LMFDB - Embedded newform 1170.2.j.c.781.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(391,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			781.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1170.781
Dual form			1170.2.j.c.391.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} -1.73205i q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.00000 - 1.73205i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +5.00000 q^{17} -3.00000 q^{18} +3.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.00000 + 1.73205i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(-4.00000 + 6.92820i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-2.50000 + 4.33013i) q^{34} -2.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -8.00000 q^{37} +(-1.50000 + 2.59808i) q^{38} +1.73205i q^{39} +(0.500000 + 0.866025i) q^{40} +(-3.50000 - 6.06218i) q^{41} -3.46410i q^{42} +(-2.50000 + 4.33013i) q^{43} +1.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(6.00000 - 10.3923i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(7.50000 + 4.33013i) q^{51} +(0.500000 - 0.866025i) q^{52} +2.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} -1.00000 q^{55} +(-1.00000 + 1.73205i) q^{56} +(4.50000 + 2.59808i) q^{57} +(-4.00000 - 6.92820i) q^{58} +(2.50000 + 4.33013i) q^{59} +(1.50000 - 0.866025i) q^{60} +(-7.00000 + 12.1244i) q^{61} +6.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.73205i q^{66} +(7.50000 + 12.9904i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(1.00000 - 1.73205i) q^{70} -2.00000 q^{71} +(1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.50000 - 2.59808i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-1.50000 - 0.866025i) q^{78} +(-1.00000 + 1.73205i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(3.00000 + 1.73205i) q^{84} +(2.50000 + 4.33013i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(-12.0000 + 6.92820i) q^{87} +(-0.500000 + 0.866025i) q^{88} +10.0000 q^{89} +(-1.50000 - 2.59808i) q^{90} -2.00000 q^{91} -10.3923i q^{93} +(6.00000 + 10.3923i) q^{94} +(1.50000 + 2.59808i) q^{95} -1.73205i q^{96} +(6.50000 - 11.2583i) q^{97} -3.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{13} - 2 q^{14} - q^{16} + 10 q^{17} - 6 q^{18} + 6 q^{19} + q^{20} - 6 q^{21} - q^{22} + 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 3 * q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + q^13 - 2 * q^14 - q^16 + 10 * q^17 - 6 * q^18 + 6 * q^19 + q^20 - 6 * q^21 - q^22 + 3 * q^24 - q^25 - 2 * q^26 + 4 * q^28 - 8 * q^29 - 3 * q^30 - 6 * q^31 - q^32 - 3 * q^33 - 5 * q^34 - 4 * q^35 + 3 * q^36 - 16 * q^37 - 3 * q^38 + q^40 - 7 * q^41 - 5 * q^43 + 2 * q^44 - 3 * q^45 + 12 * q^47 - 3 * q^48 + 3 * q^49 - q^50 + 15 * q^51 + q^52 + 4 * q^53 - 9 * q^54 - 2 * q^55 - 2 * q^56 + 9 * q^57 - 8 * q^58 + 5 * q^59 + 3 * q^60 - 14 * q^61 + 12 * q^62 - 12 * q^63 + 2 * q^64 - q^65 + 15 * q^67 - 5 * q^68 + 2 * q^70 - 4 * q^71 + 3 * q^72 - 22 * q^73 + 8 * q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 - 3 * q^78 - 2 * q^79 - 2 * q^80 - 9 * q^81 + 14 * q^82 + 12 * q^83 + 6 * q^84 + 5 * q^85 - 5 * q^86 - 24 * q^87 - q^88 + 20 * q^89 - 3 * q^90 - 4 * q^91 + 12 * q^94 + 3 * q^95 + 13 * q^97 - 6 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000			−0.316228
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		−	1.73205i		−	0.500000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−1.00000	−	1.73205i	−0.267261	−	0.462910i
$15$			1.73205i			0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.00000			1.21268			0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000			1.21268			0.606339	+	0.795206i	$0.292637\pi$
$18$	−3.00000			−0.707107
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−3.00000	+	1.73205i	−0.654654	+	0.377964i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.00000			−0.196116
$27$			5.19615i			1.00000i
$28$	2.00000			0.377964
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	0.208443	+	0.978035i	$0.433160\pi$
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	−0.951224	+	0.308500i	$0.900173\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$	−2.50000	+	4.33013i	−0.428746	+	0.742611i
$35$	−2.00000			−0.338062
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−1.50000	+	2.59808i	−0.243332	+	0.421464i
$39$			1.73205i			0.277350i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	−0.998504	−	0.0546823i	$-0.982585\pi$
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	0.451896	−	0.892071i	$-0.350748\pi$
$42$		−	3.46410i		−	0.534522i
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$	1.00000			0.150756
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.0186297	−	0.999826i	$-0.494070\pi$
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.856560	−	0.516047i	$-0.172597\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	7.50000	+	4.33013i	1.05021	+	0.606339i
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−1.00000			−0.134840
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	4.50000	+	2.59808i	0.596040	+	0.344124i
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	6.00000			0.762001
$63$	−6.00000			−0.755929
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		−	1.73205i		−	0.213201i
$67$	7.50000	+	12.9904i	0.916271	+	1.58703i	0.805030	+	0.593234i	$0.202149\pi$
$67$	7.50000	+	12.9904i	0.916271	+	1.58703i	0.111241	+	0.993793i	$0.464517\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$		0			0
$70$	1.00000	−	1.73205i	0.119523	−	0.207020i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−1.50000	−	2.59808i	−0.172062	−	0.298020i
$77$	−1.00000	−	1.73205i	−0.113961	−	0.197386i
$78$	−1.50000	−	0.866025i	−0.169842	−	0.0980581i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	7.00000			0.773021
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$	3.00000	+	1.73205i	0.327327	+	0.188982i
$85$	2.50000	+	4.33013i	0.271163	+	0.469668i
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$	−12.0000	+	6.92820i	−1.28654	+	0.742781i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	−2.00000			−0.209657
$92$		0			0
$93$		−	10.3923i		−	1.07763i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	1.50000	+	2.59808i	0.153897	+	0.266557i
$96$		−	1.73205i		−	0.176777i
