LMFDB - Embedded newform 390.2.y.e.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(139,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("390.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.y (of order $6$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.139
Dual form			390.2.y.e.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.23205 + 1.86603i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(2.59808 + 2.50000i) q^{13} -5.00000 q^{14} +(-1.23205 - 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +1.00000i q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.133975 + 2.23205i) q^{20} +5.00000 q^{21} +(-2.59808 + 1.50000i) q^{22} +(0.500000 - 0.866025i) q^{24} +(3.00000 + 4.00000i) q^{25} +(1.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-4.33013 - 2.50000i) q^{28} +(1.00000 - 1.73205i) q^{29} +(-0.133975 - 2.23205i) q^{30} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +4.00000 q^{34} +(-11.1603 + 0.669873i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-7.79423 - 4.50000i) q^{37} -1.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(-1.00000 + 2.00000i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(4.33013 + 2.50000i) q^{42} +(10.3923 - 6.00000i) q^{43} -3.00000 q^{44} +(0.133975 + 2.23205i) q^{45} +7.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(9.00000 - 15.5885i) q^{49} +(0.598076 + 4.96410i) q^{50} -4.00000 q^{51} +(-0.866025 + 3.50000i) q^{52} -3.00000i q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.59808 + 3.69615i) q^{55} +(-2.50000 - 4.33013i) q^{56} +1.00000i q^{57} +(1.73205 - 1.00000i) q^{58} +(1.00000 - 2.00000i) q^{60} +(3.46410 + 2.00000i) q^{62} +(-4.33013 - 2.50000i) q^{63} -1.00000 q^{64} +(2.69615 + 7.59808i) q^{65} +3.00000 q^{66} +(5.19615 + 3.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-10.0000 - 5.00000i) q^{70} +(-6.00000 - 10.3923i) q^{71} +(-0.866025 + 0.500000i) q^{72} -16.0000i q^{73} +(-4.50000 - 7.79423i) q^{74} +(-0.598076 - 4.96410i) q^{75} +(0.500000 - 0.866025i) q^{76} -15.0000i q^{77} +(0.866025 - 3.50000i) q^{78} +14.0000 q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -10.0000i q^{83} +(2.50000 + 4.33013i) q^{84} +(8.92820 - 0.535898i) q^{85} +12.0000 q^{86} +(-1.73205 + 1.00000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-1.00000 + 2.00000i) q^{90} +(-17.5000 - 4.33013i) q^{91} +(-3.46410 - 2.00000i) q^{93} +(-3.50000 + 6.06218i) q^{94} +(-0.133975 - 2.23205i) q^{95} +1.00000 q^{96} +(8.66025 - 5.00000i) q^{97} +(15.5885 - 9.00000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{19} + 4 q^{20} + 20 q^{21} + 2 q^{24} + 12 q^{25} + 4 q^{26} + 4 q^{29} - 4 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} - 2 q^{36} - 4 q^{39} - 4 q^{40} - 20 q^{41} - 12 q^{44} + 4 q^{45} + 36 q^{49} - 8 q^{50} - 16 q^{51} + 2 q^{54} - 12 q^{55} - 10 q^{56} + 4 q^{60} - 4 q^{64} - 10 q^{65} + 12 q^{66} - 40 q^{70} - 24 q^{71} - 18 q^{74} + 8 q^{75} + 2 q^{76} + 56 q^{79} - 4 q^{80} - 2 q^{81} + 10 q^{84} + 8 q^{85} + 48 q^{86} - 2 q^{89} - 4 q^{90} - 70 q^{91} - 14 q^{94} - 4 q^{95} + 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^19 + 4 * q^20 + 20 * q^21 + 2 * q^24 + 12 * q^25 + 4 * q^26 + 4 * q^29 - 4 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 - 2 * q^36 - 4 * q^39 - 4 * q^40 - 20 * q^41 - 12 * q^44 + 4 * q^45 + 36 * q^49 - 8 * q^50 - 16 * q^51 + 2 * q^54 - 12 * q^55 - 10 * q^56 + 4 * q^60 - 4 * q^64 - 10 * q^65 + 12 * q^66 - 40 * q^70 - 24 * q^71 - 18 * q^74 + 8 * q^75 + 2 * q^76 + 56 * q^79 - 4 * q^80 - 2 * q^81 + 10 * q^84 + 8 * q^85 + 48 * q^86 - 2 * q^89 - 4 * q^90 - 70 * q^91 - 14 * q^94 - 4 * q^95 + 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−4.33013	+	2.50000i	−1.63663	+	0.944911i	−0.654654	+	0.755929i	$0.727186\pi$
