LMFDB - Embedded newform 630.2.j.e.421.1

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			421.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.e.211.1

$q$-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} +(1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +3.00000 q^{18} +5.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(2.50000 + 4.33013i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(1.50000 + 0.866025i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(3.50000 - 6.06218i) q^{34} -1.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +3.46410i q^{39} +(-0.500000 - 0.866025i) q^{40} +(2.50000 + 4.33013i) q^{41} +1.73205i q^{42} +(4.50000 - 7.79423i) q^{43} +5.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} -8.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(10.5000 + 6.06218i) q^{51} +(1.00000 - 1.73205i) q^{52} +(4.50000 + 2.59808i) q^{54} -5.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(7.50000 + 4.33013i) q^{57} +(-2.50000 - 4.33013i) q^{59} +(1.50000 - 0.866025i) q^{60} +(4.00000 - 6.92820i) q^{61} -10.0000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +8.66025i q^{66} +(1.50000 + 2.59808i) q^{67} +(-3.50000 - 6.06218i) q^{68} -13.8564i q^{69} +(-0.500000 + 0.866025i) q^{70} +4.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(3.00000 + 1.73205i) q^{78} +(3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(1.50000 + 0.866025i) q^{84} +(3.50000 + 6.06218i) q^{85} +(-4.50000 - 7.79423i) q^{86} +(2.50000 - 4.33013i) q^{88} -14.0000 q^{89} +(1.50000 + 2.59808i) q^{90} -2.00000 q^{91} +(-4.00000 + 6.92820i) q^{92} -17.3205i q^{93} +(4.00000 + 6.92820i) q^{94} +(2.50000 + 4.33013i) q^{95} +1.73205i q^{96} +(8.50000 - 14.7224i) 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} + 2 q^{13} + q^{14} - q^{16} + 14 q^{17} + 6 q^{18} + 10 q^{19} + q^{20} - 3 q^{21} + 5 q^{22} - 8 q^{23} - 3 q^{24} - q^{25} + 4 q^{26} + 2 q^{28} + 3 q^{30} - 10 q^{31} + q^{32} - 15 q^{33} + 7 q^{34} - 2 q^{35} + 3 q^{36} - 4 q^{37} + 5 q^{38} - q^{40} + 5 q^{41} + 9 q^{43} + 10 q^{44} - 3 q^{45} - 16 q^{46} - 8 q^{47} - 3 q^{48} - q^{49} + q^{50} + 21 q^{51} + 2 q^{52} + 9 q^{54} - 10 q^{55} + q^{56} + 15 q^{57} - 5 q^{59} + 3 q^{60} + 8 q^{61} - 20 q^{62} - 6 q^{63} + 2 q^{64} - 2 q^{65} + 3 q^{67} - 7 q^{68} - q^{70} + 8 q^{71} - 3 q^{72} - 22 q^{73} - 2 q^{74} - 3 q^{75} - 5 q^{76} - 5 q^{77} + 6 q^{78} + 6 q^{79} - 2 q^{80} - 9 q^{81} + 10 q^{82} + 3 q^{84} + 7 q^{85} - 9 q^{86} + 5 q^{88} - 28 q^{89} + 3 q^{90} - 4 q^{91} - 8 q^{92} + 8 q^{94} + 5 q^{95} + 17 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 + 2 * q^13 + q^14 - q^16 + 14 * q^17 + 6 * q^18 + 10 * q^19 + q^20 - 3 * q^21 + 5 * q^22 - 8 * q^23 - 3 * q^24 - q^25 + 4 * q^26 + 2 * q^28 + 3 * q^30 - 10 * q^31 + q^32 - 15 * q^33 + 7 * q^34 - 2 * q^35 + 3 * q^36 - 4 * q^37 + 5 * q^38 - q^40 + 5 * q^41 + 9 * q^43 + 10 * q^44 - 3 * q^45 - 16 * q^46 - 8 * q^47 - 3 * q^48 - q^49 + q^50 + 21 * q^51 + 2 * q^52 + 9 * q^54 - 10 * q^55 + q^56 + 15 * q^57 - 5 * q^59 + 3 * q^60 + 8 * q^61 - 20 * q^62 - 6 * q^63 + 2 * q^64 - 2 * q^65 + 3 * q^67 - 7 * q^68 - q^70 + 8 * q^71 - 3 * q^72 - 22 * q^73 - 2 * q^74 - 3 * q^75 - 5 * q^76 - 5 * q^77 + 6 * q^78 + 6 * q^79 - 2 * q^80 - 9 * q^81 + 10 * q^82 + 3 * q^84 + 7 * q^85 - 9 * q^86 + 5 * q^88 - 28 * q^89 + 3 * q^90 - 4 * q^91 - 8 * q^92 + 8 * q^94 + 5 * q^95 + 17 * q^97 - 2 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		−	1.73205i		−	0.500000i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$			1.73205i			0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$	3.00000			0.707107
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	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
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000			0.392232
$27$			5.19615i			1.00000i
$28$	1.00000			0.188982
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	1.50000	+	0.866025i	0.273861	+	0.158114i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−7.50000	+	4.33013i	−1.30558	+	0.753778i
$34$	3.50000	−	6.06218i	0.600245	−	1.03965i
$35$	−1.00000			−0.169031
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$			3.46410i			0.554700i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$			1.73205i			0.267261i
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	0.973044	−	0.230618i	$-0.0740749\pi$
$44$	5.00000			0.753778
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	−8.00000			−1.17954
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$	−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
$51$	10.5000	+	6.06218i	1.47029	+	0.848875i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	−5.00000			−0.674200
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	7.50000	+	4.33013i	0.993399	+	0.573539i
$58$		0			0
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−10.0000			−1.27000
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$			8.66025i			1.06600i
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$		−	13.8564i		−	1.66812i
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	−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	$0.722612\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−2.50000	−	4.33013i	−0.284901	−	0.493464i
$78$	3.00000	+	1.73205i	0.339683	+	0.196116i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.00000			0.552158
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$	1.50000	+	0.866025i	0.163663	+	0.0944911i
$85$	3.50000	+	6.06218i	0.379628	+	0.657536i
$86$	−4.50000	−	7.79423i	−0.485247	−	0.840473i
$87$		0			0
$88$	2.50000	−	4.33013i	0.266501	−	0.461593i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$	−2.00000			−0.209657
$92$	−4.00000	+	6.92820i	−0.417029	+	0.722315i
$93$		−	17.3205i		−	1.79605i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	2.50000	+	4.33013i	0.256495	+	0.444262i
$96$			1.73205i			0.176777i
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	−0.00593185	−	0.999982i	$-0.501888\pi$
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	0.868976	−	0.494854i	$-0.164778\pi$
$98$	−1.00000			−0.101015
$99$	−15.0000			−1.50756
$100$	1.00000			0.100000
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	10.5000	−	6.06218i	1.03965	−	0.600245i
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	0.812545	−	0.582899i	$-0.198082\pi$
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	−0.911078	+	0.412235i	$0.864748\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	−1.50000	−	0.866025i	−0.146385	−	0.0845154i
$106$		0			0
$107$	11.0000			1.06341			0.531705	−	0.846930i	$-0.321551\pi$
