LMFDB - Embedded newform 66.2.b.a.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(65,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("66.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.b (of order $2$, degree $1$, 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:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.2
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	66.65
Dual form			66.2.b.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} +4.24264i q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} +4.24264i q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.41421i q^{10} +(3.00000 - 1.41421i) q^{11} +(-1.00000 + 1.41421i) q^{12} -4.24264i q^{13} -4.24264i q^{14} +(-2.00000 - 1.41421i) q^{15} +1.00000 q^{16} +(1.00000 + 2.82843i) q^{18} +1.41421i q^{20} +(-6.00000 - 4.24264i) q^{21} +(-3.00000 + 1.41421i) q^{22} +1.41421i q^{23} +(1.00000 - 1.41421i) q^{24} +3.00000 q^{25} +4.24264i q^{26} +(5.00000 + 1.41421i) q^{27} +4.24264i q^{28} +6.00000 q^{29} +(2.00000 + 1.41421i) q^{30} -4.00000 q^{31} -1.00000 q^{32} +(-1.00000 + 5.65685i) q^{33} -6.00000 q^{35} +(-1.00000 - 2.82843i) q^{36} +2.00000 q^{37} +(6.00000 + 4.24264i) q^{39} -1.41421i q^{40} -6.00000 q^{41} +(6.00000 + 4.24264i) q^{42} -8.48528i q^{43} +(3.00000 - 1.41421i) q^{44} +(4.00000 - 1.41421i) q^{45} -1.41421i q^{46} +9.89949i q^{47} +(-1.00000 + 1.41421i) q^{48} -11.0000 q^{49} -3.00000 q^{50} -4.24264i q^{52} -7.07107i q^{53} +(-5.00000 - 1.41421i) q^{54} +(2.00000 + 4.24264i) q^{55} -4.24264i q^{56} -6.00000 q^{58} -11.3137i q^{59} +(-2.00000 - 1.41421i) q^{60} +4.24264i q^{61} +4.00000 q^{62} +(12.0000 - 4.24264i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(1.00000 - 5.65685i) q^{66} -4.00000 q^{67} +(-2.00000 - 1.41421i) q^{69} +6.00000 q^{70} -7.07107i q^{71} +(1.00000 + 2.82843i) q^{72} -2.00000 q^{74} +(-3.00000 + 4.24264i) q^{75} +(6.00000 + 12.7279i) q^{77} +(-6.00000 - 4.24264i) q^{78} +4.24264i q^{79} +1.41421i q^{80} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{82} -12.0000 q^{83} +(-6.00000 - 4.24264i) q^{84} +8.48528i q^{86} +(-6.00000 + 8.48528i) q^{87} +(-3.00000 + 1.41421i) q^{88} +5.65685i q^{89} +(-4.00000 + 1.41421i) q^{90} +18.0000 q^{91} +1.41421i q^{92} +(4.00000 - 5.65685i) q^{93} -9.89949i q^{94} +(1.00000 - 1.41421i) q^{96} +8.00000 q^{97} +11.0000 q^{98} +(-7.00000 - 7.07107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{8} - 2 q^{9} + 6 q^{11} - 2 q^{12} - 4 q^{15} + 2 q^{16} + 2 q^{18} - 12 q^{21} - 6 q^{22} + 2 q^{24} + 6 q^{25} + 10 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} - 2 q^{36} + 4 q^{37} + 12 q^{39} - 12 q^{41} + 12 q^{42} + 6 q^{44} + 8 q^{45} - 2 q^{48} - 22 q^{49} - 6 q^{50} - 10 q^{54} + 4 q^{55} - 12 q^{58} - 4 q^{60} + 8 q^{62} + 24 q^{63} + 2 q^{64} + 12 q^{65} + 2 q^{66} - 8 q^{67} - 4 q^{69} + 12 q^{70} + 2 q^{72} - 4 q^{74} - 6 q^{75} + 12 q^{77} - 12 q^{78} - 14 q^{81} + 12 q^{82} - 24 q^{83} - 12 q^{84} - 12 q^{87} - 6 q^{88} - 8 q^{90} + 36 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{97} + 22 q^{98} - 14 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^8 - 2 * q^9 + 6 * q^11 - 2 * q^12 - 4 * q^15 + 2 * q^16 + 2 * q^18 - 12 * q^21 - 6 * q^22 + 2 * q^24 + 6 * q^25 + 10 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 - 2 * q^36 + 4 * q^37 + 12 * q^39 - 12 * q^41 + 12 * q^42 + 6 * q^44 + 8 * q^45 - 2 * q^48 - 22 * q^49 - 6 * q^50 - 10 * q^54 + 4 * q^55 - 12 * q^58 - 4 * q^60 + 8 * q^62 + 24 * q^63 + 2 * q^64 + 12 * q^65 + 2 * q^66 - 8 * q^67 - 4 * q^69 + 12 * q^70 + 2 * q^72 - 4 * q^74 - 6 * q^75 + 12 * q^77 - 12 * q^78 - 14 * q^81 + 12 * q^82 - 24 * q^83 - 12 * q^84 - 12 * q^87 - 6 * q^88 - 8 * q^90 + 36 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^97 + 22 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$	1.00000			0.500000
$5$			1.41421i			0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$5$			1.41421i			0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$	1.00000	−	1.41421i	0.408248	−	0.577350i
$7$			4.24264i			1.60357i	0.597614	+	0.801784i	$0.296115\pi$
$7$			4.24264i			1.60357i	−0.597614	+	0.801784i	$0.703885\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		−	1.41421i		−	0.447214i
$11$	3.00000	−	1.41421i	0.904534	−	0.426401i
$11$	3.00000	−	1.41421i	0.904534	−	0.426401i
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$		−	4.24264i		−	1.17670i	−0.808608	−	0.588348i	$-0.799778\pi$
$13$		−	4.24264i		−	1.17670i	0.808608	−	0.588348i	$-0.200222\pi$
$14$		−	4.24264i		−	1.13389i
$15$	−2.00000	−	1.41421i	−0.516398	−	0.365148i
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$			1.41421i			0.316228i
$21$	−6.00000	−	4.24264i	−1.30931	−	0.925820i
$22$	−3.00000	+	1.41421i	−0.639602	+	0.301511i
$23$			1.41421i			0.294884i	0.989071	+	0.147442i	$0.0471040\pi$
$23$			1.41421i			0.294884i	−0.989071	+	0.147442i	$0.952896\pi$
$24$	1.00000	−	1.41421i	0.204124	−	0.288675i
$25$	3.00000			0.600000
$26$			4.24264i			0.832050i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$			4.24264i			0.801784i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	2.00000	+	1.41421i	0.365148	+	0.258199i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000			−0.176777
$33$	−1.00000	+	5.65685i	−0.174078	+	0.984732i
$34$		0			0
$35$	−6.00000			−1.01419
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	6.00000	+	4.24264i	0.960769	+	0.679366i
$40$		−	1.41421i		−	0.223607i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	6.00000	+	4.24264i	0.925820	+	0.654654i
$43$		−	8.48528i		−	1.29399i	−0.762493	−	0.646997i	$-0.776025\pi$
$43$		−	8.48528i		−	1.29399i	0.762493	−	0.646997i	$-0.223975\pi$
$44$	3.00000	−	1.41421i	0.452267	−	0.213201i
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		−	1.41421i		−	0.208514i
$47$			9.89949i			1.44399i	0.691898	+	0.721995i	$0.256775\pi$
$47$			9.89949i			1.44399i	−0.691898	+	0.721995i	$0.743225\pi$
$48$	−1.00000	+	1.41421i	−0.144338	+	0.204124i
$49$	−11.0000			−1.57143
$50$	−3.00000			−0.424264
$51$		0			0
$52$		−	4.24264i		−	0.588348i
$53$		−	7.07107i		−	0.971286i	−0.874157	−	0.485643i	$-0.838586\pi$
$53$		−	7.07107i		−	0.971286i	0.874157	−	0.485643i	$-0.161414\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$	2.00000	+	4.24264i	0.269680	+	0.572078i
$56$		−	4.24264i		−	0.566947i
$57$		0			0
$58$	−6.00000			−0.787839
$59$		−	11.3137i		−	1.47292i	−0.676481	−	0.736460i	$-0.736496\pi$
$59$		−	11.3137i		−	1.47292i	0.676481	−	0.736460i	$-0.263504\pi$
$60$	−2.00000	−	1.41421i	−0.258199	−	0.182574i
$61$			4.24264i			0.543214i	0.962408	+	0.271607i	$0.0875552\pi$
$61$			4.24264i			0.543214i	−0.962408	+	0.271607i	$0.912445\pi$
$62$	4.00000			0.508001
$63$	12.0000	−	4.24264i	1.51186	−	0.534522i
$64$	1.00000			0.125000
