LMFDB - Embedded newform 630.2.j.c.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.c.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +(-2.00000 + 3.46410i) q^{13} +(-0.500000 + 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{18} +1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(-2.50000 + 4.33013i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{26} +5.19615i q^{27} -1.00000 q^{28} +(-1.00000 - 1.73205i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.50000 - 4.33013i) q^{33} +(-2.50000 - 4.33013i) q^{34} +1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +(0.500000 + 0.866025i) q^{38} -6.92820i q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} -1.73205i q^{42} +(0.500000 + 0.866025i) q^{43} -5.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} -2.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.50000 - 4.33013i) q^{51} +(-2.00000 - 3.46410i) q^{52} -2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +5.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(1.00000 - 1.73205i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(5.00000 + 8.66025i) q^{61} -6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} -8.66025i q^{66} +(-4.50000 + 7.79423i) q^{67} +(2.50000 - 4.33013i) q^{68} -3.46410i q^{69} +(0.500000 + 0.866025i) q^{70} +14.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +1.00000 q^{73} +(1.50000 + 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(6.00000 - 3.46410i) q^{78} +(7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(1.50000 - 0.866025i) q^{84} +(-2.50000 + 4.33013i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(3.00000 + 1.73205i) q^{87} +(-2.50000 - 4.33013i) q^{88} -10.0000 q^{89} +(1.50000 - 2.59808i) q^{90} -4.00000 q^{91} +(-1.00000 - 1.73205i) q^{92} -10.3923i q^{93} +(6.00000 - 10.3923i) q^{94} +(0.500000 - 0.866025i) q^{95} +1.73205i q^{96} +(6.50000 + 11.2583i) q^{97} -1.00000 q^{98} +15.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{10} + 5 q^{11} - 4 q^{13} - q^{14} - q^{16} - 10 q^{17} + 6 q^{18} + 2 q^{19} + q^{20} - 3 q^{21} - 5 q^{22} - 2 q^{23} + 3 q^{24} - q^{25} - 8 q^{26} - 2 q^{28} - 2 q^{29} - 3 q^{30} - 6 q^{31} + q^{32} - 15 q^{33} - 5 q^{34} + 2 q^{35} + 3 q^{36} + q^{38} - q^{40} - 9 q^{41} + q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 12 q^{47} + 3 q^{48} - q^{49} + q^{50} + 15 q^{51} - 4 q^{52} - 4 q^{53} - 9 q^{54} + 10 q^{55} - q^{56} - 3 q^{57} + 2 q^{58} + 15 q^{59} - 3 q^{60} + 10 q^{61} - 12 q^{62} + 6 q^{63} + 2 q^{64} + 4 q^{65} - 9 q^{67} + 5 q^{68} + q^{70} + 28 q^{71} - 3 q^{72} + 2 q^{73} + 3 q^{75} - q^{76} - 5 q^{77} + 12 q^{78} + 14 q^{79} - 2 q^{80} - 9 q^{81} - 18 q^{82} + 12 q^{83} + 3 q^{84} - 5 q^{85} - q^{86} + 6 q^{87} - 5 q^{88} - 20 q^{89} + 3 q^{90} - 8 q^{91} - 2 q^{92} + 12 q^{94} + q^{95} + 13 q^{97} - 2 q^{98} + 30 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9 + 2 * q^10 + 5 * q^11 - 4 * q^13 - q^14 - q^16 - 10 * q^17 + 6 * q^18 + 2 * q^19 + q^20 - 3 * q^21 - 5 * q^22 - 2 * q^23 + 3 * q^24 - q^25 - 8 * q^26 - 2 * q^28 - 2 * q^29 - 3 * q^30 - 6 * q^31 + q^32 - 15 * q^33 - 5 * q^34 + 2 * q^35 + 3 * q^36 + q^38 - q^40 - 9 * q^41 + q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 12 * q^47 + 3 * q^48 - q^49 + q^50 + 15 * q^51 - 4 * q^52 - 4 * q^53 - 9 * q^54 + 10 * q^55 - q^56 - 3 * q^57 + 2 * q^58 + 15 * q^59 - 3 * q^60 + 10 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 4 * q^65 - 9 * q^67 + 5 * q^68 + q^70 + 28 * q^71 - 3 * q^72 + 2 * q^73 + 3 * q^75 - q^76 - 5 * q^77 + 12 * q^78 + 14 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 + 3 * q^84 - 5 * q^85 - q^86 + 6 * q^87 - 5 * q^88 - 20 * q^89 + 3 * q^90 - 8 * q^91 - 2 * q^92 + 12 * q^94 + q^95 + 13 * q^97 - 2 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	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
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.00000			0.316228
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$			1.73205i			0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.00000			−1.21268			−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000			−1.21268			−0.606339	+	0.795206i	$0.707363\pi$
$18$	3.00000			0.707107
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.00000			−0.784465
$27$			5.19615i			1.00000i
$28$	−1.00000			−0.188982
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.50000	−	4.33013i	−1.30558	−	0.753778i
$34$	−2.50000	−	4.33013i	−0.428746	−	0.742611i
$35$	1.00000			0.169031
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$		−	6.92820i		−	1.10940i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		−	1.73205i		−	0.267261i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−5.00000			−0.753778
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	−2.00000			−0.294884
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	7.50000	−	4.33013i	1.05021	−	0.606339i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	5.00000			0.674200
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−1.50000	+	0.866025i	−0.198680	+	0.114708i
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.301239	−	0.953549i	$-0.402600\pi$
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.675178	−	0.737655i	$-0.264067\pi$
$60$	−1.50000	−	0.866025i	−0.193649	−	0.111803i
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−6.00000			−0.762001
$63$	3.00000			0.377964
$64$	1.00000			0.125000
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		−	8.66025i		−	1.06600i
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	0.448528	+	0.893769i	$0.351948\pi$
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	−0.998290	+	0.0584478i	$0.981385\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$		−	3.46410i		−	0.417029i
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	14.0000			1.66149			0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000			1.66149			0.830747	+	0.556650i	$0.187914\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$		0			0
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	−2.50000	+	4.33013i	−0.284901	+	0.493464i
$78$	6.00000	−	3.46410i	0.679366	−	0.392232i
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−9.00000			−0.993884
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	1.50000	−	0.866025i	0.163663	−	0.0944911i
$85$	−2.50000	+	4.33013i	−0.271163	+	0.469668i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	3.00000	+	1.73205i	0.321634	+	0.185695i
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	−4.00000			−0.419314
$92$	−1.00000	−	1.73205i	−0.104257	−	0.180579i
$93$		−	10.3923i		−	1.07763i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$			1.73205i			0.176777i
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	0.980622	+	0.195911i	$0.0627665\pi$
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	−0.320647	+	0.947199i	$0.603900\pi$
$98$	−1.00000			−0.101015
$99$	15.0000			1.50756