$107$	11.0000			1.06341			0.531705	+	0.846930i	$0.321551\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−2.50000	+	4.33013i	−0.238366	+	0.412861i
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	0.999425	−	0.0338931i	$-0.0107906\pi$
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	−0.529065	+	0.848581i	$0.677457\pi$
$114$	7.50000	−	4.33013i	0.702439	−	0.405554i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$		0			0
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$	−5.00000			−0.460287
$119$	−3.50000	+	6.06218i	−0.320844	+	0.555719i
$120$		−	1.73205i		−	0.158114i
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$			8.66025i			0.780869i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	−1.00000			−0.0894427
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	13.5000	−	7.79423i	1.18861	−	0.686244i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	7.50000	+	4.33013i	0.652791	+	0.376889i
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	3.00000			0.259161
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	−7.00000			−0.600245
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	0.232273	+	0.972651i	$0.425384\pi$
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	−0.958477	+	0.285171i	$0.907949\pi$
$138$	−12.0000	−	6.92820i	−1.02151	−	0.589768i
$139$	−11.5000	−	19.9186i	−0.975417	−	1.68947i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−11.5000	−	19.9186i	−0.975417	−	1.68947i	−0.296866	−	0.954919i	$-0.595942\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$	−12.0000	+	6.92820i	−1.01058	+	0.583460i
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	−10.0000			−0.836242
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		−	1.73205i		−	0.142857i
$148$	1.00000	+	1.73205i	0.0821995	+	0.142374i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$			1.73205i			0.141421i
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−5.00000			−0.405554
$153$	10.5000	+	18.1865i	0.848875	+	1.47029i
$154$	−5.00000			−0.402911
$155$	5.00000	−	8.66025i	0.401610	−	0.695608i
$156$	3.00000	−	1.73205i	0.240192	−	0.138675i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	8.00000			0.630488
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$	2.50000	−	4.33013i	0.195217	−	0.338126i
$165$	−7.50000	−	4.33013i	−0.583874	−	0.337100i
$166$		0			0
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$	1.50000	−	0.866025i	0.115728	−	0.0668153i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	7.00000			0.536875
$171$	7.50000	+	12.9904i	0.573539	+	0.993399i
$172$	−9.00000			−0.686244
$173$	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	$-0.0119679\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.50000	−	4.33013i	−0.188445	−	0.326396i
$177$		−	8.66025i		−	0.650945i
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$	−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
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−1.00000	+	1.73205i	−0.0741249	+	0.128388i
$183$	12.0000	−	6.92820i	0.887066	−	0.512148i
$184$	4.00000	+	6.92820i	0.294884	+	0.510754i
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−15.0000	−	8.66025i	−1.09985	−	0.635001i
$187$	−17.5000	+	30.3109i	−1.27973	+	2.21655i
$188$	8.00000			0.583460
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$	5.00000			0.362738
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$	−8.50000	−	14.7224i	−0.610264	−	1.05701i
$195$	−3.00000	+	1.73205i	−0.214834	+	0.124035i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−7.50000	+	12.9904i	−0.533002	+	0.923186i
$199$	−22.0000			−1.55954			−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000			−1.55954			−0.779769	+	0.626067i	$0.784664\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$			5.19615i			0.366508i
$202$	6.00000	+	10.3923i	0.422159	+	0.731200i
$203$		0			0
$204$		−	12.1244i		−	0.848875i
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	−2.00000			−0.139347
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	−2.00000			−0.138675
$209$	−12.5000	+	21.6506i	−0.864643	+	1.49761i
$210$	−1.50000	+	0.866025i	−0.103510	+	0.0597614i
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$		0			0
$213$	6.00000	+	3.46410i	0.411113	+	0.237356i
$214$	5.50000	−	9.52628i	0.375972	−	0.651203i
$215$	9.00000			0.613795
$216$		−	5.19615i		−	0.353553i
$217$	10.0000			0.678844
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	−16.5000	−	9.52628i	−1.11497	−	0.643726i
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$	−3.00000	+	1.73205i	−0.201347	+	0.116248i
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$	−1.00000			−0.0668153
$225$	−3.00000			−0.200000
$226$	10.0000			0.665190
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$		−	8.66025i		−	0.573539i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	−4.00000	−	6.92820i	−0.263752	−	0.456832i
$231$		−	8.66025i		−	0.569803i
$232$		0			0
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−8.00000			−0.521862
$236$	−2.50000	+	4.33013i	−0.162736	+	0.281867i
$237$	9.00000	−	5.19615i	0.584613	−	0.337526i
$238$	3.50000	+	6.06218i	0.226871	+	0.392953i
$239$	−11.0000	−	19.0526i	−0.711531	−	1.23241i	−0.964282	−	0.264876i	$-0.914669\pi$
$239$	−11.0000	−	19.0526i	−0.711531	−	1.23241i	0.252752	−	0.967531i	$-0.418664\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	−0.683908	−	0.729568i	$-0.739721\pi$
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	0.973779	+	0.227498i	$0.0730544\pi$
$242$	−14.0000			−0.899954
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−8.00000			−0.512148
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	7.50000	+	4.33013i	0.478183	+	0.276079i
$247$	5.00000	+	8.66025i	0.318142	+	0.551039i
$248$	5.00000	+	8.66025i	0.317500	+	0.549927i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	23.0000			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$252$	1.50000	+	2.59808i	0.0944911	+	0.163663i
$253$	40.0000			2.51478
$254$		0			0
$255$			12.1244i			0.759257i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.50000	+	9.52628i	0.343081	+	0.594233i	0.985003	−	0.172536i	$-0.0551963\pi$
$257$	5.50000	+	9.52628i	0.343081	+	0.594233i	−0.641923	+	0.766769i	$0.721863\pi$
$258$		−	15.5885i		−	0.970495i
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$	2.00000			0.124035
$261$		0			0
$262$	−12.0000			−0.741362
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$	7.50000	−	4.33013i	0.461593	−	0.266501i
$265$		0			0
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$	−21.0000	−	12.1244i	−1.28518	−	0.741999i
$268$	1.50000	−	2.59808i	0.0916271	−	0.158703i