$65$	6.00000			0.744208
$66$	1.00000	−	5.65685i	0.123091	−	0.696311i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	−2.00000	−	1.41421i	−0.240772	−	0.170251i
$70$	6.00000			0.717137
$71$		−	7.07107i		−	0.839181i	−0.907713	−	0.419591i	$-0.862174\pi$
$71$		−	7.07107i		−	0.839181i	0.907713	−	0.419591i	$-0.137826\pi$
$72$	1.00000	+	2.82843i	0.117851	+	0.333333i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−2.00000			−0.232495
$75$	−3.00000	+	4.24264i	−0.346410	+	0.489898i
$76$		0			0
$77$	6.00000	+	12.7279i	0.683763	+	1.45048i
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$			4.24264i			0.477334i	0.971101	+	0.238667i	$0.0767105\pi$
$79$			4.24264i			0.477334i	−0.971101	+	0.238667i	$0.923290\pi$
$80$			1.41421i			0.158114i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	6.00000			0.662589
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	−6.00000	−	4.24264i	−0.654654	−	0.462910i
$85$		0			0
$86$			8.48528i			0.914991i
$87$	−6.00000	+	8.48528i	−0.643268	+	0.909718i
$88$	−3.00000	+	1.41421i	−0.319801	+	0.150756i
$89$			5.65685i			0.599625i	0.953998	+	0.299813i	$0.0969242\pi$
$89$			5.65685i			0.599625i	−0.953998	+	0.299813i	$0.903076\pi$
$90$	−4.00000	+	1.41421i	−0.421637	+	0.149071i
$91$	18.0000			1.88691
$92$			1.41421i			0.147442i
$93$	4.00000	−	5.65685i	0.414781	−	0.586588i
$94$		−	9.89949i		−	1.02105i
$95$		0			0
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	11.0000			1.11117
$99$	−7.00000	−	7.07107i	−0.703526	−	0.710669i
$100$	3.00000			0.300000
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$			4.24264i			0.416025i
$105$	6.00000	−	8.48528i	0.585540	−	0.828079i
$106$			7.07107i			0.686803i
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$			12.7279i			1.21911i	0.792742	+	0.609557i	$0.208653\pi$
$109$			12.7279i			1.21911i	−0.792742	+	0.609557i	$0.791347\pi$
$110$	−2.00000	−	4.24264i	−0.190693	−	0.404520i
$111$	−2.00000	+	2.82843i	−0.189832	+	0.268462i
$112$			4.24264i			0.400892i
$113$		−	11.3137i		−	1.06430i	−0.846649	−	0.532152i	$-0.821383\pi$
$113$		−	11.3137i		−	1.06430i	0.846649	−	0.532152i	$-0.178617\pi$
$114$		0			0
$115$	−2.00000			−0.186501
$116$	6.00000			0.557086
$117$	−12.0000	+	4.24264i	−1.10940	+	0.392232i
$118$			11.3137i			1.04151i
$119$		0			0
$120$	2.00000	+	1.41421i	0.182574	+	0.129099i
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$		−	4.24264i		−	0.384111i
$123$	6.00000	−	8.48528i	0.541002	−	0.765092i
$124$	−4.00000			−0.359211
$125$			11.3137i			1.01193i
$126$	−12.0000	+	4.24264i	−1.06904	+	0.377964i
$127$		−	12.7279i		−	1.12942i	−0.825289	−	0.564710i	$-0.808988\pi$
$127$		−	12.7279i		−	1.12942i	0.825289	−	0.564710i	$-0.191012\pi$
$128$	−1.00000			−0.0883883
$129$	12.0000	+	8.48528i	1.05654	+	0.747087i
$130$	−6.00000			−0.526235
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−1.00000	+	5.65685i	−0.0870388	+	0.492366i
$133$		0			0
$134$	4.00000			0.345547
$135$	−2.00000	+	7.07107i	−0.172133	+	0.608581i
$136$		0			0
$137$		−	2.82843i		−	0.241649i	−0.992674	−	0.120824i	$-0.961446\pi$
$137$		−	2.82843i		−	0.241649i	0.992674	−	0.120824i	$-0.0385538\pi$
$138$	2.00000	+	1.41421i	0.170251	+	0.120386i
$139$		−	16.9706i		−	1.43942i	−0.694273	−	0.719712i	$-0.744274\pi$
$139$		−	16.9706i		−	1.43942i	0.694273	−	0.719712i	$-0.255726\pi$
$140$	−6.00000			−0.507093
$141$	−14.0000	−	9.89949i	−1.17901	−	0.833688i
$142$			7.07107i			0.593391i
$143$	−6.00000	−	12.7279i	−0.501745	−	1.06436i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$			8.48528i			0.704664i
$146$		0			0
$147$	11.0000	−	15.5563i	0.907265	−	1.28307i
$148$	2.00000			0.164399
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	3.00000	−	4.24264i	0.244949	−	0.346410i
$151$			4.24264i			0.345261i	0.984987	+	0.172631i	$0.0552267\pi$
$151$			4.24264i			0.345261i	−0.984987	+	0.172631i	$0.944773\pi$
$152$		0			0
$153$		0			0
$154$	−6.00000	−	12.7279i	−0.483494	−	1.02565i
$155$		−	5.65685i		−	0.454369i
$156$	6.00000	+	4.24264i	0.480384	+	0.339683i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$		−	4.24264i		−	0.337526i
$159$	10.0000	+	7.07107i	0.793052	+	0.560772i
$160$		−	1.41421i		−	0.111803i
$161$	−6.00000			−0.472866
$162$	7.00000	−	5.65685i	0.549972	−	0.444444i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	−6.00000			−0.468521
$165$	−8.00000	−	1.41421i	−0.622799	−	0.110096i
$166$	12.0000			0.931381
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	6.00000	+	4.24264i	0.462910	+	0.327327i
$169$	−5.00000			−0.384615
$170$		0			0
$171$		0			0
$172$		−	8.48528i		−	0.646997i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	6.00000	−	8.48528i	0.454859	−	0.643268i
$175$			12.7279i			0.962140i
$176$	3.00000	−	1.41421i	0.226134	−	0.106600i
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$		−	5.65685i		−	0.423999i
$179$			5.65685i			0.422813i	0.977398	+	0.211407i	$0.0678044\pi$
$179$			5.65685i			0.422813i	−0.977398	+	0.211407i	$0.932196\pi$
$180$	4.00000	−	1.41421i	0.298142	−	0.105409i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−18.0000			−1.33425
$183$	−6.00000	−	4.24264i	−0.443533	−	0.313625i
$184$		−	1.41421i		−	0.104257i
$185$			2.82843i			0.207950i
$186$	−4.00000	+	5.65685i	−0.293294	+	0.414781i
$187$		0			0
$188$			9.89949i			0.721995i
$189$	−6.00000	+	21.2132i	−0.436436	+	1.54303i
$190$		0			0
$191$			9.89949i			0.716302i	0.933664	+	0.358151i	$0.116593\pi$
$191$			9.89949i			0.716302i	−0.933664	+	0.358151i	$0.883407\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$			8.48528i			0.610784i	0.952227	+	0.305392i	$0.0987875\pi$
$193$			8.48528i			0.610784i	−0.952227	+	0.305392i	$0.901213\pi$
$194$	−8.00000			−0.574367
$195$	−6.00000	+	8.48528i	−0.429669	+	0.607644i
$196$	−11.0000			−0.785714
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	7.00000	+	7.07107i	0.497468	+	0.502519i
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−3.00000			−0.212132
$201$	4.00000	−	5.65685i	0.282138	−	0.399004i
$202$	−6.00000			−0.422159
$203$			25.4558i			1.78665i
$204$		0			0
$205$		−	8.48528i		−	0.592638i
$206$	4.00000			0.278693
$207$	4.00000	−	1.41421i	0.278019	−	0.0982946i
$208$		−	4.24264i		−	0.294174i
$209$		0			0
$210$	−6.00000	+	8.48528i	−0.414039	+	0.585540i
$211$			8.48528i			0.584151i	0.956395	+	0.292075i	$0.0943458\pi$
$211$			8.48528i			0.584151i	−0.956395	+	0.292075i	$0.905654\pi$
$212$		−	7.07107i		−	0.485643i
$213$	10.0000	+	7.07107i	0.685189	+	0.484502i
$214$	18.0000			1.23045
$215$	12.0000			0.818393
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$		−	16.9706i		−	1.15204i
$218$		−	12.7279i		−	0.862044i
$219$		0			0
$220$	2.00000	+	4.24264i	0.134840	+	0.286039i
$221$		0			0
$222$	2.00000	−	2.82843i	0.134231	−	0.189832i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		−	4.24264i		−	0.283473i