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	−0.320647	−	0.947199i	$-0.603900\pi$
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	0.980622	−	0.195911i	$-0.0627665\pi$
$98$	−3.00000			−0.303046
$99$	−3.00000			−0.301511
$100$	1.00000			0.100000
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$	−7.50000	+	4.33013i	−0.742611	+	0.428746i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$	−3.00000	−	1.73205i	−0.292770	−	0.169031i
$106$	−1.00000	+	1.73205i	−0.0971286	+	0.168232i
$107$	9.00000			0.870063			0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000			0.870063			0.435031	+	0.900415i	$0.356737\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−12.0000	−	6.92820i	−1.13899	−	0.657596i
$112$	−1.00000	−	1.73205i	−0.0944911	−	0.163663i
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$	−4.50000	+	2.59808i	−0.421464	+	0.243332i
$115$		0			0
$116$	8.00000			0.742781
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$	−5.00000			−0.460287
$119$	−5.00000	+	8.66025i	−0.458349	+	0.793884i
$120$			1.73205i			0.158114i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$		−	12.1244i		−	1.09322i
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	−1.00000			−0.0894427
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	22.0000			1.95218			0.976092	−	0.217357i	$-0.0697436\pi$
$127$	22.0000			1.95218			0.976092	+	0.217357i	$0.0697436\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−7.50000	+	4.33013i	−0.660338	+	0.381246i
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	1.50000	+	0.866025i	0.130558	+	0.0753778i
$133$	−3.00000	+	5.19615i	−0.260133	+	0.450564i
$134$	−15.0000			−1.29580
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	5.00000			0.428746
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	18.0000	−	10.3923i	1.51587	−	0.875190i
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	−1.00000			−0.0836242
$144$	−3.00000			−0.250000
$145$	−8.00000			−0.664364
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$			5.19615i			0.428571i
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$		−	1.73205i		−	0.141421i
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	3.00000			0.243332
$153$	7.50000	+	12.9904i	0.606339	+	1.05021i
$154$	2.00000			0.161165
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$	1.50000	−	0.866025i	0.120096	−	0.0693375i
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	3.00000	+	1.73205i	0.237915	+	0.137361i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$	−1.50000	−	0.866025i	−0.116775	−	0.0674200i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$	−3.00000	+	1.73205i	−0.231455	+	0.133631i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−5.00000			−0.383482
$171$	4.50000	+	7.79423i	0.344124	+	0.596040i
$172$	5.00000			0.381246
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$		−	13.8564i		−	1.05045i
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$			8.66025i			0.650945i
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	3.00000			0.223607
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	1.00000	−	1.73205i	0.0741249	−	0.128388i
$183$	−21.0000	+	12.1244i	−1.55236	+	0.896258i
$184$		0			0
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$	−2.50000	+	4.33013i	−0.182818	+	0.316650i
$188$	−12.0000			−0.875190
$189$	−9.00000	−	5.19615i	−0.654654	−	0.377964i
$190$	−3.00000			−0.217643
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$	6.50000	+	11.2583i	0.466673	+	0.808301i
$195$	−1.50000	+	0.866025i	−0.107417	+	0.0620174i
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	18.0000			1.27599			0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000			1.27599			0.637993	+	0.770042i	$0.279765\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$			25.9808i			1.83254i
$202$	−1.00000	−	1.73205i	−0.0703598	−	0.121867i
$203$	−8.00000	−	13.8564i	−0.561490	−	0.972529i
$204$		−	8.66025i		−	0.606339i
$205$	3.50000	−	6.06218i	0.244451	−	0.423401i
$206$		0			0
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−1.50000	+	2.59808i	−0.103757	+	0.179713i
$210$	3.00000	−	1.73205i	0.207020	−	0.119523i
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$	−3.00000	−	1.73205i	−0.205557	−	0.118678i
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$	−5.00000			−0.340997
$216$			5.19615i			0.353553i
$217$	12.0000			0.814613
$218$	−3.00000	+	5.19615i	−0.203186	+	0.351928i
$219$	−16.5000	−	9.52628i	−1.11497	−	0.643726i
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$	12.0000	−	6.92820i	0.805387	−	0.464991i
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	−0.530607	−	0.847618i	$-0.678036\pi$
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	0.999362	+	0.0357107i	$0.0113695\pi$
$224$	2.00000			0.133631
$225$	−3.00000			−0.200000
$226$	14.0000			0.931266
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	0.432962	+	0.901412i	$0.357468\pi$
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	−0.997127	+	0.0757500i	$0.975865\pi$
$228$		−	5.19615i		−	0.344124i
$229$	4.00000	+	6.92820i	0.264327	+	0.457829i	0.967387	−	0.253302i	$-0.0815167\pi$
$229$	4.00000	+	6.92820i	0.264327	+	0.457829i	−0.703060	+	0.711131i	$0.748183\pi$
$230$		0			0
$231$		−	3.46410i		−	0.227921i
$232$	−4.00000	+	6.92820i	−0.262613	+	0.454859i
$233$	15.0000			0.982683			0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000			0.982683			0.491341	+	0.870967i	$0.336507\pi$
$234$	−1.50000	−	2.59808i	−0.0980581	−	0.169842i
$235$	12.0000			0.782794
$236$	2.50000	−	4.33013i	0.162736	−	0.281867i
$237$	−3.00000	+	1.73205i	−0.194871	+	0.112509i
$238$	−5.00000	−	8.66025i	−0.324102	−	0.561361i
$239$	1.00000	+	1.73205i	0.0646846	+	0.112037i	0.896554	−	0.442934i	$-0.146063\pi$
$239$	1.00000	+	1.73205i	0.0646846	+	0.112037i	−0.831869	+	0.554971i	$0.812729\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	−10.0000			−0.642824
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	14.0000			0.896258
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$	10.5000	+	6.06218i	0.669456	+	0.386510i
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$	18.0000	−	10.3923i	1.14070	−	0.658586i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	27.0000			1.70422			0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000			1.70422			0.852112	+	0.523359i	$0.175321\pi$
