	0.554343i	$-0.187031\pi$
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	−0.554343	+	0.832288i	$0.687031\pi$
$234$	2.82843	+	8.00000i	0.184900	+	0.522976i
$235$	−12.0000	−	24.0000i	−0.782794	−	1.56559i
$236$		−	1.41421i		−	0.0920575i
$237$	4.10051	+	23.8995i	0.266356	+	1.55244i
$238$	18.0000	−	18.0000i	1.16677	−	1.16677i
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$	−0.585786	+	3.82843i	−0.0378124	+	0.247124i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	4.94975	−	4.94975i	0.318182	−	0.318182i
$243$	10.2929	−	11.7071i	0.660289	−	0.751011i
$244$			10.0000i			0.640184i
$245$	23.3345	+	7.77817i	1.49079	+	0.496929i
$246$	8.00000	+	5.65685i	0.510061	+	0.360668i
$247$	−8.00000	−	8.00000i	−0.509028	−	0.509028i
$248$	1.41421	+	1.41421i	0.0898027	+	0.0898027i
$249$	−16.9706	−	12.0000i	−1.07547	−	0.760469i
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$			18.3848i			1.16044i	0.814461	+	0.580218i	$0.197033\pi$
$251$			18.3848i			1.16044i	−0.814461	+	0.580218i	$0.802967\pi$
$252$	5.48528	−	11.4853i	0.345540	−	0.723505i
$253$	−3.00000	+	3.00000i	−0.188608	+	0.188608i
$254$	12.7279			0.798621
$255$	13.7574	+	18.7279i	0.861519	+	1.17279i
$256$	1.00000			0.0625000
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	−0.661622	−	0.749838i	$-0.730131\pi$
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	0.749838	+	0.661622i	$0.230131\pi$
$258$		0			0
$259$			36.0000i			2.23693i
$260$	−5.65685	+	2.82843i	−0.350823	+	0.175412i
$261$	−20.0000	+	7.07107i	−1.23797	+	0.437688i
$262$	−1.00000	−	1.00000i	−0.0617802	−	0.0617802i
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.998867	+	0.0475824i	$0.0151517\pi$
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.0475824	+	0.998867i	$0.484848\pi$
$264$	−4.24264	+	6.00000i	−0.261116	+	0.369274i
$265$	−8.00000	+	4.00000i	−0.491436	+	0.245718i
$266$			16.9706i			1.04053i
$267$	19.3137	−	3.31371i	1.18198	−	0.202796i
$268$	−10.0000	+	10.0000i	−0.610847	+	0.610847i
$269$	−21.2132			−1.29339			−0.646696	−	0.762748i	$-0.723850\pi$
$269$	−21.2132			−1.29339			−0.646696	+	0.762748i	$0.723850\pi$
$270$	9.60660	+	6.53553i	0.584639	+	0.397740i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	4.24264	−	4.24264i	0.257248	−	0.257248i
$273$	20.4853	−	3.51472i	1.23983	−	0.212720i
$274$		−	2.00000i		−	0.120824i
$275$	12.7279	−	16.9706i	0.767523	−	1.02336i
$276$	1.00000	−	1.41421i	0.0601929	−	0.0851257i
$277$	4.00000	+	4.00000i	0.240337	+	0.240337i	0.816989	−	0.576653i	$-0.195641\pi$
$277$	4.00000	+	4.00000i	0.240337	+	0.240337i	−0.576653	+	0.816989i	$0.695641\pi$
$278$	−8.48528	−	8.48528i	−0.508913	−	0.508913i
$279$	5.65685	−	2.00000i	0.338667	−	0.119737i
$280$	9.00000	+	3.00000i	0.537853	+	0.179284i
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$	3.51472	+	20.4853i	0.209298	+	1.21988i
$283$	18.0000	−	18.0000i	1.06999	−	1.06999i	0.0726300	−	0.997359i	$-0.476861\pi$
$283$	18.0000	−	18.0000i	1.06999	−	1.06999i	0.997359	−	0.0726300i	$-0.0231392\pi$
$284$	5.65685			0.335673
$285$	−15.3137	−	2.34315i	−0.907106	−	0.138796i
$286$	−12.0000			−0.709575
$287$	16.9706	−	16.9706i	1.00174	−	1.00174i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$		−	19.0000i		−	1.11765i
$290$	−7.07107	−	14.1421i	−0.415227	−	0.830455i
$291$	−6.00000	−	4.24264i	−0.351726	−	0.248708i
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	−11.3137	−	11.3137i	−0.660954	−	0.660954i	0.294651	−	0.955605i	$-0.404797\pi$
$293$	−11.3137	−	11.3137i	−0.660954	−	0.660954i	−0.955605	+	0.294651i	$0.904797\pi$
$294$	−15.5563	−	11.0000i	−0.907265	−	0.641533i
$295$	1.00000	−	3.00000i	0.0582223	−	0.174667i
$296$			8.48528i			0.493197i
$297$	10.7574	+	19.2426i	0.624205	+	1.11657i
$298$	1.00000	−	1.00000i	0.0579284	−	0.0579284i
$299$	2.82843			0.163572
$300$	−3.94975	+	7.70711i	−0.228039	+	0.444970i
$301$		0			0
$302$	16.9706	−	16.9706i	0.976546	−	0.976546i
$303$	−3.72792	−	21.7279i	−0.214164	−	1.24824i
$304$			4.00000i			0.229416i
$305$	−7.07107	+	21.2132i	−0.404888	+	1.21466i
$306$	−6.00000	−	16.9706i	−0.342997	−	0.970143i
$307$	−2.00000	−	2.00000i	−0.114146	−	0.114146i	0.647727	−	0.761873i	$-0.275720\pi$
$307$	−2.00000	−	2.00000i	−0.114146	−	0.114146i	−0.761873	+	0.647727i	$0.775720\pi$
$308$	12.7279	+	12.7279i	0.725241	+	0.725241i
$309$	7.07107	−	10.0000i	0.402259	−	0.568880i
$310$	2.00000	+	4.00000i	0.113592	+	0.227185i
$311$		−	22.6274i		−	1.28308i	−0.767088	−	0.641542i	$-0.778295\pi$
$311$		−	22.6274i		−	1.28308i	0.767088	−	0.641542i	$-0.221705\pi$
$312$	4.82843	−	0.828427i	0.273356	−	0.0469005i
$313$	7.00000	−	7.00000i	0.395663	−	0.395663i	−0.481037	−	0.876700i	$-0.659740\pi$
$313$	7.00000	−	7.00000i	0.395663	−	0.395663i	0.876700	+	0.481037i	$0.159740\pi$
$314$	16.9706			0.957704
$315$	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	$0.232113\pi$
$318$	6.82843	−	1.17157i	0.382919	−	0.0656985i
$319$		−	30.0000i		−	1.67968i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$	−4.00000	+	5.65685i	−0.223258	+	0.315735i
$322$	−3.00000	−	3.00000i	−0.167183	−	0.167183i
$323$	16.9706	+	16.9706i	0.944267	+	0.944267i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−14.0000	+	2.00000i	−0.776580	+	0.110940i
$326$			22.6274i			1.25322i
$327$	1.75736	+	10.2426i	0.0971822	+	0.566419i
$328$	4.00000	−	4.00000i	0.220863	−	0.220863i
$329$	50.9117			2.80685
$330$	−13.2426	+	9.72792i	−0.728983	+	0.535504i
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	22.9706	+	10.9706i	1.25878	+	0.601183i
$334$		−	12.0000i		−	0.656611i
$335$	−28.2843	+	14.1421i	−1.54533	+	0.772667i
$336$	−6.00000	−	4.24264i	−0.327327	−	0.231455i
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$	−3.53553	−	3.53553i	−0.192308	−	0.192308i
$339$	8.48528	+	6.00000i	0.460857	+	0.325875i
$340$	12.0000	−	6.00000i	0.650791	−	0.325396i
$341$			8.48528i			0.459504i