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$			5.19615i			0.316228i
$271$	−18.0000			−1.09342			−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000			−1.09342			−0.546711	+	0.837321i	$0.684120\pi$
$272$	−3.50000	+	6.06218i	−0.212219	+	0.367574i
$273$	−3.00000	−	1.73205i	−0.181568	−	0.104828i
$274$	8.50000	+	14.7224i	0.513504	+	0.889415i
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$	−12.0000	+	6.92820i	−0.722315	+	0.417029i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−23.0000			−1.37945
$279$	15.0000	−	25.9808i	0.898027	−	1.55543i
$280$	1.00000			0.0597614
$281$	5.00000	−	8.66025i	0.298275	−	0.516627i	−0.677466	−	0.735554i	$-0.736922\pi$
$281$	5.00000	−	8.66025i	0.298275	−	0.516627i	0.975741	+	0.218926i	$0.0702554\pi$
$282$			13.8564i			0.825137i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$			8.66025i			0.512989i
$286$	−5.00000	+	8.66025i	−0.295656	+	0.512092i
$287$	−5.00000			−0.295141
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	32.0000			1.88235
$290$		0			0
$291$	25.5000	−	14.7224i	1.49484	−	0.863044i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$	−1.50000	−	0.866025i	−0.0874818	−	0.0505076i
$295$	2.50000	−	4.33013i	0.145556	−	0.252110i
$296$	2.00000			0.116248
$297$	−22.5000	−	12.9904i	−1.30558	−	0.753778i
$298$		0			0
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	1.50000	+	0.866025i	0.0866025	+	0.0500000i
$301$	4.50000	+	7.79423i	0.259376	+	0.449252i
$302$	1.00000	+	1.73205i	0.0575435	+	0.0996683i
$303$	−18.0000	+	10.3923i	−1.03407	+	0.597022i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	8.00000			0.458079
$306$	21.0000			1.20049
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$	−2.50000	+	4.33013i	−0.142451	+	0.246732i
$309$		−	3.46410i		−	0.197066i
$310$	−5.00000	−	8.66025i	−0.283981	−	0.491869i
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	0.688726	−	0.725022i	$-0.258170\pi$
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	−0.972250	+	0.233944i	$0.924837\pi$
$312$		−	3.46410i		−	0.196116i
$313$	2.50000	−	4.33013i	0.141308	−	0.244753i	−0.786681	−	0.617359i	$-0.788202\pi$
$313$	2.50000	−	4.33013i	0.141308	−	0.244753i	0.927990	+	0.372606i	$0.121536\pi$
$314$	10.0000			0.564333
$315$	−1.50000	−	2.59808i	−0.0845154	−	0.146385i
$316$	−6.00000			−0.337526
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	−0.226665	−	0.973973i	$-0.572782\pi$
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	0.956818	−	0.290689i	$-0.0938844\pi$
$318$		0			0
$319$		0			0
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	16.5000	+	9.52628i	0.920940	+	0.531705i
$322$	4.00000	−	6.92820i	0.222911	−	0.386094i
$323$	35.0000			1.94745
$324$	9.00000			0.500000
$325$	−2.00000			−0.110940
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$	15.0000	+	8.66025i	0.829502	+	0.478913i
$328$	−2.50000	−	4.33013i	−0.138039	−	0.239091i
$329$	−4.00000	−	6.92820i	−0.220527	−	0.381964i
$330$	−7.50000	+	4.33013i	−0.412861	+	0.238366i
$331$	−8.00000	+	13.8564i	−0.439720	+	0.761617i	−0.997668	−	0.0682590i	$-0.978256\pi$
$331$	−8.00000	+	13.8564i	−0.439720	+	0.761617i	0.557948	+	0.829876i	$0.311589\pi$
$332$		0			0
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$	8.00000			0.437741
$335$	−1.50000	+	2.59808i	−0.0819538	+	0.141948i
$336$		−	1.73205i		−	0.0944911i
$337$	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	$0.718128\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$			17.3205i			0.940721i
$340$	3.50000	−	6.06218i	0.189814	−	0.328768i
$341$	50.0000			2.70765
$342$	15.0000			0.811107
$343$	1.00000			0.0539949
$344$	−4.50000	+	7.79423i	−0.242624	+	0.420237i
$345$	12.0000	−	6.92820i	0.646058	−	0.373002i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	0.959090	+	0.283101i	$0.0913633\pi$
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	−0.234372	+	0.972147i	$0.575303\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	−1.00000			−0.0534522
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	−5.00000			−0.266501
$353$	13.5000	−	23.3827i	0.718532	−	1.24453i	−0.243049	−	0.970014i	$-0.578147\pi$
$353$	13.5000	−	23.3827i	0.718532	−	1.24453i	0.961581	−	0.274521i	$-0.0885192\pi$
$354$	−7.50000	−	4.33013i	−0.398621	−	0.230144i
$355$	2.00000	+	3.46410i	0.106149	+	0.183855i
$356$	7.00000	+	12.1244i	0.370999	+	0.642590i
$357$	−10.5000	+	6.06218i	−0.555719	+	0.320844i
$358$	−8.00000	+	13.8564i	−0.422813	+	0.732334i
$359$	14.0000			0.738892			0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000			0.738892			0.369446	+	0.929252i	$0.379548\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	6.00000			0.315789
$362$	4.00000	−	6.92820i	0.210235	−	0.364138i
$363$		−	24.2487i		−	1.27273i
$364$	1.00000	+	1.73205i	0.0524142	+	0.0907841i
$365$	−5.50000	−	9.52628i	−0.287883	−	0.498628i
$366$		−	13.8564i		−	0.724286i
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$	8.00000			0.417029
$369$	−7.50000	+	12.9904i	−0.390434	+	0.676252i
$370$	−2.00000			−0.103975
$371$		0			0
$372$	−15.0000	+	8.66025i	−0.777714	+	0.449013i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	17.5000	+	30.3109i	0.904903	+	1.56734i
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$		0			0
$378$	−4.50000	+	2.59808i	−0.231455	+	0.133631i
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$	2.50000	−	4.33013i	0.128247	−	0.222131i
$381$		0			0
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	11.0000			0.559885
$387$	27.0000			1.37249
$388$	−17.0000			−0.863044
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$			3.46410i			0.175412i
$391$	−28.0000	−	48.4974i	−1.41602	−	2.45262i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		−	20.7846i		−	1.04844i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	6.00000			0.301893
$396$	7.50000	+	12.9904i	0.376889	+	0.652791i
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	−11.0000	+	19.0526i	−0.551380	+	0.955018i
$399$	−7.50000	+	4.33013i	−0.375470	+	0.216777i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.683892	+	0.729583i	$0.260286\pi$
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.289891	+	0.957060i	$0.406381\pi$
$402$	4.50000	+	2.59808i	0.224440	+	0.129580i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	12.0000			0.597022
$405$	−9.00000			−0.447214
$406$		0			0
$407$	5.00000	−	8.66025i	0.247841	−	0.429273i
$408$	−10.5000	−	6.06218i	−0.519827	−	0.300123i
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$	2.50000	+	4.33013i	0.123466	+	0.213850i
$411$	−25.5000	+	14.7224i	−1.25782	+	0.726204i
$412$	−1.00000	+	1.73205i	−0.0492665	+	0.0853320i
$413$	5.00000			0.246034