$225$	−3.00000	−	8.48528i	−0.200000	−	0.565685i
$226$			11.3137i			0.752577i
$227$	6.00000			0.398234			0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000			0.398234			0.199117	+	0.979976i	$0.436193\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	2.00000			0.131876
$231$	−24.0000	−	4.24264i	−1.57908	−	0.279145i
$232$	−6.00000			−0.393919
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	12.0000	−	4.24264i	0.784465	−	0.277350i
$235$	−14.0000			−0.913259
$236$		−	11.3137i		−	0.736460i
$237$	−6.00000	−	4.24264i	−0.389742	−	0.275589i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	−2.00000	−	1.41421i	−0.129099	−	0.0912871i
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$	−7.00000	+	8.48528i	−0.449977	+	0.545455i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$			4.24264i			0.271607i
$245$		−	15.5563i		−	0.993859i
$246$	−6.00000	+	8.48528i	−0.382546	+	0.541002i
$247$		0			0
$248$	4.00000			0.254000
$249$	12.0000	−	16.9706i	0.760469	−	1.07547i
$250$		−	11.3137i		−	0.715542i
$251$			5.65685i			0.357057i	0.983935	+	0.178529i	$0.0571337\pi$
$251$			5.65685i			0.357057i	−0.983935	+	0.178529i	$0.942866\pi$
$252$	12.0000	−	4.24264i	0.755929	−	0.267261i
$253$	2.00000	+	4.24264i	0.125739	+	0.266733i
$254$			12.7279i			0.798621i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	11.3137i		−	0.705730i	−0.935674	−	0.352865i	$-0.885208\pi$
$257$		−	11.3137i		−	0.705730i	0.935674	−	0.352865i	$-0.114792\pi$
$258$	−12.0000	−	8.48528i	−0.747087	−	0.528271i
$259$			8.48528i			0.527250i
$260$	6.00000			0.372104
$261$	−6.00000	−	16.9706i	−0.371391	−	1.05045i
$262$	−12.0000			−0.741362
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$	1.00000	−	5.65685i	0.0615457	−	0.348155i
$265$	10.0000			0.614295
$266$		0			0
$267$	−8.00000	−	5.65685i	−0.489592	−	0.346194i
$268$	−4.00000			−0.244339
$269$		−	7.07107i		−	0.431131i	−0.976489	−	0.215565i	$-0.930841\pi$
$269$		−	7.07107i		−	0.431131i	0.976489	−	0.215565i	$-0.0691594\pi$
$270$	2.00000	−	7.07107i	0.121716	−	0.430331i
$271$			12.7279i			0.773166i	0.922255	+	0.386583i	$0.126345\pi$
$271$			12.7279i			0.773166i	−0.922255	+	0.386583i	$0.873655\pi$
$272$		0			0
$273$	−18.0000	+	25.4558i	−1.08941	+	1.54066i
$274$			2.82843i			0.170872i
$275$	9.00000	−	4.24264i	0.542720	−	0.255841i
$276$	−2.00000	−	1.41421i	−0.120386	−	0.0851257i
$277$		−	21.2132i		−	1.27458i	−0.770625	−	0.637289i	$-0.780056\pi$
$277$		−	21.2132i		−	1.27458i	0.770625	−	0.637289i	$-0.219944\pi$
$278$			16.9706i			1.01783i
$279$	4.00000	+	11.3137i	0.239474	+	0.677334i
$280$	6.00000			0.358569
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	14.0000	+	9.89949i	0.833688	+	0.589506i
$283$			8.48528i			0.504398i	0.967675	+	0.252199i	$0.0811537\pi$
$283$			8.48528i			0.504398i	−0.967675	+	0.252199i	$0.918846\pi$
$284$		−	7.07107i		−	0.419591i
$285$		0			0
$286$	6.00000	+	12.7279i	0.354787	+	0.752618i
$287$		−	25.4558i		−	1.50261i
$288$	1.00000	+	2.82843i	0.0589256	+	0.166667i
$289$	−17.0000			−1.00000
$290$		−	8.48528i		−	0.498273i
$291$	−8.00000	+	11.3137i	−0.468968	+	0.663221i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	−11.0000	+	15.5563i	−0.641533	+	0.907265i
$295$	16.0000			0.931556
$296$	−2.00000			−0.116248
$297$	17.0000	−	2.82843i	0.986440	−	0.164122i
$298$	6.00000			0.347571
$299$	6.00000			0.346989
$300$	−3.00000	+	4.24264i	−0.173205	+	0.244949i
$301$	36.0000			2.07501
$302$		−	4.24264i		−	0.244137i
$303$	−6.00000	+	8.48528i	−0.344691	+	0.487467i
$304$		0			0
$305$	−6.00000			−0.343559
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	6.00000	+	12.7279i	0.341882	+	0.725241i
$309$	4.00000	−	5.65685i	0.227552	−	0.321807i
$310$			5.65685i			0.321288i
$311$			26.8701i			1.52366i	0.647776	+	0.761831i	$0.275699\pi$
$311$			26.8701i			1.52366i	−0.647776	+	0.761831i	$0.724301\pi$
$312$	−6.00000	−	4.24264i	−0.339683	−	0.240192i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	22.0000			1.24153
$315$	6.00000	+	16.9706i	0.338062	+	0.956183i
$316$			4.24264i			0.238667i
$317$			9.89949i			0.556011i	0.960579	+	0.278006i	$0.0896734\pi$
$317$			9.89949i			0.556011i	−0.960579	+	0.278006i	$0.910327\pi$
$318$	−10.0000	−	7.07107i	−0.560772	−	0.396526i
$319$	18.0000	−	8.48528i	1.00781	−	0.475085i
$320$			1.41421i			0.0790569i
$321$	18.0000	−	25.4558i	1.00466	−	1.42081i
$322$	6.00000			0.334367
$323$		0			0
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$		−	12.7279i		−	0.706018i
$326$	−2.00000			−0.110770
$327$	−18.0000	−	12.7279i	−0.995402	−	0.703856i
$328$	6.00000			0.331295
$329$	−42.0000			−2.31553
$330$	8.00000	+	1.41421i	0.440386	+	0.0778499i
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$	−12.0000			−0.658586
$333$	−2.00000	−	5.65685i	−0.109599	−	0.309994i
$334$	−12.0000			−0.656611
$335$		−	5.65685i		−	0.309067i
$336$	−6.00000	−	4.24264i	−0.327327	−	0.231455i
$337$			33.9411i			1.84889i	0.381314	+	0.924445i	$0.375472\pi$
$337$			33.9411i			1.84889i	−0.381314	+	0.924445i	$0.624528\pi$
$338$	5.00000			0.271964
$339$	16.0000	+	11.3137i	0.869001	+	0.614476i
$340$		0			0
$341$	−12.0000	+	5.65685i	−0.649836	+	0.306336i
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$			8.48528i			0.457496i
$345$	2.00000	−	2.82843i	0.107676	−	0.152277i
$346$	−6.00000			−0.322562
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$	−6.00000	+	8.48528i	−0.321634	+	0.454859i
$349$			29.6985i			1.58972i	0.606791	+	0.794862i	$0.292457\pi$
$349$			29.6985i			1.58972i	−0.606791	+	0.794862i	$0.707543\pi$
$350$		−	12.7279i		−	0.680336i
$351$	6.00000	−	21.2132i	0.320256	−	1.13228i
$352$	−3.00000	+	1.41421i	−0.159901	+	0.0753778i
$353$			22.6274i			1.20434i	0.798369	+	0.602168i	$0.205696\pi$
$353$			22.6274i			1.20434i	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−16.0000	−	11.3137i	−0.850390	−	0.601317i
$355$	10.0000			0.530745
$356$			5.65685i			0.299813i
$357$		0			0
$358$		−	5.65685i		−	0.298974i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−4.00000	+	1.41421i	−0.210819	+	0.0745356i
$361$	19.0000			1.00000
$362$	−2.00000			−0.105118
$363$	5.00000	+	18.3848i	0.262432	+	0.964951i
$364$	18.0000			0.943456
$365$		0			0
$366$	6.00000	+	4.24264i	0.313625	+	0.221766i
$367$	−28.0000			−1.46159			−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000			−1.46159			−0.730794	+	0.682598i	$0.760850\pi$
$368$			1.41421i			0.0737210i
$369$	6.00000	+	16.9706i	0.312348	+	0.883452i
$370$		−	2.82843i		−	0.147043i
$371$	30.0000			1.55752
$372$	4.00000	−	5.65685i	0.207390	−	0.293294i
$373$		−	29.6985i		−	1.53773i	−0.639412	−	0.768865i	$-0.720822\pi$
$373$		−	29.6985i		−	1.53773i	0.639412	−	0.768865i	$-0.279178\pi$
$374$		0			0
$375$	−16.0000	−	11.3137i	−0.826236	−	0.584237i
$376$		−	9.89949i		−	0.510527i