$342$	10.8284	+	5.17157i	0.585534	+	0.279647i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	3.12132	−	2.29289i	0.168046	−	0.123445i
$346$	14.0000			0.752645
$347$	−4.24264	+	4.24264i	−0.227757	+	0.227757i	−0.811755	−	0.583998i	$-0.801488\pi$
$347$	−4.24264	+	4.24264i	−0.227757	+	0.227757i	0.583998	+	0.811755i	$0.301488\pi$
$348$	2.07107	+	12.0711i	0.111021	+	0.647077i
$349$			34.0000i			1.81998i	0.414632	+	0.909989i	$0.363910\pi$
$349$			34.0000i			1.81998i	−0.414632	+	0.909989i	$0.636090\pi$
$350$	16.9706	+	12.7279i	0.907115	+	0.680336i
$351$	4.00000	−	14.1421i	0.213504	−	0.754851i
$352$	3.00000	+	3.00000i	0.159901	+	0.159901i
$353$	9.89949	+	9.89949i	0.526897	+	0.526897i	0.919646	−	0.392749i	$-0.128476\pi$
$353$	9.89949	+	9.89949i	0.526897	+	0.526897i	−0.392749	+	0.919646i	$0.628476\pi$
$354$	−1.41421	+	2.00000i	−0.0751646	+	0.106299i
$355$	12.0000	+	4.00000i	0.636894	+	0.212298i
$356$		−	11.3137i		−	0.599625i
$357$	−43.4558	+	7.45584i	−2.29993	+	0.394605i
$358$	3.00000	−	3.00000i	0.158555	−	0.158555i
$359$	−11.3137			−0.597115			−0.298557	−	0.954392i	$-0.596505\pi$
$359$	−11.3137			−0.597115			−0.298557	+	0.954392i	$0.596505\pi$
$360$	4.65685	−	4.82843i	0.245438	−	0.254480i
$361$	3.00000			0.157895
$362$	−4.24264	+	4.24264i	−0.222988	+	0.222988i
$363$	−11.9497	+	2.05025i	−0.627199	+	0.107610i
$364$		−	12.0000i		−	0.628971i
$365$	1.41421	+	2.82843i	0.0740233	+	0.148047i
$366$	10.0000	−	14.1421i	0.522708	−	0.739221i
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	0.994272	−	0.106879i	$-0.0340858\pi$
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	−0.106879	+	0.994272i	$0.534086\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−5.65685	−	16.0000i	−0.294484	−	0.832927i
$370$	−6.00000	+	18.0000i	−0.311925	+	0.935775i
$371$		−	16.9706i		−	0.881068i
$372$	−0.585786	−	3.41421i	−0.0303716	−	0.177019i
$373$	−16.0000	+	16.0000i	−0.828449	+	0.828449i	−0.987302	−	0.158854i	$-0.949220\pi$
$373$	−16.0000	+	16.0000i	−0.828449	+	0.828449i	0.158854	+	0.987302i	$0.449220\pi$
$374$	25.4558			1.31629
$375$	−13.8284	+	13.5563i	−0.714097	+	0.700047i
$376$	12.0000			0.618853
$377$	−14.1421	+	14.1421i	−0.728357	+	0.728357i
$378$	−19.2426	+	10.7574i	−0.989735	+	0.553299i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−2.82843	+	8.48528i	−0.145095	+	0.435286i
$381$	−18.0000	−	12.7279i	−0.922168	−	0.652071i
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	5.65685	+	5.65685i	0.289052	+	0.289052i	0.836705	−	0.547653i	$-0.184479\pi$
$383$	5.65685	+	5.65685i	0.289052	+	0.289052i	−0.547653	+	0.836705i	$0.684479\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	18.0000	+	36.0000i	0.917365	+	1.83473i
$386$		−	21.2132i		−	1.07972i
$387$		0			0
$388$	−3.00000	+	3.00000i	−0.152302	+	0.152302i
$389$	1.41421			0.0717035			0.0358517	−	0.999357i	$-0.488586\pi$
$389$	1.41421			0.0717035			0.0358517	+	0.999357i	$0.488586\pi$
$390$	10.8284	+	1.65685i	0.548319	+	0.0838981i
$391$	−6.00000			−0.303433
$392$	−7.77817	+	7.77817i	−0.392857	+	0.392857i
$393$	0.414214	+	2.41421i	0.0208943	+	0.121781i
$394$			12.0000i			0.604551i
$395$	29.6985	+	9.89949i	1.49429	+	0.498098i
$396$	12.0000	−	4.24264i	0.603023	−	0.213201i
$397$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	−5.65685	−	5.65685i	−0.283552	−	0.283552i
$399$	16.9706	−	24.0000i	0.849591	−	1.20150i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$			22.6274i			1.12996i	0.825105	+	0.564980i	$0.191116\pi$
$401$			22.6274i			1.12996i	−0.825105	+	0.564980i	$0.808884\pi$
$402$	24.1421	−	4.14214i	1.20410	−	0.206591i
$403$	4.00000	−	4.00000i	0.199254	−	0.199254i
$404$	−12.7279			−0.633238
$405$	−7.05025	−	18.8492i	−0.350330	−	0.936626i
$406$	30.0000			1.48888
$407$	−25.4558	+	25.4558i	−1.26180	+	1.26180i
$408$	−10.2426	+	1.75736i	−0.507086	+	0.0870023i
$409$			8.00000i			0.395575i	0.980245	+	0.197787i	$0.0633755\pi$
$409$			8.00000i			0.395575i	−0.980245	+	0.197787i	$0.936624\pi$
$410$	11.3137	−	5.65685i	0.558744	−	0.279372i
$411$	−2.00000	+	2.82843i	−0.0986527	+	0.139516i
$412$	−5.00000	−	5.00000i	−0.246332	−	0.246332i
$413$	4.24264	+	4.24264i	0.208767	+	0.208767i
$414$	−2.82843	+	1.00000i	−0.139010	+	0.0491473i
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$		−	2.82843i		−	0.138675i
$417$	3.51472	+	20.4853i	0.172117	+	1.00317i
$418$	−12.0000	+	12.0000i	−0.586939	+	0.586939i
$419$	−24.0416			−1.17451			−0.587255	−	0.809402i	$-0.699792\pi$
$419$	−24.0416			−1.17451			−0.587255	+	0.809402i	$0.699792\pi$
$420$	−9.72792	−	13.2426i	−0.474674	−	0.646175i
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$	2.82843	−	2.82843i	0.137686	−	0.137686i
$423$	15.5147	−	32.4853i	0.754351	−	1.57949i
$424$		−	4.00000i		−	0.194257i
$425$	29.6985	−	4.24264i	1.44059	−	0.205798i
$426$	−8.00000	−	5.65685i	−0.387601	−	0.274075i
$427$	−30.0000	−	30.0000i	−1.45180	−	1.45180i
$428$	2.82843	+	2.82843i	0.136717	+	0.136717i
$429$	16.9706	+	12.0000i	0.819346	+	0.579365i
$430$		0			0
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$	−4.53553	+	2.53553i	−0.218216	+	0.121991i
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.00923827	−	0.999957i	$-0.497059\pi$
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.999957	−	0.00923827i	$-0.00294067\pi$
$434$	−8.48528			−0.407307
$435$	−4.14214	+	27.0711i	−0.198600	+	1.29796i
$436$	6.00000			0.287348
$437$	2.82843	−	2.82843i	0.135302	−	0.135302i
$438$	−0.414214	−	2.41421i	−0.0197919	−	0.115356i
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$	4.24264	+	8.48528i	0.202260	+	0.404520i
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$	−12.0000	−	12.0000i	−0.570782	−	0.570782i
$443$	21.2132	+	21.2132i	1.00787	+	1.00787i	0.999969	+	0.00790092i	$0.00251497\pi$
$443$	21.2132	+	21.2132i	1.00787	+	1.00787i	0.00790092	+	0.999969i	$0.497485\pi$