$100$	1.00000			0.100000
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	7.50000	+	4.33013i	0.742611	+	0.428746i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$	−1.50000	+	0.866025i	−0.146385	+	0.0845154i
$106$	−1.00000	−	1.73205i	−0.0971286	−	0.168232i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−1.50000	−	0.866025i	−0.140488	−	0.0811107i
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	2.00000			0.185695
$117$	6.00000	+	10.3923i	0.554700	+	0.960769i
$118$	15.0000			1.38086
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$		−	1.73205i		−	0.158114i
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		−	15.5885i		−	1.40556i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	−1.00000			−0.0894427
$126$	1.50000	+	2.59808i	0.133631	+	0.231455i
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$	7.50000	−	4.33013i	0.652791	−	0.376889i
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	−9.00000			−0.777482
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	5.00000			0.428746
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	0.997878	+	0.0651178i	$0.0207423\pi$
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	−0.442545	+	0.896746i	$0.645924\pi$
$138$	3.00000	−	1.73205i	0.255377	−	0.147442i
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	18.0000	+	10.3923i	1.51587	+	0.875190i
$142$	7.00000	+	12.1244i	0.587427	+	1.01745i
$143$	−20.0000			−1.67248
$144$	−3.00000			−0.250000
$145$	−2.00000			−0.166091
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$		−	1.73205i		−	0.142857i
$148$		0			0
$149$	10.0000	−	17.3205i	0.819232	−	1.41895i	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	10.0000	−	17.3205i	0.819232	−	1.41895i	0.906249	−	0.422744i	$-0.138933\pi$
$150$			1.73205i			0.141421i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−1.00000			−0.0811107
$153$	−7.50000	+	12.9904i	−0.606339	+	1.05021i
$154$	−5.00000			−0.402911
$155$	3.00000	+	5.19615i	0.240966	+	0.417365i
$156$	6.00000	+	3.46410i	0.480384	+	0.277350i
$157$	6.00000	−	10.3923i	0.478852	−	0.829396i	−0.520854	−	0.853646i	$-0.674386\pi$
$157$	6.00000	−	10.3923i	0.478852	−	0.829396i	0.999706	+	0.0242497i	$0.00771967\pi$
$158$	−7.00000	+	12.1244i	−0.556890	+	0.964562i
$159$	3.00000	−	1.73205i	0.237915	−	0.137361i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.00000			−0.157622
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	−7.50000	+	4.33013i	−0.583874	+	0.337100i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	0.457132	+	0.889399i	$0.348877\pi$
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	−0.998808	+	0.0488118i	$0.984457\pi$
$168$	1.50000	+	0.866025i	0.115728	+	0.0668153i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−5.00000			−0.383482
$171$	1.50000	−	2.59808i	0.114708	−	0.198680i
$172$	−1.00000			−0.0762493
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$			3.46410i			0.262613i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$			25.9808i			1.95283i
$178$	−5.00000	−	8.66025i	−0.374766	−	0.649113i
$179$	−16.0000			−1.19590			−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000			−1.19590			−0.597948	+	0.801535i	$0.704017\pi$
$180$	3.00000			0.223607
$181$	−12.0000			−0.891953			−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000			−0.891953			−0.445976	+	0.895045i	$0.647144\pi$
$182$	−2.00000	−	3.46410i	−0.148250	−	0.256776i
$183$	−15.0000	−	8.66025i	−1.10883	−	0.640184i
$184$	1.00000	−	1.73205i	0.0737210	−	0.127688i
$185$		0			0
$186$	9.00000	−	5.19615i	0.659912	−	0.381000i
$187$	−12.5000	−	21.6506i	−0.914091	−	1.58325i
$188$	12.0000			0.875190
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	1.00000			0.0725476
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	−6.00000	−	3.46410i	−0.429669	−	0.248069i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	7.50000	+	12.9904i	0.533002	+	0.923186i
$199$	12.0000			0.850657			0.425329	−	0.905039i	$-0.360158\pi$
$199$	12.0000			0.850657			0.425329	+	0.905039i	$0.360158\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		−	15.5885i		−	1.09952i
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$	1.00000	−	1.73205i	0.0701862	−	0.121566i
$204$			8.66025i			0.606339i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−4.00000			−0.278693
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	4.00000			0.277350
$209$	2.50000	+	4.33013i	0.172929	+	0.299521i
$210$	−1.50000	−	0.866025i	−0.103510	−	0.0597614i
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	−21.0000	+	12.1244i	−1.43890	+	0.830747i
$214$	1.50000	+	2.59808i	0.102538	+	0.177601i
$215$	1.00000			0.0681994
$216$		−	5.19615i		−	0.353553i
$217$	−6.00000			−0.407307
$218$	4.00000	+	6.92820i	0.270914	+	0.469237i
$219$	−1.50000	+	0.866025i	−0.101361	+	0.0585206i
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$	10.0000	−	17.3205i	0.672673	−	1.16510i
$222$		0			0
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	0.530607	−	0.847618i	$-0.321964\pi$
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	−0.999362	+	0.0357107i	$0.988630\pi$
$224$	1.00000			0.0668153
$225$	−3.00000			−0.200000
$226$	6.00000			0.399114
$227$	9.50000	+	16.4545i	0.630537	+	1.09212i	0.987442	+	0.157982i	$0.0504987\pi$
$227$	9.50000	+	16.4545i	0.630537	+	1.09212i	−0.356905	+	0.934141i	$0.616168\pi$
$228$		−	1.73205i		−	0.114708i
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$	−1.00000	+	1.73205i	−0.0659380	+	0.114208i
$231$		−	8.66025i		−	0.569803i
$232$	1.00000	+	1.73205i	0.0656532	+	0.113715i
$233$	1.00000			0.0655122			0.0327561	−	0.999463i	$-0.489572\pi$
$233$	1.00000			0.0655122			0.0327561	+	0.999463i	$0.489572\pi$
$234$	−6.00000	+	10.3923i	−0.392232	+	0.679366i
$235$	−12.0000			−0.782794
$236$	7.50000	+	12.9904i	0.488208	+	0.845602i
$237$	−21.0000	−	12.1244i	−1.36410	−	0.787562i
$238$	2.50000	−	4.33013i	0.162051	−	0.280680i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	−14.0000			−0.899954
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−10.0000			−0.640184
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	13.5000	−	7.79423i	0.860729	−	0.496942i
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	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
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$	−1.50000	+	2.59808i	−0.0944911	+	0.163663i
$253$	−10.0000			−0.628695
$254$	7.00000	+	12.1244i	0.439219	+	0.760750i
$255$		−	8.66025i		−	0.542326i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	−0.735972	−	0.677012i	$-0.763274\pi$
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	0.954296	+	0.298864i	$0.0966077\pi$
$258$		−	1.73205i		−	0.107833i
$259$		0			0
$260$	−4.00000			−0.248069
$261$	−6.00000			−0.371391
$262$	20.0000			1.23560
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$	7.50000	+	4.33013i	0.461593	+	0.266501i
$265$	−1.00000	+	1.73205i	−0.0614295	+	0.106399i
$266$	−0.500000	+	0.866025i	−0.0306570	+	0.0530994i