$414$	−12.0000	−	20.7846i	−0.589768	−	1.02151i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		−	39.8372i		−	1.95083i
$418$	12.5000	+	21.6506i	0.611395	+	1.05897i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$			1.73205i			0.0845154i
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−8.00000			−0.389434
$423$	−24.0000			−1.16692
$424$		0			0
$425$	−3.50000	+	6.06218i	−0.169775	+	0.294059i
$426$	6.00000	−	3.46410i	0.290701	−	0.167836i
$427$	4.00000	+	6.92820i	0.193574	+	0.335279i
$428$	−5.50000	−	9.52628i	−0.265853	−	0.460470i
$429$	−15.0000	−	8.66025i	−0.724207	−	0.418121i
$430$	4.50000	−	7.79423i	0.217009	−	0.375871i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−21.0000			−1.00920			−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000			−1.00920			−0.504598	+	0.863355i	$0.668359\pi$
$434$	5.00000	−	8.66025i	0.240008	−	0.415705i
$435$		0			0
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$	−20.0000	−	34.6410i	−0.956730	−	1.65710i
$438$	−16.5000	+	9.52628i	−0.788400	+	0.455183i
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$	5.00000			0.238366
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	14.0000			0.665912
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	−0.937113	−	0.349027i	$-0.886512\pi$
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	0.770823	+	0.637050i	$0.219845\pi$
$444$			3.46410i			0.164399i
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$		0			0
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−7.00000			−0.330350			−0.165175	−	0.986264i	$-0.552819\pi$
$449$	−7.00000			−0.330350			−0.165175	+	0.986264i	$0.552819\pi$
$450$	−1.50000	+	2.59808i	−0.0707107	+	0.122474i
$451$	−25.0000			−1.17720
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	−3.00000	+	1.73205i	−0.140952	+	0.0813788i
$454$	13.5000	+	23.3827i	0.633586	+	1.09740i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	−7.50000	−	4.33013i	−0.351220	−	0.202777i
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	0.00126243	+	0.999999i	$0.499598\pi$
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	−0.866656	+	0.498906i	$0.833735\pi$
$458$	−10.0000			−0.467269
$459$			36.3731i			1.69775i
$460$	−8.00000			−0.373002
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	−0.958652	−	0.284579i	$-0.908146\pi$
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	0.725779	+	0.687928i	$0.241479\pi$
$462$	−7.50000	−	4.33013i	−0.348932	−	0.201456i
$463$	8.00000	+	13.8564i	0.371792	+	0.643962i	0.989841	−	0.142177i	$-0.0454103\pi$
$463$	8.00000	+	13.8564i	0.371792	+	0.643962i	−0.618050	+	0.786139i	$0.712077\pi$
$464$		0			0
$465$	15.0000	−	8.66025i	0.695608	−	0.401610i
$466$	−0.500000	+	0.866025i	−0.0231621	+	0.0401179i
$467$	11.0000			0.509019			0.254510	−	0.967070i	$-0.418086\pi$
$467$	11.0000			0.509019			0.254510	+	0.967070i	$0.418086\pi$
$468$	6.00000			0.277350
$469$	−3.00000			−0.138527
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$			17.3205i			0.798087i
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	22.5000	+	38.9711i	1.03455	+	1.79190i
$474$		−	10.3923i		−	0.477334i
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$	7.00000			0.320844
$477$		0			0
$478$	−22.0000			−1.00626
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$	−1.50000	+	0.866025i	−0.0684653	+	0.0395285i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−4.50000	−	7.79423i	−0.204969	−	0.355017i
$483$	12.0000	+	6.92820i	0.546019	+	0.315244i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	17.0000			0.771930
$486$			15.5885i			0.707107i
$487$	−18.0000			−0.815658			−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000			−0.815658			−0.407829	+	0.913058i	$0.633714\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	18.0000	+	10.3923i	0.813988	+	0.469956i
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	0.897886	−	0.440228i	$-0.145102\pi$
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	−0.830192	+	0.557478i	$0.811769\pi$
$492$	7.50000	−	4.33013i	0.338126	−	0.195217i
$493$		0			0
$494$	10.0000			0.449921
$495$	−7.50000	−	12.9904i	−0.337100	−	0.583874i
$496$	10.0000			0.449013
$497$	−2.00000	+	3.46410i	−0.0897123	+	0.155386i
$498$		0			0
$499$	20.5000	+	35.5070i	0.917706	+	1.58951i	0.802890	+	0.596127i	$0.203294\pi$
$499$	20.5000	+	35.5070i	0.917706	+	1.58951i	0.114816	+	0.993387i	$0.463372\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$			13.8564i			0.619059i
$502$	11.5000	−	19.9186i	0.513270	−	0.889010i
$503$	−10.0000			−0.445878			−0.222939	−	0.974832i	$-0.571565\pi$
$503$	−10.0000			−0.445878			−0.222939	+	0.974832i	$0.571565\pi$
$504$	3.00000			0.133631
$505$	−12.0000			−0.533993
$506$	20.0000	−	34.6410i	0.889108	−	1.53998i
$507$	13.5000	−	7.79423i	0.599556	−	0.346154i
$508$		0			0
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$	10.5000	+	6.06218i	0.464948	+	0.268438i
$511$	5.50000	−	9.52628i	0.243306	−	0.421418i
$512$	−1.00000			−0.0441942
$513$			25.9808i			1.14708i
$514$	11.0000			0.485189
$515$	1.00000	−	1.73205i	0.0440653	−	0.0763233i
$516$	−13.5000	−	7.79423i	−0.594304	−	0.343122i
$517$	−20.0000	−	34.6410i	−0.879599	−	1.52351i
$518$	−1.00000	−	1.73205i	−0.0439375	−	0.0761019i
$519$	21.0000	−	12.1244i	0.921798	−	0.532200i
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$		0			0
$523$	−28.0000			−1.22435			−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000			−1.22435			−0.612177	+	0.790721i	$0.709706\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		−	1.73205i		−	0.0755929i
$526$	3.00000	+	5.19615i	0.130806	+	0.226563i
$527$	−35.0000	−	60.6218i	−1.52462	−	2.64073i
$528$		−	8.66025i		−	0.376889i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	7.50000	−	12.9904i	0.325472	−	0.563735i
$532$	5.00000			0.216777
$533$	−5.00000	+	8.66025i	−0.216574	+	0.375117i
$534$	−21.0000	+	12.1244i	−0.908759	+	0.524672i
$535$	5.50000	+	9.52628i	0.237786	+	0.411857i
$536$	−1.50000	−	2.59808i	−0.0647901	−	0.112220i
$537$	−24.0000	−	13.8564i	−1.03568	−	0.597948i
$538$	12.0000	−	20.7846i	0.517357	−	0.896088i
$539$	5.00000			0.215365
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	−9.00000	+	15.5885i	−0.386583	+	0.669582i
$543$	12.0000	+	6.92820i	0.514969	+	0.297318i
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$	5.00000	+	8.66025i	0.214176	+	0.370965i
$546$	−3.00000	+	1.73205i	−0.128388	+	0.0741249i
$547$	−9.50000	+	16.4545i	−0.406191	+	0.703543i	−0.994459	−	0.105123i	$-0.966476\pi$
$547$	−9.50000	+	16.4545i	−0.406191	+	0.703543i	0.588269	+	0.808666i	$0.299810\pi$
$548$	17.0000			0.726204
$549$	24.0000			1.02430
$550$	−5.00000			−0.213201
$551$		0			0
$552$			13.8564i			0.589768i