$7$	−4.33013	+	2.50000i	−1.63663	+	0.944911i	−0.981981	+	0.188982i	$0.939481\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.23205	+	1.86603i	0.389609	+	0.590089i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		−	1.00000i		−	0.288675i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−5.00000			−1.33631
$15$	−1.23205	−	1.86603i	−0.318114	−	0.481806i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$			1.00000i			0.235702i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0.133975	+	2.23205i	0.0299576	+	0.499102i
$21$	5.00000			1.09109
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$		−	1.00000i		−	0.192450i
$28$	−4.33013	−	2.50000i	−0.818317	−	0.472456i
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$	−0.133975	−	2.23205i	−0.0244603	−	0.407515i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.59808	−	1.50000i	0.452267	−	0.261116i
$34$	4.00000			0.685994
$35$	−11.1603	+	0.669873i	−1.88643	+	0.113229i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−7.79423	−	4.50000i	−1.28136	−	0.739795i	−0.304266	−	0.952587i	$-0.598411\pi$
$37$	−7.79423	−	4.50000i	−1.28136	−	0.739795i	−0.977098	+	0.212792i	$0.931744\pi$
$38$		−	1.00000i		−	0.162221i
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	4.33013	+	2.50000i	0.668153	+	0.385758i
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.590669	−	0.806914i	$-0.298864\pi$
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.994142	−	0.108078i	$-0.0344695\pi$
$44$	−3.00000			−0.452267
$45$	0.133975	+	2.23205i	0.0199718	+	0.332734i
$46$		0			0
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	9.00000	−	15.5885i	1.28571	−	2.22692i
$50$	0.598076	+	4.96410i	0.0845807	+	0.702030i
$51$	−4.00000			−0.560112
$52$	−0.866025	+	3.50000i	−0.120096	+	0.485363i
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−5.59808	+	3.69615i	−0.754844	+	0.498389i
$56$	−2.50000	−	4.33013i	−0.334077	−	0.578638i
$57$			1.00000i			0.132453i
$58$	1.73205	−	1.00000i	0.227429	−	0.131306i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$	−4.33013	−	2.50000i	−0.545545	−	0.314970i
$64$	−1.00000			−0.125000
$65$	2.69615	+	7.59808i	0.334417	+	0.942425i
$66$	3.00000			0.369274
$67$	5.19615	+	3.00000i	0.634811	+	0.366508i	0.782613	−	0.622509i	$-0.213886\pi$
$67$	5.19615	+	3.00000i	0.634811	+	0.366508i	−0.147802	+	0.989017i	$0.547220\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$		0			0
$70$	−10.0000	−	5.00000i	−1.19523	−	0.597614i
$71$	−6.00000	−	10.3923i	−0.712069	−	1.23334i	−0.964079	−	0.265615i	$-0.914425\pi$
$71$	−6.00000	−	10.3923i	−0.712069	−	1.23334i	0.252010	−	0.967725i	$-0.418908\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$		−	16.0000i		−	1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$		−	16.0000i		−	1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	−4.50000	−	7.79423i	−0.523114	−	0.906061i
$75$	−0.598076	−	4.96410i	−0.0690599	−	0.573205i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		−	15.0000i		−	1.70941i
$78$	0.866025	−	3.50000i	0.0980581	−	0.396297i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.86603	+	1.23205i	−0.208628	+	0.137747i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−8.66025	+	5.00000i	−0.956365	+	0.552158i
$83$		−	10.0000i		−	1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$		−	10.0000i		−	1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$	2.50000	+	4.33013i	0.272772	+	0.472456i
$85$	8.92820	−	0.535898i	0.968400	−	0.0581263i
$86$	12.0000			1.29399
$87$	−1.73205	+	1.00000i	−0.185695	+	0.107211i
$88$	−2.59808	−	1.50000i	−0.276956	−	0.159901i
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$	−1.00000	+	2.00000i	−0.105409	+	0.210819i
$91$	−17.5000	−	4.33013i	−1.83450	−	0.453921i
$92$		0			0
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−0.133975	−	2.23205i	−0.0137455	−	0.229004i