$267$	15.0000	−	8.66025i	0.917985	−	0.529999i
$268$	−4.50000	−	7.79423i	−0.274881	−	0.476108i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$			5.19615i			0.316228i
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	2.50000	+	4.33013i	0.151585	+	0.262553i
$273$	6.00000	−	3.46410i	0.363137	−	0.209657i
$274$	−6.50000	+	11.2583i	−0.392679	+	0.680141i
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$	3.00000	+	1.73205i	0.180579	+	0.104257i
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$	13.0000			0.779688
$279$	9.00000	+	15.5885i	0.538816	+	0.933257i
$280$	−1.00000			−0.0597614
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$			20.7846i			1.23771i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−7.00000	+	12.1244i	−0.415374	+	0.719448i
$285$			1.73205i			0.102598i
$286$	−10.0000	−	17.3205i	−0.591312	−	1.02418i
$287$	−9.00000			−0.531253
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	8.00000			0.470588
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	−19.5000	−	11.2583i	−1.14311	−	0.659975i
$292$	−0.500000	+	0.866025i	−0.0292603	+	0.0506803i
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$	1.50000	−	0.866025i	0.0874818	−	0.0505076i
$295$	−7.50000	−	12.9904i	−0.436667	−	0.756329i
$296$		0			0
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	20.0000			1.15857
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$	−1.50000	+	0.866025i	−0.0866025	+	0.0500000i
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$	−1.00000	+	1.73205i	−0.0575435	+	0.0996683i
$303$	18.0000	+	10.3923i	1.03407	+	0.597022i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	10.0000			0.572598
$306$	−15.0000			−0.857493
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$	−2.50000	−	4.33013i	−0.142451	−	0.246732i
$309$		−	6.92820i		−	0.394132i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	−0.892984	−	0.450088i	$-0.851393\pi$
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	0.836280	+	0.548303i	$0.184726\pi$
$312$			6.92820i			0.392232i
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	0.964720	−	0.263278i	$-0.0848035\pi$
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	−0.710365	+	0.703833i	$0.751470\pi$
$314$	12.0000			0.677199
$315$	1.50000	−	2.59808i	0.0845154	−	0.146385i
$316$	−14.0000			−0.787562
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$	3.00000	+	1.73205i	0.168232	+	0.0971286i
$319$	5.00000	−	8.66025i	0.279946	−	0.484881i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	−1.00000	−	1.73205i	−0.0557278	−	0.0965234i
$323$	−5.00000			−0.278207
$324$	9.00000			0.500000
$325$	4.00000			0.221880
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	−12.0000	+	6.92820i	−0.663602	+	0.383131i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	−7.50000	−	4.33013i	−0.412861	−	0.238366i
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	0.982470	−	0.186421i	$-0.0596888\pi$
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	−14.0000			−0.766046
$335$	4.50000	+	7.79423i	0.245861	+	0.425844i
$336$			1.73205i			0.0944911i
$337$	1.50000	−	2.59808i	0.0817102	−	0.141526i	−0.822274	−	0.569091i	$-0.807295\pi$
$337$	1.50000	−	2.59808i	0.0817102	−	0.141526i	0.903985	+	0.427565i	$0.140628\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$			10.3923i			0.564433i
$340$	−2.50000	−	4.33013i	−0.135582	−	0.234834i
$341$	−30.0000			−1.62459
$342$	3.00000			0.162221
$343$	−1.00000			−0.0539949
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$	−3.00000	−	1.73205i	−0.161515	−	0.0932505i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	11.5000	−	19.9186i	0.617352	−	1.06929i	−0.372615	−	0.927986i	$-0.621539\pi$
$347$	11.5000	−	19.9186i	0.617352	−	1.06929i	0.989967	−	0.141299i	$-0.0451280\pi$
$348$	−3.00000	+	1.73205i	−0.160817	+	0.0928477i
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	0.914577	−	0.404412i	$-0.132524\pi$
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	−0.807519	+	0.589841i	$0.799190\pi$
$350$	1.00000			0.0534522
$351$	−18.0000	−	10.3923i	−0.960769	−	0.554700i
$352$	5.00000			0.266501
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	0.546126	−	0.837703i	$-0.316102\pi$
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	−0.998535	+	0.0541072i	$0.982769\pi$
$354$	−22.5000	+	12.9904i	−1.19586	+	0.690431i
$355$	7.00000	−	12.1244i	0.371521	−	0.643494i
$356$	5.00000	−	8.66025i	0.264999	−	0.458993i
$357$	7.50000	+	4.33013i	0.396942	+	0.229175i
$358$	−8.00000	−	13.8564i	−0.422813	−	0.732334i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	−18.0000			−0.947368
$362$	−6.00000	−	10.3923i	−0.315353	−	0.546207i
$363$		−	24.2487i		−	1.27273i
$364$	2.00000	−	3.46410i	0.104828	−	0.181568i
$365$	0.500000	−	0.866025i	0.0261712	−	0.0453298i
$366$		−	17.3205i		−	0.905357i
$367$	10.0000	+	17.3205i	0.521996	+	0.904123i	0.999673	+	0.0255875i	$0.00814566\pi$
$367$	10.0000	+	17.3205i	0.521996	+	0.904123i	−0.477677	+	0.878536i	$0.658521\pi$
$368$	2.00000			0.104257
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$		0			0
$371$	−1.00000	−	1.73205i	−0.0519174	−	0.0899236i
$372$	9.00000	+	5.19615i	0.466628	+	0.269408i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	12.5000	−	21.6506i	0.646360	−	1.11953i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	8.00000			0.412021
$378$	−4.50000	−	2.59808i	−0.231455	−	0.133631i
$379$	−35.0000			−1.79783			−0.898915	−	0.438124i	$-0.855643\pi$
$379$	−35.0000			−1.79783			−0.898915	+	0.438124i	$0.855643\pi$
$380$	0.500000	+	0.866025i	0.0256495	+	0.0444262i
$381$	−21.0000	+	12.1244i	−1.07586	+	0.621150i
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	−10.0000	+	17.3205i	−0.510976	+	0.885037i	0.488943	+	0.872316i	$0.337383\pi$
$383$	−10.0000	+	17.3205i	−0.510976	+	0.885037i	−0.999919	+	0.0127209i	$0.995951\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$	2.50000	+	4.33013i	0.127412	+	0.220684i
$386$	25.0000			1.27247
$387$	3.00000			0.152499
$388$	−13.0000			−0.659975
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337237\pi$
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$390$		−	6.92820i		−	0.350823i
$391$	5.00000	−	8.66025i	0.252861	−	0.437968i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$			34.6410i			1.74741i
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$	14.0000			0.704416
$396$	−7.50000	+	12.9904i	−0.376889	+	0.652791i
$397$	−12.0000			−0.602263			−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000			−0.602263			−0.301131	+	0.953583i	$0.597364\pi$
$398$	6.00000	+	10.3923i	0.300753	+	0.520919i
$399$	−1.50000	−	0.866025i	−0.0750939	−	0.0433555i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	−0.996371	−	0.0851195i	$-0.972873\pi$
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	0.571901	+	0.820323i	$0.306206\pi$
$402$	13.5000	−	7.79423i	0.673319	−	0.388741i
$403$	−12.0000	−	20.7846i	−0.597763	−	1.03536i
$404$	12.0000			0.597022
$405$	−9.00000			−0.447214