$252$	3.00000	+	5.19615i	0.188982	+	0.327327i
$253$		0			0
$254$	−11.0000	+	19.0526i	−0.690201	+	1.19546i
$255$			8.66025i			0.542326i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		−	8.66025i		−	0.539164i
$259$	8.00000	−	13.8564i	0.497096	−	0.860995i
$260$	1.00000			0.0620174
$261$	−24.0000			−1.48556
$262$	4.00000			0.247121
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$	−1.50000	+	0.866025i	−0.0923186	+	0.0533002i
$265$	1.00000	+	1.73205i	0.0614295	+	0.106399i
$266$	−3.00000	−	5.19615i	−0.183942	−	0.318597i
$267$	15.0000	+	8.66025i	0.917985	+	0.529999i
$268$	7.50000	−	12.9904i	0.458135	−	0.793514i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		−	5.19615i		−	0.316228i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	−2.50000	+	4.33013i	−0.151585	+	0.262553i
$273$	−3.00000	−	1.73205i	−0.181568	−	0.104828i
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	7.00000			0.419832
$279$	9.00000	−	15.5885i	0.538816	−	0.933257i
$280$	−2.00000			−0.119523
$281$	15.0000	−	25.9808i	0.894825	−	1.54988i	0.0608039	−	0.998150i	$-0.480634\pi$
$281$	15.0000	−	25.9808i	0.894825	−	1.54988i	0.834021	−	0.551733i	$-0.186033\pi$
$282$			20.7846i			1.23771i
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.208053	−	0.978117i	$-0.566713\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$			5.19615i			0.307794i
$286$	0.500000	−	0.866025i	0.0295656	−	0.0512092i
$287$	14.0000			0.826394
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	8.00000			0.470588
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$	19.5000	−	11.2583i	1.14311	−	0.659975i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	1.00000	+	1.73205i	0.0584206	+	0.101187i	0.893757	−	0.448552i	$-0.148060\pi$
$293$	1.00000	+	1.73205i	0.0584206	+	0.101187i	−0.835336	+	0.549740i	$0.814727\pi$
$294$	−4.50000	−	2.59808i	−0.262445	−	0.151523i
$295$	−2.50000	+	4.33013i	−0.145556	+	0.252110i
$296$	−8.00000			−0.464991
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$	14.0000			0.810998
$299$		0			0
$300$	1.50000	+	0.866025i	0.0866025	+	0.0500000i
$301$	−5.00000	−	8.66025i	−0.288195	−	0.499169i
$302$		0			0
$303$	−3.00000	+	1.73205i	−0.172345	+	0.0995037i
$304$	−1.50000	+	2.59808i	−0.0860309	+	0.149010i
$305$	−14.0000			−0.801638
$306$	−15.0000			−0.857493
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$		0			0
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$			1.73205i			0.0980581i
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	−0.964720	−	0.263278i	$-0.915197\pi$
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	0.710365	+	0.703833i	$0.248530\pi$
$314$	22.0000			1.24153
$315$	−3.00000	−	5.19615i	−0.169031	−	0.292770i
$316$	2.00000			0.112509
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−3.00000	+	1.73205i	−0.168232	+	0.0971286i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	13.5000	+	7.79423i	0.753497	+	0.435031i
$322$		0			0
$323$	15.0000			0.834622
$324$	9.00000			0.500000
$325$	−1.00000			−0.0554700
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$	9.00000	+	5.19615i	0.497701	+	0.287348i
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$	1.50000	−	0.866025i	0.0825723	−	0.0476731i
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	−12.0000			−0.658586
$333$	−12.0000	−	20.7846i	−0.657596	−	1.13899i
$334$	8.00000			0.437741
$335$	−7.50000	+	12.9904i	−0.409769	+	0.709740i
$336$		−	3.46410i		−	0.188982i
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	−0.500000	−	0.866025i	−0.0271964	−	0.0471056i
$339$		−	24.2487i		−	1.31701i
$340$	2.50000	−	4.33013i	0.135582	−	0.234834i
$341$	6.00000			0.324918
$342$	−9.00000			−0.486664
$343$	−20.0000			−1.07990
$344$	−2.50000	+	4.33013i	−0.134791	+	0.233465i
$345$		0			0
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	0.961162	−	0.275983i	$-0.0890035\pi$
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	−0.719590	+	0.694399i	$0.755670\pi$
$348$	12.0000	+	6.92820i	0.643268	+	0.371391i
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$	2.00000			0.106904
$351$	−4.50000	+	2.59808i	−0.240192	+	0.138675i
$352$	1.00000			0.0533002
$353$	5.50000	−	9.52628i	0.292735	−	0.507033i	−0.681720	−	0.731613i	$-0.738768\pi$
$353$	5.50000	−	9.52628i	0.292735	−	0.507033i	0.974456	+	0.224580i	$0.0721011\pi$
$354$	−7.50000	−	4.33013i	−0.398621	−	0.230144i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−5.00000	−	8.66025i	−0.264999	−	0.458993i
$357$	−15.0000	+	8.66025i	−0.793884	+	0.458349i
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	−10.0000			−0.526316
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$			17.3205i			0.909091i
$364$	1.00000	+	1.73205i	0.0524142	+	0.0907841i
$365$	−5.50000	−	9.52628i	−0.287883	−	0.498628i
$366$		−	24.2487i		−	1.26750i
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	−0.665855	−	0.746081i	$-0.731933\pi$
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	0.979053	+	0.203607i	$0.0652665\pi$
$368$		0			0
$369$	10.5000	−	18.1865i	0.546608	−	0.946753i
$370$	8.00000			0.415900
$371$	−2.00000	+	3.46410i	−0.103835	+	0.179847i
$372$	−9.00000	+	5.19615i	−0.466628	+	0.269408i
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	−2.50000	−	4.33013i	−0.129272	−	0.223906i
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	−8.00000			−0.412021
$378$	9.00000	−	5.19615i	0.462910	−	0.267261i
$379$	15.0000			0.770498			0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000			0.770498			0.385249	+	0.922813i	$0.374116\pi$
$380$	1.50000	−	2.59808i	0.0769484	−	0.133278i
$381$	33.0000	+	19.0526i	1.69064	+	0.976092i
$382$		0			0
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	1.00000	−	1.73205i	0.0509647	−	0.0882735i
$386$	−13.0000			−0.661683
$387$	−15.0000			−0.762493
$388$	−13.0000			−0.659975
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$		−	1.73205i		−	0.0877058i
$391$		0			0
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$		−	6.92820i		−	0.349482i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−2.00000			−0.100631
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−9.00000	+	15.5885i	−0.451129	+	0.781379i
$399$	−9.00000	+	5.19615i	−0.450564	+	0.260133i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$	−22.5000	−	12.9904i	−1.12220	−	0.647901i