$96$	1.00000			0.102062
$97$	8.66025	−	5.00000i	0.879316	−	0.507673i	0.00888289	−	0.999961i	$-0.497172\pi$
$97$	8.66025	−	5.00000i	0.879316	−	0.507673i	0.870433	+	0.492287i	$0.163839\pi$
$98$	15.5885	−	9.00000i	1.57467	−	0.909137i
$99$	−3.00000			−0.301511
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$			7.00000i			0.689730i	0.938652	+	0.344865i	$0.112075\pi$
$103$			7.00000i			0.689730i	−0.938652	+	0.344865i	$0.887925\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$	10.0000	+	5.00000i	0.975900	+	0.487950i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−6.69615	+	0.401924i	−0.638453	+	0.0383219i
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$		−	5.00000i		−	0.472456i
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	−0.654008	−	0.756487i	$-0.726914\pi$
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	0.328133	+	0.944632i	$0.393581\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$		0			0
$116$	2.00000			0.185695
$117$	−0.866025	+	3.50000i	−0.0800641	+	0.323575i
$118$		0			0
$119$	−10.0000	+	17.3205i	−0.916698	+	1.58777i
$120$	1.86603	−	1.23205i	0.170344	−	0.112470i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	8.66025	−	5.00000i	0.780869	−	0.450835i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−2.50000	−	4.33013i	−0.222718	−	0.385758i
$127$	14.7224	+	8.50000i	1.30640	+	0.754253i	0.981494	−	0.191492i	$-0.0613325\pi$
$127$	14.7224	+	8.50000i	1.30640	+	0.754253i	0.324910	+	0.945745i	$0.394666\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−12.0000			−1.05654
$130$	−1.46410	+	7.92820i	−0.128410	+	0.695349i
$131$	7.00000			0.611593			0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000			0.611593			0.305796	+	0.952097i	$0.401077\pi$
$132$	2.59808	+	1.50000i	0.226134	+	0.130558i
$133$	4.33013	+	2.50000i	0.375470	+	0.216777i
$134$	3.00000	+	5.19615i	0.259161	+	0.448879i
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	−0.822031	−	0.569442i	$-0.807159\pi$
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	0.0821359	+	0.996621i	$0.473826\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	−6.16025	−	9.33013i	−0.520636	−	0.788540i
$141$	3.50000	−	6.06218i	0.294753	−	0.510527i
$142$		−	12.0000i		−	1.00702i
$143$	−10.3923	+	3.00000i	−0.869048	+	0.250873i
$144$	−1.00000			−0.0833333
$145$	3.73205	−	2.46410i	0.309930	−	0.204633i
$146$	8.00000	−	13.8564i	0.662085	−	1.14676i
$147$	−15.5885	+	9.00000i	−1.28571	+	0.742307i
$148$		−	9.00000i		−	0.739795i
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	0.981797	+	0.189933i	$0.0608272\pi$
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	−0.326411	+	0.945228i	$0.605840\pi$
$150$	1.96410	−	4.59808i	0.160368	−	0.375431i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	0.866025	−	0.500000i	0.0702439	−	0.0405554i
$153$	3.46410	+	2.00000i	0.280056	+	0.161690i
$154$	7.50000	−	12.9904i	0.604367	−	1.04679i
$155$	8.00000	+	4.00000i	0.642575	+	0.321288i
$156$	2.50000	−	2.59808i	0.200160	−	0.208013i
$157$			3.00000i			0.239426i	0.992809	+	0.119713i	$0.0381975\pi$
$157$			3.00000i			0.239426i	−0.992809	+	0.119713i	$0.961803\pi$
$158$	12.1244	+	7.00000i	0.964562	+	0.556890i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$	−2.23205	+	0.133975i	−0.176459	+	0.0105916i
$161$		0			0
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	−0.203497	−	0.979076i	$-0.565231\pi$
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	0.746156	+	0.665771i	$0.231897\pi$
$164$	−10.0000			−0.780869
$165$	6.69615	−	0.401924i	0.521295	−	0.0312897i
$166$	5.00000	−	8.66025i	0.388075	−	0.672166i
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.297681	−	0.954665i	$-0.596213\pi$
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.975605	+	0.219533i	$0.929547\pi$