$406$	2.00000			0.0992583
$407$		0			0
$408$	−7.50000	+	4.33013i	−0.371305	+	0.214373i
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	−0.00141047	−	0.999999i	$-0.500449\pi$
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	0.866730	−	0.498778i	$-0.166218\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	−19.5000	−	11.2583i	−0.961864	−	0.555332i
$412$	−2.00000	−	3.46410i	−0.0985329	−	0.170664i
$413$	15.0000			0.738102
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	12.0000			0.589057
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$			22.5167i			1.10265i
$418$	−2.50000	+	4.33013i	−0.122279	+	0.211793i
$419$	−20.0000	+	34.6410i	−0.977064	+	1.69232i	−0.304115	+	0.952635i	$0.598361\pi$
$419$	−20.0000	+	34.6410i	−0.977064	+	1.69232i	−0.672949	+	0.739689i	$0.734973\pi$
$420$		−	1.73205i		−	0.0845154i
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	0.984648	−	0.174550i	$-0.0558472\pi$
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	−0.643489	+	0.765455i	$0.722514\pi$
$422$	−12.0000			−0.584151
$423$	−36.0000			−1.75038
$424$	2.00000			0.0971286
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$	−21.0000	−	12.1244i	−1.01745	−	0.587427i
$427$	−5.00000	+	8.66025i	−0.241967	+	0.419099i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$	30.0000	−	17.3205i	1.44841	−	0.836242i
$430$	0.500000	+	0.866025i	0.0241121	+	0.0417635i
$431$	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
$433$	19.0000			0.913082			0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000			0.913082			0.456541	+	0.889702i	$0.349088\pi$
$434$	−3.00000	−	5.19615i	−0.144005	−	0.249423i
$435$	3.00000	−	1.73205i	0.143839	−	0.0830455i
$436$	−4.00000	+	6.92820i	−0.191565	+	0.331801i
$437$	−1.00000	+	1.73205i	−0.0478365	+	0.0828552i
$438$	−1.50000	−	0.866025i	−0.0716728	−	0.0413803i
$439$	1.00000	+	1.73205i	0.0477274	+	0.0826663i	0.888902	−	0.458097i	$-0.151469\pi$
$439$	1.00000	+	1.73205i	0.0477274	+	0.0826663i	−0.841175	+	0.540763i	$0.818135\pi$
$440$	−5.00000			−0.238366
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$	20.0000			0.951303
$443$	16.5000	+	28.5788i	0.783939	+	1.35782i	0.929631	+	0.368492i	$0.120126\pi$
$443$	16.5000	+	28.5788i	0.783939	+	1.35782i	−0.145692	+	0.989330i	$0.546541\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	7.00000	−	12.1244i	0.331460	−	0.574105i
$447$			34.6410i			1.63846i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$	−1.50000	−	2.59808i	−0.0707107	−	0.122474i
$451$	−45.0000			−2.11897
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−3.00000	−	1.73205i	−0.140952	−	0.0813788i
$454$	−9.50000	+	16.4545i	−0.445857	+	0.772247i
$455$	−2.00000	+	3.46410i	−0.0937614	+	0.162400i
$456$	1.50000	−	0.866025i	0.0702439	−	0.0405554i
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	0.553618	−	0.832771i	$-0.313247\pi$
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	−0.998010	+	0.0630623i	$0.979913\pi$
$458$	4.00000			0.186908
$459$		−	25.9808i		−	1.21268i
$460$	−2.00000			−0.0932505
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	0.950104	+	0.311933i	$0.100977\pi$
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	−0.204910	+	0.978781i	$0.565690\pi$
$462$	7.50000	−	4.33013i	0.348932	−	0.201456i
$463$	−6.00000	+	10.3923i	−0.278844	+	0.482971i	−0.971098	−	0.238683i	$-0.923284\pi$
$463$	−6.00000	+	10.3923i	−0.278844	+	0.482971i	0.692254	+	0.721654i	$0.256618\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	−9.00000	−	5.19615i	−0.417365	−	0.240966i
$466$	0.500000	+	0.866025i	0.0231621	+	0.0401179i
$467$	21.0000			0.971764			0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000			0.971764			0.485882	+	0.874024i	$0.338498\pi$
$468$	−12.0000			−0.554700
$469$	−9.00000			−0.415581
$470$	−6.00000	−	10.3923i	−0.276759	−	0.479361i
$471$			20.7846i			0.957704i
$472$	−7.50000	+	12.9904i	−0.345215	+	0.597931i
$473$	−2.50000	+	4.33013i	−0.114950	+	0.199099i
$474$		−	24.2487i		−	1.11378i
$475$	−0.500000	−	0.866025i	−0.0229416	−	0.0397360i
$476$	5.00000			0.229175
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$	−6.00000			−0.274434
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	0.993689	+	0.112168i	$0.0357796\pi$
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	−0.399704	+	0.916644i	$0.630887\pi$
$480$	1.50000	+	0.866025i	0.0684653	+	0.0395285i
$481$		0			0
$482$	−5.50000	+	9.52628i	−0.250518	+	0.433910i
$483$	3.00000	−	1.73205i	0.136505	−	0.0788110i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	13.0000			0.590300
$486$			15.5885i			0.707107i
$487$	−14.0000			−0.634401			−0.317200	−	0.948359i	$-0.602743\pi$
$487$	−14.0000			−0.634401			−0.317200	+	0.948359i	$0.602743\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	−12.0000	+	6.92820i	−0.542659	+	0.313304i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	16.5000	−	28.5788i	0.744635	−	1.28974i	−0.205731	−	0.978609i	$-0.565957\pi$
$491$	16.5000	−	28.5788i	0.744635	−	1.28974i	0.950365	−	0.311136i	$-0.100710\pi$
$492$	13.5000	+	7.79423i	0.608627	+	0.351391i
$493$	5.00000	+	8.66025i	0.225189	+	0.390038i
$494$	−4.00000			−0.179969
$495$	7.50000	−	12.9904i	0.337100	−	0.583874i
$496$	6.00000			0.269408
$497$	7.00000	+	12.1244i	0.313993	+	0.543852i
$498$		−	20.7846i		−	0.931381i
$499$	−4.50000	+	7.79423i	−0.201448	+	0.348918i	−0.948995	−	0.315291i	$-0.897898\pi$
$499$	−4.50000	+	7.79423i	−0.201448	+	0.348918i	0.747547	+	0.664208i	$0.231231\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		−	24.2487i		−	1.08335i
$502$	7.50000	+	12.9904i	0.334741	+	0.579789i
$503$	26.0000			1.15928			0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000			1.15928			0.579641	+	0.814872i	$0.303193\pi$
$504$	−3.00000			−0.133631
$505$	−12.0000			−0.533993
$506$	−5.00000	−	8.66025i	−0.222277	−	0.384995i
$507$	4.50000	+	2.59808i	0.199852	+	0.115385i
$508$	−7.00000	+	12.1244i	−0.310575	+	0.537931i
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$	7.50000	−	4.33013i	0.332106	−	0.191741i
$511$	0.500000	+	0.866025i	0.0221187	+	0.0383107i
$512$	−1.00000			−0.0441942
$513$			5.19615i			0.229416i
$514$	7.00000			0.308757
$515$	2.00000	+	3.46410i	0.0881305	+	0.152647i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	30.0000	−	51.9615i	1.31940	−	2.28527i
$518$		0			0
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	28.0000			1.22435			0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000			1.22435			0.612177	+	0.790721i	$0.290294\pi$
$524$	10.0000	+	17.3205i	0.436852	+	0.756650i
$525$			1.73205i			0.0755929i
$526$	−4.00000	+	6.92820i	−0.174408	+	0.302084i
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$			8.66025i			0.376889i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$	−2.00000			−0.0868744
$531$	−22.5000	−	38.9711i	−0.976417	−	1.69120i
$532$	−1.00000			−0.0433555
$533$	−18.0000	−	31.1769i	−0.779667	−	1.35042i
$534$	15.0000	+	8.66025i	0.649113	+	0.374766i