$444$	8.48528	−	12.0000i	0.402694	−	0.569495i
$445$	8.00000	−	24.0000i	0.379236	−	1.13771i
$446$		−	15.5563i		−	0.736614i
$447$	−2.41421	+	0.414214i	−0.114188	+	0.0195916i
$448$	−3.00000	+	3.00000i	−0.141737	+	0.141737i
$449$	2.82843			0.133482			0.0667409	−	0.997770i	$-0.478740\pi$
$449$	2.82843			0.133482			0.0667409	+	0.997770i	$0.478740\pi$
$450$	13.2929	−	6.94975i	0.626633	−	0.327614i
$451$	24.0000			1.13012
$452$	4.24264	−	4.24264i	0.199557	−	0.199557i
$453$	−40.9706	+	7.02944i	−1.92496	+	0.330272i
$454$			14.0000i			0.657053i
$455$	8.48528	−	25.4558i	0.397796	−	1.19339i
$456$	4.00000	−	5.65685i	0.187317	−	0.264906i
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	0.964769	−	0.263099i	$-0.0847444\pi$
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	−0.263099	+	0.964769i	$0.584744\pi$
$458$	−7.07107	−	7.07107i	−0.330409	−	0.330409i
$459$	−8.48528	+	30.0000i	−0.396059	+	1.40028i
$460$	−1.00000	−	2.00000i	−0.0466252	−	0.0932505i
$461$			12.7279i			0.592798i	0.955064	+	0.296399i	$0.0957859\pi$
$461$			12.7279i			0.592798i	−0.955064	+	0.296399i	$0.904214\pi$
$462$	−5.27208	−	30.7279i	−0.245279	−	1.42959i
$463$	−13.0000	+	13.0000i	−0.604161	+	0.604161i	−0.941414	−	0.337253i	$-0.890502\pi$
$463$	−13.0000	+	13.0000i	−0.604161	+	0.604161i	0.337253	+	0.941414i	$0.390502\pi$
$464$	7.07107			0.328266
$465$	1.17157	−	7.65685i	0.0543304	−	0.355078i
$466$	−6.00000			−0.277945
$467$	−14.1421	+	14.1421i	−0.654420	+	0.654420i	−0.954054	−	0.299634i	$-0.903135\pi$
$467$	−14.1421	+	14.1421i	−0.654420	+	0.654420i	0.299634	+	0.954054i	$0.403135\pi$
$468$	−7.65685	−	3.65685i	−0.353938	−	0.169038i
$469$		−	60.0000i		−	2.77054i
$470$	25.4558	+	8.48528i	1.17419	+	0.391397i
$471$	−24.0000	−	16.9706i	−1.10586	−	0.781962i
$472$	1.00000	+	1.00000i	0.0460287	+	0.0460287i
$473$		0			0
$474$	−19.7990	−	14.0000i	−0.909398	−	0.643041i
$475$	−12.0000	+	16.0000i	−0.550598	+	0.734130i
$476$			25.4558i			1.16677i
$477$	−10.8284	−	5.17157i	−0.495800	−	0.236790i
$478$	8.00000	−	8.00000i	0.365911	−	0.365911i
$479$	2.82843			0.129234			0.0646171	−	0.997910i	$-0.479417\pi$
$479$	2.82843			0.129234			0.0646171	+	0.997910i	$0.479417\pi$
$480$	−2.29289	−	3.12132i	−0.104656	−	0.142468i
$481$	24.0000			1.09431
$482$		0			0
$483$	1.24264	+	7.24264i	0.0565421	+	0.329552i
$484$			7.00000i			0.318182i
$485$	−8.48528	+	4.24264i	−0.385297	+	0.192648i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	0.473152	−	0.880981i	$-0.343116\pi$
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	−0.880981	+	0.473152i	$0.843116\pi$
$488$	−7.07107	−	7.07107i	−0.320092	−	0.320092i
$489$	22.6274	−	32.0000i	1.02325	−	1.44709i
$490$	−22.0000	+	11.0000i	−0.993859	+	0.496929i
$491$		−	32.5269i		−	1.46792i	−0.679193	−	0.733959i	$-0.737670\pi$
$491$		−	32.5269i		−	1.46792i	0.679193	−	0.733959i	$-0.262330\pi$
$492$	−9.65685	+	1.65685i	−0.435365	+	0.0746968i
$493$	30.0000	−	30.0000i	1.35113	−	1.35113i
$494$	11.3137			0.509028
$495$	28.4558	−	0.514719i	1.27900	−	0.0231349i
$496$	−2.00000			−0.0898027
$497$	−16.9706	+	16.9706i	−0.761234	+	0.761234i
$498$	20.4853	−	3.51472i	0.917967	−	0.157498i
$499$		−	8.00000i		−	0.358129i	−0.983837	−	0.179065i	$-0.942693\pi$
$499$		−	8.00000i		−	0.358129i	0.983837	−	0.179065i	$-0.0573071\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$	−12.0000	+	16.9706i	−0.536120	+	0.758189i
$502$	−13.0000	−	13.0000i	−0.580218	−	0.580218i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$	4.24264	+	12.0000i	0.188982	+	0.534522i
$505$	−27.0000	−	9.00000i	−1.20148	−	0.400495i
$506$		−	4.24264i		−	0.188608i
$507$	1.46447	+	8.53553i	0.0650392	+	0.379076i
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	21.2132			0.940259			0.470129	−	0.882598i	$-0.344207\pi$
$509$	21.2132			0.940259			0.470129	+	0.882598i	$0.344207\pi$
$510$	−22.9706	−	3.51472i	−1.01715	−	0.155634i
$511$	−6.00000			−0.265424
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−10.1421	−	18.1421i	−0.447786	−	0.800995i
$514$			2.00000i			0.0882162i
$515$	−7.07107	−	14.1421i	−0.311588	−	0.623177i
$516$		0			0
$517$	36.0000	+	36.0000i	1.58328	+	1.58328i
$518$	−25.4558	−	25.4558i	−1.11847	−	1.11847i
$519$	−19.7990	−	14.0000i	−0.869079	−	0.614532i
$520$	2.00000	−	6.00000i	0.0877058	−	0.263117i
$521$		−	28.2843i		−	1.23916i	−0.784935	−	0.619578i	$-0.787304\pi$
$521$		−	28.2843i		−	1.23916i	0.784935	−	0.619578i	$-0.212696\pi$
$522$	9.14214	−	19.1421i	0.400140	−	0.837829i
$523$	18.0000	−	18.0000i	0.787085	−	0.787085i	−0.193930	−	0.981015i	$-0.562124\pi$
$523$	18.0000	−	18.0000i	0.787085	−	0.787085i	0.981015	+	0.193930i	$0.0621236\pi$
$524$	1.41421			0.0617802
$525$	−11.2721	−	34.9706i	−0.491954	−	1.52624i
$526$	−24.0000			−1.04645
$527$	−8.48528	+	8.48528i	−0.369625	+	0.369625i
$528$	−1.24264	−	7.24264i	−0.0540790	−	0.315195i
$529$			1.00000i			0.0434783i
$530$	2.82843	−	8.48528i	0.122859	−	0.368577i
$531$	4.00000	−	1.41421i	0.173585	−	0.0613716i
$532$	−12.0000	−	12.0000i	−0.520266	−	0.520266i
$533$	−11.3137	−	11.3137i	−0.490051	−	0.490051i
$534$	−11.3137	+	16.0000i	−0.489592	+	0.692388i
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$		−	14.1421i		−	0.610847i
$537$	−7.24264	+	1.24264i	−0.312543	+	0.0536239i
$538$	15.0000	−	15.0000i	0.646696	−	0.646696i
$539$	−46.6690			−2.01018
$540$	−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	$0.458830\pi$
$542$	−11.3137	+	11.3137i	−0.485965	+	0.485965i
$543$	10.2426	−	1.75736i	0.439554	−	0.0754155i
$544$			6.00000i			0.257248i
$545$	12.7279	+	4.24264i	0.545204	+	0.181735i
$546$	−12.0000	+	16.9706i	−0.513553	+	0.726273i
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	0.208416	−	0.978040i	$-0.433169\pi$
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	−0.978040	+	0.208416i	$0.933169\pi$
$548$	1.41421	+	1.41421i	0.0604122	+	0.0604122i
$549$	−28.2843	+	10.0000i	−1.20714	+	0.426790i