$168$			5.00000i			0.385758i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	8.00000	+	4.00000i	0.613572	+	0.306786i
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	10.3923	+	6.00000i	0.792406	+	0.457496i
$173$	−6.06218	+	3.50000i	−0.460899	+	0.266100i	−0.712422	−	0.701751i	$-0.752402\pi$
$173$	−6.06218	+	3.50000i	−0.460899	+	0.266100i	0.251523	+	0.967851i	$0.419068\pi$
$174$	−2.00000			−0.151620
$175$	−22.9904	−	9.82051i	−1.73791	−	0.742361i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−0.866025	+	0.500000i	−0.0649113	+	0.0374766i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	−1.86603	+	1.23205i	−0.139085	+	0.0918316i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	−12.9904	−	12.5000i	−0.962911	−	0.926562i
$183$		0			0
$184$		0			0
$185$	−11.0885	−	16.7942i	−0.815240	−	1.23474i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$			12.0000i			0.877527i
$188$	−6.06218	+	3.50000i	−0.442130	+	0.255264i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$	1.00000	−	2.00000i	0.0725476	−	0.145095i
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−3.46410	−	2.00000i	−0.249351	−	0.143963i	0.370116	−	0.928986i	$-0.379318\pi$
$193$	−3.46410	−	2.00000i	−0.249351	−	0.143963i	−0.619467	+	0.785022i	$0.712651\pi$
$194$	10.0000			0.717958
$195$	1.46410	−	7.92820i	0.104846	−	0.567750i
$196$	18.0000			1.28571
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.885394	−	0.464841i	$-0.153889\pi$
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.0401324	+	0.999194i	$0.487222\pi$
$198$	−2.59808	−	1.50000i	−0.184637	−	0.106600i
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	−3.00000	−	5.19615i	−0.211604	−	0.366508i
$202$	−8.66025	+	5.00000i	−0.609333	+	0.351799i
$203$			10.0000i			0.701862i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	−18.6603	+	12.3205i	−1.30329	+	0.860502i
$206$	−3.50000	+	6.06218i	−0.243857	+	0.422372i
$207$		0			0
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	3.00000			0.207514
$210$	6.16025	+	9.33013i	0.425098	+	0.643840i
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	2.59808	−	1.50000i	0.178437	−	0.103020i
$213$			12.0000i			0.822226i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	26.7846	−	1.60770i	1.82670	−	0.109644i
$216$	1.00000			0.0680414
$217$	−17.3205	+	10.0000i	−1.17579	+	0.678844i
$218$	−8.66025	−	5.00000i	−0.586546	−	0.338643i
$219$	−8.00000	+	13.8564i	−0.540590	+	0.936329i
$220$	−6.00000	−	3.00000i	−0.404520	−	0.202260i
$221$	14.0000	+	3.46410i	0.941742	+	0.233021i
$222$			9.00000i			0.604040i
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	0.528716	−	0.848799i	$-0.322674\pi$
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	−0.470723	+	0.882281i	$0.656007\pi$
$224$	2.50000	−	4.33013i	0.167038	−	0.289319i
$225$	−1.96410	+	4.59808i	−0.130940	+	0.306538i
$226$	−4.00000			−0.266076
$227$	−1.73205	+	1.00000i	−0.114960	+	0.0663723i	−0.556378	−	0.830930i	$-0.687809\pi$
$227$	−1.73205	+	1.00000i	−0.114960	+	0.0663723i	0.441417	+	0.897302i	$0.354476\pi$
$228$	−0.866025	+	0.500000i	−0.0573539	+	0.0331133i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−7.50000	+	12.9904i	−0.493464	+	0.854704i
$232$	1.73205	+	1.00000i	0.113715	+	0.0656532i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$	−7.00000	+	14.0000i	−0.456630	+	0.913259i
$236$		0			0
$237$	−12.1244	−	7.00000i	−0.787562	−	0.454699i
$238$	−17.3205	+	10.0000i	−1.12272	+	0.648204i
$239$	−14.0000			−0.905585			−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000			−0.905585			−0.452792	+	0.891616i	$0.649572\pi$
$240$	2.23205	−	0.133975i	0.144078	−	0.00864802i
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	0.813662	−	0.581339i	$-0.197471\pi$
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	−0.910285	+	0.413982i	$0.864138\pi$