$535$	1.50000	−	2.59808i	0.0648507	−	0.112325i
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$	24.0000	−	13.8564i	1.03568	−	0.597948i
$538$	3.00000	+	5.19615i	0.129339	+	0.224022i
$539$	−5.00000			−0.215365
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	−16.0000			−0.687894			−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000			−0.687894			−0.343947	+	0.938989i	$0.611764\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	18.0000	−	10.3923i	0.772454	−	0.445976i
$544$	−2.50000	+	4.33013i	−0.107187	+	0.185653i
$545$	4.00000	−	6.92820i	0.171341	−	0.296772i
$546$	6.00000	+	3.46410i	0.256776	+	0.148250i
$547$	−13.5000	−	23.3827i	−0.577218	−	0.999771i	−0.995797	−	0.0915908i	$-0.970805\pi$
$547$	−13.5000	−	23.3827i	−0.577218	−	0.999771i	0.418578	−	0.908181i	$-0.362529\pi$
$548$	−13.0000			−0.555332
$549$	30.0000			1.28037
$550$	5.00000			0.213201
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$			3.46410i			0.147442i
$553$	−7.00000	+	12.1244i	−0.297670	+	0.515580i
$554$	5.00000	−	8.66025i	0.212430	−	0.367939i
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	−9.00000	+	15.5885i	−0.381000	+	0.659912i
$559$	−4.00000			−0.169182
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	37.5000	+	21.6506i	1.58325	+	0.914091i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	0.152443	+	0.988312i	$0.451286\pi$
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	−0.932125	+	0.362137i	$0.882047\pi$
$564$	−18.0000	+	10.3923i	−0.757937	+	0.437595i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−4.00000			−0.168133
$567$	4.50000	−	7.79423i	0.188982	−	0.327327i
$568$	−14.0000			−0.587427
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	−0.999609	−	0.0279702i	$-0.991096\pi$
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	0.475581	−	0.879672i	$-0.342238\pi$
$570$	−1.50000	+	0.866025i	−0.0628281	+	0.0362738i
$571$	17.5000	−	30.3109i	0.732352	−	1.26847i	−0.223523	−	0.974699i	$-0.571756\pi$
$571$	17.5000	−	30.3109i	0.732352	−	1.26847i	0.955875	−	0.293773i	$-0.0949108\pi$
$572$	10.0000	−	17.3205i	0.418121	−	0.724207i
$573$	6.00000	+	3.46410i	0.250654	+	0.144715i
$574$	−4.50000	−	7.79423i	−0.187826	−	0.325325i
$575$	2.00000			0.0834058
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−23.0000			−0.957503			−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000			−0.957503			−0.478751	+	0.877951i	$0.658910\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$			43.3013i			1.79954i
$580$	1.00000	−	1.73205i	0.0415227	−	0.0719195i
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$		−	22.5167i		−	0.933346i
$583$	−5.00000	−	8.66025i	−0.207079	−	0.358671i
$584$	−1.00000			−0.0413803
$585$	12.0000			0.496139
$586$	6.00000			0.247858
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	0.943824	−	0.330449i	$-0.107200\pi$
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	−0.758089	+	0.652151i	$0.773867\pi$
$588$	1.50000	+	0.866025i	0.0618590	+	0.0357143i
$589$	−3.00000	+	5.19615i	−0.123613	+	0.214104i
$590$	7.50000	−	12.9904i	0.308770	−	0.534806i
$591$	18.0000	−	10.3923i	0.740421	−	0.427482i
$592$		0			0
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$	−22.5000	−	12.9904i	−0.923186	−	0.533002i
$595$	−5.00000			−0.204980
$596$	10.0000	+	17.3205i	0.409616	+	0.709476i
$597$	−18.0000	+	10.3923i	−0.736691	+	0.425329i
$598$	4.00000	−	6.92820i	0.163572	−	0.283315i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−1.50000	−	0.866025i	−0.0612372	−	0.0353553i
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	0.994035	+	0.109061i	$0.0347845\pi$
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	−0.402568	+	0.915390i	$0.631882\pi$
$602$	−1.00000			−0.0407570
$603$	13.5000	+	23.3827i	0.549762	+	0.952217i
$604$	−2.00000			−0.0813788
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$			20.7846i			0.844317i
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	0.500000	−	0.866025i	0.0202777	−	0.0351220i
$609$			3.46410i			0.140372i
$610$	5.00000	+	8.66025i	0.202444	+	0.350643i
$611$	48.0000			1.94187
$612$	−7.50000	−	12.9904i	−0.303170	−	0.525105i
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	8.50000	+	14.7224i	0.343032	+	0.594149i
$615$	−13.5000	−	7.79423i	−0.544373	−	0.314294i
$616$	2.50000	−	4.33013i	0.100728	−	0.174466i
$617$	−6.50000	+	11.2583i	−0.261680	+	0.453243i	−0.966689	−	0.255956i	$-0.917610\pi$
$617$	−6.50000	+	11.2583i	−0.261680	+	0.453243i	0.705008	+	0.709199i	$0.250943\pi$
$618$	6.00000	−	3.46410i	0.241355	−	0.139347i
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	0.988924	+	0.148420i	$0.0474187\pi$
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	−0.365927	+	0.930644i	$0.619248\pi$
$620$	−6.00000			−0.240966
$621$	−9.00000	−	5.19615i	−0.361158	−	0.208514i
$622$	−2.00000			−0.0801927
$623$	−5.00000	−	8.66025i	−0.200321	−	0.346966i
$624$	−6.00000	+	3.46410i	−0.240192	+	0.138675i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.50000	+	7.79423i	−0.179856	+	0.311520i
$627$	−7.50000	−	4.33013i	−0.299521	−	0.172929i
$628$	6.00000	+	10.3923i	0.239426	+	0.414698i
$629$		0			0
$630$	3.00000			0.119523
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−7.00000	−	12.1244i	−0.278445	−	0.482281i
$633$		−	20.7846i		−	0.826114i
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$	7.00000	−	12.1244i	0.277787	−	0.481140i
$636$			3.46410i			0.137361i
$637$	−2.00000	−	3.46410i	−0.0792429	−	0.137253i
$638$	10.0000			0.395904
$639$	21.0000	−	36.3731i	0.830747	−	1.43890i
$640$	1.00000			0.0395285
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$	−4.50000	−	2.59808i	−0.177601	−	0.102538i
$643$	0.500000	−	0.866025i	0.0197181	−	0.0341527i	−0.855998	−	0.516979i	$-0.827056\pi$
$643$	0.500000	−	0.866025i	0.0197181	−	0.0341527i	0.875716	+	0.482826i	$0.160390\pi$
$644$	1.00000	−	1.73205i	0.0394055	−	0.0682524i
$645$	−1.50000	+	0.866025i	−0.0590624	+	0.0340997i
$646$	−2.50000	−	4.33013i	−0.0983612	−	0.170367i
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	75.0000			2.94401
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$	9.00000	−	5.19615i	0.352738	−	0.203653i
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	−0.695934	−	0.718106i	$-0.745009\pi$
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	0.969865	+	0.243643i	$0.0783426\pi$
$654$	−12.0000	−	6.92820i	−0.469237	−	0.270914i
$655$	−10.0000	−	17.3205i	−0.390732	−	0.676768i
$656$	9.00000			0.351391
$657$	1.50000	−	2.59808i	0.0585206	−	0.101361i
$658$	12.0000			0.467809
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		−	8.66025i		−	0.337100i
$661$	8.00000	−	13.8564i	0.311164	−	0.538952i	−0.667451	−	0.744654i	$-0.732615\pi$
$661$	8.00000	−	13.8564i	0.311164	−	0.538952i	0.978615	+	0.205702i	$0.0659478\pi$
$662$	−6.00000	+	10.3923i	−0.233197	+	0.403908i
$663$			34.6410i			1.34535i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	1.00000			0.0387783
$666$		0			0
$667$	4.00000			0.154881