$377$		−	25.4558i		−	1.31104i
$378$	6.00000	−	21.2132i	0.308607	−	1.09109i
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$	18.0000	+	12.7279i	0.922168	+	0.652071i
$382$		−	9.89949i		−	0.506502i
$383$			1.41421i			0.0722629i	0.999347	+	0.0361315i	$0.0115035\pi$
$383$			1.41421i			0.0722629i	−0.999347	+	0.0361315i	$0.988496\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$	−18.0000	+	8.48528i	−0.917365	+	0.432450i
$386$		−	8.48528i		−	0.431889i
$387$	−24.0000	+	8.48528i	−1.21999	+	0.431331i
$388$	8.00000			0.406138
$389$			9.89949i			0.501924i	0.967997	+	0.250962i	$0.0807470\pi$
$389$			9.89949i			0.501924i	−0.967997	+	0.250962i	$0.919253\pi$
$390$	6.00000	−	8.48528i	0.303822	−	0.429669i
$391$		0			0
$392$	11.0000			0.555584
$393$	−12.0000	+	16.9706i	−0.605320	+	0.856052i
$394$	−18.0000			−0.906827
$395$	−6.00000			−0.301893
$396$	−7.00000	−	7.07107i	−0.351763	−	0.355335i
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	3.00000			0.150000
$401$		−	36.7696i		−	1.83618i	−0.396368	−	0.918092i	$-0.629729\pi$
$401$		−	36.7696i		−	1.83618i	0.396368	−	0.918092i	$-0.370271\pi$
$402$	−4.00000	+	5.65685i	−0.199502	+	0.282138i
$403$			16.9706i			0.845364i
$404$	6.00000			0.298511
$405$	−8.00000	−	9.89949i	−0.397523	−	0.491910i
$406$		−	25.4558i		−	1.26335i
$407$	6.00000	−	2.82843i	0.297409	−	0.140200i
$408$		0			0
$409$			8.48528i			0.419570i	0.977748	+	0.209785i	$0.0672764\pi$
$409$			8.48528i			0.419570i	−0.977748	+	0.209785i	$0.932724\pi$
$410$			8.48528i			0.419058i
$411$	4.00000	+	2.82843i	0.197305	+	0.139516i
$412$	−4.00000			−0.197066
$413$	48.0000			2.36193
$414$	−4.00000	+	1.41421i	−0.196589	+	0.0695048i
$415$		−	16.9706i		−	0.833052i
$416$			4.24264i			0.208013i
$417$	24.0000	+	16.9706i	1.17529	+	0.831052i
$418$		0			0
$419$		−	11.3137i		−	0.552711i	−0.961056	−	0.276355i	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$	6.00000	−	8.48528i	0.292770	−	0.414039i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		−	8.48528i		−	0.413057i
$423$	28.0000	−	9.89949i	1.36141	−	0.481330i
$424$			7.07107i			0.343401i
$425$		0			0
$426$	−10.0000	−	7.07107i	−0.484502	−	0.342594i
$427$	−18.0000			−0.871081
$428$	−18.0000			−0.870063
$429$	24.0000	+	4.24264i	1.15873	+	0.204837i
$430$	−12.0000			−0.578691
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$	5.00000	+	1.41421i	0.240563	+	0.0680414i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$			16.9706i			0.814613i
$435$	−12.0000	−	8.48528i	−0.575356	−	0.406838i
$436$			12.7279i			0.609557i
$437$		0			0
$438$		0			0
$439$		−	21.2132i		−	1.01245i	−0.862401	−	0.506225i	$-0.831040\pi$
$439$		−	21.2132i		−	1.01245i	0.862401	−	0.506225i	$-0.168960\pi$
$440$	−2.00000	−	4.24264i	−0.0953463	−	0.202260i
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$		0			0
$443$		−	28.2843i		−	1.34383i	−0.740630	−	0.671913i	$-0.765473\pi$
$443$		−	28.2843i		−	1.34383i	0.740630	−	0.671913i	$-0.234527\pi$
$444$	−2.00000	+	2.82843i	−0.0949158	+	0.134231i
$445$	−8.00000			−0.379236
$446$	−8.00000			−0.378811
$447$	6.00000	−	8.48528i	0.283790	−	0.401340i
$448$			4.24264i			0.200446i
$449$			31.1127i			1.46830i	0.678988	+	0.734150i	$0.262419\pi$
$449$			31.1127i			1.46830i	−0.678988	+	0.734150i	$0.737581\pi$
$450$	3.00000	+	8.48528i	0.141421	+	0.400000i
$451$	−18.0000	+	8.48528i	−0.847587	+	0.399556i
$452$		−	11.3137i		−	0.532152i
$453$	−6.00000	−	4.24264i	−0.281905	−	0.199337i
$454$	−6.00000			−0.281594
$455$			25.4558i			1.19339i
$456$		0			0
$457$		−	8.48528i		−	0.396925i	−0.980109	−	0.198462i	$-0.936405\pi$
$457$		−	8.48528i		−	0.396925i	0.980109	−	0.198462i	$-0.0635948\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$	−2.00000			−0.0932505
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	24.0000	+	4.24264i	1.11658	+	0.197386i
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	6.00000			0.278543
$465$	8.00000	+	5.65685i	0.370991	+	0.262330i
$466$	18.0000			0.833834
$467$			31.1127i			1.43972i	0.694117	+	0.719862i	$0.255795\pi$
$467$			31.1127i			1.43972i	−0.694117	+	0.719862i	$0.744205\pi$
$468$	−12.0000	+	4.24264i	−0.554700	+	0.196116i
$469$		−	16.9706i		−	0.783628i
$470$	14.0000			0.645772
$471$	22.0000	−	31.1127i	1.01371	−	1.43360i
$472$			11.3137i			0.520756i
$473$	−12.0000	−	25.4558i	−0.551761	−	1.17046i
$474$	6.00000	+	4.24264i	0.275589	+	0.194871i
$475$		0			0
$476$		0			0
$477$	−20.0000	+	7.07107i	−0.915737	+	0.323762i
$478$	−12.0000			−0.548867
$479$	−12.0000			−0.548294			−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000			−0.548294			−0.274147	+	0.961688i	$0.588395\pi$
$480$	2.00000	+	1.41421i	0.0912871	+	0.0645497i
$481$		−	8.48528i		−	0.386896i
$482$			8.48528i			0.386494i
$483$	6.00000	−	8.48528i	0.273009	−	0.386094i
$484$	7.00000	−	8.48528i	0.318182	−	0.385695i
$485$			11.3137i			0.513729i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$		−	4.24264i		−	0.192055i
$489$	−2.00000	+	2.82843i	−0.0904431	+	0.127906i
$490$			15.5563i			0.702764i
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$	6.00000	−	8.48528i	0.270501	−	0.382546i
$493$		0			0
$494$		0			0
$495$	10.0000	−	9.89949i	0.449467	−	0.444949i
$496$	−4.00000			−0.179605
$497$	30.0000			1.34568
$498$	−12.0000	+	16.9706i	−0.537733	+	0.760469i
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$			11.3137i			0.505964i
$501$	−12.0000	+	16.9706i	−0.536120	+	0.758189i
$502$		−	5.65685i		−	0.252478i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−12.0000	+	4.24264i	−0.534522	+	0.188982i
$505$			8.48528i			0.377590i
$506$	−2.00000	−	4.24264i	−0.0889108	−	0.188608i
$507$	5.00000	−	7.07107i	0.222058	−	0.314037i
$508$		−	12.7279i		−	0.564710i
$509$			1.41421i			0.0626839i	0.999509	+	0.0313420i	$0.00997809\pi$
$509$			1.41421i			0.0626839i	−0.999509	+	0.0313420i	$0.990022\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			11.3137i			0.499026i
$515$		−	5.65685i		−	0.249271i
$516$	12.0000	+	8.48528i	0.528271	+	0.373544i
$517$	14.0000	+	29.6985i	0.615719	+	1.30614i
$518$		−	8.48528i		−	0.372822i
$519$	−6.00000	+	8.48528i	−0.263371	+	0.372463i
$520$	−6.00000			−0.263117
$521$		−	19.7990i		−	0.867409i	−0.901055	−	0.433705i	$-0.857206\pi$
$521$		−	19.7990i		−	0.867409i	0.901055	−	0.433705i	$-0.142794\pi$
$522$	6.00000	+	16.9706i	0.262613	+	0.742781i
$523$			25.4558i			1.11311i	0.830812	+	0.556553i	$0.187876\pi$
$523$			25.4558i			1.11311i	−0.830812	+	0.556553i	$0.812124\pi$
$524$	12.0000			0.524222
$525$	−18.0000	−	12.7279i	−0.785584	−	0.555492i
$526$	12.0000			0.523225
$527$		0			0
$528$	−1.00000	+	5.65685i	−0.0435194	+	0.246183i
$529$	21.0000			0.913043
$530$	−10.0000			−0.434372
$531$	−32.0000	+	11.3137i	−1.38868	+	0.490973i
$532$		0			0
$533$			25.4558i			1.10262i
$534$	8.00000	+	5.65685i	0.346194	+	0.244796i