$242$			2.00000i			0.128565i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	33.5885	−	22.1769i	2.14589	−	1.41683i
$246$	10.0000			0.637577
$247$	0.866025	−	3.50000i	0.0551039	−	0.222700i
$248$			4.00000i			0.254000i
$249$	−5.00000	+	8.66025i	−0.316862	+	0.548821i
$250$	−3.76795	+	10.5263i	−0.238306	+	0.665740i
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	0.584643	−	0.811290i	$-0.301234\pi$
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	−0.994920	+	0.100671i	$0.967901\pi$
$252$		−	5.00000i		−	0.314970i
$253$		0			0
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$	−8.00000	−	4.00000i	−0.500979	−	0.250490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.66025	+	5.00000i	0.540212	+	0.311891i	0.745165	−	0.666880i	$-0.232371\pi$
$257$	8.66025	+	5.00000i	0.540212	+	0.311891i	−0.204953	+	0.978772i	$0.565704\pi$
$258$	−10.3923	−	6.00000i	−0.646997	−	0.373544i
$259$	45.0000			2.79616
$260$	−5.23205	+	6.13397i	−0.324478	+	0.380413i
$261$	2.00000			0.123797
$262$	6.06218	+	3.50000i	0.374523	+	0.216231i
$263$	6.06218	+	3.50000i	0.373810	+	0.215819i	0.675122	−	0.737706i	$-0.264091\pi$
$263$	6.06218	+	3.50000i	0.373810	+	0.215819i	−0.301312	+	0.953526i	$0.597424\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$	3.00000	−	6.00000i	0.184289	−	0.368577i
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$	0.866025	−	0.500000i	0.0529999	−	0.0305995i
$268$			6.00000i			0.366508i
$269$	−4.00000	−	6.92820i	−0.243884	−	0.422420i	0.717933	−	0.696112i	$-0.245088\pi$
$269$	−4.00000	−	6.92820i	−0.243884	−	0.422420i	−0.961817	+	0.273692i	$0.911755\pi$
$270$	1.86603	−	1.23205i	0.113563	−	0.0749802i
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$			4.00000i			0.242536i
$273$	12.9904	+	12.5000i	0.786214	+	0.756534i
$274$	−10.0000			−0.604122
$275$	−14.8923	+	1.79423i	−0.898040	+	0.108196i
$276$		0			0
$277$	14.7224	−	8.50000i	0.884585	−	0.510716i	0.0124177	−	0.999923i	$-0.496047\pi$
$277$	14.7224	−	8.50000i	0.884585	−	0.510716i	0.872167	+	0.489207i	$0.162714\pi$
$278$		−	5.00000i		−	0.299880i
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$	−0.669873	−	11.1603i	−0.0400326	−	0.666953i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	6.06218	−	3.50000i	0.360997	−	0.208422i
$283$	−5.19615	−	3.00000i	−0.308879	−	0.178331i	0.337546	−	0.941309i	$-0.390403\pi$
$283$	−5.19615	−	3.00000i	−0.308879	−	0.178331i	−0.646425	+	0.762978i	$0.723737\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$	−1.00000	+	2.00000i	−0.0592349	+	0.118470i
$286$	−10.5000	−	2.59808i	−0.620878	−	0.153627i
$287$		−	50.0000i		−	2.95141i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	4.46410	−	0.267949i	0.262141	−	0.0157345i
$291$	−10.0000			−0.586210
$292$	13.8564	−	8.00000i	0.810885	−	0.468165i
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	−0.422186	−	0.906509i	$-0.638737\pi$
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	0.573967	+	0.818878i	$0.305404\pi$
$294$	−18.0000			−1.04978
$295$		0			0
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	2.59808	+	1.50000i	0.150756	+	0.0870388i
$298$			16.0000i			0.926855i
$299$		0			0
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	−30.0000	+	51.9615i	−1.72917	+	2.99501i
$302$	−6.92820	−	4.00000i	−0.398673	−	0.230174i
$303$	8.66025	−	5.00000i	0.497519	−	0.287242i
$304$	1.00000			0.0573539
$305$		0			0
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$	12.9904	−	7.50000i	0.740196	−	0.427352i
$309$	3.50000	−	6.06218i	0.199108	−	0.344865i
$310$	4.92820	+	7.46410i	0.279903	+	0.423932i
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$	3.46410	−	1.00000i	0.196116	−	0.0566139i
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$	−6.16025	−	9.33013i	−0.347091	−	0.525693i
$316$	7.00000	+	12.1244i	0.393781	+	0.682048i