$668$	−7.00000	−	12.1244i	−0.270838	−	0.469105i
$669$	21.0000	+	12.1244i	0.811907	+	0.468755i
$670$	−4.50000	+	7.79423i	−0.173850	+	0.301117i
$671$	−25.0000	+	43.3013i	−0.965114	+	1.67163i
$672$	−1.50000	+	0.866025i	−0.0578638	+	0.0334077i
$673$	21.0000	+	36.3731i	0.809491	+	1.40208i	0.913217	+	0.407473i	$0.133590\pi$
$673$	21.0000	+	36.3731i	0.809491	+	1.40208i	−0.103727	+	0.994606i	$0.533077\pi$
$674$	3.00000			0.115556
$675$	4.50000	−	2.59808i	0.173205	−	0.100000i
$676$	3.00000			0.115385
$677$	−16.0000	−	27.7128i	−0.614930	−	1.06509i	−0.990397	−	0.138254i	$-0.955851\pi$
$677$	−16.0000	−	27.7128i	−0.614930	−	1.06509i	0.375467	−	0.926836i	$-0.377482\pi$
$678$	−9.00000	+	5.19615i	−0.345643	+	0.199557i
$679$	−6.50000	+	11.2583i	−0.249447	+	0.432055i
$680$	2.50000	−	4.33013i	0.0958706	−	0.166053i
$681$	−28.5000	−	16.4545i	−1.09212	−	0.630537i
$682$	−15.0000	−	25.9808i	−0.574380	−	0.994855i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	1.50000	+	2.59808i	0.0573539	+	0.0993399i
$685$	13.0000			0.496704
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$			6.92820i			0.264327i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	4.00000	−	6.92820i	0.152388	−	0.263944i
$690$		−	3.46410i		−	0.131876i
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	6.00000			0.228086
$693$	7.50000	+	12.9904i	0.284901	+	0.493464i
$694$	23.0000			0.873068
$695$	−6.50000	−	11.2583i	−0.246559	−	0.427053i
$696$	−3.00000	−	1.73205i	−0.113715	−	0.0656532i
$697$	22.5000	−	38.9711i	0.852248	−	1.47614i
$698$	−2.00000	+	3.46410i	−0.0757011	+	0.131118i
$699$	−1.50000	+	0.866025i	−0.0567352	+	0.0327561i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		−	20.7846i		−	0.784465i
$703$		0			0
$704$	2.50000	+	4.33013i	0.0942223	+	0.163198i
$705$	18.0000	−	10.3923i	0.677919	−	0.391397i
$706$	8.50000	−	14.7224i	0.319902	−	0.554086i
$707$	6.00000	−	10.3923i	0.225653	−	0.390843i
$708$	−22.5000	−	12.9904i	−0.845602	−	0.488208i
$709$	−23.0000	−	39.8372i	−0.863783	−	1.49612i	−0.868250	−	0.496126i	$-0.834755\pi$
$709$	−23.0000	−	39.8372i	−0.863783	−	1.49612i	0.00446726	−	0.999990i	$-0.498578\pi$
$710$	14.0000			0.525411
$711$	42.0000			1.57512
$712$	10.0000			0.374766
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$			8.66025i			0.324102i
$715$	−10.0000	+	17.3205i	−0.373979	+	0.647750i
$716$	8.00000	−	13.8564i	0.298974	−	0.517838i
$717$		−	10.3923i		−	0.388108i
$718$		0			0
$719$	−44.0000			−1.64092			−0.820462	−	0.571702i	$-0.806283\pi$
$719$	−44.0000			−1.64092			−0.820462	+	0.571702i	$0.806283\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	−4.00000			−0.148968
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$	−16.5000	−	9.52628i	−0.613642	−	0.354286i
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$	21.0000	−	12.1244i	0.779383	−	0.449977i
$727$	−22.0000	−	38.1051i	−0.815935	−	1.41324i	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−22.0000	−	38.1051i	−0.815935	−	1.41324i	0.0927199	−	0.995692i	$-0.470444\pi$
$728$	4.00000			0.148250
$729$	−27.0000			−1.00000
$730$	1.00000			0.0370117
$731$	−2.50000	−	4.33013i	−0.0924658	−	0.160156i
$732$	15.0000	−	8.66025i	0.554416	−	0.320092i
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	−0.782650	−	0.622462i	$-0.786132\pi$
$733$	4.00000	−	6.92820i	0.147743	−	0.255899i	0.930393	+	0.366563i	$0.119466\pi$
$734$	−10.0000	+	17.3205i	−0.369107	+	0.639312i
$735$	−1.50000	−	0.866025i	−0.0553283	−	0.0319438i
$736$	1.00000	+	1.73205i	0.0368605	+	0.0638442i
$737$	−45.0000			−1.65760
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	−43.0000			−1.58178			−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000			−1.58178			−0.790890	+	0.611958i	$0.790382\pi$
$740$		0			0
$741$		−	6.92820i		−	0.254514i
$742$	1.00000	−	1.73205i	0.0367112	−	0.0635856i
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$			10.3923i			0.381000i
$745$	−10.0000	−	17.3205i	−0.366372	−	0.634574i
$746$	−14.0000			−0.512576
$747$	36.0000			1.31717
$748$	25.0000			0.914091
$749$	1.50000	+	2.59808i	0.0548088	+	0.0949316i
$750$	1.50000	+	0.866025i	0.0547723	+	0.0316228i
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	0.227153	+	0.973859i	$0.427058\pi$
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	−0.956963	+	0.290209i	$0.906275\pi$
$752$	−6.00000	+	10.3923i	−0.218797	+	0.378968i
$753$	−22.5000	+	12.9904i	−0.819946	+	0.473396i
$754$	4.00000	+	6.92820i	0.145671	+	0.252310i
$755$	2.00000			0.0727875
$756$		−	5.19615i		−	0.188982i
$757$	34.0000			1.23575			0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000			1.23575			0.617876	+	0.786276i	$0.287994\pi$
$758$	−17.5000	−	30.3109i	−0.635629	−	1.10094i
$759$	15.0000	−	8.66025i	0.544466	−	0.314347i
$760$	−0.500000	+	0.866025i	−0.0181369	+	0.0314140i
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	−0.999459	−	0.0328858i	$-0.989530\pi$
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	0.528209	+	0.849114i	$0.322864\pi$
$762$	−21.0000	−	12.1244i	−0.760750	−	0.439219i
$763$	4.00000	+	6.92820i	0.144810	+	0.250818i
$764$	4.00000			0.144715
$765$	7.50000	+	12.9904i	0.271163	+	0.469668i
$766$	−20.0000			−0.722629
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		−	1.73205i		−	0.0625000i
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$	−2.50000	+	4.33013i	−0.0900937	+	0.156047i
$771$			12.1244i			0.436648i
$772$	12.5000	+	21.6506i	0.449885	+	0.779223i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	6.00000			0.215526
$776$	−6.50000	−	11.2583i	−0.233336	−	0.404151i
$777$		0			0
$778$	−8.00000	+	13.8564i	−0.286814	+	0.496776i
$779$	−4.50000	+	7.79423i	−0.161229	+	0.279257i
$780$	6.00000	−	3.46410i	0.214834	−	0.124035i
$781$	35.0000	+	60.6218i	1.25240	+	2.16922i
$782$	10.0000			0.357599
$783$	9.00000	−	5.19615i	0.321634	−	0.185695i
$784$	1.00000			0.0357143
$785$	−6.00000	−	10.3923i	−0.214149	−	0.370917i
$786$	−30.0000	+	17.3205i	−1.07006	+	0.617802i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	6.00000	−	10.3923i	0.213741	−	0.370211i
$789$	−12.0000	−	6.92820i	−0.427211	−	0.246651i
$790$	7.00000	+	12.1244i	0.249049	+	0.431365i
$791$	6.00000			0.213335
$792$	−15.0000			−0.533002
$793$	−40.0000			−1.42044
$794$	−6.00000	−	10.3923i	−0.212932	−	0.368809i
$795$		−	3.46410i		−	0.122859i
$796$	−6.00000	+	10.3923i	−0.212664	+	0.368345i
$797$	24.0000	−	41.5692i	0.850124	−	1.47246i	−0.0309726	−	0.999520i	$-0.509860\pi$
$797$	24.0000	−	41.5692i	0.850124	−	1.47246i	0.881096	−	0.472937i	$-0.156806\pi$
$798$		−	1.73205i		−	0.0613139i
$799$	30.0000	+	51.9615i	1.06132	+	1.83827i
$800$	−1.00000			−0.0353553
$801$	−15.0000	+	25.9808i	−0.529999	+	0.917985i
$802$	−17.0000			−0.600291
$803$	2.50000	+	4.33013i	0.0882231	+	0.152807i
$804$	13.5000	+	7.79423i	0.476108	+	0.274881i
$805$	−1.00000	+	1.73205i	−0.0352454	+	0.0610468i
$806$	12.0000	−	20.7846i	0.422682	−	0.732107i
$807$	−9.00000	+	5.19615i	−0.316815	+	0.182913i