$535$		−	25.4558i		−	1.10055i
$536$	4.00000			0.172774
$537$	−8.00000	−	5.65685i	−0.345225	−	0.244111i
$538$			7.07107i			0.304855i
$539$	−33.0000	+	15.5563i	−1.42141	+	0.670059i
$540$	−2.00000	+	7.07107i	−0.0860663	+	0.304290i
$541$			12.7279i			0.547216i	0.961841	+	0.273608i	$0.0882171\pi$
$541$			12.7279i			0.547216i	−0.961841	+	0.273608i	$0.911783\pi$
$542$		−	12.7279i		−	0.546711i
$543$	−2.00000	+	2.82843i	−0.0858282	+	0.121379i
$544$		0			0
$545$	−18.0000			−0.771035
$546$	18.0000	−	25.4558i	0.770329	−	1.08941i
$547$		−	33.9411i		−	1.45122i	−0.688107	−	0.725609i	$-0.741558\pi$
$547$		−	33.9411i		−	1.45122i	0.688107	−	0.725609i	$-0.258442\pi$
$548$		−	2.82843i		−	0.120824i
$549$	12.0000	−	4.24264i	0.512148	−	0.181071i
$550$	−9.00000	+	4.24264i	−0.383761	+	0.180907i
$551$		0			0
$552$	2.00000	+	1.41421i	0.0851257	+	0.0601929i
$553$	−18.0000			−0.765438
$554$			21.2132i			0.901263i
$555$	−4.00000	−	2.82843i	−0.169791	−	0.120060i
$556$		−	16.9706i		−	0.719712i
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$	−4.00000	−	11.3137i	−0.169334	−	0.478947i
$559$	−36.0000			−1.52264
$560$	−6.00000			−0.253546
$561$		0			0
$562$	12.0000			0.506189
$563$	30.0000			1.26435			0.632175	−	0.774826i	$-0.282163\pi$
$563$	30.0000			1.26435			0.632175	+	0.774826i	$0.282163\pi$
$564$	−14.0000	−	9.89949i	−0.589506	−	0.416844i
$565$	16.0000			0.673125
$566$		−	8.48528i		−	0.356663i
$567$	−24.0000	−	29.6985i	−1.00791	−	1.24722i
$568$			7.07107i			0.296695i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$			33.9411i			1.42039i	0.704004	+	0.710196i	$0.251394\pi$
$571$			33.9411i			1.42039i	−0.704004	+	0.710196i	$0.748606\pi$
$572$	−6.00000	−	12.7279i	−0.250873	−	0.532181i
$573$	−14.0000	−	9.89949i	−0.584858	−	0.413557i
$574$			25.4558i			1.06251i
$575$			4.24264i			0.176930i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$	17.0000			0.707107
$579$	−12.0000	−	8.48528i	−0.498703	−	0.352636i
$580$			8.48528i			0.352332i
$581$		−	50.9117i		−	2.11217i
$582$	8.00000	−	11.3137i	0.331611	−	0.468968i
$583$	−10.0000	−	21.2132i	−0.414158	−	0.878561i
$584$		0			0
$585$	−6.00000	−	16.9706i	−0.248069	−	0.701646i
$586$	6.00000			0.247858
$587$		−	28.2843i		−	1.16742i	−0.811963	−	0.583708i	$-0.801601\pi$
$587$		−	28.2843i		−	1.16742i	0.811963	−	0.583708i	$-0.198399\pi$
$588$	11.0000	−	15.5563i	0.453632	−	0.641533i
$589$		0			0
$590$	−16.0000			−0.658710
$591$	−18.0000	+	25.4558i	−0.740421	+	1.04711i
$592$	2.00000			0.0821995
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$	−17.0000	+	2.82843i	−0.697518	+	0.116052i
$595$		0			0
$596$	−6.00000			−0.245770
$597$	16.0000	−	22.6274i	0.654836	−	0.926079i
$598$	−6.00000			−0.245358
$599$		−	24.0416i		−	0.982314i	−0.871071	−	0.491157i	$-0.836574\pi$
$599$		−	24.0416i		−	0.982314i	0.871071	−	0.491157i	$-0.163426\pi$
$600$	3.00000	−	4.24264i	0.122474	−	0.173205i
$601$		−	33.9411i		−	1.38449i	−0.721664	−	0.692244i	$-0.756622\pi$
$601$		−	33.9411i		−	1.38449i	0.721664	−	0.692244i	$-0.243378\pi$
$602$	−36.0000			−1.46725
$603$	4.00000	+	11.3137i	0.162893	+	0.460730i
$604$			4.24264i			0.172631i
$605$	12.0000	+	9.89949i	0.487869	+	0.402472i
$606$	6.00000	−	8.48528i	0.243733	−	0.344691i
$607$		−	4.24264i		−	0.172203i	−0.996286	−	0.0861017i	$-0.972559\pi$
$607$		−	4.24264i		−	0.172203i	0.996286	−	0.0861017i	$-0.0274410\pi$
$608$		0			0
$609$	−36.0000	−	25.4558i	−1.45879	−	1.03152i
$610$	6.00000			0.242933
$611$	42.0000			1.69914
$612$		0			0
$613$			12.7279i			0.514076i	0.966401	+	0.257038i	$0.0827465\pi$
$613$			12.7279i			0.514076i	−0.966401	+	0.257038i	$0.917253\pi$
$614$		0			0
$615$	12.0000	+	8.48528i	0.483887	+	0.342160i
$616$	−6.00000	−	12.7279i	−0.241747	−	0.512823i
$617$			39.5980i			1.59415i	0.603877	+	0.797077i	$0.293622\pi$
$617$			39.5980i			1.59415i	−0.603877	+	0.797077i	$0.706378\pi$
$618$	−4.00000	+	5.65685i	−0.160904	+	0.227552i
$619$	44.0000			1.76851			0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000			1.76851			0.884255	+	0.467005i	$0.154667\pi$
$620$		−	5.65685i		−	0.227185i
$621$	−2.00000	+	7.07107i	−0.0802572	+	0.283752i
$622$		−	26.8701i		−	1.07739i
$623$	−24.0000			−0.961540
$624$	6.00000	+	4.24264i	0.240192	+	0.169842i
$625$	−1.00000			−0.0400000
$626$	10.0000			0.399680
$627$		0			0
$628$	−22.0000			−0.877896
$629$		0			0
$630$	−6.00000	−	16.9706i	−0.239046	−	0.676123i
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$		−	4.24264i		−	0.168763i
$633$	−12.0000	−	8.48528i	−0.476957	−	0.337260i
$634$		−	9.89949i		−	0.393159i
$635$	18.0000			0.714308
$636$	10.0000	+	7.07107i	0.396526	+	0.280386i
$637$			46.6690i			1.84909i
$638$	−18.0000	+	8.48528i	−0.712627	+	0.335936i
$639$	−20.0000	+	7.07107i	−0.791188	+	0.279727i
$640$		−	1.41421i		−	0.0559017i
$641$			48.0833i			1.89917i	0.313503	+	0.949587i	$0.398498\pi$
$641$			48.0833i			1.89917i	−0.313503	+	0.949587i	$0.601502\pi$
$642$	−18.0000	+	25.4558i	−0.710403	+	1.00466i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−6.00000			−0.236433
$645$	−12.0000	+	16.9706i	−0.472500	+	0.668215i
$646$		0			0
$647$		−	7.07107i		−	0.277992i	−0.990293	−	0.138996i	$-0.955612\pi$
$647$		−	7.07107i		−	0.277992i	0.990293	−	0.138996i	$-0.0443876\pi$
$648$	7.00000	−	5.65685i	0.274986	−	0.222222i
$649$	−16.0000	−	33.9411i	−0.628055	−	1.33231i
$650$			12.7279i			0.499230i
$651$	24.0000	+	16.9706i	0.940634	+	0.665129i
$652$	2.00000			0.0783260
$653$			26.8701i			1.05151i	0.850637	+	0.525753i	$0.176216\pi$
$653$			26.8701i			1.05151i	−0.850637	+	0.525753i	$0.823784\pi$
$654$	18.0000	+	12.7279i	0.703856	+	0.497701i
$655$			16.9706i			0.663095i
$656$	−6.00000			−0.234261
$657$		0			0
$658$	42.0000			1.63733
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	−8.00000	−	1.41421i	−0.311400	−	0.0550482i
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	10.0000			0.388661
$663$		0			0
$664$	12.0000			0.465690
$665$		0			0
$666$	2.00000	+	5.65685i	0.0774984	+	0.219199i
$667$			8.48528i			0.328551i
$668$	12.0000			0.464294
$669$	−8.00000	+	11.3137i	−0.309298	+	0.437413i
$670$			5.65685i			0.218543i
$671$	6.00000	+	12.7279i	0.231627	+	0.491356i
$672$	6.00000	+	4.24264i	0.231455	+	0.163663i
$673$			42.4264i			1.63542i	0.575632	+	0.817709i	$0.304756\pi$
$673$			42.4264i			1.63542i	−0.575632	+	0.817709i	$0.695244\pi$
$674$		−	33.9411i		−	1.30736i
$675$	15.0000	+	4.24264i	0.577350	+	0.163299i
$676$	−5.00000			−0.192308
$677$	−30.0000			−1.15299			−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000			−1.15299			−0.576497	+	0.817099i	$0.695581\pi$
$678$	−16.0000	−	11.3137i	−0.614476	−	0.434500i
$679$			33.9411i			1.30254i
$680$		0			0
$681$	−6.00000	+	8.48528i	−0.229920	+	0.325157i
$682$	12.0000	−	5.65685i	0.459504	−	0.216612i
$683$			5.65685i			0.216454i	0.994126	+	0.108227i	$0.0345173\pi$