$317$			7.00000i			0.393159i	0.980488	+	0.196580i	$0.0629834\pi$
$317$			7.00000i			0.393159i	−0.980488	+	0.196580i	$0.937017\pi$
$318$	−2.59808	+	1.50000i	−0.145693	+	0.0841158i
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$		0			0
$323$	−3.46410	−	2.00000i	−0.192748	−	0.111283i
$324$	−1.00000			−0.0555556
$325$	−2.20577	+	17.8923i	−0.122354	+	0.992487i
$326$	8.00000			0.443079
$327$	8.66025	+	5.00000i	0.478913	+	0.276501i
$328$	−8.66025	−	5.00000i	−0.478183	−	0.276079i
$329$	−17.5000	−	30.3109i	−0.964806	−	1.67109i
$330$	6.00000	+	3.00000i	0.330289	+	0.165145i
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	8.66025	−	5.00000i	0.475293	−	0.274411i
$333$		−	9.00000i		−	0.493197i
$334$	−9.50000	−	16.4545i	−0.519817	−	0.900349i
$335$	7.39230	+	11.1962i	0.403885	+	0.611711i
$336$	−2.50000	+	4.33013i	−0.136386	+	0.236228i
$337$		−	10.0000i		−	0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$	−6.06218	+	11.5000i	−0.329739	+	0.625518i
$339$	4.00000			0.217250
$340$	4.92820	+	7.46410i	0.267269	+	0.404798i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$	0.866025	−	0.500000i	0.0468293	−	0.0270369i
$343$			55.0000i			2.96972i
$344$	6.00000	+	10.3923i	0.323498	+	0.560316i
$345$		0			0
$346$	−7.00000			−0.376322
$347$	−19.0526	+	11.0000i	−1.02279	+	0.590511i	−0.914912	−	0.403653i	$-0.867740\pi$
$347$	−19.0526	+	11.0000i	−1.02279	+	0.590511i	−0.107883	+	0.994164i	$0.534407\pi$
$348$	−1.73205	−	1.00000i	−0.0928477	−	0.0536056i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	−15.0000	−	20.0000i	−0.801784	−	1.06904i
$351$	2.50000	−	2.59808i	0.133440	−	0.138675i
$352$		−	3.00000i		−	0.159901i
$353$	−29.4449	−	17.0000i	−1.56719	−	0.904819i	−0.996495	−	0.0836583i	$-0.973340\pi$
$353$	−29.4449	−	17.0000i	−1.56719	−	0.904819i	−0.570697	−	0.821160i	$-0.693327\pi$
$354$		0			0
$355$	−1.60770	−	26.7846i	−0.0853276	−	1.42158i
$356$	−1.00000			−0.0529999
$357$	17.3205	−	10.0000i	0.916698	−	0.529256i
$358$	10.3923	−	6.00000i	0.549250	−	0.317110i
$359$	20.0000			1.05556			0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$	−2.23205	+	0.133975i	−0.117639	+	0.00706108i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−5.19615	−	3.00000i	−0.273104	−	0.157676i
$363$		−	2.00000i		−	0.104973i
$364$	−5.00000	−	17.3205i	−0.262071	−	0.907841i
$365$	16.0000	−	32.0000i	0.837478	−	1.67496i
$366$		0			0
$367$	−20.7846	−	12.0000i	−1.08495	−	0.626395i	−0.152721	−	0.988269i	$-0.548804\pi$
$367$	−20.7846	−	12.0000i	−1.08495	−	0.626395i	−0.932227	+	0.361874i	$0.882137\pi$
$368$		0			0
$369$	−10.0000			−0.520579
$370$	−1.20577	−	20.0885i	−0.0626851	−	1.04435i
$371$	7.50000	+	12.9904i	0.389381	+	0.674427i
$372$		−	4.00000i		−	0.207390i
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	−0.359408	−	0.933181i	$-0.617021\pi$
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	0.628454	+	0.777847i	$0.283688\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$	3.76795	−	10.5263i	0.194576	−	0.543575i
$376$	−7.00000			−0.360997
$377$	6.92820	−	2.00000i	0.356821	−	0.103005i
$378$			5.00000i			0.257172i
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	−0.511922	−	0.859032i	$-0.671066\pi$
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	0.999904	+	0.0138218i	$0.00439975\pi$
$380$	1.86603	−	1.23205i	0.0957251	−	0.0632029i
$381$	−8.50000	−	14.7224i	−0.435468	−	0.754253i
$382$		−	12.0000i		−	0.613973i
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	−0.810331	−	0.585973i	$-0.800713\pi$
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	0.102302	+	0.994753i	$0.467379\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	15.0000	−	30.0000i	0.764471	−	1.52894i
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	10.3923	+	6.00000i	0.528271	+	0.304997i