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$	2.00000			0.0995037
$405$	−9.00000			−0.447214
$406$	16.0000			0.794067
$407$	4.00000	−	6.92820i	0.198273	−	0.343418i
$408$	7.50000	+	4.33013i	0.371305	+	0.214373i
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$	3.50000	+	6.06218i	0.172853	+	0.299390i
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$		0			0
$413$	−10.0000			−0.492068
$414$		0			0
$415$	12.0000			0.589057
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		−	12.1244i		−	0.593732i
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	10.0000	+	17.3205i	0.488532	+	0.846162i	0.999913	−	0.0131919i	$-0.00419923\pi$
$419$	10.0000	+	17.3205i	0.488532	+	0.846162i	−0.511381	+	0.859354i	$0.670866\pi$
$420$			3.46410i			0.169031i
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	0.291953	+	0.956433i	$0.405695\pi$
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	−0.974272	+	0.225377i	$0.927639\pi$
$422$	−20.0000			−0.973585
$423$	36.0000			1.75038
$424$	2.00000			0.0971286
$425$	−2.50000	+	4.33013i	−0.121268	+	0.210042i
$426$	3.00000	−	1.73205i	0.145350	−	0.0839181i
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$	−4.50000	−	7.79423i	−0.217516	−	0.376748i
$429$	−1.50000	−	0.866025i	−0.0724207	−	0.0418121i
$430$	2.50000	−	4.33013i	0.120561	−	0.208817i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	−6.00000	+	10.3923i	−0.288009	+	0.498847i
$435$	−12.0000	−	6.92820i	−0.575356	−	0.332182i
$436$	−3.00000	−	5.19615i	−0.143674	−	0.248851i
$437$		0			0
$438$	16.5000	−	9.52628i	0.788400	−	0.455183i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−1.00000			−0.0476731
$441$	−4.50000	+	7.79423i	−0.214286	+	0.371154i
$442$	−5.00000			−0.237826
$443$	−0.500000	+	0.866025i	−0.0237557	+	0.0411461i	−0.877659	−	0.479286i	$-0.840896\pi$
$443$	−0.500000	+	0.866025i	−0.0237557	+	0.0411461i	0.853903	+	0.520432i	$0.174229\pi$
$444$			13.8564i			0.657596i
$445$	5.00000	+	8.66025i	0.237023	+	0.410535i
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$		−	24.2487i		−	1.14692i
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	7.00000			0.329617
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	−8.50000	−	14.7224i	−0.398925	−	0.690958i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	4.50000	+	2.59808i	0.210732	+	0.121666i
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	0.0880870	+	0.996113i	$0.471925\pi$
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	−0.906702	+	0.421771i	$0.861409\pi$
$458$	−8.00000			−0.373815
$459$			25.9808i			1.21268i
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$	3.00000	+	1.73205i	0.139573	+	0.0805823i
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	0.618050	−	0.786139i	$-0.287923\pi$
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$	9.00000	−	5.19615i	0.417365	−	0.240966i
$466$	−7.50000	+	12.9904i	−0.347431	+	0.601768i
$467$	7.00000			0.323921			0.161961	−	0.986797i	$-0.448218\pi$
$467$	7.00000			0.323921			0.161961	+	0.986797i	$0.448218\pi$
$468$	3.00000			0.138675
$469$	−30.0000			−1.38527
$470$	−6.00000	+	10.3923i	−0.276759	+	0.479361i
$471$		−	38.1051i		−	1.75579i
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	−2.50000	−	4.33013i	−0.114950	−	0.199099i
$474$		−	3.46410i		−	0.159111i
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$	10.0000			0.458349
$477$	3.00000	+	5.19615i	0.137361	+	0.237915i
$478$	−2.00000			−0.0914779
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$	1.50000	−	0.866025i	0.0684653	−	0.0395285i
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	0.500000	+	0.866025i	0.0227744	+	0.0394464i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	13.0000			0.590300
$486$		−	15.5885i		−	0.707107i
$487$	−34.0000			−1.54069			−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000			−1.54069			−0.770344	+	0.637629i	$0.779915\pi$
$488$	−7.00000	+	12.1244i	−0.316875	+	0.548844i
$489$	−24.0000	−	13.8564i	−1.08532	−	0.626608i
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$492$	−10.5000	+	6.06218i	−0.473377	+	0.273304i
$493$	−20.0000	+	34.6410i	−0.900755	+	1.56015i
$494$	−3.00000			−0.134976
$495$	−1.50000	−	2.59808i	−0.0674200	−	0.116775i
$496$	6.00000			0.269408
$497$	2.00000	−	3.46410i	0.0897123	−	0.155386i
$498$			20.7846i			0.931381i
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		−	13.8564i		−	0.619059i
$502$	−13.5000	+	23.3827i	−0.602534	+	1.04362i
$503$	−2.00000			−0.0891756			−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000			−0.0891756			−0.0445878	+	0.999005i	$0.514197\pi$
$504$	−6.00000			−0.267261
$505$	−2.00000			−0.0889988
$506$		0			0
$507$	−1.50000	+	0.866025i	−0.0666173	+	0.0384615i
$508$	−11.0000	−	19.0526i	−0.488046	−	0.845321i
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$	−7.50000	−	4.33013i	−0.332106	−	0.191741i
$511$	11.0000	−	19.0526i	0.486611	−	0.842836i
$512$	1.00000			0.0441942
$513$			15.5885i			0.688247i
$514$	15.0000			0.661622
$515$		0			0
$516$	7.50000	+	4.33013i	0.330169	+	0.190623i
$517$	6.00000	+	10.3923i	0.263880	+	0.457053i
$518$	8.00000	+	13.8564i	0.351500	+	0.608816i
$519$	21.0000	−	12.1244i	0.921798	−	0.532200i
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−23.0000			−1.00765			−0.503824	−	0.863806i	$-0.668074\pi$
$521$	−23.0000			−1.00765			−0.503824	+	0.863806i	$0.668074\pi$
$522$	12.0000	−	20.7846i	0.525226	−	0.909718i
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$		−	3.46410i		−	0.151186i
$526$	2.00000	+	3.46410i	0.0872041	+	0.151042i
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$		−	1.73205i		−	0.0753778i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−2.00000			−0.0868744
$531$	−7.50000	+	12.9904i	−0.325472	+	0.563735i
$532$	6.00000			0.260133
$533$	3.50000	−	6.06218i	0.151602	−	0.262582i
$534$	−15.0000	+	8.66025i	−0.649113	+	0.374766i
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$	7.50000	+	12.9904i	0.323951	+	0.561099i
$537$	30.0000	+	17.3205i	1.29460	+	0.747435i
$538$		0			0
$539$	−3.00000			−0.129219
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	−21.0000	−	12.1244i	−0.901196	−	0.520306i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	3.00000	+	5.19615i	0.128506	+	0.222579i
$546$	3.00000	−	1.73205i	0.128388	−	0.0741249i