$550$	3.00000	+	21.0000i	0.127920	+	0.895443i
$551$			28.2843i			1.20495i
$552$	0.292893	+	1.70711i	0.0124664	+	0.0726593i
$553$	−42.0000	+	42.0000i	−1.78602	+	1.78602i
$554$	−5.65685			−0.240337
$555$	26.4853	−	19.4558i	1.12424	−	0.825855i
$556$	12.0000			0.508913
$557$	16.9706	−	16.9706i	0.719066	−	0.719066i	−0.249348	−	0.968414i	$-0.580216\pi$
$557$	16.9706	−	16.9706i	0.719066	−	0.719066i	0.968414	+	0.249348i	$0.0802163\pi$
$558$	−2.58579	+	5.41421i	−0.109465	+	0.229202i
$559$		0			0
$560$	−8.48528	+	4.24264i	−0.358569	+	0.179284i
$561$	−36.0000	−	25.4558i	−1.51992	−	1.07475i
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	4.24264	+	4.24264i	0.178806	+	0.178806i	0.790835	−	0.612029i	$-0.209647\pi$
$563$	4.24264	+	4.24264i	0.178806	+	0.178806i	−0.612029	+	0.790835i	$0.709647\pi$
$564$	−16.9706	−	12.0000i	−0.714590	−	0.505291i
$565$	12.0000	−	6.00000i	0.504844	−	0.252422i
$566$			25.4558i			1.06999i
$567$	37.9706	+	4.02944i	1.59461	+	0.169220i
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	−5.65685			−0.237148			−0.118574	−	0.992945i	$-0.537832\pi$
$569$	−5.65685			−0.237148			−0.118574	+	0.992945i	$0.537832\pi$
$570$	12.4853	−	9.17157i	0.522951	−	0.384155i
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$	8.48528	−	8.48528i	0.354787	−	0.354787i
$573$	−0.828427	−	4.82843i	−0.0346080	−	0.201710i
$574$			24.0000i			1.00174i
$575$	−0.707107	−	4.94975i	−0.0294884	−	0.206419i
$576$	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	$0.664649\pi$
$578$	13.4350	+	13.4350i	0.558824	+	0.558824i
$579$	−21.2132	+	30.0000i	−0.881591	+	1.24676i
$580$	15.0000	+	5.00000i	0.622841	+	0.207614i
$581$		−	50.9117i		−	2.11217i
$582$	7.24264	−	1.24264i	0.300217	−	0.0515091i
$583$	12.0000	−	12.0000i	0.496989	−	0.496989i
$584$	−1.41421			−0.0585206
$585$	−13.6569	−	13.1716i	−0.564641	−	0.544578i
$586$	16.0000			0.660954
$587$	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	$0.170343\pi$
$588$	18.7782	−	3.22183i	0.774399	−	0.132866i
$589$		−	8.00000i		−	0.329634i
$590$	1.41421	+	2.82843i	0.0582223	+	0.116445i
$591$	12.0000	−	16.9706i	0.493614	−	0.698076i
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$	−18.3848	−	18.3848i	−0.754972	−	0.754972i	0.220430	−	0.975403i	$-0.429254\pi$
$593$	−18.3848	−	18.3848i	−0.754972	−	0.754972i	−0.975403	+	0.220430i	$0.929254\pi$
$594$	−21.2132	−	6.00000i	−0.870388	−	0.246183i
$595$	−18.0000	+	54.0000i	−0.737928	+	2.21378i
$596$			1.41421i			0.0579284i
$597$	2.34315	+	13.6569i	0.0958986	+	0.558938i
$598$	−2.00000	+	2.00000i	−0.0817861	+	0.0817861i
$599$	−19.7990			−0.808965			−0.404482	−	0.914546i	$-0.632548\pi$
$599$	−19.7990			−0.808965			−0.404482	+	0.914546i	$0.632548\pi$
$600$	−2.65685	−	8.24264i	−0.108466	−	0.336504i
$601$	6.00000			0.244745			0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000			0.244745			0.122373	+	0.992484i	$0.460950\pi$
$602$		0			0
$603$	−38.2843	−	18.2843i	−1.55906	−	0.744593i
$604$			24.0000i			0.976546i
$605$	−4.94975	+	14.8492i	−0.201236	+	0.603708i
$606$	18.0000	+	12.7279i	0.731200	+	0.517036i
$607$	−27.0000	−	27.0000i	−1.09590	−	1.09590i	−0.994885	−	0.101011i	$-0.967792\pi$
$607$	−27.0000	−	27.0000i	−1.09590	−	1.09590i	−0.101011	−	0.994885i	$-0.532208\pi$
$608$	−2.82843	−	2.82843i	−0.114708	−	0.114708i
$609$	−42.4264	−	30.0000i	−1.71920	−	1.21566i
$610$	−10.0000	−	20.0000i	−0.404888	−	0.809776i
$611$		−	33.9411i		−	1.37311i
$612$	16.2426	+	7.75736i	0.656570	+	0.313573i
$613$	−26.0000	+	26.0000i	−1.05013	+	1.05013i	−0.0514548	+	0.998675i	$0.516386\pi$
$613$	−26.0000	+	26.0000i	−1.05013	+	1.05013i	−0.998675	+	0.0514548i	$0.983614\pi$
$614$	2.82843			0.114146
$615$	−21.6569	−	3.31371i	−0.873289	−	0.133622i
$616$	−18.0000			−0.725241
$617$	29.6985	−	29.6985i	1.19562	−	1.19562i	0.220150	−	0.975466i	$-0.429345\pi$
$617$	29.6985	−	29.6985i	1.19562	−	1.19562i	0.975466	−	0.220150i	$-0.0706547\pi$
$618$	2.07107	+	12.0711i	0.0833106	+	0.485570i
$619$		−	44.0000i		−	1.76851i	−0.467005	−	0.884255i	$-0.654667\pi$
$619$		−	44.0000i		−	1.76851i	0.467005	−	0.884255i	$-0.345333\pi$
$620$	−4.24264	−	1.41421i	−0.170389	−	0.0567962i
$621$	5.00000	+	1.41421i	0.200643	+	0.0567504i
$622$	16.0000	+	16.0000i	0.641542	+	0.641542i
$623$	33.9411	+	33.9411i	1.35982	+	1.35982i
$624$	−2.82843	+	4.00000i	−0.113228	+	0.160128i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			9.89949i			0.395663i
$627$	28.9706	−	4.97056i	1.15697	−	0.198505i
$628$	−12.0000	+	12.0000i	−0.478852	+	0.478852i
$629$	−50.9117			−2.02998
$630$	0.514719	+	28.4558i	0.0205069	+	1.13371i
$631$	−38.0000			−1.51276			−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000			−1.51276			−0.756378	+	0.654135i	$0.773033\pi$
$632$	−9.89949	+	9.89949i	−0.393781	+	0.393781i
$633$	−6.82843	+	1.17157i	−0.271406	+	0.0465658i
$634$			2.00000i			0.0794301i
$635$	−25.4558	+	12.7279i	−1.01018	+	0.505092i
$636$	−4.00000	+	5.65685i	−0.158610	+	0.224309i
$637$	22.0000	+	22.0000i	0.871672	+	0.871672i
$638$	21.2132	+	21.2132i	0.839839	+	0.839839i
$639$	5.65685	+	16.0000i	0.223782	+	0.632950i
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$		−	14.1421i		−	0.558581i	−0.960207	−	0.279290i	$-0.909901\pi$
$641$		−	14.1421i		−	0.558581i	0.960207	−	0.279290i	$-0.0900992\pi$
$642$	−1.17157	−	6.82843i	−0.0462383	−	0.269497i
$643$	6.00000	−	6.00000i	0.236617	−	0.236617i	−0.578831	−	0.815448i	$-0.696491\pi$
$643$	6.00000	−	6.00000i	0.236617	−	0.236617i	0.815448	+	0.578831i	$0.196491\pi$
$644$	4.24264			0.167183
$645$		0			0
$646$	−24.0000			−0.944267
$647$	22.6274	−	22.6274i	0.889576	−	0.889576i	−0.104907	−	0.994482i	$-0.533454\pi$
$647$	22.6274	−	22.6274i	0.889576	−	0.889576i	0.994482	+	0.104907i	$0.0334543\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$			6.00000i			0.235521i
$650$	8.48528	−	11.3137i	0.332820	−	0.443760i