$388$	8.66025	+	5.00000i	0.439658	+	0.253837i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$	5.23205	−	6.13397i	0.264935	−	0.310606i
$391$		0			0
$392$	15.5885	+	9.00000i	0.787336	+	0.454569i
$393$	−6.06218	−	3.50000i	−0.305796	−	0.176552i
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$	28.0000	+	14.0000i	1.40883	+	0.704416i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−19.9186	+	11.5000i	−0.999685	+	0.577168i	−0.908155	−	0.418634i	$-0.862509\pi$
$397$	−19.9186	+	11.5000i	−0.999685	+	0.577168i	−0.0915300	+	0.995802i	$0.529176\pi$
$398$		−	14.0000i		−	0.701757i
$399$	−2.50000	−	4.33013i	−0.125157	−	0.216777i
$400$	−4.96410	+	0.598076i	−0.248205	+	0.0299038i
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	−0.475253	−	0.879849i	$-0.657644\pi$
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	0.999598	−	0.0283431i	$-0.00902310\pi$
$402$		−	6.00000i		−	0.299253i
$403$	10.3923	+	10.0000i	0.517678	+	0.498135i
$404$	−10.0000			−0.497519
$405$	−1.86603	+	1.23205i	−0.0927235	+	0.0612211i
$406$	−5.00000	+	8.66025i	−0.248146	+	0.429801i
$407$	23.3827	−	13.5000i	1.15904	−	0.669170i
$408$		−	4.00000i		−	0.198030i
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$	−22.3205	+	1.33975i	−1.10233	+	0.0661653i
$411$	10.0000			0.493264
$412$	−6.06218	+	3.50000i	−0.298662	+	0.172433i
$413$		0			0
$414$		0			0
$415$	10.0000	−	20.0000i	0.490881	−	0.981761i
$416$	−3.50000	−	0.866025i	−0.171602	−	0.0424604i
$417$			5.00000i			0.244851i
$418$	2.59808	+	1.50000i	0.127076	+	0.0733674i
$419$	−14.0000	+	24.2487i	−0.683945	+	1.18463i	0.289822	+	0.957080i	$0.406404\pi$
$419$	−14.0000	+	24.2487i	−0.683945	+	1.18463i	−0.973767	+	0.227547i	$0.926930\pi$
$420$	0.669873	+	11.1603i	0.0326865	+	0.544565i
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	−11.2583	+	6.50000i	−0.548047	+	0.316415i
$423$	−6.06218	+	3.50000i	−0.294753	+	0.170176i
$424$	3.00000			0.145693
$425$	18.3923	+	7.85641i	0.892158	+	0.381092i
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$		0			0
$428$			12.0000i			0.580042i
$429$	10.5000	+	2.59808i	0.506945	+	0.125436i
$430$	24.0000	+	12.0000i	1.15738	+	0.578691i
$431$	20.0000	−	34.6410i	0.963366	−	1.66860i	0.249424	−	0.968394i	$-0.419759\pi$
$431$	20.0000	−	34.6410i	0.963366	−	1.66860i	0.713942	−	0.700205i	$-0.246908\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−6.92820	+	4.00000i	−0.332948	+	0.192228i	−0.657149	−	0.753760i	$-0.728238\pi$
$433$	−6.92820	+	4.00000i	−0.332948	+	0.192228i	0.324201	+	0.945988i	$0.394905\pi$
$434$	−20.0000			−0.960031
$435$	−4.46410	+	0.267949i	−0.214037	+	0.0128472i
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$		0			0
$438$	−13.8564	+	8.00000i	−0.662085	+	0.382255i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	−3.69615	−	5.59808i	−0.176207	−	0.266878i
$441$	18.0000			0.857143
$442$	10.3923	+	10.0000i	0.494312	+	0.475651i
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$	−4.50000	+	7.79423i	−0.213561	+	0.369898i
$445$	−1.86603	+	1.23205i	−0.0884581	+	0.0584048i
$446$	0.500000	+	0.866025i	0.0236757	+	0.0410075i
$447$		−	16.0000i		−	0.756774i
$448$	4.33013	−	2.50000i	0.204579	−	0.118114i
$449$	−6.50000	−	11.2583i	−0.306754	−	0.531313i	0.670896	−	0.741551i	$-0.265910\pi$
$449$	−6.50000	−	11.2583i	−0.306754	−	0.531313i	−0.977650	+	0.210238i	$0.932576\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−15.0000	−	25.9808i	−0.706322	−	1.22339i
$452$	−3.46410	−	2.00000i	−0.162938	−	0.0940721i
$453$	6.92820	+	4.00000i	0.325515	+	0.187936i
$454$	−2.00000			−0.0938647
$455$	−30.6699	−	26.1603i	−1.43783	−	1.22641i
$456$	−1.00000			−0.0468293
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.189292	−	0.981921i	$-0.560619\pi$
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.945015	+	0.327028i	$0.893953\pi$