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	−47.0000			−1.65243			−0.826216	−	0.563353i	$-0.809511\pi$
$809$	−47.0000			−1.65243			−0.826216	+	0.563353i	$0.809511\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	55.0000			1.93131			0.965656	−	0.259825i	$-0.0836650\pi$
$811$	55.0000			1.93131			0.965656	+	0.259825i	$0.0836650\pi$
$812$	1.00000	+	1.73205i	0.0350931	+	0.0607831i
$813$	30.0000	−	17.3205i	1.05215	−	0.607457i
$814$		0			0
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$	−7.50000	−	4.33013i	−0.262553	−	0.151585i
$817$	0.500000	+	0.866025i	0.0174928	+	0.0302984i
$818$	35.0000			1.22375
$819$	−6.00000	+	10.3923i	−0.209657	+	0.363137i
$820$	−9.00000			−0.314294
$821$	−16.0000	−	27.7128i	−0.558404	−	0.967184i	−0.997630	−	0.0688073i	$-0.978081\pi$
$821$	−16.0000	−	27.7128i	−0.558404	−	0.967184i	0.439226	−	0.898377i	$-0.355253\pi$
$822$		−	22.5167i		−	0.785359i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$			8.66025i			0.301511i
$826$	7.50000	+	12.9904i	0.260958	+	0.451993i
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$	−6.00000			−0.208514
$829$	24.0000			0.833554			0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000			0.833554			0.416777	+	0.909009i	$0.363160\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	15.0000	+	8.66025i	0.520344	+	0.300421i
$832$	−2.00000	+	3.46410i	−0.0693375	+	0.120096i
$833$	2.50000	−	4.33013i	0.0866199	−	0.150030i
$834$	−19.5000	+	11.2583i	−0.675230	+	0.389844i
$835$	7.00000	+	12.1244i	0.242245	+	0.419581i
$836$	−5.00000			−0.172929
$837$	−27.0000	−	15.5885i	−0.933257	−	0.538816i
$838$	−40.0000			−1.38178
$839$	−5.00000	−	8.66025i	−0.172619	−	0.298985i	0.766716	−	0.641987i	$-0.221890\pi$
$839$	−5.00000	−	8.66025i	−0.172619	−	0.298985i	−0.939335	+	0.343002i	$0.888556\pi$
$840$	1.50000	−	0.866025i	0.0517549	−	0.0298807i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−7.00000	+	12.1244i	−0.241236	+	0.417833i
$843$	−9.00000	−	5.19615i	−0.309976	−	0.178965i
$844$	−6.00000	−	10.3923i	−0.206529	−	0.357718i
$845$	−3.00000			−0.103203
$846$	−18.0000	−	31.1769i	−0.618853	−	1.07188i
$847$	−14.0000			−0.481046
$848$	1.00000	+	1.73205i	0.0343401	+	0.0594789i
$849$		−	6.92820i		−	0.237775i
$850$	−2.50000	+	4.33013i	−0.0857493	+	0.148522i
$851$		0			0
$852$		−	24.2487i		−	0.830747i
$853$	−20.0000	−	34.6410i	−0.684787	−	1.18609i	−0.973504	−	0.228671i	$-0.926562\pi$
$853$	−20.0000	−	34.6410i	−0.684787	−	1.18609i	0.288717	−	0.957415i	$-0.406771\pi$
$854$	−10.0000			−0.342193
$855$	−1.50000	−	2.59808i	−0.0512989	−	0.0888523i
$856$	−3.00000			−0.102538
$857$	13.0000	+	22.5167i	0.444072	+	0.769154i	0.997987	−	0.0634184i	$-0.0202003\pi$
$857$	13.0000	+	22.5167i	0.444072	+	0.769154i	−0.553915	+	0.832573i	$0.686867\pi$
$858$	30.0000	+	17.3205i	1.02418	+	0.591312i
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	0.0573424	+	0.998355i	$0.481737\pi$
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	−0.893272	+	0.449517i	$0.851596\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	13.5000	−	7.79423i	0.460079	−	0.265627i
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	−50.0000			−1.70202			−0.851010	−	0.525150i	$-0.824009\pi$
$863$	−50.0000			−1.70202			−0.851010	+	0.525150i	$0.824009\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−6.00000			−0.204006
$866$	9.50000	+	16.4545i	0.322823	+	0.559146i
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	3.00000	−	5.19615i	0.101827	−	0.176369i
$869$	−35.0000	+	60.6218i	−1.18729	+	2.05645i
$870$	3.00000	+	1.73205i	0.101710	+	0.0587220i
$871$	−18.0000	−	31.1769i	−0.609907	−	1.05639i
$872$	−8.00000			−0.270914
$873$	39.0000			1.31995
$874$	−2.00000			−0.0676510
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$		−	1.73205i		−	0.0585206i
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−1.00000	+	1.73205i	−0.0337484	+	0.0584539i
$879$			10.3923i			0.350524i
$880$	−2.50000	−	4.33013i	−0.0842750	−	0.145969i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	10.0000	+	17.3205i	0.336336	+	0.582552i
$885$	22.5000	+	12.9904i	0.756329	+	0.436667i
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	−17.0000	+	29.4449i	−0.570804	+	0.988662i	0.425679	+	0.904874i	$0.360035\pi$
$887$	−17.0000	+	29.4449i	−0.570804	+	0.988662i	−0.996484	+	0.0837878i	$0.973298\pi$
$888$		0			0
$889$	7.00000	+	12.1244i	0.234772	+	0.406638i
$890$	−10.0000			−0.335201
$891$	22.5000	−	38.9711i	0.753778	−	1.30558i
$892$	14.0000			0.468755
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$	−30.0000	+	17.3205i	−1.00335	+	0.579284i
$895$	−8.00000	+	13.8564i	−0.267411	+	0.463169i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	12.0000	+	6.92820i	0.400668	+	0.231326i
$898$	−11.5000	−	19.9186i	−0.383760	−	0.664692i
$899$	12.0000			0.400222
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$	10.0000			0.333148
$902$	−22.5000	−	38.9711i	−0.749168	−	1.29760i
$903$		−	1.73205i		−	0.0576390i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−6.00000	+	10.3923i	−0.199447	+	0.345452i
$906$		−	3.46410i		−	0.115087i
$907$	11.5000	+	19.9186i	0.381851	+	0.661386i	0.991327	−	0.131419i	$-0.0419533\pi$
$907$	11.5000	+	19.9186i	0.381851	+	0.661386i	−0.609476	+	0.792805i	$0.708620\pi$
$908$	−19.0000			−0.630537
$909$	−36.0000			−1.19404
$910$	−4.00000			−0.132599
$911$	−17.0000	−	29.4449i	−0.563235	−	0.975552i	−0.997211	−	0.0746276i	$-0.976223\pi$
$911$	−17.0000	−	29.4449i	−0.563235	−	0.975552i	0.433976	−	0.900924i	$-0.357110\pi$
$912$	1.50000	+	0.866025i	0.0496700	+	0.0286770i
$913$	−30.0000	+	51.9615i	−0.992855	+	1.71968i
$914$	9.50000	−	16.4545i	0.314232	−	0.544266i
$915$	−15.0000	+	8.66025i	−0.495885	+	0.286299i
$916$	2.00000	+	3.46410i	0.0660819	+	0.114457i
$917$	20.0000			0.660458
$918$	22.5000	−	12.9904i	0.742611	−	0.428746i
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$	−1.00000	−	1.73205i	−0.0329690	−	0.0571040i
$921$	−25.5000	+	14.7224i	−0.840254	+	0.485121i
$922$	−16.0000	+	27.7128i	−0.526932	+	0.912673i
$923$	−28.0000	+	48.4974i	−0.921631	+	1.59631i
$924$	7.50000	+	4.33013i	0.246732	+	0.142451i
$925$		0			0
$926$	−12.0000			−0.394344
$927$	6.00000	+	10.3923i	0.197066	+	0.341328i
$928$	−2.00000			−0.0656532
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		−	10.3923i		−	0.340777i
$931$	−0.500000	+	0.866025i	−0.0163868	+	0.0283828i
$932$	−0.500000	+	0.866025i	−0.0163780	+	0.0283676i
$933$		−	3.46410i		−	0.113410i
$934$	10.5000	+	18.1865i	0.343570	+	0.595082i
$935$	−25.0000			−0.817587
$936$	−6.00000	−	10.3923i	−0.196116	−	0.339683i
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$	−4.50000	−	7.79423i	−0.146930	−	0.254491i
$939$	−13.5000	−	7.79423i	−0.440556	−	0.254355i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$	−18.0000	+	10.3923i	−0.586472	+	0.338600i
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$	−15.0000			−0.488208
$945$			5.19615i			0.169031i
$946$	−5.00000			−0.162564
$947$	−11.5000	−	19.9186i	−0.373700	−	0.647267i	0.616432	−	0.787408i	$-0.288578\pi$