$553$	3.00000	+	5.19615i	0.127573	+	0.220963i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		−	3.46410i		−	0.147043i
$556$	−11.5000	+	19.9186i	−0.487709	+	0.844736i
$557$	−4.00000			−0.169485			−0.0847427	−	0.996403i	$-0.527007\pi$
$557$	−4.00000			−0.169485			−0.0847427	+	0.996403i	$0.527007\pi$
$558$	−15.0000	−	25.9808i	−0.635001	−	1.09985i
$559$	18.0000			0.761319
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$	−52.5000	+	30.3109i	−2.21655	+	1.27973i
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	−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	$0.935703\pi$
$564$	12.0000	+	6.92820i	0.505291	+	0.291730i
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$	4.00000			0.168133
$567$	−4.50000	−	7.79423i	−0.188982	−	0.327327i
$568$	−4.00000			−0.167836
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$	7.50000	+	4.33013i	0.314140	+	0.181369i
$571$	−9.50000	−	16.4545i	−0.397563	−	0.688599i	0.595862	−	0.803087i	$-0.296811\pi$
$571$	−9.50000	−	16.4545i	−0.397563	−	0.688599i	−0.993425	+	0.114488i	$0.963477\pi$
$572$	5.00000	+	8.66025i	0.209061	+	0.362103i
$573$	30.0000	−	17.3205i	1.25327	−	0.723575i
$574$	−2.50000	+	4.33013i	−0.104348	+	0.180736i
$575$	8.00000			0.333623
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	17.0000			0.707719			0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000			0.707719			0.353860	+	0.935299i	$0.384869\pi$
$578$	16.0000	−	27.7128i	0.665512	−	1.15270i
$579$			19.0526i			0.791797i
$580$		0			0
$581$		0			0
$582$		−	29.4449i		−	1.22053i
$583$		0			0
$584$	11.0000			0.455183
$585$	−6.00000			−0.248069
$586$	−12.0000			−0.495715
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	−0.668708	−	0.743525i	$-0.733152\pi$
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	0.978266	+	0.207355i	$0.0664855\pi$
$588$	−1.50000	+	0.866025i	−0.0618590	+	0.0357143i
$589$	−25.0000	−	43.3013i	−1.03011	−	1.78420i
$590$	−2.50000	−	4.33013i	−0.102923	−	0.178269i
$591$	−27.0000	−	15.5885i	−1.11063	−	0.641223i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$	−22.5000	+	12.9904i	−0.923186	+	0.533002i
$595$	−7.00000			−0.286972
$596$		0			0
$597$	−33.0000	−	19.0526i	−1.35060	−	0.779769i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	−0.907754	−	0.419504i	$-0.862204\pi$
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	0.0905757	−	0.995890i	$-0.471129\pi$
$600$	1.50000	−	0.866025i	0.0612372	−	0.0353553i
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	−0.912499	−	0.409079i	$-0.865850\pi$
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	0.810522	+	0.585708i	$0.199184\pi$
$602$	9.00000			0.366813
$603$	−4.50000	+	7.79423i	−0.183254	+	0.317406i
$604$	2.00000			0.0813788
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$			20.7846i			0.844317i
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	0.999889	−	0.0148722i	$-0.00473415\pi$
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	−0.512824	+	0.858494i	$0.671401\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$		0			0
$610$	4.00000	−	6.92820i	0.161955	−	0.280515i
$611$	−16.0000			−0.647291
$612$	10.5000	−	18.1865i	0.424437	−	0.735147i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	11.5000	−	19.9186i	0.464102	−	0.803849i
$615$	−7.50000	+	4.33013i	−0.302429	+	0.174608i
$616$	2.50000	+	4.33013i	0.100728	+	0.174466i
$617$	18.5000	+	32.0429i	0.744782	+	1.29000i	0.950297	+	0.311346i	$0.100780\pi$
$617$	18.5000	+	32.0429i	0.744782	+	1.29000i	−0.205515	+	0.978654i	$0.565887\pi$
$618$	−3.00000	−	1.73205i	−0.120678	−	0.0696733i
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	−0.875899	−	0.482495i	$-0.839731\pi$
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	0.855802	+	0.517303i	$0.173064\pi$
$620$	−10.0000			−0.401610
$621$	36.0000	−	20.7846i	1.44463	−	0.834058i
$622$	−10.0000			−0.400963
$623$	7.00000	−	12.1244i	0.280449	−	0.485752i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.50000	−	4.33013i	−0.0999201	−	0.173067i
$627$	−37.5000	+	21.6506i	−1.49761	+	0.864643i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	−14.0000			−0.558217
$630$	−3.00000			−0.119523
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$		−	13.8564i		−	0.550743i
$634$	−13.0000	−	22.5167i	−0.516296	−	0.894251i
$635$		0			0
$636$		0			0
$637$	1.00000	−	1.73205i	0.0396214	−	0.0686264i
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$	1.00000			0.0395285
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$	16.5000	−	9.52628i	0.651203	−	0.375972i
$643$	−0.500000	−	0.866025i	−0.0197181	−	0.0341527i	0.855998	−	0.516979i	$-0.172944\pi$
$643$	−0.500000	−	0.866025i	−0.0197181	−	0.0341527i	−0.875716	+	0.482826i	$0.839610\pi$
$644$	−4.00000	−	6.92820i	−0.157622	−	0.273009i
$645$	13.5000	+	7.79423i	0.531562	+	0.306897i
$646$	17.5000	−	30.3109i	0.688528	−	1.19257i
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	25.0000			0.981336
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$	15.0000	+	8.66025i	0.587896	+	0.339422i
$652$	−6.00000	−	10.3923i	−0.234978	−	0.406994i
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	0.751453	−	0.659786i	$-0.229353\pi$
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	−0.947118	+	0.320884i	$0.896020\pi$
$654$	15.0000	−	8.66025i	0.586546	−	0.338643i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	−5.00000			−0.195217
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$	−8.00000			−0.311872
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	−0.933357	−	0.358951i	$-0.883135\pi$
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	0.777539	+	0.628835i	$0.216468\pi$
$660$			8.66025i			0.337100i
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	0.603354	−	0.797473i	$-0.293830\pi$
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	−0.992309	+	0.123784i	$0.960497\pi$
$662$	8.00000	+	13.8564i	0.310929	+	0.538545i
$663$			24.2487i			0.941742i
$664$		0			0
$665$	−5.00000			−0.193892
$666$	−6.00000			−0.232495
$667$		0			0
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$		0			0
$670$	1.50000	+	2.59808i	0.0579501	+	0.100372i
$671$	20.0000	+	34.6410i	0.772091	+	1.33730i
$672$	−1.50000	−	0.866025i	−0.0578638	−	0.0334077i
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	13.0000			0.500741
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	−9.00000			−0.346154
$677$	−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	$0.279092\pi$
$678$	15.0000	+	8.66025i	0.576072	+	0.332595i
$679$	8.50000	+	14.7224i	0.326200	+	0.564995i
$680$	−3.50000	−	6.06218i	−0.134219	−	0.232474i
$681$	−40.5000	+	23.3827i	−1.55196	+	0.896026i
$682$	25.0000	−	43.3013i	0.957299	−	1.65809i