$547$	11.5000	−	19.9186i	0.491704	−	0.851657i	−0.508250	−	0.861210i	$-0.669707\pi$
$547$	11.5000	−	19.9186i	0.491704	−	0.851657i	0.999954	+	0.00955248i	$0.00304070\pi$
$548$	3.00000			0.128154
$549$	−42.0000			−1.79252
$550$	1.00000			0.0426401
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	8.00000	+	13.8564i	0.339887	+	0.588702i
$555$		−	13.8564i		−	0.588172i
$556$	−3.50000	+	6.06218i	−0.148433	+	0.257094i
$557$	−16.0000			−0.677942			−0.338971	−	0.940797i	$-0.610079\pi$
$557$	−16.0000			−0.677942			−0.338971	+	0.940797i	$0.610079\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$	−5.00000			−0.211477
$560$	1.00000	−	1.73205i	0.0422577	−	0.0731925i
$561$	−7.50000	+	4.33013i	−0.316650	+	0.182818i
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	0.663581	−	0.748105i	$-0.269036\pi$
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	−0.979668	+	0.200625i	$0.935703\pi$
$564$	−18.0000	−	10.3923i	−0.757937	−	0.437595i
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	32.0000			1.34506
$567$	−9.00000	−	15.5885i	−0.377964	−	0.654654i
$568$	−2.00000			−0.0839181
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.184030	+	0.982921i	$0.558914\pi$
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.759220	+	0.650835i	$0.774419\pi$
$570$	−4.50000	−	2.59808i	−0.188484	−	0.108821i
$571$	−6.50000	−	11.2583i	−0.272017	−	0.471146i	0.697362	−	0.716720i	$-0.254357\pi$
$571$	−6.50000	−	11.2583i	−0.272017	−	0.471146i	−0.969378	+	0.245573i	$0.921024\pi$
$572$	0.500000	+	0.866025i	0.0209061	+	0.0362103i
$573$		0			0
$574$	−7.00000	+	12.1244i	−0.292174	+	0.506061i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	21.0000			0.874241			0.437121	−	0.899403i	$-0.355998\pi$
$577$	21.0000			0.874241			0.437121	+	0.899403i	$0.355998\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$			22.5167i			0.935760i
$580$	4.00000	+	6.92820i	0.166091	+	0.287678i
$581$	12.0000	+	20.7846i	0.497844	+	0.862291i
$582$			22.5167i			0.933346i
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	−11.0000			−0.455183
$585$	−3.00000			−0.124035
$586$	−2.00000			−0.0826192
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$	4.50000	−	2.59808i	0.185577	−	0.107143i
$589$	−9.00000	−	15.5885i	−0.370839	−	0.642311i
$590$	−2.50000	−	4.33013i	−0.102923	−	0.178269i
$591$	27.0000	+	15.5885i	1.11063	+	0.641223i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	46.0000			1.88899			0.944497	−	0.328521i	$-0.106550\pi$
$593$	46.0000			1.88899			0.944497	+	0.328521i	$0.106550\pi$
$594$	4.50000	−	2.59808i	0.184637	−	0.106600i
$595$	−10.0000			−0.409960
$596$	−7.00000	+	12.1244i	−0.286731	+	0.496633i
$597$	27.0000	+	15.5885i	1.10504	+	0.637993i
$598$		0			0
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$	−1.50000	+	0.866025i	−0.0612372	+	0.0353553i
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$	10.0000			0.407570
$603$	−22.5000	+	38.9711i	−0.916271	+	1.58703i
$604$		0			0
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		−	3.46410i		−	0.140720i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	−1.50000	−	2.59808i	−0.0608330	−	0.105366i
$609$		−	27.7128i		−	1.12298i
$610$	7.00000	−	12.1244i	0.283422	−	0.490901i
$611$	12.0000			0.485468
$612$	7.50000	−	12.9904i	0.303170	−	0.525105i
$613$	−4.00000			−0.161558			−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$	−4.50000	+	7.79423i	−0.181605	+	0.314549i
$615$	10.5000	−	6.06218i	0.423401	−	0.244451i
$616$	−1.00000	−	1.73205i	−0.0402911	−	0.0697863i
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	0.761114	−	0.648618i	$-0.224653\pi$
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	−0.942277	+	0.334835i	$0.891320\pi$
$618$		0			0
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	−0.705319	−	0.708890i	$-0.749196\pi$
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	0.966576	+	0.256379i	$0.0825296\pi$
$620$	−6.00000			−0.240966
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−10.0000	+	17.3205i	−0.400642	+	0.693932i
$624$	−1.50000	−	0.866025i	−0.0600481	−	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.50000	−	7.79423i	−0.179856	−	0.311520i
$627$	−4.50000	+	2.59808i	−0.179713	+	0.103757i
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$	−40.0000			−1.59490
$630$	6.00000			0.239046
$631$	−48.0000			−1.91085			−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000			−1.91085			−0.955425	+	0.295234i	$0.904602\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$			34.6410i			1.37686i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	11.0000	+	19.0526i	0.436522	+	0.756078i
$636$		−	3.46410i		−	0.137361i
$637$	−1.50000	+	2.59808i	−0.0594322	+	0.102940i
$638$	8.00000			0.316723
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	−1.00000			−0.0395285
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.0472793	+	0.998882i	$0.515055\pi$
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.841417	+	0.540386i	$0.818278\pi$
$642$	−13.5000	+	7.79423i	−0.532803	+	0.307614i
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	0.875716	−	0.482826i	$-0.160390\pi$
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	−0.855998	+	0.516979i	$0.827056\pi$
$644$		0			0
$645$	−7.50000	−	4.33013i	−0.295312	−	0.170499i
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−5.00000			−0.196267
$650$	0.500000	−	0.866025i	0.0196116	−	0.0339683i
$651$	18.0000	+	10.3923i	0.705476	+	0.407307i
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$	−9.00000	+	5.19615i	−0.351928	+	0.203186i
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	7.00000			0.273304
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$	−24.0000			−0.935617
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$			1.73205i			0.0674200i
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$			8.66025i			0.336336i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$	−6.00000			−0.232670
$666$	24.0000			0.929981
$667$		0			0
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	21.0000	−	12.1244i	0.811907	−	0.468755i
$670$	−7.50000	−	12.9904i	−0.289750	−	0.501862i
$671$	−7.00000	−	12.1244i	−0.270232	−	0.468056i
$672$	3.00000	+	1.73205i	0.115728	+	0.0668153i
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$	−13.0000			−0.500741
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	1.00000			0.0384615