$651$	12.0000	+	8.48528i	0.470317	+	0.332564i
$652$	−16.0000	−	16.0000i	−0.626608	−	0.626608i
$653$	24.0416	+	24.0416i	0.940822	+	0.940822i	0.998344	−	0.0575225i	$-0.0183201\pi$
$653$	24.0416	+	24.0416i	0.940822	+	0.940822i	−0.0575225	+	0.998344i	$0.518320\pi$
$654$	−8.48528	−	6.00000i	−0.331801	−	0.234619i
$655$	3.00000	+	1.00000i	0.117220	+	0.0390732i
$656$			5.65685i			0.220863i
$657$	−1.82843	+	3.82843i	−0.0713337	+	0.149361i
$658$	−36.0000	+	36.0000i	−1.40343	+	1.40343i
$659$	43.8406			1.70779			0.853894	−	0.520447i	$-0.174235\pi$
$659$	43.8406			1.70779			0.853894	+	0.520447i	$0.174235\pi$
$660$	2.48528	−	16.2426i	0.0967394	−	0.632244i
$661$	26.0000			1.01128			0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000			1.01128			0.505641	+	0.862744i	$0.331256\pi$
$662$	−2.82843	+	2.82843i	−0.109930	+	0.109930i
$663$	4.97056	+	28.9706i	0.193041	+	1.12512i
$664$		−	12.0000i		−	0.465690i
$665$	−16.9706	−	33.9411i	−0.658090	−	1.31618i
$666$	−24.0000	+	8.48528i	−0.929981	+	0.328798i
$667$	−5.00000	−	5.00000i	−0.193601	−	0.193601i
$668$	8.48528	+	8.48528i	0.328305	+	0.328305i
$669$	−15.5563	+	22.0000i	−0.601443	+	0.850569i
$670$	10.0000	−	30.0000i	0.386334	−	1.15900i
$671$		−	42.4264i		−	1.63785i
$672$	7.24264	−	1.24264i	0.279391	−	0.0479359i
$673$	9.00000	−	9.00000i	0.346925	−	0.346925i	−0.512038	−	0.858963i	$-0.671109\pi$
$673$	9.00000	−	9.00000i	0.346925	−	0.346925i	0.858963	+	0.512038i	$0.171109\pi$
$674$	−12.7279			−0.490261
$675$	−25.7487	−	3.46447i	−0.991069	−	0.133347i
$676$	5.00000			0.192308
$677$	4.24264	−	4.24264i	0.163058	−	0.163058i	−0.620862	−	0.783920i	$-0.713217\pi$
$677$	4.24264	−	4.24264i	0.163058	−	0.163058i	0.783920	+	0.620862i	$0.213217\pi$
$678$	−10.2426	+	1.75736i	−0.393366	+	0.0674910i
$679$		−	18.0000i		−	0.690777i
$680$	−4.24264	+	12.7279i	−0.162698	+	0.488094i
$681$	14.0000	−	19.7990i	0.536481	−	0.758699i
$682$	−6.00000	−	6.00000i	−0.229752	−	0.229752i
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	0.850559	−	0.525879i	$-0.176264\pi$
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	−0.525879	+	0.850559i	$0.676264\pi$
$684$	−11.3137	+	4.00000i	−0.432590	+	0.152944i
$685$	2.00000	+	4.00000i	0.0764161	+	0.152832i
$686$		−	16.9706i		−	0.647939i
$687$	2.92893	+	17.0711i	0.111746	+	0.651302i
$688$		0			0
$689$	−11.3137			−0.431018
$690$	−0.585786	+	3.82843i	−0.0223005	+	0.145746i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−9.89949	+	9.89949i	−0.376322	+	0.376322i
$693$	−23.2721	+	48.7279i	−0.884033	+	1.85102i
$694$		−	6.00000i		−	0.227757i
$695$	25.4558	+	8.48528i	0.965595	+	0.321865i
$696$	−10.0000	−	7.07107i	−0.379049	−	0.268028i
$697$	24.0000	+	24.0000i	0.909065	+	0.909065i
$698$	−24.0416	−	24.0416i	−0.909989	−	0.909989i
$699$	8.48528	+	6.00000i	0.320943	+	0.226941i
$700$	−21.0000	+	3.00000i	−0.793725	+	0.113389i
$701$			43.8406i			1.65584i	0.560848	+	0.827919i	$0.310475\pi$
$701$			43.8406i			1.65584i	−0.560848	+	0.827919i	$0.689525\pi$
$702$	7.17157	+	12.8284i	0.270674	+	0.484178i
$703$	24.0000	−	24.0000i	0.905177	−	0.905177i
$704$	−4.24264			−0.159901
$705$	−27.5147	−	37.4558i	−1.03626	−	1.41067i
$706$	−14.0000			−0.526897
$707$	38.1838	−	38.1838i	1.43605	−	1.43605i
$708$	−0.414214	−	2.41421i	−0.0155671	−	0.0907317i
$709$			18.0000i			0.676004i	0.941145	+	0.338002i	$0.109751\pi$
$709$			18.0000i			0.676004i	−0.941145	+	0.338002i	$0.890249\pi$
$710$	−11.3137	+	5.65685i	−0.424596	+	0.212298i
$711$	14.0000	+	39.5980i	0.525041	+	1.48504i
$712$	8.00000	+	8.00000i	0.299813	+	0.299813i
$713$	1.41421	+	1.41421i	0.0529627	+	0.0529627i
$714$	25.4558	−	36.0000i	0.952661	−	1.34727i
$715$	24.0000	−	12.0000i	0.897549	−	0.448775i
$716$			4.24264i			0.158555i
$717$	−19.3137	+	3.31371i	−0.721284	+	0.123753i
$718$	8.00000	−	8.00000i	0.298557	−	0.298557i
$719$	31.1127			1.16031			0.580154	−	0.814507i	$-0.302992\pi$
$719$	31.1127			1.16031			0.580154	+	0.814507i	$0.302992\pi$
$720$	0.121320	+	6.70711i	0.00452134	+	0.249959i
$721$	30.0000			1.11726
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$		0			0
$724$		−	6.00000i		−	0.222988i
$725$	28.2843	+	21.2132i	1.05045	+	0.787839i
$726$	7.00000	−	9.89949i	0.259794	−	0.367405i
$727$	−27.0000	−	27.0000i	−1.00137	−	1.00137i	−0.999999	−	0.00137552i	$-0.999562\pi$
$727$	−27.0000	−	27.0000i	−1.00137	−	1.00137i	−0.00137552	−	0.999999i	$-0.500438\pi$
$728$	8.48528	+	8.48528i	0.314485	+	0.314485i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−3.00000	−	1.00000i	−0.111035	−	0.0370117i
$731$		0			0
$732$	2.92893	+	17.0711i	0.108256	+	0.630965i
$733$	14.0000	−	14.0000i	0.517102	−	0.517102i	−0.399592	−	0.916693i	$-0.630848\pi$
$733$	14.0000	−	14.0000i	0.517102	−	0.517102i	0.916693	+	0.399592i	$0.130848\pi$
$734$	−24.0416			−0.887393
$735$	42.1127	+	6.44365i	1.55335	+	0.237678i
$736$	1.00000			0.0368605
$737$	42.4264	−	42.4264i	1.56280	−	1.56280i
$738$	15.3137	+	7.31371i	0.563705	+	0.269221i
$739$		−	24.0000i		−	0.882854i	−0.897297	−	0.441427i	$-0.854472\pi$
$739$		−	24.0000i		−	0.882854i	0.897297	−	0.441427i	$-0.145528\pi$
$740$	−8.48528	−	16.9706i	−0.311925	−	0.623850i
$741$	−16.0000	−	11.3137i	−0.587775	−	0.415619i
$742$	12.0000	+	12.0000i	0.440534	+	0.440534i
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.988192	+	0.153222i	$0.0489651\pi$
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.153222	+	0.988192i	$0.451035\pi$
$744$	2.82843	+	2.00000i	0.103695	+	0.0733236i
$745$	−1.00000	+	3.00000i	−0.0366372	+	0.109911i
$746$		−	22.6274i		−	0.828449i
$747$	−32.4853	−	15.5147i	−1.18857	−	0.567654i
$748$	−18.0000	+	18.0000i	−0.658145	+	0.658145i
$749$	−16.9706			−0.620091
$750$	0.192388	−	19.3640i	0.00702502	−	0.707072i
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$	−8.48528	+	8.48528i	−0.309426	+	0.309426i
$753$	5.38478	+	31.3848i	0.196232	+	1.14372i