$683$	−17.0000			−0.650487			−0.325243	−	0.945630i	$-0.605446\pi$
$683$	−17.0000			−0.650487			−0.325243	+	0.945630i	$0.605446\pi$
$684$	7.50000	−	12.9904i	0.286770	−	0.496700i
$685$	−17.0000			−0.649537
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		−	17.3205i		−	0.660819i
$688$	4.50000	+	7.79423i	0.171561	+	0.297152i
$689$		0			0
$690$		−	13.8564i		−	0.527504i
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	0.181584	+	0.983375i	$0.441877\pi$
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	−0.942420	+	0.334431i	$0.891456\pi$
$692$	−14.0000			−0.532200
$693$	7.50000	−	12.9904i	0.284901	−	0.493464i
$694$	27.0000			1.02491
$695$	11.5000	−	19.9186i	0.436220	−	0.755555i
$696$		0			0
$697$	17.5000	+	30.3109i	0.662860	+	1.14811i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	−1.50000	−	0.866025i	−0.0567352	−	0.0327561i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$			10.3923i			0.392232i
$703$	−10.0000			−0.377157
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−12.0000	−	6.92820i	−0.451946	−	0.260931i
$706$	−13.5000	−	23.3827i	−0.508079	−	0.880019i
$707$	−6.00000	−	10.3923i	−0.225653	−	0.390843i
$708$	−7.50000	+	4.33013i	−0.281867	+	0.162736i
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$	4.00000			0.150117
$711$	18.0000			0.675053
$712$	14.0000			0.524672
$713$	−40.0000	+	69.2820i	−1.49801	+	2.59463i
$714$			12.1244i			0.453743i
$715$	−5.00000	−	8.66025i	−0.186989	−	0.323875i
$716$	8.00000	+	13.8564i	0.298974	+	0.517838i
$717$		−	38.1051i		−	1.42306i
$718$	7.00000	−	12.1244i	0.261238	−	0.452477i
$719$	18.0000			0.671287			0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000			0.671287			0.335643	+	0.941989i	$0.391046\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	2.00000			0.0744839
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	13.5000	−	7.79423i	0.502070	−	0.289870i
$724$	−4.00000	−	6.92820i	−0.148659	−	0.257485i
$725$		0			0
$726$	−21.0000	−	12.1244i	−0.779383	−	0.449977i
$727$	−15.0000	+	25.9808i	−0.556319	+	0.963573i	0.441480	+	0.897271i	$0.354453\pi$
$727$	−15.0000	+	25.9808i	−0.556319	+	0.963573i	−0.997800	+	0.0663022i	$0.978880\pi$
$728$	2.00000			0.0741249
$729$	−27.0000			−1.00000
$730$	−11.0000			−0.407128
$731$	31.5000	−	54.5596i	1.16507	−	2.01796i
$732$	−12.0000	−	6.92820i	−0.443533	−	0.256074i
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	0.650564	−	0.759452i	$-0.274533\pi$
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	−0.982986	+	0.183679i	$0.941199\pi$
$734$	11.0000	+	19.0526i	0.406017	+	0.703243i
$735$	1.50000	−	0.866025i	0.0553283	−	0.0319438i
$736$	4.00000	−	6.92820i	0.147442	−	0.255377i
$737$	−15.0000			−0.552532
$738$	7.50000	+	12.9904i	0.276079	+	0.478183i
$739$	−21.0000			−0.772497			−0.386249	−	0.922395i	$-0.626229\pi$
$739$	−21.0000			−0.772497			−0.386249	+	0.922395i	$0.626229\pi$
$740$	−1.00000	+	1.73205i	−0.0367607	+	0.0636715i
$741$			17.3205i			0.636285i
$742$		0			0
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	−0.937336	−	0.348428i	$-0.886716\pi$
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	0.166920	−	0.985970i	$-0.446618\pi$
$744$			17.3205i			0.635001i
$745$		0			0
$746$	10.0000			0.366126
$747$		0			0
$748$	35.0000			1.27973
$749$	−5.50000	+	9.52628i	−0.200966	+	0.348083i
$750$	−1.50000	+	0.866025i	−0.0547723	+	0.0316228i
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	0.965013	−	0.262201i	$-0.0844484\pi$
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	−0.709580	+	0.704625i	$0.751115\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	34.5000	+	19.9186i	1.25725	+	0.725874i
$754$		0			0
$755$	−2.00000			−0.0727875
$756$			5.19615i			0.188982i
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−14.5000	+	25.1147i	−0.526664	+	0.912208i
$759$	60.0000	+	34.6410i	2.17786	+	1.25739i
$760$	−2.50000	−	4.33013i	−0.0906845	−	0.157070i
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	0.761057	−	0.648686i	$-0.224681\pi$
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	−0.942306	+	0.334752i	$0.891348\pi$
$762$		0			0
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$	−20.0000			−0.723575
$765$	−10.5000	+	18.1865i	−0.379628	+	0.657536i
$766$	12.0000			0.433578
$767$	5.00000	−	8.66025i	0.180540	−	0.312704i
$768$		−	1.73205i		−	0.0625000i
$769$	−11.0000	−	19.0526i	−0.396670	−	0.687053i	0.596643	−	0.802507i	$-0.296501\pi$
$769$	−11.0000	−	19.0526i	−0.396670	−	0.687053i	−0.993313	+	0.115454i	$0.963168\pi$
$770$	−2.50000	−	4.33013i	−0.0900937	−	0.156047i
$771$			19.0526i			0.686161i
$772$	5.50000	−	9.52628i	0.197949	−	0.342858i
$773$	−40.0000			−1.43870			−0.719350	−	0.694648i	$-0.755560\pi$
$773$	−40.0000			−1.43870			−0.719350	+	0.694648i	$0.755560\pi$
$774$	13.5000	−	23.3827i	0.485247	−	0.840473i
$775$	10.0000			0.359211
$776$	−8.50000	+	14.7224i	−0.305132	+	0.528505i
$777$	3.00000	−	1.73205i	0.107624	−	0.0621370i
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$	12.5000	+	21.6506i	0.447859	+	0.775715i
$780$	3.00000	+	1.73205i	0.107417	+	0.0620174i
$781$	−10.0000	+	17.3205i	−0.357828	+	0.619777i
$782$	−56.0000			−2.00256
$783$		0			0
$784$	1.00000			0.0357143
$785$	−5.00000	+	8.66025i	−0.178458	+	0.309098i
$786$	−18.0000	−	10.3923i	−0.642039	−	0.370681i
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	−0.929467	−	0.368906i	$-0.879732\pi$
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	0.145251	−	0.989395i	$-0.453601\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	−9.00000	+	5.19615i	−0.320408	+	0.184988i
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	−10.0000			−0.355559
$792$	15.0000			0.533002
$793$	16.0000			0.568177
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	11.0000	+	19.0526i	0.389885	+	0.675300i
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$			8.66025i			0.306570i
$799$	−28.0000	+	48.4974i	−0.990569	+	1.71572i
$800$	−1.00000			−0.0353553
$801$	−21.0000	−	36.3731i	−0.741999	−	1.28518i
$802$	39.0000			1.37714
$803$	27.5000	−	47.6314i	0.970454	−	1.68088i
$804$	4.50000	−	2.59808i	0.158703	−	0.0916271i
$805$	4.00000	+	6.92820i	0.140981	+	0.244187i
$806$	−10.0000	−	17.3205i	−0.352235	−	0.610089i
$807$	36.0000	+	20.7846i	1.26726	+	0.731653i
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	−19.0000			−0.668004			−0.334002	−	0.942572i	$-0.608399\pi$
$809$	−19.0000			−0.668004			−0.334002	+	0.942572i	$0.608399\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	−21.0000			−0.737410			−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000			−0.737410			−0.368705	+	0.929547i	$0.620199\pi$
$812$		0			0
$813$	−27.0000	−	15.5885i	−0.946931	−	0.546711i