$683$			5.65685i			0.216454i	−0.994126	+	0.108227i	$0.965483\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$			16.9706i			0.647939i
$687$	−14.0000	+	19.7990i	−0.534133	+	0.755379i
$688$		−	8.48528i		−	0.323498i
$689$	−30.0000			−1.14291
$690$	−2.00000	+	2.82843i	−0.0761387	+	0.107676i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	6.00000			0.228086
$693$	30.0000	−	29.6985i	1.13961	−	1.12815i
$694$	−12.0000			−0.455514
$695$	24.0000			0.910372
$696$	6.00000	−	8.48528i	0.227429	−	0.321634i
$697$		0			0
$698$		−	29.6985i		−	1.12410i
$699$	18.0000	−	25.4558i	0.680823	−	0.962828i
$700$			12.7279i			0.481070i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−6.00000	+	21.2132i	−0.226455	+	0.800641i
$703$		0			0
$704$	3.00000	−	1.41421i	0.113067	−	0.0533002i
$705$	14.0000	−	19.7990i	0.527271	−	0.745673i
$706$		−	22.6274i		−	0.851594i
$707$			25.4558i			0.957366i
$708$	16.0000	+	11.3137i	0.601317	+	0.425195i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−10.0000			−0.375293
$711$	12.0000	−	4.24264i	0.450035	−	0.159111i
$712$		−	5.65685i		−	0.212000i
$713$		−	5.65685i		−	0.211851i
$714$		0			0
$715$	18.0000	−	8.48528i	0.673162	−	0.317332i
$716$			5.65685i			0.211407i
$717$	−12.0000	+	16.9706i	−0.448148	+	0.633777i
$718$		0			0
$719$		−	32.5269i		−	1.21305i	−0.795065	−	0.606525i	$-0.792563\pi$
$719$		−	32.5269i		−	1.21305i	0.795065	−	0.606525i	$-0.207437\pi$
$720$	4.00000	−	1.41421i	0.149071	−	0.0527046i
$721$		−	16.9706i		−	0.632017i
$722$	−19.0000			−0.707107
$723$	12.0000	+	8.48528i	0.446285	+	0.315571i
$724$	2.00000			0.0743294
$725$	18.0000			0.668503
$726$	−5.00000	−	18.3848i	−0.185567	−	0.682323i
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$	−18.0000			−0.667124
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$		0			0
$732$	−6.00000	−	4.24264i	−0.221766	−	0.156813i
$733$		−	4.24264i		−	0.156706i	−0.996926	−	0.0783528i	$-0.975034\pi$
$733$		−	4.24264i		−	0.156706i	0.996926	−	0.0783528i	$-0.0249660\pi$
$734$	28.0000			1.03350
$735$	22.0000	+	15.5563i	0.811482	+	0.573805i
$736$		−	1.41421i		−	0.0521286i
$737$	−12.0000	+	5.65685i	−0.442026	+	0.208373i
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$		−	25.4558i		−	0.936408i	−0.883620	−	0.468204i	$-0.844901\pi$
$739$		−	25.4558i		−	0.936408i	0.883620	−	0.468204i	$-0.155099\pi$
$740$			2.82843i			0.103975i
$741$		0			0
$742$	−30.0000			−1.10133
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	−4.00000	+	5.65685i	−0.146647	+	0.207390i
$745$		−	8.48528i		−	0.310877i
$746$			29.6985i			1.08734i
$747$	12.0000	+	33.9411i	0.439057	+	1.24184i
$748$		0			0
$749$		−	76.3675i		−	2.79041i
$750$	16.0000	+	11.3137i	0.584237	+	0.413118i
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$			9.89949i			0.360997i
$753$	−8.00000	−	5.65685i	−0.291536	−	0.206147i
$754$			25.4558i			0.927047i
$755$	−6.00000			−0.218362
$756$	−6.00000	+	21.2132i	−0.218218	+	0.771517i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−2.00000			−0.0726433
$759$	−8.00000	−	1.41421i	−0.290382	−	0.0513327i
$760$		0			0
$761$	−24.0000			−0.869999			−0.435000	−	0.900431i	$-0.643252\pi$
$761$	−24.0000			−0.869999			−0.435000	+	0.900431i	$0.643252\pi$
$762$	−18.0000	−	12.7279i	−0.652071	−	0.461084i
$763$	−54.0000			−1.95493
$764$			9.89949i			0.358151i
$765$		0			0
$766$		−	1.41421i		−	0.0510976i
$767$	−48.0000			−1.73318
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$		−	42.4264i		−	1.52994i	−0.644069	−	0.764968i	$-0.722755\pi$
$769$		−	42.4264i		−	1.52994i	0.644069	−	0.764968i	$-0.277245\pi$
$770$	18.0000	−	8.48528i	0.648675	−	0.305788i
$771$	16.0000	+	11.3137i	0.576226	+	0.407453i
$772$			8.48528i			0.305392i
$773$			18.3848i			0.661254i	0.943761	+	0.330627i	$0.107260\pi$
$773$			18.3848i			0.661254i	−0.943761	+	0.330627i	$0.892740\pi$
$774$	24.0000	−	8.48528i	0.862662	−	0.304997i
$775$	−12.0000			−0.431053
$776$	−8.00000			−0.287183
$777$	−12.0000	−	8.48528i	−0.430498	−	0.304408i
$778$		−	9.89949i		−	0.354914i
$779$		0			0
$780$	−6.00000	+	8.48528i	−0.214834	+	0.303822i
$781$	−10.0000	−	21.2132i	−0.357828	−	0.759068i
$782$		0			0
$783$	30.0000	+	8.48528i	1.07211	+	0.303239i
$784$	−11.0000			−0.392857
$785$		−	31.1127i		−	1.11046i
$786$	12.0000	−	16.9706i	0.428026	−	0.605320i
$787$		−	42.4264i		−	1.51234i	−0.654376	−	0.756169i	$-0.727069\pi$
$787$		−	42.4264i		−	1.51234i	0.654376	−	0.756169i	$-0.272931\pi$
$788$	18.0000			0.641223
$789$	12.0000	−	16.9706i	0.427211	−	0.604168i
$790$	6.00000			0.213470
$791$	48.0000			1.70668
$792$	7.00000	+	7.07107i	0.248734	+	0.251259i
$793$	18.0000			0.639199
$794$	34.0000			1.20661
$795$	−10.0000	+	14.1421i	−0.354663	+	0.501570i
$796$	−16.0000			−0.567105
$797$			1.41421i			0.0500940i	0.999686	+	0.0250470i	$0.00797354\pi$
$797$			1.41421i			0.0500940i	−0.999686	+	0.0250470i	$0.992026\pi$
$798$		0			0
$799$		0			0
$800$	−3.00000			−0.106066
$801$	16.0000	−	5.65685i	0.565332	−	0.199875i
$802$			36.7696i			1.29838i
$803$		0			0
$804$	4.00000	−	5.65685i	0.141069	−	0.199502i
$805$		−	8.48528i		−	0.299067i
$806$		−	16.9706i		−	0.597763i
$807$	10.0000	+	7.07107i	0.352017	+	0.248913i
$808$	−6.00000			−0.211079
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$	8.00000	+	9.89949i	0.281091	+	0.347833i
$811$			25.4558i			0.893876i	0.894565	+	0.446938i	$0.147485\pi$
$811$			25.4558i			0.893876i	−0.894565	+	0.446938i	$0.852515\pi$
$812$			25.4558i			0.893325i
$813$	−18.0000	−	12.7279i	−0.631288	−	0.446388i
$814$	−6.00000	+	2.82843i	−0.210300	+	0.0991363i
$815$			2.82843i			0.0990755i
$816$		0			0
$817$		0			0
$818$		−	8.48528i		−	0.296681i
$819$	−18.0000	−	50.9117i	−0.628971	−	1.77900i
$820$		−	8.48528i		−	0.296319i
$821$	−30.0000			−1.04701			−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000			−1.04701			−0.523504	+	0.852023i	$0.675375\pi$
$822$	−4.00000	−	2.82843i	−0.139516	−	0.0986527i
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$	4.00000			0.139347
$825$	−3.00000	+	16.9706i	−0.104447	+	0.590839i
$826$	−48.0000			−1.67013
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	4.00000	−	1.41421i	0.139010	−	0.0491473i
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$			16.9706i			0.589057i
$831$	30.0000	+	21.2132i	1.04069	+	0.735878i
$832$		−	4.24264i		−	0.147087i
$833$		0			0
$834$	−24.0000	−	16.9706i	−0.831052	−	0.587643i
$835$			16.9706i			0.587291i
$836$		0			0
$837$	−20.0000	−	5.65685i	−0.691301	−	0.195529i
$838$			11.3137i			0.390826i
$839$		−	15.5563i		−	0.537065i	−0.963271	−	0.268532i	$-0.913461\pi$
$839$		−	15.5563i		−	0.537065i	0.963271	−	0.268532i	$-0.0865386\pi$
$840$	−6.00000	+	8.48528i	−0.207020	+	0.292770i
$841$	7.00000			0.241379
$842$	10.0000			0.344623
$843$	12.0000	−	16.9706i	0.413302	−	0.584497i
$844$			8.48528i			0.292075i