$754$		−	20.0000i		−	0.728357i
$755$	−16.9706	+	50.9117i	−0.617622	+	1.85287i
$756$	6.00000	−	21.2132i	0.218218	−	0.771517i
$757$	10.0000	+	10.0000i	0.363456	+	0.363456i	0.865084	−	0.501628i	$-0.167265\pi$
$757$	10.0000	+	10.0000i	0.363456	+	0.363456i	−0.501628	+	0.865084i	$0.667265\pi$
$758$		0			0
$759$	−4.24264	+	6.00000i	−0.153998	+	0.217786i
$760$	−4.00000	−	8.00000i	−0.145095	−	0.290191i
$761$		−	25.4558i		−	0.922774i	−0.887199	−	0.461387i	$-0.847352\pi$
$761$		−	25.4558i		−	0.922774i	0.887199	−	0.461387i	$-0.152648\pi$
$762$	21.7279	−	3.72792i	0.787120	−	0.135048i
$763$	−18.0000	+	18.0000i	−0.651644	+	0.651644i
$764$	−2.82843			−0.102329
$765$	28.9706	+	27.9411i	1.04743	+	1.01021i
$766$	−8.00000			−0.289052
$767$	2.82843	−	2.82843i	0.102129	−	0.102129i
$768$	1.70711	−	0.292893i	0.0615999	−	0.0105689i
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$	−38.1838	−	12.7279i	−1.37605	−	0.458682i
$771$	2.00000	−	2.82843i	0.0720282	−	0.101863i
$772$	15.0000	+	15.0000i	0.539862	+	0.539862i
$773$	15.5563	+	15.5563i	0.559523	+	0.559523i	0.929172	−	0.369649i	$-0.120522\pi$
$773$	15.5563	+	15.5563i	0.559523	+	0.559523i	−0.369649	+	0.929172i	$0.620522\pi$
$774$		0			0
$775$	−8.00000	−	6.00000i	−0.287368	−	0.215526i
$776$		−	4.24264i		−	0.152302i
$777$	10.5442	+	61.4558i	0.378269	+	2.20472i
$778$	−1.00000	+	1.00000i	−0.0358517	+	0.0358517i
$779$	−22.6274			−0.810711
$780$	−8.82843	+	6.48528i	−0.316108	+	0.232210i
$781$	−24.0000			−0.858788
$782$	4.24264	−	4.24264i	0.151717	−	0.151717i
$783$	−32.0711	+	17.9289i	−1.14613	+	0.640728i
$784$		−	11.0000i		−	0.392857i
$785$	−33.9411	+	16.9706i	−1.21141	+	0.605705i
$786$	−2.00000	−	1.41421i	−0.0713376	−	0.0504433i
$787$	18.0000	+	18.0000i	0.641631	+	0.641631i	0.950956	−	0.309326i	$-0.100103\pi$
$787$	18.0000	+	18.0000i	0.641631	+	0.641631i	−0.309326	+	0.950956i	$0.600103\pi$
$788$	−8.48528	−	8.48528i	−0.302276	−	0.302276i
$789$	33.9411	+	24.0000i	1.20834	+	0.854423i
$790$	−28.0000	+	14.0000i	−0.996195	+	0.498098i
$791$			25.4558i			0.905106i
$792$	−5.48528	+	11.4853i	−0.194911	+	0.408112i
$793$	−20.0000	+	20.0000i	−0.710221	+	0.710221i
$794$		0			0
$795$	−12.4853	+	9.17157i	−0.442807	+	0.325282i
$796$	8.00000			0.283552
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	−0.731710	−	0.681616i	$-0.761277\pi$
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	0.681616	+	0.731710i	$0.261277\pi$
$798$	4.97056	+	28.9706i	0.175956	+	1.02555i
$799$			72.0000i			2.54718i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$	32.0000	−	11.3137i	1.13066	−	0.399750i
$802$	−16.0000	−	16.0000i	−0.564980	−	0.564980i
$803$	−4.24264	−	4.24264i	−0.149720	−	0.149720i
$804$	−14.1421	+	20.0000i	−0.498755	+	0.705346i
$805$	9.00000	+	3.00000i	0.317208	+	0.105736i
$806$			5.65685i			0.199254i
$807$	−36.2132	+	6.21320i	−1.27477	+	0.218715i
$808$	9.00000	−	9.00000i	0.316619	−	0.316619i
$809$	5.65685			0.198884			0.0994422	−	0.995043i	$-0.468294\pi$
$809$	5.65685			0.198884			0.0994422	+	0.995043i	$0.468294\pi$
$810$	18.3137	+	8.34315i	0.643478	+	0.293148i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−21.2132	+	21.2132i	−0.744438	+	0.744438i
$813$	27.3137	−	4.68629i	0.957934	−	0.164355i
$814$		−	36.0000i		−	1.26180i
$815$	−22.6274	−	45.2548i	−0.792604	−	1.58521i
$816$	6.00000	−	8.48528i	0.210042	−	0.297044i
$817$		0			0
$818$	−5.65685	−	5.65685i	−0.197787	−	0.197787i
$819$	33.9411	−	12.0000i	1.18600	−	0.419314i
$820$	−4.00000	+	12.0000i	−0.139686	+	0.419058i
$821$		−	38.1838i		−	1.33262i	−0.745674	−	0.666311i	$-0.767872\pi$
$821$		−	38.1838i		−	1.33262i	0.745674	−	0.666311i	$-0.232128\pi$
$822$	−0.585786	−	3.41421i	−0.0204316	−	0.119084i
$823$	13.0000	−	13.0000i	0.453152	−	0.453152i	−0.443248	−	0.896399i	$-0.646174\pi$
$823$	13.0000	−	13.0000i	0.453152	−	0.453152i	0.896399	+	0.443248i	$0.146174\pi$
$824$	7.07107			0.246332
$825$	16.7574	−	32.6985i	0.583416	−	1.13842i
$826$	−6.00000			−0.208767
$827$	4.24264	−	4.24264i	0.147531	−	0.147531i	−0.629483	−	0.777014i	$-0.716733\pi$
$827$	4.24264	−	4.24264i	0.147531	−	0.147531i	0.777014	+	0.629483i	$0.216733\pi$
$828$	1.29289	−	2.70711i	0.0449311	−	0.0940785i
$829$			30.0000i			1.04194i	0.853574	+	0.520972i	$0.174430\pi$
$829$			30.0000i			1.04194i	−0.853574	+	0.520972i	$0.825570\pi$
$830$	8.48528	−	25.4558i	0.294528	−	0.883585i
$831$	8.00000	+	5.65685i	0.277517	+	0.196234i
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	−46.6690	−	46.6690i	−1.61699	−	1.61699i
$834$	−16.9706	−	12.0000i	−0.587643	−	0.415526i
$835$	12.0000	+	24.0000i	0.415277	+	0.830554i
$836$		−	16.9706i		−	0.586939i
$837$	9.07107	−	5.07107i	0.313542	−	0.175282i
$838$	17.0000	−	17.0000i	0.587255	−	0.587255i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	16.2426	+	2.48528i	0.560424	+	0.0857504i
$841$	21.0000			0.724138
$842$	21.2132	−	21.2132i	0.731055	−	0.731055i
$843$	1.65685	+	9.65685i	0.0570651	+	0.332600i
$844$			4.00000i			0.137686i
$845$	10.6066	+	3.53553i	0.364878	+	0.121626i
$846$	12.0000	+	33.9411i	0.412568	+	1.16692i
$847$	−21.0000	−	21.0000i	−0.721569	−	0.721569i
$848$	2.82843	+	2.82843i	0.0971286	+	0.0971286i
$849$	25.4558	−	36.0000i	0.873642	−	1.23552i
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$			8.48528i			0.290872i
$852$	9.65685	−	1.65685i	0.330838	−	0.0567629i
$853$	12.0000	−	12.0000i	0.410872	−	0.410872i	−0.471170	−	0.882042i	$-0.656168\pi$
$853$	12.0000	−	12.0000i	0.410872	−	0.410872i	0.882042	+	0.471170i	$0.156168\pi$
$854$	42.4264			1.45180
$855$	−26.8284	+	0.485281i	−0.917513	+	0.0165963i
$856$	−4.00000			−0.136717
$857$	−29.6985	+	29.6985i	−1.01448	+	1.01448i	−0.0145873	+	0.999894i	$0.504643\pi$
$857$	−29.6985	+	29.6985i	−1.01448	+	1.01448i	−0.999894	+	0.0145873i	$0.995357\pi$
$858$	−20.4853	+	3.51472i	−0.699356	+	0.119991i
$859$		−	32.0000i		−	1.09183i	−0.837842	−	0.545913i	$-0.816183\pi$