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$	21.0000	+	12.1244i	0.806500	+	0.465633i
$679$	13.0000	+	22.5167i	0.498894	+	0.864110i
$680$	2.50000	+	4.33013i	0.0958706	+	0.166053i
$681$	−25.5000	+	14.7224i	−0.977162	+	0.564165i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	−5.00000			−0.191320			−0.0956598	−	0.995414i	$-0.530496\pi$
$683$	−5.00000			−0.191320			−0.0956598	+	0.995414i	$0.530496\pi$
$684$	4.50000	−	7.79423i	0.172062	−	0.298020i
$685$	−3.00000			−0.114624
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$			13.8564i			0.528655i
$688$	−2.50000	−	4.33013i	−0.0953116	−	0.165085i
$689$	1.00000	+	1.73205i	0.0380970	+	0.0659859i
$690$		0			0
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	−0.901557	−	0.432660i	$-0.857575\pi$
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	0.825473	+	0.564441i	$0.190908\pi$
$692$	−14.0000			−0.532200
$693$	3.00000	−	5.19615i	0.113961	−	0.197386i
$694$	−9.00000			−0.341635
$695$	3.50000	−	6.06218i	0.132763	−	0.229952i
$696$	−12.0000	+	6.92820i	−0.454859	+	0.262613i
$697$	−17.5000	−	30.3109i	−0.662860	−	1.14811i
$698$	−4.00000	−	6.92820i	−0.151402	−	0.262236i
$699$	22.5000	+	12.9904i	0.851028	+	0.491341i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	−46.0000			−1.73740			−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000			−1.73740			−0.868698	+	0.495342i	$0.835043\pi$
$702$		−	5.19615i		−	0.196116i
$703$	−24.0000			−0.905177
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	18.0000	+	10.3923i	0.677919	+	0.391397i
$706$	5.50000	+	9.52628i	0.206995	+	0.358526i
$707$	−2.00000	−	3.46410i	−0.0752177	−	0.130281i
$708$	7.50000	−	4.33013i	0.281867	−	0.162736i
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	2.00000			0.0750587
$711$	−6.00000			−0.225018
$712$	10.0000			0.374766
$713$		0			0
$714$		−	17.3205i		−	0.648204i
$715$	−0.500000	−	0.866025i	−0.0186989	−	0.0323875i
$716$	−10.0000	−	17.3205i	−0.373718	−	0.647298i
$717$			3.46410i			0.129369i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$		0			0
$722$	5.00000	−	8.66025i	0.186081	−	0.322301i
$723$	1.50000	−	0.866025i	0.0557856	−	0.0322078i
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$	−15.0000	−	8.66025i	−0.556702	−	0.321412i
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.139212	−	0.990263i	$-0.455543\pi$
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.787986	−	0.615693i	$-0.211124\pi$
$728$	−2.00000			−0.0741249
$729$	−27.0000			−1.00000
$730$	11.0000			0.407128
$731$	−12.5000	+	21.6506i	−0.462329	+	0.800778i
$732$	21.0000	+	12.1244i	0.776182	+	0.448129i
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	6.00000	+	10.3923i	0.221464	+	0.383587i
$735$	−4.50000	+	2.59808i	−0.165985	+	0.0958315i
$736$		0			0
$737$	−15.0000			−0.552532
$738$	10.5000	+	18.1865i	0.386510	+	0.669456i
$739$	27.0000			0.993211			0.496606	−	0.867976i	$-0.334580\pi$
$739$	27.0000			0.993211			0.496606	+	0.867976i	$0.334580\pi$
$740$	−4.00000	+	6.92820i	−0.147043	+	0.254686i
$741$			5.19615i			0.190885i
$742$	−2.00000	−	3.46410i	−0.0734223	−	0.127171i
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		−	10.3923i		−	0.381000i
$745$	7.00000	−	12.1244i	0.256460	−	0.444202i
$746$	−14.0000			−0.512576
$747$	36.0000			1.31717
$748$	5.00000			0.182818
$749$	−9.00000	+	15.5885i	−0.328853	+	0.569590i
$750$	1.50000	−	0.866025i	0.0547723	−	0.0316228i
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	40.5000	+	23.3827i	1.47590	+	0.852112i
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$		0			0
$756$			10.3923i			0.377964i
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	−7.50000	+	12.9904i	−0.272412	+	0.471832i
$759$		0			0
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$	−33.0000	+	19.0526i	−1.19546	+	0.690201i
$763$	−6.00000	+	10.3923i	−0.217215	+	0.376227i
$764$		0			0
$765$	−7.50000	+	12.9904i	−0.271163	+	0.469668i
$766$	18.0000			0.650366
$767$	−2.50000	+	4.33013i	−0.0902698	+	0.156352i
$768$		−	1.73205i		−	0.0625000i
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$	1.00000	+	1.73205i	0.0360375	+	0.0624188i
$771$		−	25.9808i		−	0.935674i
$772$	6.50000	−	11.2583i	0.233940	−	0.405196i
$773$	−40.0000			−1.43870			−0.719350	−	0.694648i	$-0.755560\pi$
$773$	−40.0000			−1.43870			−0.719350	+	0.694648i	$0.755560\pi$
$774$	7.50000	−	12.9904i	0.269582	−	0.466930i
$775$	6.00000			0.215526
$776$	6.50000	−	11.2583i	0.233336	−	0.404151i
$777$	24.0000	−	13.8564i	0.860995	−	0.497096i
$778$	5.00000	+	8.66025i	0.179259	+	0.310485i
$779$	−10.5000	−	18.1865i	−0.376202	−	0.651600i
$780$	1.50000	+	0.866025i	0.0537086	+	0.0310087i
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$		0			0
$783$	−36.0000	−	20.7846i	−1.28654	−	0.742781i
$784$	−3.00000			−0.107143
$785$	11.0000	−	19.0526i	0.392607	−	0.680015i
$786$	6.00000	+	3.46410i	0.214013	+	0.123560i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$	6.00000	−	3.46410i	0.213606	−	0.123325i
$790$	1.00000	−	1.73205i	0.0355784	−	0.0616236i
$791$	28.0000			0.995565
$792$	−3.00000			−0.106600
$793$	−14.0000			−0.497155
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$			3.46410i			0.122859i
$796$	−9.00000	−	15.5885i	−0.318997	−	0.552518i
$797$	−19.0000	−	32.9090i	−0.673015	−	1.16570i	−0.977045	−	0.213033i	$-0.931666\pi$
$797$	−19.0000	−	32.9090i	−0.673015	−	1.16570i	0.304030	−	0.952662i	$-0.401668\pi$
$798$		−	10.3923i		−	0.367884i
$799$	30.0000	−	51.9615i	1.06132	−	1.83827i
$800$	1.00000			0.0353553
$801$	15.0000	+	25.9808i	0.529999	+	0.917985i
$802$	3.00000			0.105934
$803$	5.50000	−	9.52628i	0.194091	−	0.336175i
$804$	22.5000	−	12.9904i	0.793514	−	0.458135i
$805$		0			0
$806$	3.00000	+	5.19615i	0.105670	+	0.183027i
$807$		0			0
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	5.00000			0.175791			0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000			0.175791			0.0878953	+	0.996130i	$0.471986\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−47.0000			−1.65039			−0.825197	−	0.564846i	$-0.808936\pi$
$811$	−47.0000			−1.65039			−0.825197	+	0.564846i	$0.808936\pi$
$812$	−8.00000	+	13.8564i	−0.280745	+	0.486265i
$813$	24.0000	+	13.8564i	0.841717	+	0.485965i
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$	−7.50000	+	4.33013i	−0.262553	+	0.151585i