$814$	−5.00000	−	8.66025i	−0.175250	−	0.303542i
$815$	6.00000	+	10.3923i	0.210171	+	0.364027i
$816$	−10.5000	+	6.06218i	−0.367574	+	0.212219i
$817$	22.5000	−	38.9711i	0.787175	−	1.36343i
$818$	5.00000			0.174821
$819$	−3.00000	−	5.19615i	−0.104828	−	0.181568i
$820$	5.00000			0.174608
$821$	−13.0000	+	22.5167i	−0.453703	+	0.785837i	−0.998613	−	0.0526580i	$-0.983231\pi$
$821$	−13.0000	+	22.5167i	−0.453703	+	0.785837i	0.544909	+	0.838495i	$0.316564\pi$
$822$			29.4449i			1.02701i
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	0.998580	−	0.0532760i	$-0.0169663\pi$
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	−0.545428	+	0.838157i	$0.683633\pi$
$824$	1.00000	+	1.73205i	0.0348367	+	0.0603388i
$825$		−	8.66025i		−	0.301511i
$826$	2.50000	−	4.33013i	0.0869861	−	0.150664i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−24.0000			−0.834058
$829$	44.0000			1.52818			0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000			1.52818			0.764092	+	0.645108i	$0.223188\pi$
$830$		0			0
$831$	−3.00000	+	1.73205i	−0.104069	+	0.0600842i
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$	−3.50000	−	6.06218i	−0.121268	−	0.210042i
$834$	−34.5000	−	19.9186i	−1.19464	−	0.689724i
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	25.0000			0.864643
$837$	45.0000	−	25.9808i	1.55543	−	0.898027i
$838$	−12.0000			−0.414533
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	0.0705865	+	0.997506i	$0.477513\pi$
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	−0.899158	+	0.437623i	$0.855820\pi$
$840$	1.50000	+	0.866025i	0.0517549	+	0.0298807i
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−4.00000	−	6.92820i	−0.137849	−	0.238762i
$843$	15.0000	−	8.66025i	0.516627	−	0.298275i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	9.00000			0.309609
$846$	−12.0000	+	20.7846i	−0.412568	+	0.714590i
$847$	14.0000			0.481046
$848$		0			0
$849$			6.92820i			0.237775i
$850$	3.50000	+	6.06218i	0.120049	+	0.207931i
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$		−	6.92820i		−	0.237356i
$853$	−2.00000	+	3.46410i	−0.0684787	+	0.118609i	−0.898232	−	0.439522i	$-0.855148\pi$
$853$	−2.00000	+	3.46410i	−0.0684787	+	0.118609i	0.829753	+	0.558131i	$0.188481\pi$
$854$	8.00000			0.273754
$855$	−7.50000	+	12.9904i	−0.256495	+	0.444262i
$856$	−11.0000			−0.375972
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	−0.990439	−	0.137948i	$-0.955949\pi$
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	0.614687	+	0.788771i	$0.289283\pi$
$858$	−15.0000	+	8.66025i	−0.512092	+	0.295656i
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	0.919537	−	0.393003i	$-0.128564\pi$
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	−0.800119	+	0.599841i	$0.795230\pi$
$860$	−4.50000	−	7.79423i	−0.153449	−	0.265781i
$861$	−7.50000	−	4.33013i	−0.255599	−	0.147570i
$862$	−12.0000	+	20.7846i	−0.408722	+	0.707927i
$863$	−42.0000			−1.42970			−0.714848	−	0.699280i	$-0.753504\pi$
$863$	−42.0000			−1.42970			−0.714848	+	0.699280i	$0.753504\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	14.0000			0.476014
$866$	−10.5000	+	18.1865i	−0.356805	+	0.618004i
$867$	48.0000	+	27.7128i	1.63017	+	0.941176i
$868$	−5.00000	−	8.66025i	−0.169711	−	0.293948i
$869$	15.0000	+	25.9808i	0.508840	+	0.881337i
$870$		0			0
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$	−10.0000			−0.338643
$873$	51.0000			1.72609
$874$	−40.0000			−1.35302
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$			19.0526i			0.643726i
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	0.646319	−	0.763067i	$-0.276307\pi$
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	−0.983995	+	0.178195i	$0.942974\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$		−	20.7846i		−	0.701047i
$880$	2.50000	−	4.33013i	0.0842750	−	0.145969i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	13.0000			0.437485			0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000			0.437485			0.218742	+	0.975783i	$0.429805\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$	7.50000	−	4.33013i	0.252110	−	0.145556i
$886$	3.50000	+	6.06218i	0.117585	+	0.203663i
$887$	−1.00000	−	1.73205i	−0.0335767	−	0.0581566i	0.848749	−	0.528796i	$-0.177356\pi$
$887$	−1.00000	−	1.73205i	−0.0335767	−	0.0581566i	−0.882325	+	0.470640i	$0.844023\pi$
$888$	3.00000	+	1.73205i	0.100673	+	0.0581238i
$889$		0			0
$890$	−14.0000			−0.469281
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$		0			0
$893$	−20.0000	+	34.6410i	−0.669274	+	1.15922i
$894$		0			0
$895$	−8.00000	−	13.8564i	−0.267411	−	0.463169i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	24.0000	−	13.8564i	0.801337	−	0.462652i
$898$	−3.50000	+	6.06218i	−0.116797	+	0.202297i
$899$		0			0
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$		0			0
$902$	−12.5000	+	21.6506i	−0.416204	+	0.720887i
$903$			15.5885i			0.518751i
$904$	−5.00000	−	8.66025i	−0.166298	−	0.288036i
$905$	4.00000	+	6.92820i	0.132964	+	0.230301i
$906$			3.46410i			0.115087i
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	−0.550013	−	0.835156i	$-0.685377\pi$
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	0.998273	+	0.0587469i	$0.0187105\pi$
$908$	27.0000			0.896026
$909$	−36.0000			−1.19404
$910$	−2.00000			−0.0662994
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	−0.749347	−	0.662177i	$-0.769633\pi$
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	0.948136	+	0.317865i	$0.102966\pi$
$912$	−7.50000	+	4.33013i	−0.248350	+	0.143385i
$913$		0			0
$914$	18.5000	+	32.0429i	0.611926	+	1.05989i
$915$	12.0000	+	6.92820i	0.396708	+	0.229039i
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	12.0000			0.396275
$918$	31.5000	+	18.1865i	1.03965	+	0.600245i
$919$	52.0000			1.71532			0.857661	−	0.514216i	$-0.171917\pi$
$919$	52.0000			1.71532			0.857661	+	0.514216i	$0.171917\pi$
$920$	−4.00000	+	6.92820i	−0.131876	+	0.228416i
$921$	34.5000	+	19.9186i	1.13681	+	0.656340i
$922$	5.00000	+	8.66025i	0.164666	+	0.285210i
$923$	4.00000	+	6.92820i	0.131662	+	0.228045i
$924$	−7.50000	+	4.33013i	−0.246732	+	0.142451i
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	16.0000			0.525793
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$		0			0
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		−	17.3205i		−	0.567962i
$931$	−2.50000	−	4.33013i	−0.0819342	−	0.141914i
$932$	0.500000	+	0.866025i	0.0163780	+	0.0283676i
$933$		−	17.3205i		−	0.567048i
$934$	5.50000	−	9.52628i	0.179965	−	0.311709i
$935$	−35.0000			−1.14462
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	−1.50000	+	2.59808i	−0.0489767	+	0.0848302i
$939$	7.50000	−	4.33013i	0.244753	−	0.141308i