$845$		−	7.07107i		−	0.243252i
$846$	−28.0000	+	9.89949i	−0.962660	+	0.340352i
$847$	36.0000	+	29.6985i	1.23697	+	1.02045i
$848$		−	7.07107i		−	0.242821i
$849$	−12.0000	−	8.48528i	−0.411839	−	0.291214i
$850$		0			0
$851$			2.82843i			0.0969572i
$852$	10.0000	+	7.07107i	0.342594	+	0.242251i
$853$		−	21.2132i		−	0.726326i	−0.931726	−	0.363163i	$-0.881697\pi$
$853$		−	21.2132i		−	0.726326i	0.931726	−	0.363163i	$-0.118303\pi$
$854$	18.0000			0.615947
$855$		0			0
$856$	18.0000			0.615227
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$	−24.0000	−	4.24264i	−0.819346	−	0.144841i
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	12.0000			0.409197
$861$	36.0000	+	25.4558i	1.22688	+	0.867533i
$862$	36.0000			1.22616
$863$		−	7.07107i		−	0.240702i	−0.992731	−	0.120351i	$-0.961598\pi$
$863$		−	7.07107i		−	0.240702i	0.992731	−	0.120351i	$-0.0384020\pi$
$864$	−5.00000	−	1.41421i	−0.170103	−	0.0481125i
$865$			8.48528i			0.288508i
$866$	−2.00000			−0.0679628
$867$	17.0000	−	24.0416i	0.577350	−	0.816497i
$868$		−	16.9706i		−	0.576018i
$869$	6.00000	+	12.7279i	0.203536	+	0.431765i
$870$	12.0000	+	8.48528i	0.406838	+	0.287678i
$871$			16.9706i			0.575026i
$872$		−	12.7279i		−	0.431022i
$873$	−8.00000	−	22.6274i	−0.270759	−	0.765822i
$874$		0			0
$875$	−48.0000			−1.62270
$876$		0			0
$877$		−	29.6985i		−	1.00285i	−0.865202	−	0.501423i	$-0.832810\pi$
$877$		−	29.6985i		−	1.00285i	0.865202	−	0.501423i	$-0.167190\pi$
$878$			21.2132i			0.715911i
$879$	6.00000	−	8.48528i	0.202375	−	0.286201i
$880$	2.00000	+	4.24264i	0.0674200	+	0.143019i
$881$			5.65685i			0.190584i	0.995449	+	0.0952921i	$0.0303785\pi$
$881$			5.65685i			0.190584i	−0.995449	+	0.0952921i	$0.969621\pi$
$882$	−11.0000	−	31.1127i	−0.370389	−	1.04762i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−16.0000	+	22.6274i	−0.537834	+	0.760612i
$886$			28.2843i			0.950229i
$887$	48.0000			1.61168			0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000			1.61168			0.805841	+	0.592132i	$0.201714\pi$
$888$	2.00000	−	2.82843i	0.0671156	−	0.0949158i
$889$	54.0000			1.81110
$890$	8.00000			0.268161
$891$	−13.0000	+	26.8701i	−0.435516	+	0.900181i
$892$	8.00000			0.267860
$893$		0			0
$894$	−6.00000	+	8.48528i	−0.200670	+	0.283790i
$895$	−8.00000			−0.267411
$896$		−	4.24264i		−	0.141737i
$897$	−6.00000	+	8.48528i	−0.200334	+	0.283315i
$898$		−	31.1127i		−	1.03824i
$899$	−24.0000			−0.800445
$900$	−3.00000	−	8.48528i	−0.100000	−	0.282843i
$901$		0			0
$902$	18.0000	−	8.48528i	0.599334	−	0.282529i
$903$	−36.0000	+	50.9117i	−1.19800	+	1.69423i
$904$			11.3137i			0.376288i
$905$			2.82843i			0.0940201i
$906$	6.00000	+	4.24264i	0.199337	+	0.140952i
$907$	44.0000			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$908$	6.00000			0.199117
$909$	−6.00000	−	16.9706i	−0.199007	−	0.562878i
$910$		−	25.4558i		−	0.843853i
$911$			9.89949i			0.327985i	0.986462	+	0.163992i	$0.0524373\pi$
$911$			9.89949i			0.327985i	−0.986462	+	0.163992i	$0.947563\pi$
$912$		0			0
$913$	−36.0000	+	16.9706i	−1.19143	+	0.561644i
$914$			8.48528i			0.280668i
$915$	6.00000	−	8.48528i	0.198354	−	0.280515i
$916$	14.0000			0.462573
$917$			50.9117i			1.68125i
$918$		0			0
$919$			38.1838i			1.25957i	0.776771	+	0.629783i	$0.216856\pi$
$919$			38.1838i			1.25957i	−0.776771	+	0.629783i	$0.783144\pi$
$920$	2.00000			0.0659380
$921$		0			0
$922$	30.0000			0.987997
$923$	−30.0000			−0.987462
$924$	−24.0000	−	4.24264i	−0.789542	−	0.139573i
$925$	6.00000			0.197279
$926$	−32.0000			−1.05159
$927$	4.00000	+	11.3137i	0.131377	+	0.371591i
$928$	−6.00000			−0.196960
$929$		−	2.82843i		−	0.0927977i	−0.998923	−	0.0463988i	$-0.985225\pi$
$929$		−	2.82843i		−	0.0927977i	0.998923	−	0.0463988i	$-0.0147745\pi$
$930$	−8.00000	−	5.65685i	−0.262330	−	0.185496i
$931$		0			0
$932$	−18.0000			−0.589610
$933$	−38.0000	−	26.8701i	−1.24406	−	0.879686i
$934$		−	31.1127i		−	1.01804i
$935$		0			0
$936$	12.0000	−	4.24264i	0.392232	−	0.138675i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$			16.9706i			0.554109i
$939$	10.0000	−	14.1421i	0.326338	−	0.461511i
$940$	−14.0000			−0.456630
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$	−22.0000	+	31.1127i	−0.716799	+	1.01371i
$943$		−	8.48528i		−	0.276319i
$944$		−	11.3137i		−	0.368230i
$945$	−30.0000	−	8.48528i	−0.975900	−	0.276026i
$946$	12.0000	+	25.4558i	0.390154	+	0.827641i
$947$			48.0833i			1.56250i	0.624221	+	0.781248i	$0.285417\pi$
$947$			48.0833i			1.56250i	−0.624221	+	0.781248i	$0.714583\pi$
$948$	−6.00000	−	4.24264i	−0.194871	−	0.137795i
$949$		0			0
$950$		0			0
$951$	−14.0000	−	9.89949i	−0.453981	−	0.321013i
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$	20.0000	−	7.07107i	0.647524	−	0.228934i
$955$	−14.0000			−0.453029
$956$	12.0000			0.388108
$957$	−6.00000	+	33.9411i	−0.193952	+	1.09716i
$958$	12.0000			0.387702
$959$	12.0000			0.387500
$960$	−2.00000	−	1.41421i	−0.0645497	−	0.0456435i
$961$	−15.0000			−0.483871
$962$			8.48528i			0.273576i
$963$	18.0000	+	50.9117i	0.580042	+	1.64061i
$964$		−	8.48528i		−	0.273293i
$965$	−12.0000			−0.386294
$966$	−6.00000	+	8.48528i	−0.193047	+	0.273009i
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$	−7.00000	+	8.48528i	−0.224989	+	0.272727i
$969$		0			0
$970$		−	11.3137i		−	0.363261i
$971$		−	45.2548i		−	1.45230i	−0.687538	−	0.726148i	$-0.741309\pi$
$971$		−	45.2548i		−	1.45230i	0.687538	−	0.726148i	$-0.258691\pi$
$972$	−1.00000	−	15.5563i	−0.0320750	−	0.498970i
$973$	72.0000			2.30821
$974$	−20.0000			−0.640841
$975$	18.0000	+	12.7279i	0.576461	+	0.407620i
$976$			4.24264i			0.135804i
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$	2.00000	−	2.82843i	0.0639529	−	0.0904431i
$979$	8.00000	+	16.9706i	0.255681	+	0.542382i
$980$		−	15.5563i		−	0.496929i
$981$	36.0000	−	12.7279i	1.14939	−	0.406371i
$982$	6.00000			0.191468
$983$			9.89949i			0.315745i	0.987460	+	0.157872i	$0.0504635\pi$
$983$			9.89949i			0.315745i	−0.987460	+	0.157872i	$0.949537\pi$
$984$	−6.00000	+	8.48528i	−0.191273	+	0.270501i
$985$			25.4558i			0.811091i
$986$		0			0
$987$	42.0000	−	59.3970i	1.33687	−	1.89063i
$988$		0			0
$989$	12.0000			0.381578
$990$	−10.0000	+	9.89949i	−0.317821	+	0.314627i
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	4.00000			0.127000
$993$	10.0000	−	14.1421i	0.317340	−	0.448787i
$994$	−30.0000			−0.951542
$995$		−	22.6274i		−	0.717337i
$996$	12.0000	−	16.9706i	0.380235	−	0.537733i
$997$			29.6985i			0.940560i	0.882517	+	0.470280i	$0.155847\pi$
$997$			29.6985i			0.940560i	−0.882517	+	0.470280i	$0.844153\pi$
$998$	−14.0000			−0.443162
$999$	10.0000	+	2.82843i	0.316386	+	0.0894875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.2.b.a.65.2	yes	2
3.2	odd	2		66.2.b.b.65.1	yes	2
4.3	odd	2		528.2.b.b.65.1		2
5.2	odd	4		1650.2.f.b.1649.2		4