$947$	−11.5000	−	19.9186i	−0.373700	−	0.647267i	−0.990132	+	0.140141i	$0.955244\pi$
$948$	21.0000	−	12.1244i	0.682048	−	0.393781i
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$	0.500000	−	0.866025i	0.0162221	−	0.0280976i
$951$	48.0000	+	27.7128i	1.55651	+	0.898650i
$952$	2.50000	+	4.33013i	0.0810255	+	0.140340i
$953$	31.0000			1.00419			0.502094	−	0.864813i	$-0.332563\pi$
$953$	31.0000			1.00419			0.502094	+	0.864813i	$0.332563\pi$
$954$	−6.00000			−0.194257
$955$	−4.00000			−0.129437
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$			17.3205i			0.559893i
$958$	−13.0000	+	22.5167i	−0.420011	+	0.727480i
$959$	−6.50000	+	11.2583i	−0.209896	+	0.363550i
$960$			1.73205i			0.0559017i
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	−11.0000			−0.354286
$965$	−12.5000	−	21.6506i	−0.402389	−	0.696959i
$966$	3.00000	+	1.73205i	0.0965234	+	0.0557278i
$967$	19.0000	−	32.9090i	0.610999	−	1.05828i	−0.380074	−	0.924956i	$-0.624101\pi$
$967$	19.0000	−	32.9090i	0.610999	−	1.05828i	0.991072	−	0.133325i	$-0.0425653\pi$
$968$	7.00000	−	12.1244i	0.224989	−	0.389692i
$969$	7.50000	−	4.33013i	0.240935	−	0.139104i
$970$	6.50000	+	11.2583i	0.208702	+	0.361483i
$971$	−28.0000			−0.898563			−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000			−0.898563			−0.449281	+	0.893390i	$0.648320\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	13.0000			0.416761
$974$	−7.00000	−	12.1244i	−0.224294	−	0.388489i
$975$	−6.00000	+	3.46410i	−0.192154	+	0.110940i
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	−0.889022	−	0.457864i	$-0.848615\pi$
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	0.841033	+	0.540984i	$0.181948\pi$
$978$	−12.0000	−	6.92820i	−0.383718	−	0.221540i
$979$	−25.0000	−	43.3013i	−0.799003	−	1.38391i
$980$	−1.00000			−0.0319438
$981$	12.0000	−	20.7846i	0.383131	−	0.663602i
$982$	33.0000			1.05307
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.730073	−	0.683369i	$-0.760514\pi$
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.226778	−	0.973946i	$-0.572819\pi$
$984$			15.5885i			0.496942i
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$	−5.00000	+	8.66025i	−0.159232	+	0.275799i
$987$			20.7846i			0.661581i
$988$	−2.00000	−	3.46410i	−0.0636285	−	0.110208i
$989$	−2.00000			−0.0635963
$990$	15.0000			0.476731
$991$	28.0000			0.889449			0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000			0.889449			0.444725	+	0.895667i	$0.353302\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$	−18.0000	−	10.3923i	−0.571213	−	0.329790i
$994$	−7.00000	+	12.1244i	−0.222027	+	0.384561i
$995$	6.00000	−	10.3923i	0.190213	−	0.329458i
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$	−9.00000			−0.284890
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.c.211.1	✓	2
3.2	odd	2		1890.2.j.c.631.1		2
9.2	odd	6		1890.2.j.c.1261.1		2
9.4	even	3		5670.2.a.a.1.1		1
9.5	odd	6		5670.2.a.o.1.1		1
9.7	even	3	inner	630.2.j.c.421.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.c.211.1	✓	2	1.1	even	1	trivial
630.2.j.c.421.1	yes	2	9.7	even	3	inner
1890.2.j.c.631.1		2	3.2	odd	2
1890.2.j.c.1261.1		2	9.2	odd	6
5670.2.a.a.1.1		1	9.4	even	3
5670.2.a.o.1.1		1	9.5	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +(-2.00000 + 3.46410i) q^{13} +(-0.500000 + 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{18} +1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(-2.50000 + 4.33013i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{26} +5.19615i q^{27} -1.00000 q^{28} +(-1.00000 - 1.73205i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.50000 - 4.33013i) q^{33} +(-2.50000 - 4.33013i) q^{34} +1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +(0.500000 + 0.866025i) q^{38} -6.92820i q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} -1.73205i q^{42} +(0.500000 + 0.866025i) q^{43} -5.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} -2.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.50000 - 4.33013i) q^{51} +(-2.00000 - 3.46410i) q^{52} -2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +5.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(1.00000 - 1.73205i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(5.00000 + 8.66025i) q^{61} -6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} -8.66025i q^{66} +(-4.50000 + 7.79423i) q^{67} +(2.50000 - 4.33013i) q^{68} -3.46410i q^{69} +(0.500000 + 0.866025i) q^{70} +14.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +1.00000 q^{73} +(1.50000 + 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(6.00000 - 3.46410i) q^{78} +(7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(1.50000 - 0.866025i) q^{84} +(-2.50000 + 4.33013i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(3.00000 + 1.73205i) q^{87} +(-2.50000 - 4.33013i) q^{88} -10.0000 q^{89} +(1.50000 - 2.59808i) q^{90} -4.00000 q^{91} +(-1.00000 - 1.73205i) q^{92} -10.3923i q^{93} +(6.00000 - 10.3923i) q^{94} +(0.500000 - 0.866025i) q^{95} +1.73205i q^{96} +(6.50000 + 11.2583i) q^{97} -1.00000 q^{98} +15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{10} + 5 q^{11} - 4 q^{13} - q^{14} - q^{16} - 10 q^{17} + 6 q^{18} + 2 q^{19} + q^{20} - 3 q^{21} - 5 q^{22} - 2 q^{23} + 3 q^{24} - q^{25} - 8 q^{26} - 2 q^{28} - 2 q^{29} - 3 q^{30} - 6 q^{31} + q^{32} - 15 q^{33} - 5 q^{34} + 2 q^{35} + 3 q^{36} + q^{38} - q^{40} - 9 q^{41} + q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 12 q^{47} + 3 q^{48} - q^{49} + q^{50} + 15 q^{51} - 4 q^{52} - 4 q^{53} - 9 q^{54} + 10 q^{55} - q^{56} - 3 q^{57} + 2 q^{58} + 15 q^{59} - 3 q^{60} + 10 q^{61} - 12 q^{62} + 6 q^{63} + 2 q^{64} + 4 q^{65} - 9 q^{67} + 5 q^{68} + q^{70} + 28 q^{71} - 3 q^{72} + 2 q^{73} + 3 q^{75} - q^{76} - 5 q^{77} + 12 q^{78} + 14 q^{79} - 2 q^{80} - 9 q^{81} - 18 q^{82} + 12 q^{83} + 3 q^{84} - 5 q^{85} - q^{86} + 6 q^{87} - 5 q^{88} - 20 q^{89} + 3 q^{90} - 8 q^{91} - 2 q^{92} + 12 q^{94} + q^{95} + 13 q^{97} - 2 q^{98} + 30 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9 + 2 * q^10 + 5 * q^11 - 4 * q^13 - q^14 - q^16 - 10 * q^17 + 6 * q^18 + 2 * q^19 + q^20 - 3 * q^21 - 5 * q^22 - 2 * q^23 + 3 * q^24 - q^25 - 8 * q^26 - 2 * q^28 - 2 * q^29 - 3 * q^30 - 6 * q^31 + q^32 - 15 * q^33 - 5 * q^34 + 2 * q^35 + 3 * q^36 + q^38 - q^40 - 9 * q^41 + q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 12 * q^47 + 3 * q^48 - q^49 + q^50 + 15 * q^51 - 4 * q^52 - 4 * q^53 - 9 * q^54 + 10 * q^55 - q^56 - 3 * q^57 + 2 * q^58 + 15 * q^59 - 3 * q^60 + 10 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 4 * q^65 - 9 * q^67 + 5 * q^68 + q^70 + 28 * q^71 - 3 * q^72 + 2 * q^73 + 3 * q^75 - q^76 - 5 * q^77 + 12 * q^78 + 14 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 + 3 * q^84 - 5 * q^85 - q^86 + 6 * q^87 - 5 * q^88 - 20 * q^89 + 3 * q^90 - 8 * q^91 - 2 * q^92 + 12 * q^94 + q^95 + 13 * q^97 - 2 * q^98 + 30 * q^99

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