$859$		−	32.0000i		−	1.09183i	0.837842	−	0.545913i	$-0.183817\pi$
$860$		0			0
$861$	24.0000	−	33.9411i	0.817918	−	1.15671i
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	−31.1127	−	31.1127i	−1.05909	−	1.05909i	−0.998141	−	0.0609476i	$-0.980588\pi$
$863$	−31.1127	−	31.1127i	−1.05909	−	1.05909i	−0.0609476	−	0.998141i	$-0.519412\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	−28.0000	+	14.0000i	−0.952029	+	0.476014i
$866$			29.6985i			1.00920i
$867$	−5.56497	−	32.4350i	−0.188996	−	1.10155i
$868$	6.00000	−	6.00000i	0.203653	−	0.203653i
$869$	−59.3970			−2.01490
$870$	−16.2132	−	22.0711i	−0.549679	−	0.748279i
$871$	−40.0000			−1.35535
$872$	−4.24264	+	4.24264i	−0.143674	+	0.143674i
$873$	−11.4853	−	5.48528i	−0.388718	−	0.185649i
$874$			4.00000i			0.135302i
$875$	−46.6690	−	8.48528i	−1.57770	−	0.286855i
$876$	2.00000	+	1.41421i	0.0675737	+	0.0477818i
$877$	14.0000	+	14.0000i	0.472746	+	0.472746i	0.902802	−	0.430056i	$-0.141506\pi$
$877$	14.0000	+	14.0000i	0.472746	+	0.472746i	−0.430056	+	0.902802i	$0.641506\pi$
$878$	5.65685	+	5.65685i	0.190910	+	0.190910i
$879$	−22.6274	−	16.0000i	−0.763204	−	0.539667i
$880$	−9.00000	−	3.00000i	−0.303390	−	0.101130i
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$	−29.7782	−	14.2218i	−1.00268	−	0.478874i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$	16.9706			0.570782
$885$	0.828427	−	5.41421i	0.0278473	−	0.181997i
$886$	−30.0000			−1.00787
$887$	19.7990	−	19.7990i	0.664785	−	0.664785i	−0.291719	−	0.956504i	$-0.594227\pi$
$887$	19.7990	−	19.7990i	0.664785	−	0.664785i	0.956504	+	0.291719i	$0.0942272\pi$
$888$	2.48528	+	14.4853i	0.0834006	+	0.486094i
$889$		−	54.0000i		−	1.81110i
$890$	11.3137	+	22.6274i	0.379236	+	0.758473i
$891$	24.0000	+	29.6985i	0.804030	+	0.994937i
$892$	11.0000	+	11.0000i	0.368307	+	0.368307i
$893$	−33.9411	−	33.9411i	−1.13580	−	1.13580i
$894$	1.41421	−	2.00000i	0.0472984	−	0.0668900i
$895$	−3.00000	+	9.00000i	−0.100279	+	0.300837i
$896$		−	4.24264i		−	0.141737i
$897$	4.82843	−	0.828427i	0.161216	−	0.0276604i
$898$	−2.00000	+	2.00000i	−0.0667409	+	0.0667409i
$899$	−14.1421			−0.471667
$900$	−4.48528	+	14.3137i	−0.149509	+	0.477124i
$901$	24.0000			0.799556
$902$	−16.9706	+	16.9706i	−0.565058	+	0.565058i
$903$		0			0
$904$			6.00000i			0.199557i
$905$	4.24264	−	12.7279i	0.141030	−	0.423090i
$906$	24.0000	−	33.9411i	0.797347	−	1.12762i
$907$	32.0000	+	32.0000i	1.06254	+	1.06254i	0.997909	+	0.0646335i	$0.0205878\pi$
$907$	32.0000	+	32.0000i	1.06254	+	1.06254i	0.0646335	+	0.997909i	$0.479412\pi$
$908$	−9.89949	−	9.89949i	−0.328526	−	0.328526i
$909$	−12.7279	−	36.0000i	−0.422159	−	1.19404i
$910$	12.0000	+	24.0000i	0.397796	+	0.795592i
$911$			50.9117i			1.68678i	0.537302	+	0.843390i	$0.319443\pi$
$911$			50.9117i			1.68678i	−0.537302	+	0.843390i	$0.680557\pi$
$912$	1.17157	+	6.82843i	0.0387947	+	0.226112i
$913$	36.0000	−	36.0000i	1.19143	−	1.19143i
$914$	−21.2132			−0.701670
$915$	−5.85786	+	38.2843i	−0.193655	+	1.26564i
$916$	10.0000			0.330409
$917$	−4.24264	+	4.24264i	−0.140104	+	0.140104i
$918$	−15.2132	−	27.2132i	−0.502111	−	0.898170i
$919$		−	34.0000i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$919$		−	34.0000i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$920$	2.12132	+	0.707107i	0.0699379	+	0.0233126i
$921$	−4.00000	−	2.82843i	−0.131804	−	0.0931998i
$922$	−9.00000	−	9.00000i	−0.296399	−	0.296399i
$923$	11.3137	+	11.3137i	0.372395	+	0.372395i
$924$	25.4558	+	18.0000i	0.837436	+	0.592157i
$925$	−6.00000	−	42.0000i	−0.197279	−	1.38095i
$926$		−	18.3848i		−	0.604161i
$927$	9.14214	−	19.1421i	0.300267	−	0.628710i
$928$	−5.00000	+	5.00000i	−0.164133	+	0.164133i
$929$	2.82843			0.0927977			0.0463988	−	0.998923i	$-0.485225\pi$
$929$	2.82843			0.0927977			0.0463988	+	0.998923i	$0.485225\pi$
$930$	4.58579	+	6.24264i	0.150374	+	0.204704i
$931$	44.0000			1.44204
$932$	4.24264	−	4.24264i	0.138972	−	0.138972i
$933$	−6.62742	−	38.6274i	−0.216972	−	1.26460i
$934$		−	20.0000i		−	0.654420i
$935$	−50.9117	+	25.4558i	−1.66499	+	0.832495i
$936$	8.00000	−	2.82843i	0.261488	−	0.0924500i
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.987824	−	0.155576i	$-0.950277\pi$
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.155576	−	0.987824i	$-0.549723\pi$
$938$	42.4264	+	42.4264i	1.38527	+	1.38527i
$939$	9.89949	−	14.0000i	0.323058	−	0.456873i
$940$	−24.0000	+	12.0000i	−0.782794	+	0.391397i
$941$		−	32.5269i		−	1.06035i	−0.847889	−	0.530174i	$-0.822127\pi$
$941$		−	32.5269i		−	1.06035i	0.847889	−	0.530174i	$-0.177873\pi$
$942$	28.9706	−	4.97056i	0.943912	−	0.161950i
$943$	4.00000	−	4.00000i	0.130258	−	0.130258i
$944$	−1.41421			−0.0460287
$945$	27.7279	−	40.7574i	0.901989	−	1.32584i
$946$		0			0
$947$	12.7279	−	12.7279i	0.413602	−	0.413602i	−0.469389	−	0.882991i	$-0.655526\pi$
$947$	12.7279	−	12.7279i	0.413602	−	0.413602i	0.882991	+	0.469389i	$0.155526\pi$
$948$	23.8995	−	4.10051i	0.776220	−	0.133178i
$949$			4.00000i			0.129845i
$950$	−2.82843	−	19.7990i	−0.0917663	−	0.642364i
$951$	2.00000	−	2.82843i	0.0648544	−	0.0917180i
$952$	−18.0000	−	18.0000i	−0.583383	−	0.583383i
$953$	24.0416	+	24.0416i	0.778785	+	0.778785i	0.979624	−	0.200839i	$-0.0643669\pi$
$953$	24.0416	+	24.0416i	0.778785	+	0.778785i	−0.200839	+	0.979624i	$0.564367\pi$
$954$	11.3137	−	4.00000i	0.366295	−	0.129505i
$955$	−6.00000	−	2.00000i	−0.194155	−	0.0647185i
$956$			11.3137i			0.365911i
$957$	−8.78680	−	51.2132i	−0.284037	−	1.65549i
$958$	−2.00000	+	2.00000i	−0.0646171	+	0.0646171i
$959$	−8.48528			−0.274004
$960$	3.82843	+	0.585786i	0.123562	+	0.0189062i
$961$	−27.0000			−0.870968
$962$	−16.9706	+	16.9706i	−0.547153	+	0.547153i
$963$	−5.17157	+	10.8284i	−0.166652	+	0.348941i
$964$		0			0
$965$	21.2132	+	42.4264i	0.682877	+	1.36575i
$966$	−6.00000	−	4.24264i	−0.193047	−	0.136505i