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−6.00000	−	10.3923i	−0.195594	−	0.338779i	0.751501	−	0.659732i	$-0.229330\pi$
$941$	−6.00000	−	10.3923i	−0.195594	−	0.338779i	−0.947095	+	0.320953i	$0.895997\pi$
$942$	15.0000	+	8.66025i	0.488726	+	0.282166i
$943$	20.0000	−	34.6410i	0.651290	−	1.12807i
$944$	5.00000			0.162736
$945$		−	5.19615i		−	0.169031i
$946$	45.0000			1.46308
$947$	10.5000	−	18.1865i	0.341204	−	0.590983i	−0.643452	−	0.765486i	$-0.722499\pi$
$947$	10.5000	−	18.1865i	0.341204	−	0.590983i	0.984657	+	0.174503i	$0.0558319\pi$
$948$	−9.00000	−	5.19615i	−0.292306	−	0.168763i
$949$	−11.0000	−	19.0526i	−0.357075	−	0.618472i
$950$	2.50000	+	4.33013i	0.0811107	+	0.140488i
$951$	39.0000	−	22.5167i	1.26466	−	0.730153i
$952$	3.50000	−	6.06218i	0.113436	−	0.196476i
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$		0			0
$955$	20.0000			0.647185
$956$	−11.0000	+	19.0526i	−0.355765	+	0.616204i
$957$		0			0
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$	−8.50000	−	14.7224i	−0.274479	−	0.475412i
$960$			1.73205i			0.0559017i
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	−4.00000			−0.128965
$963$	16.5000	+	28.5788i	0.531705	+	0.920940i
$964$	−9.00000			−0.289870
$965$	−5.50000	+	9.52628i	−0.177051	+	0.306662i
$966$	12.0000	−	6.92820i	0.386094	−	0.222911i
$967$	13.0000	+	22.5167i	0.418052	+	0.724087i	0.995743	−	0.0921681i	$-0.0293797\pi$
$967$	13.0000	+	22.5167i	0.418052	+	0.724087i	−0.577692	+	0.816255i	$0.696046\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$	52.5000	+	30.3109i	1.68654	+	0.973726i
$970$	8.50000	−	14.7224i	0.272919	−	0.472709i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	23.0000			0.737346
$974$	−9.00000	+	15.5885i	−0.288379	+	0.499486i
$975$	−3.00000	−	1.73205i	−0.0960769	−	0.0554700i
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	−22.5000	−	38.9711i	−0.719839	−	1.24680i	−0.961063	−	0.276328i	$-0.910882\pi$
$977$	−22.5000	−	38.9711i	−0.719839	−	1.24680i	0.241225	−	0.970469i	$-0.422451\pi$
$978$	18.0000	−	10.3923i	0.575577	−	0.332309i
$979$	35.0000	−	60.6218i	1.11860	−	1.93748i
$980$	−1.00000			−0.0319438
$981$	15.0000	+	25.9808i	0.478913	+	0.829502i
$982$	3.00000			0.0957338
$983$	−26.0000	+	45.0333i	−0.829271	+	1.43634i	0.0693395	+	0.997593i	$0.477911\pi$
$983$	−26.0000	+	45.0333i	−0.829271	+	1.43634i	−0.898611	+	0.438747i	$0.855423\pi$
$984$		−	8.66025i		−	0.276079i
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$		−	13.8564i		−	0.441054i
$988$	5.00000	−	8.66025i	0.159071	−	0.275519i
$989$	−72.0000			−2.28947
$990$	−15.0000			−0.476731
$991$	52.0000			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$	−24.0000	+	13.8564i	−0.761617	+	0.439720i
$994$	2.00000	+	3.46410i	0.0634361	+	0.109875i
$995$	−11.0000	−	19.0526i	−0.348723	−	0.604007i
$996$		0			0
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$	41.0000			1.29783
$999$		−	10.3923i		−	0.328798i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.e.211.1	✓	2	9.4	even	3	inner
630.2.j.e.421.1	yes	2	1.1	even	1	trivial
1890.2.j.b.631.1		2	9.5	odd	6
1890.2.j.b.1261.1		2	3.2	odd	2
5670.2.a.f.1.1		1	9.7	even	3
5670.2.a.p.1.1		1	9.2	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} +(1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +3.00000 q^{18} +5.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(2.50000 + 4.33013i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(1.50000 + 0.866025i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(3.50000 - 6.06218i) q^{34} -1.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +3.46410i q^{39} +(-0.500000 - 0.866025i) q^{40} +(2.50000 + 4.33013i) q^{41} +1.73205i q^{42} +(4.50000 - 7.79423i) q^{43} +5.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} -8.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(10.5000 + 6.06218i) q^{51} +(1.00000 - 1.73205i) q^{52} +(4.50000 + 2.59808i) q^{54} -5.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(7.50000 + 4.33013i) q^{57} +(-2.50000 - 4.33013i) q^{59} +(1.50000 - 0.866025i) q^{60} +(4.00000 - 6.92820i) q^{61} -10.0000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +8.66025i q^{66} +(1.50000 + 2.59808i) q^{67} +(-3.50000 - 6.06218i) q^{68} -13.8564i q^{69} +(-0.500000 + 0.866025i) q^{70} +4.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(3.00000 + 1.73205i) q^{78} +(3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(1.50000 + 0.866025i) q^{84} +(3.50000 + 6.06218i) q^{85} +(-4.50000 - 7.79423i) q^{86} +(2.50000 - 4.33013i) q^{88} -14.0000 q^{89} +(1.50000 + 2.59808i) q^{90} -2.00000 q^{91} +(-4.00000 + 6.92820i) q^{92} -17.3205i q^{93} +(4.00000 + 6.92820i) q^{94} +(2.50000 + 4.33013i) q^{95} +1.73205i q^{96} +(8.50000 - 14.7224i) 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	\( 2 q + q^{2} + 3 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{10} - 5 q^{11} + 2 q^{13} + q^{14} - q^{16} + 14 q^{17} + 6 q^{18} + 10 q^{19} + q^{20} - 3 q^{21} + 5 q^{22} - 8 q^{23} - 3 q^{24} - q^{25} + 4 q^{26} + 2 q^{28} + 3 q^{30} - 10 q^{31} + q^{32} - 15 q^{33} + 7 q^{34} - 2 q^{35} + 3 q^{36} - 4 q^{37} + 5 q^{38} - q^{40} + 5 q^{41} + 9 q^{43} + 10 q^{44} - 3 q^{45} - 16 q^{46} - 8 q^{47} - 3 q^{48} - q^{49} + q^{50} + 21 q^{51} + 2 q^{52} + 9 q^{54} - 10 q^{55} + q^{56} + 15 q^{57} - 5 q^{59} + 3 q^{60} + 8 q^{61} - 20 q^{62} - 6 q^{63} + 2 q^{64} - 2 q^{65} + 3 q^{67} - 7 q^{68} - q^{70} + 8 q^{71} - 3 q^{72} - 22 q^{73} - 2 q^{74} - 3 q^{75} - 5 q^{76} - 5 q^{77} + 6 q^{78} + 6 q^{79} - 2 q^{80} - 9 q^{81} + 10 q^{82} + 3 q^{84} + 7 q^{85} - 9 q^{86} + 5 q^{88} - 28 q^{89} + 3 q^{90} - 4 q^{91} - 8 q^{92} + 8 q^{94} + 5 q^{95} + 17 q^{97} - 2 q^{98} - 30 q^{99}+O(q^{100}) \) 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 + 2 * q^13 + q^14 - q^16 + 14 * q^17 + 6 * q^18 + 10 * q^19 + q^20 - 3 * q^21 + 5 * q^22 - 8 * q^23 - 3 * q^24 - q^25 + 4 * q^26 + 2 * q^28 + 3 * q^30 - 10 * q^31 + q^32 - 15 * q^33 + 7 * q^34 - 2 * q^35 + 3 * q^36 - 4 * q^37 + 5 * q^38 - q^40 + 5 * q^41 + 9 * q^43 + 10 * q^44 - 3 * q^45 - 16 * q^46 - 8 * q^47 - 3 * q^48 - q^49 + q^50 + 21 * q^51 + 2 * q^52 + 9 * q^54 - 10 * q^55 + q^56 + 15 * q^57 - 5 * q^59 + 3 * q^60 + 8 * q^61 - 20 * q^62 - 6 * q^63 + 2 * q^64 - 2 * q^65 + 3 * q^67 - 7 * q^68 - q^70 + 8 * q^71 - 3 * q^72 - 22 * q^73 - 2 * q^74 - 3 * q^75 - 5 * q^76 - 5 * q^77 + 6 * q^78 + 6 * q^79 - 2 * q^80 - 9 * q^81 + 10 * q^82 + 3 * q^84 + 7 * q^85 - 9 * q^86 + 5 * q^88 - 28 * q^89 + 3 * q^90 - 4 * q^91 - 8 * q^92 + 8 * q^94 + 5 * q^95 + 17 * q^97 - 2 * q^98 - 30 * q^99

Introduction

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