5.3	odd	4		1650.2.f.b.1649.3		4
5.4	even	2		1650.2.d.b.1451.1		2
8.3	odd	2		2112.2.b.d.65.2		2
8.5	even	2		2112.2.b.g.65.1		2
9.2	odd	6		1782.2.i.c.1187.2		4
9.4	even	3		1782.2.i.f.593.2		4
9.5	odd	6		1782.2.i.c.593.1		4
9.7	even	3		1782.2.i.f.1187.1		4
11.2	odd	10		726.2.h.e.161.2		8
11.3	even	5		726.2.h.i.233.1		8
11.4	even	5		726.2.h.i.215.2		8
11.5	even	5		726.2.h.i.239.1		8
11.6	odd	10		726.2.h.e.239.1		8
11.7	odd	10		726.2.h.e.215.2		8
11.8	odd	10		726.2.h.e.233.1		8
11.9	even	5		726.2.h.i.161.2		8
11.10	odd	2		66.2.b.b.65.2	yes	2
12.11	even	2		528.2.b.c.65.2		2
15.2	even	4		1650.2.f.a.1649.3		4
15.8	even	4		1650.2.f.a.1649.2		4
15.14	odd	2		1650.2.d.a.1451.2		2
24.5	odd	2		2112.2.b.i.65.2		2
24.11	even	2		2112.2.b.b.65.1		2
33.2	even	10		726.2.h.i.161.1		8
33.5	odd	10		726.2.h.e.239.2		8
33.8	even	10		726.2.h.i.233.2		8
33.14	odd	10		726.2.h.e.233.2		8
33.17	even	10		726.2.h.i.239.2		8
33.20	odd	10		726.2.h.e.161.1		8
33.26	odd	10		726.2.h.e.215.1		8
33.29	even	10		726.2.h.i.215.1		8
33.32	even	2	inner	66.2.b.a.65.1	✓	2
44.43	even	2		528.2.b.c.65.1		2
55.32	even	4		1650.2.f.a.1649.4		4
55.43	even	4		1650.2.f.a.1649.1		4
55.54	odd	2		1650.2.d.a.1451.1		2
88.21	odd	2		2112.2.b.i.65.1		2
88.43	even	2		2112.2.b.b.65.2		2
99.32	even	6		1782.2.i.f.593.1		4
99.43	odd	6		1782.2.i.c.1187.1		4
99.65	even	6		1782.2.i.f.1187.2		4
99.76	odd	6		1782.2.i.c.593.2		4
132.131	odd	2		528.2.b.b.65.2		2
165.32	odd	4		1650.2.f.b.1649.1		4
165.98	odd	4		1650.2.f.b.1649.4		4
165.164	even	2		1650.2.d.b.1451.2		2
264.131	odd	2		2112.2.b.d.65.1		2
264.197	even	2		2112.2.b.g.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	33.32	even	2	inner
66.2.b.a.65.2	yes	2	1.1	even	1	trivial
66.2.b.b.65.1	yes	2	3.2	odd	2
66.2.b.b.65.2	yes	2	11.10	odd	2
528.2.b.b.65.1		2	4.3	odd	2
528.2.b.b.65.2		2	132.131	odd	2
528.2.b.c.65.1		2	44.43	even	2
528.2.b.c.65.2		2	12.11	even	2
726.2.h.e.161.1		8	33.20	odd	10
726.2.h.e.161.2		8	11.2	odd	10
726.2.h.e.215.1		8	33.26	odd	10
726.2.h.e.215.2		8	11.7	odd	10
726.2.h.e.233.1		8	11.8	odd	10
726.2.h.e.233.2		8	33.14	odd	10
726.2.h.e.239.1		8	11.6	odd	10
726.2.h.e.239.2		8	33.5	odd	10
726.2.h.i.161.1		8	33.2	even	10
726.2.h.i.161.2		8	11.9	even	5
726.2.h.i.215.1		8	33.29	even	10
726.2.h.i.215.2		8	11.4	even	5
726.2.h.i.233.1		8	11.3	even	5
726.2.h.i.233.2		8	33.8	even	10
726.2.h.i.239.1		8	11.5	even	5
726.2.h.i.239.2		8	33.17	even	10
1650.2.d.a.1451.1		2	55.54	odd	2
1650.2.d.a.1451.2		2	15.14	odd	2
1650.2.d.b.1451.1		2	5.4	even	2
1650.2.d.b.1451.2		2	165.164	even	2
1650.2.f.a.1649.1		4	55.43	even	4
1650.2.f.a.1649.2		4	15.8	even	4
1650.2.f.a.1649.3		4	15.2	even	4
1650.2.f.a.1649.4		4	55.32	even	4
1650.2.f.b.1649.1		4	165.32	odd	4
1650.2.f.b.1649.2		4	5.2	odd	4
1650.2.f.b.1649.3		4	5.3	odd	4
1650.2.f.b.1649.4		4	165.98	odd	4
1782.2.i.c.593.1		4	9.5	odd	6
1782.2.i.c.593.2		4	99.76	odd	6
1782.2.i.c.1187.1		4	99.43	odd	6
1782.2.i.c.1187.2		4	9.2	odd	6
1782.2.i.f.593.1		4	99.32	even	6
1782.2.i.f.593.2		4	9.4	even	3
1782.2.i.f.1187.1		4	9.7	even	3
1782.2.i.f.1187.2		4	99.65	even	6
2112.2.b.b.65.1		2	24.11	even	2
2112.2.b.b.65.2		2	88.43	even	2
2112.2.b.d.65.1		2	264.131	odd	2
2112.2.b.d.65.2		2	8.3	odd	2
2112.2.b.g.65.1		2	8.5	even	2
2112.2.b.g.65.2		2	264.197	even	2
2112.2.b.i.65.1		2	88.21	odd	2
2112.2.b.i.65.2		2	24.5	odd	2

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} +4.24264i q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} +4.24264i q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.41421i q^{10} +(3.00000 - 1.41421i) q^{11} +(-1.00000 + 1.41421i) q^{12} -4.24264i q^{13} -4.24264i q^{14} +(-2.00000 - 1.41421i) q^{15} +1.00000 q^{16} +(1.00000 + 2.82843i) q^{18} +1.41421i q^{20} +(-6.00000 - 4.24264i) q^{21} +(-3.00000 + 1.41421i) q^{22} +1.41421i q^{23} +(1.00000 - 1.41421i) q^{24} +3.00000 q^{25} +4.24264i q^{26} +(5.00000 + 1.41421i) q^{27} +4.24264i q^{28} +6.00000 q^{29} +(2.00000 + 1.41421i) q^{30} -4.00000 q^{31} -1.00000 q^{32} +(-1.00000 + 5.65685i) q^{33} -6.00000 q^{35} +(-1.00000 - 2.82843i) q^{36} +2.00000 q^{37} +(6.00000 + 4.24264i) q^{39} -1.41421i q^{40} -6.00000 q^{41} +(6.00000 + 4.24264i) q^{42} -8.48528i q^{43} +(3.00000 - 1.41421i) q^{44} +(4.00000 - 1.41421i) q^{45} -1.41421i q^{46} +9.89949i q^{47} +(-1.00000 + 1.41421i) q^{48} -11.0000 q^{49} -3.00000 q^{50} -4.24264i q^{52} -7.07107i q^{53} +(-5.00000 - 1.41421i) q^{54} +(2.00000 + 4.24264i) q^{55} -4.24264i q^{56} -6.00000 q^{58} -11.3137i q^{59} +(-2.00000 - 1.41421i) q^{60} +4.24264i q^{61} +4.00000 q^{62} +(12.0000 - 4.24264i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(1.00000 - 5.65685i) q^{66} -4.00000 q^{67} +(-2.00000 - 1.41421i) q^{69} +6.00000 q^{70} -7.07107i q^{71} +(1.00000 + 2.82843i) q^{72} -2.00000 q^{74} +(-3.00000 + 4.24264i) q^{75} +(6.00000 + 12.7279i) q^{77} +(-6.00000 - 4.24264i) q^{78} +4.24264i q^{79} +1.41421i q^{80} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{82} -12.0000 q^{83} +(-6.00000 - 4.24264i) q^{84} +8.48528i q^{86} +(-6.00000 + 8.48528i) q^{87} +(-3.00000 + 1.41421i) q^{88} +5.65685i q^{89} +(-4.00000 + 1.41421i) q^{90} +18.0000 q^{91} +1.41421i q^{92} +(4.00000 - 5.65685i) q^{93} -9.89949i q^{94} +(1.00000 - 1.41421i) q^{96} +8.00000 q^{97} +11.0000 q^{98} +(-7.00000 - 7.07107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{8} - 2 q^{9} + 6 q^{11} - 2 q^{12} - 4 q^{15} + 2 q^{16} + 2 q^{18} - 12 q^{21} - 6 q^{22} + 2 q^{24} + 6 q^{25} + 10 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} - 2 q^{36} + 4 q^{37} + 12 q^{39} - 12 q^{41} + 12 q^{42} + 6 q^{44} + 8 q^{45} - 2 q^{48} - 22 q^{49} - 6 q^{50} - 10 q^{54} + 4 q^{55} - 12 q^{58} - 4 q^{60} + 8 q^{62} + 24 q^{63} + 2 q^{64} + 12 q^{65} + 2 q^{66} - 8 q^{67} - 4 q^{69} + 12 q^{70} + 2 q^{72} - 4 q^{74} - 6 q^{75} + 12 q^{77} - 12 q^{78} - 14 q^{81} + 12 q^{82} - 24 q^{83} - 12 q^{84} - 12 q^{87} - 6 q^{88} - 8 q^{90} + 36 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{97} + 22 q^{98} - 14 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^8 - 2 * q^9 + 6 * q^11 - 2 * q^12 - 4 * q^15 + 2 * q^16 + 2 * q^18 - 12 * q^21 - 6 * q^22 + 2 * q^24 + 6 * q^25 + 10 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 - 2 * q^36 + 4 * q^37 + 12 * q^39 - 12 * q^41 + 12 * q^42 + 6 * q^44 + 8 * q^45 - 2 * q^48 - 22 * q^49 - 6 * q^50 - 10 * q^54 + 4 * q^55 - 12 * q^58 - 4 * q^60 + 8 * q^62 + 24 * q^63 + 2 * q^64 + 12 * q^65 + 2 * q^66 - 8 * q^67 - 4 * q^69 + 12 * q^70 + 2 * q^72 - 4 * q^74 - 6 * q^75 + 12 * q^77 - 12 * q^78 - 14 * q^81 + 12 * q^82 - 24 * q^83 - 12 * q^84 - 12 * q^87 - 6 * q^88 - 8 * q^90 + 36 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^97 + 22 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more