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.998000	+	0.0632081i	$0.0201332\pi$
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.0632081	+	0.998000i	$0.479867\pi$
$968$	−4.94975	−	4.94975i	−0.159091	−	0.159091i
$969$	33.9411	+	24.0000i	1.09035	+	0.770991i
$970$	3.00000	−	9.00000i	0.0963242	−	0.288973i
$971$			32.5269i			1.04384i	0.852995	+	0.521919i	$0.174784\pi$
$971$			32.5269i			1.04384i	−0.852995	+	0.521919i	$0.825216\pi$
$972$	−11.7071	−	10.2929i	−0.375506	−	0.330145i
$973$	−36.0000	+	36.0000i	−1.15411	+	1.15411i
$974$	12.7279			0.407829
$975$	−23.3137	+	7.51472i	−0.746636	+	0.240664i
$976$	10.0000			0.320092
$977$	−24.0416	+	24.0416i	−0.769160	+	0.769160i	−0.977959	−	0.208799i	$-0.933045\pi$
$977$	−24.0416	+	24.0416i	−0.769160	+	0.769160i	0.208799	+	0.977959i	$0.433045\pi$
$978$	6.62742	+	38.6274i	0.211921	+	1.23517i
$979$			48.0000i			1.53409i
$980$	7.77817	−	23.3345i	0.248465	−	0.745394i
$981$	6.00000	+	16.9706i	0.191565	+	0.541828i
$982$	23.0000	+	23.0000i	0.733959	+	0.733959i
$983$	42.4264	+	42.4264i	1.35319	+	1.35319i	0.882066	+	0.471127i	$0.156153\pi$
$983$	42.4264	+	42.4264i	1.35319	+	1.35319i	0.471127	+	0.882066i	$0.343847\pi$
$984$	5.65685	−	8.00000i	0.180334	−	0.255031i
$985$	−12.0000	−	24.0000i	−0.382352	−	0.764704i
$986$			42.4264i			1.35113i
$987$	86.9117	−	14.9117i	2.76643	−	0.474644i
$988$	−8.00000	+	8.00000i	−0.254514	+	0.254514i
$989$		0			0
$990$	−19.7574	+	20.4853i	−0.627930	+	0.651065i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	1.41421	−	1.41421i	0.0449013	−	0.0449013i
$993$	6.82843	−	1.17157i	0.216694	−	0.0371787i
$994$		−	24.0000i		−	0.761234i
$995$	16.9706	+	5.65685i	0.538003	+	0.179334i
$996$	−12.0000	+	16.9706i	−0.380235	+	0.537733i
$997$	−14.0000	−	14.0000i	−0.443384	−	0.443384i	0.449763	−	0.893148i	$-0.351508\pi$
$997$	−14.0000	−	14.0000i	−0.443384	−	0.443384i	−0.893148	+	0.449763i	$0.851508\pi$
$998$	5.65685	+	5.65685i	0.179065	+	0.179065i
$999$	42.4264	+	12.0000i	1.34231	+	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.b.47.1	✓	4
3.2	odd	2	inner	690.2.i.b.47.2	yes	4
5.3	odd	4	inner	690.2.i.b.323.2	yes	4
15.8	even	4	inner	690.2.i.b.323.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.b.47.1	✓	4	1.1	even	1	trivial
690.2.i.b.47.2	yes	4	3.2	odd	2	inner
690.2.i.b.323.1	yes	4	15.8	even	4	inner
690.2.i.b.323.2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (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} +4.24264i 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} +(-4.24264 + 4.24264i) q^{17} +(-1.29289 + 2.70711i) q^{18} -4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(6.00000 + 4.24264i) q^{21} +(-3.00000 - 3.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(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} -7.07107 q^{29} +(2.29289 + 3.12132i) q^{30} +2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.24264 + 7.24264i) q^{33} -6.00000i q^{34} +(8.48528 - 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(2.82843 - 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} -5.65685i q^{41} +(-7.24264 + 1.24264i) q^{42} +4.24264 q^{44} +(-0.121320 - 6.70711i) q^{45} -1.00000 q^{46} +(8.48528 - 8.48528i) q^{47} +(-1.70711 + 0.292893i) q^{48} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-6.00000 + 8.48528i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(-2.82843 - 2.82843i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(9.00000 + 3.00000i) q^{55} +4.24264i q^{56} +(-1.17157 - 6.82843i) q^{57} +(5.00000 - 5.00000i) q^{58} +1.41421 q^{59} +(-3.82843 - 0.585786i) q^{60} -10.0000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(11.4853 + 5.48528i) q^{63} +1.00000i q^{64} +(-2.82843 - 5.65685i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-10.0000 - 10.0000i) q^{67} +(4.24264 + 4.24264i) q^{68} +(1.41421 + 1.00000i) q^{69} +(-3.00000 + 9.00000i) q^{70} +5.65685i q^{71} +(2.70711 + 1.29289i) q^{72} +(-1.00000 + 1.00000i) q^{73} -8.48528 q^{74} +(-7.70711 - 3.94975i) q^{75} -4.00000 q^{76} +(-12.7279 + 12.7279i) q^{77} +(0.828427 + 4.82843i) q^{78} +14.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} +(4.24264 - 6.00000i) q^{84} +(6.00000 + 12.0000i) q^{85} +(-12.0711 + 2.07107i) q^{87} +(-3.00000 + 3.00000i) q^{88} +11.3137 q^{89} +(4.82843 + 4.65685i) q^{90} +12.0000 q^{91} +(0.707107 - 0.707107i) q^{92} +(3.41421 - 0.585786i) q^{93} +12.0000i q^{94} +(-8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +(4.24264 + 12.0000i) 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	\( 4 q + 4 q^{3} - 4 q^{6} + 12 q^{7} + 4 q^{10} - 4 q^{12} + 8 q^{13} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{21} - 12 q^{22} - 16 q^{25} + 4 q^{27} + 12 q^{28} + 12 q^{30} + 8 q^{31} - 12 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} - 12 q^{42} + 8 q^{45} - 4 q^{46} - 4 q^{48} - 24 q^{51} - 8 q^{52} + 36 q^{55} - 16 q^{57} + 20 q^{58} - 4 q^{60} - 40 q^{61} + 12 q^{63} - 24 q^{66} - 40 q^{67} - 12 q^{70} + 8 q^{72} - 4 q^{73} - 28 q^{75} - 16 q^{76} - 8 q^{78} + 28 q^{81} + 16 q^{82} + 24 q^{85} - 20 q^{87} - 12 q^{88} + 8 q^{90} + 48 q^{91} + 8 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) \) 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 - 12 * q^22 - 16 * q^25 + 4 * q^27 + 12 * q^28 + 12 * q^30 + 8 * q^31 - 12 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 - 12 * q^42 + 8 * q^45 - 4 * q^46 - 4 * q^48 - 24 * q^51 - 8 * q^52 + 36 * q^55 - 16 * q^57 + 20 * q^58 - 4 * q^60 - 40 * q^61 + 12 * q^63 - 24 * q^66 - 40 * q^67 - 12 * q^70 + 8 * q^72 - 4 * q^73 - 28 * q^75 - 16 * q^76 - 8 * q^78 + 28 * q^81 + 16 * q^82 + 24 * q^85 - 20 * q^87 - 12 * q^88 + 8 * q^90 + 48 * q^91 + 8 * q^93 + 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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