$817$	−7.50000	+	12.9904i	−0.262392	+	0.454476i
$818$	19.0000			0.664319
$819$	−3.00000	−	5.19615i	−0.104828	−	0.181568i
$820$	−7.00000			−0.244451
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	−0.927346	−	0.374206i	$-0.877915\pi$
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	0.787745	+	0.616002i	$0.211249\pi$
$822$		−	5.19615i		−	0.181237i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$		−	1.73205i		−	0.0603023i
$826$	5.00000	−	8.66025i	0.173972	−	0.301329i
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$		0			0
$829$	−4.00000			−0.138926			−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000			−0.138926			−0.0694629	+	0.997585i	$0.522129\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	24.0000	−	13.8564i	0.832551	−	0.480673i
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	7.50000	+	12.9904i	0.259860	+	0.450090i
$834$	10.5000	+	6.06218i	0.363585	+	0.209916i
$835$	4.00000	−	6.92820i	0.138426	−	0.239760i
$836$	3.00000			0.103757
$837$	27.0000	−	15.5885i	0.933257	−	0.538816i
$838$	−20.0000			−0.690889
$839$	8.00000	−	13.8564i	0.276191	−	0.478376i	−0.694244	−	0.719740i	$-0.744261\pi$
$839$	8.00000	−	13.8564i	0.276191	−	0.478376i	0.970435	+	0.241363i	$0.0775945\pi$
$840$	−3.00000	−	1.73205i	−0.103510	−	0.0597614i
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	−14.0000	−	24.2487i	−0.482472	−	0.835666i
$843$	45.0000	−	25.9808i	1.54988	−	0.894825i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$	−1.00000			−0.0344010
$846$	−18.0000	+	31.1769i	−0.618853	+	1.07188i
$847$	−20.0000			−0.687208
$848$	−1.00000	+	1.73205i	−0.0343401	+	0.0594789i
$849$		−	55.4256i		−	1.90220i
$850$	−2.50000	−	4.33013i	−0.0857493	−	0.148522i
$851$		0			0
$852$			3.46410i			0.118678i
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	−0.969861	−	0.243660i	$-0.921652\pi$
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	0.695946	+	0.718094i	$0.254985\pi$
$854$	28.0000			0.958140
$855$	−4.50000	+	7.79423i	−0.153897	+	0.266557i
$856$	9.00000			0.307614
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	−0.553915	−	0.832573i	$-0.686867\pi$
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	0.997987	+	0.0634184i	$0.0202003\pi$
$858$	1.50000	−	0.866025i	0.0512092	−	0.0295656i
$859$	−22.5000	−	38.9711i	−0.767690	−	1.32968i	−0.938813	−	0.344428i	$-0.888073\pi$
$859$	−22.5000	−	38.9711i	−0.767690	−	1.32968i	0.171122	−	0.985250i	$-0.445261\pi$
$860$	2.50000	+	4.33013i	0.0852493	+	0.147656i
$861$	21.0000	+	12.1244i	0.715678	+	0.413197i
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	14.0000			0.476014
$866$	5.50000	−	9.52628i	0.186898	−	0.323716i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	−1.00000	−	1.73205i	−0.0339227	−	0.0587558i
$870$	12.0000	−	6.92820i	0.406838	−	0.234888i
$871$	−7.50000	+	12.9904i	−0.254128	+	0.440162i
$872$	6.00000			0.203186
$873$	39.0000			1.31995
$874$		0			0
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$			19.0526i			0.643726i
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$			3.46410i			0.116841i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	−4.50000	−	7.79423i	−0.151523	−	0.262445i
$883$	35.0000			1.17784			0.588922	−	0.808190i	$-0.299553\pi$
$883$	35.0000			1.17784			0.588922	+	0.808190i	$0.299553\pi$
$884$	2.50000	−	4.33013i	0.0840841	−	0.145638i
$885$	−7.50000	+	4.33013i	−0.252110	+	0.145556i
$886$	−0.500000	−	0.866025i	−0.0167978	−	0.0290947i
$887$	−2.00000	−	3.46410i	−0.0671534	−	0.116313i	0.830494	−	0.557028i	$-0.188058\pi$
$887$	−2.00000	−	3.46410i	−0.0671534	−	0.116313i	−0.897647	+	0.440715i	$0.854725\pi$
$888$	−12.0000	−	6.92820i	−0.402694	−	0.232495i
$889$	−22.0000	+	38.1051i	−0.737856	+	1.27800i
$890$	−10.0000			−0.335201
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−14.0000			−0.468755
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$	21.0000	+	12.1244i	0.702345	+	0.405499i
$895$	10.0000	+	17.3205i	0.334263	+	0.578961i
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$		0			0
$898$	4.50000	−	7.79423i	0.150167	−	0.260097i
$899$	48.0000			1.60089
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	10.0000			0.333148
$902$	−3.50000	+	6.06218i	−0.116537	+	0.201848i
$903$		−	17.3205i		−	0.576390i
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	−7.00000	−	12.1244i	−0.232688	−	0.403027i
$906$		0			0
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	17.0000			0.564165
$909$	−6.00000			−0.199007
$910$	2.00000			0.0662994
$911$	16.0000	−	27.7128i	0.530104	−	0.918166i	−0.469280	−	0.883050i	$-0.655486\pi$
$911$	16.0000	−	27.7128i	0.530104	−	0.918166i	0.999383	−	0.0351168i	$-0.0111803\pi$
$912$	−4.50000	+	2.59808i	−0.149010	+	0.0860309i
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	−17.5000	−	30.3109i	−0.578849	−	1.00260i
$915$	−21.0000	−	12.1244i	−0.694239	−	0.400819i
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$	8.00000			0.264183
$918$	−22.5000	−	12.9904i	−0.742611	−	0.428746i
$919$	46.0000			1.51740			0.758700	−	0.651440i	$-0.225835\pi$
$919$	46.0000			1.51740			0.758700	+	0.651440i	$0.225835\pi$
$920$		0			0
$921$	13.5000	+	7.79423i	0.444840	+	0.256829i
$922$		0			0
$923$	−1.00000	−	1.73205i	−0.0329154	−	0.0570111i
$924$	−3.00000	+	1.73205i	−0.0986928	+	0.0569803i
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	16.0000			0.525793
$927$		0			0
$928$	8.00000			0.262613
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$			10.3923i			0.340777i
$931$	4.50000	+	7.79423i	0.147482	+	0.255446i
$932$	−7.50000	−	12.9904i	−0.245671	−	0.425514i
$933$			41.5692i			1.36092i
$934$	−3.50000	+	6.06218i	−0.114523	+	0.198361i
$935$	−5.00000			−0.163517
$936$	−1.50000	+	2.59808i	−0.0490290	+	0.0849208i
$937$	−54.0000			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$938$	15.0000	−	25.9808i	0.489767	−	0.848302i
$939$	−13.5000	+	7.79423i	−0.440556	+	0.254355i
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$	33.0000	+	19.0526i	1.07520	+	0.620766i
$943$		0			0
$944$	−5.00000			−0.162736
$945$		−	10.3923i		−	0.338062i
$946$	5.00000			0.162564
$947$	−21.5000	+	37.2391i	−0.698656	+	1.21011i	0.270276	+	0.962783i	$0.412885\pi$
$947$	−21.5000	+	37.2391i	−0.698656	+	1.21011i	−0.968933	+	0.247325i	$0.920448\pi$
$948$	3.00000	+	1.73205i	0.0974355	+	0.0562544i
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$	−1.50000	−	2.59808i	−0.0486664	−	0.0842927i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$	−5.00000	+	8.66025i	−0.162051	+	0.280680i
$953$	57.0000			1.84641			0.923206	−	0.384307i	$-0.125559\pi$
$953$	57.0000			1.84641			0.923206	+	0.384307i	$0.125559\pi$
$954$	−6.00000			−0.194257
$955$		0			0
$956$	1.00000	−	1.73205i	0.0323423	−	0.0560185i
$957$		−	13.8564i		−	0.447914i
$958$	−4.00000	−	6.92820i	−0.129234	−	0.223840i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$			1.73205i			0.0559017i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	8.00000			0.257930
$963$	13.5000	+	23.3827i	0.435031	+	0.753497i
$964$	−1.00000			−0.0322078
$965$	−6.50000	+	11.2583i	−0.209242	+	0.362418i
$966$		0			0
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	0.708245	−	0.705967i	$-0.249487\pi$
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	−0.965508	+	0.260375i	$0.916154\pi$
$968$	5.00000	+	8.66025i	0.160706	+	0.278351i
$969$	22.5000	+	12.9904i	0.722804	+	0.417311i
$970$	−6.50000	+	11.2583i	−0.208702	+	0.361483i
$971$	−16.0000			−0.513464			−0.256732	−	0.966483i	$-0.582646\pi$
$971$	−16.0000			−0.513464			−0.256732	+	0.966483i	$0.582646\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	14.0000			0.448819
$974$	17.0000	−	29.4449i	0.544715	−	0.943474i
$975$	−1.50000	−	0.866025i	−0.0480384	−	0.0277350i
$976$	−7.00000	−	12.1244i	−0.224065	−	0.388091i
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	0.841033	−	0.540984i	$-0.181948\pi$
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	−0.889022	+	0.457864i	$0.848615\pi$
$978$	24.0000	−	13.8564i	0.767435	−	0.443079i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	3.00000			0.0958315
$981$	9.00000	+	15.5885i	0.287348	+	0.497701i
$982$	3.00000			0.0957338
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	−0.551627	−	0.834091i	$-0.685993\pi$
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	0.998157	+	0.0606773i	$0.0193260\pi$
$984$		−	12.1244i		−	0.386510i
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$	−20.0000	−	34.6410i	−0.636930	−	1.10319i
$987$			41.5692i			1.32316i
$988$	1.50000	−	2.59808i	0.0477214	−	0.0826558i
$989$		0			0
$990$	3.00000			0.0953463
$991$	−30.0000			−0.952981			−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000			−0.952981			−0.476491	+	0.879180i	$0.658091\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$	30.0000	−	17.3205i	0.952021	−	0.549650i
$994$	2.00000	+	3.46410i	0.0634361	+	0.109875i
$995$	9.00000	+	15.5885i	0.285319	+	0.494187i
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	28.0000	−	48.4974i	0.886769	−	1.53593i	0.0430962	−	0.999071i	$-0.486278\pi$
$997$	28.0000	−	48.4974i	0.886769	−	1.53593i	0.843673	−	0.536858i	$-0.180389\pi$
$998$	11.0000			0.348199
$999$		−	41.5692i		−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.j.c.781.1	yes	2
3.2	odd	2		3510.2.j.e.2341.1		2
9.4	even	3	inner	1170.2.j.c.391.1	✓	2
9.5	odd	6		3510.2.j.e.1171.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.c.391.1	✓	2	9.4	even	3	inner
1170.2.j.c.781.1	yes	2	1.1	even	1	trivial
3510.2.j.e.1171.1		2	9.5	odd	6
3510.2.j.e.2341.1		2	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} -1.73205i q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.00000 - 1.73205i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +5.00000 q^{17} -3.00000 q^{18} +3.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.00000 + 1.73205i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(-4.00000 + 6.92820i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-2.50000 + 4.33013i) q^{34} -2.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -8.00000 q^{37} +(-1.50000 + 2.59808i) q^{38} +1.73205i q^{39} +(0.500000 + 0.866025i) q^{40} +(-3.50000 - 6.06218i) q^{41} -3.46410i q^{42} +(-2.50000 + 4.33013i) q^{43} +1.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(6.00000 - 10.3923i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(7.50000 + 4.33013i) q^{51} +(0.500000 - 0.866025i) q^{52} +2.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} -1.00000 q^{55} +(-1.00000 + 1.73205i) q^{56} +(4.50000 + 2.59808i) q^{57} +(-4.00000 - 6.92820i) q^{58} +(2.50000 + 4.33013i) q^{59} +(1.50000 - 0.866025i) q^{60} +(-7.00000 + 12.1244i) q^{61} +6.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -1.73205i q^{66} +(7.50000 + 12.9904i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(1.00000 - 1.73205i) q^{70} -2.00000 q^{71} +(1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.50000 - 2.59808i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-1.50000 - 0.866025i) q^{78} +(-1.00000 + 1.73205i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(3.00000 + 1.73205i) q^{84} +(2.50000 + 4.33013i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(-12.0000 + 6.92820i) q^{87} +(-0.500000 + 0.866025i) q^{88} +10.0000 q^{89} +(-1.50000 - 2.59808i) q^{90} -2.00000 q^{91} -10.3923i q^{93} +(6.00000 + 10.3923i) q^{94} +(1.50000 + 2.59808i) q^{95} -1.73205i q^{96} +(6.50000 - 11.2583i) q^{97} -3.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{13} - 2 q^{14} - q^{16} + 10 q^{17} - 6 q^{18} + 6 q^{19} + q^{20} - 6 q^{21} - q^{22} + 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 3 * q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + q^13 - 2 * q^14 - q^16 + 10 * q^17 - 6 * q^18 + 6 * q^19 + q^20 - 6 * q^21 - q^22 + 3 * q^24 - q^25 - 2 * q^26 + 4 * q^28 - 8 * q^29 - 3 * q^30 - 6 * q^31 - q^32 - 3 * q^33 - 5 * q^34 - 4 * q^35 + 3 * q^36 - 16 * q^37 - 3 * q^38 + q^40 - 7 * q^41 - 5 * q^43 + 2 * q^44 - 3 * q^45 + 12 * q^47 - 3 * q^48 + 3 * q^49 - q^50 + 15 * q^51 + q^52 + 4 * q^53 - 9 * q^54 - 2 * q^55 - 2 * q^56 + 9 * q^57 - 8 * q^58 + 5 * q^59 + 3 * q^60 - 14 * q^61 + 12 * q^62 - 12 * q^63 + 2 * q^64 - q^65 + 15 * q^67 - 5 * q^68 + 2 * q^70 - 4 * q^71 + 3 * q^72 - 22 * q^73 + 8 * q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 - 3 * q^78 - 2 * q^79 - 2 * q^80 - 9 * q^81 + 14 * q^82 + 12 * q^83 + 6 * q^84 + 5 * q^85 - 5 * q^86 - 24 * q^87 - q^88 + 20 * q^89 - 3 * q^90 - 4 * q^91 + 12 * q^94 + 3 * q^95 + 13 * q^97 - 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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