$458$	19.0526	+	11.0000i	0.890268	+	0.513996i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	11.0000	+	19.0526i	0.512321	+	0.887366i	0.999898	+	0.0142861i	$0.00454755\pi$
$461$	11.0000	+	19.0526i	0.512321	+	0.887366i	−0.487577	+	0.873080i	$0.662119\pi$
$462$	−12.9904	+	7.50000i	−0.604367	+	0.348932i
$463$		−	8.00000i		−	0.371792i	−0.982569	−	0.185896i	$-0.940481\pi$
$463$		−	8.00000i		−	0.371792i	0.982569	−	0.185896i	$-0.0595187\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$	−4.92820	−	7.46410i	−0.228540	−	0.346139i
$466$		0			0
$467$			34.0000i			1.57333i	0.617379	+	0.786666i	$0.288195\pi$
$467$			34.0000i			1.57333i	−0.617379	+	0.786666i	$0.711805\pi$
$468$	−3.46410	+	1.00000i	−0.160128	+	0.0462250i
$469$	−30.0000			−1.38527
$470$	−13.0622	+	8.62436i	−0.602513	+	0.397812i
$471$	1.50000	−	2.59808i	0.0691164	−	0.119713i
$472$		0			0
$473$			36.0000i			1.65528i
$474$	−7.00000	−	12.1244i	−0.321521	−	0.556890i
$475$	1.96410	−	4.59808i	0.0901192	−	0.210974i
$476$	−20.0000			−0.916698
$477$	2.59808	−	1.50000i	0.118958	−	0.0686803i
$478$	−12.1244	−	7.00000i	−0.554555	−	0.320173i
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	−0.728895	−	0.684626i	$-0.759966\pi$
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	0.957351	+	0.288929i	$0.0932990\pi$
$480$	2.00000	+	1.00000i	0.0912871	+	0.0456435i
$481$	−9.00000	−	31.1769i	−0.410365	−	1.42154i
$482$		−	3.00000i		−	0.136646i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	22.3205	−	1.33975i	1.01352	−	0.0608347i
$486$	1.00000			0.0453609
$487$	0.866025	−	0.500000i	0.0392434	−	0.0226572i	−0.480250	−	0.877132i	$-0.659454\pi$
$487$	0.866025	−	0.500000i	0.0392434	−	0.0226572i	0.519493	+	0.854475i	$0.326121\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$	40.1769	−	2.41154i	1.81501	−	0.108942i
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$	8.66025	+	5.00000i	0.390434	+	0.225417i
$493$		−	8.00000i		−	0.360302i
$494$	2.50000	−	2.59808i	0.112480	−	0.116893i
$495$	−6.00000	−	3.00000i	−0.269680	−	0.134840i
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	51.9615	+	30.0000i	2.33079	+	1.34568i
$498$	−8.66025	+	5.00000i	−0.388075	+	0.224055i
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	−8.52628	+	7.23205i	−0.381307	+	0.323427i
$501$	9.50000	+	16.4545i	0.424429	+	0.735132i
$502$		−	13.0000i		−	0.580218i
$503$	−9.52628	+	5.50000i	−0.424756	+	0.245233i	−0.697110	−	0.716964i	$-0.745531\pi$
$503$	−9.52628	+	5.50000i	−0.424756	+	0.245233i	0.272354	+	0.962197i	$0.412198\pi$
$504$	2.50000	−	4.33013i	0.111359	−	0.192879i
$505$	−18.6603	+	12.3205i	−0.830370	+	0.548255i
$506$		0			0
$507$	6.06218	−	11.5000i	0.269231	−	0.510733i
$508$			17.0000i			0.754253i
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	−0.887336	−	0.461123i	$-0.847447\pi$
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	0.843012	+	0.537895i	$0.180780\pi$
$510$	−4.92820	−	7.46410i	−0.218225	−	0.330516i
$511$	40.0000	+	69.2820i	1.76950	+	3.06486i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.866025	+	0.500000i	−0.0382360	+	0.0220755i
$514$	5.00000	+	8.66025i	0.220541	+	0.381987i
$515$	−7.00000	+	14.0000i	−0.308457	+	0.616914i
$516$	−6.00000	−	10.3923i	−0.264135	−	0.457496i
$517$	−18.1865	−	10.5000i	−0.799843	−	0.461789i
$518$	38.9711	+	22.5000i	1.71229	+	0.988593i
$519$	7.00000			0.307266
$520$	−7.59808	+	2.69615i	−0.333198	+	0.118234i
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$	1.73205	+	1.00000i	0.0758098	+	0.0437688i
$523$	−13.8564	−	8.00000i	−0.605898	−	0.349816i	0.165460	−	0.986216i	$-0.447089\pi$
$523$	−13.8564	−	8.00000i	−0.605898	−	0.349816i	−0.771358	+	0.636401i	$0.780422\pi$
$524$	3.50000	+	6.06218i	0.152898	+	0.264827i
$525$	15.0000	+	20.0000i	0.654654	+	0.872872i
$526$	3.50000	+	6.06218i	0.152607	+	0.264324i
$527$	13.8564	−	8.00000i	0.603595	−	0.348485i
$528$			3.00000i			0.130558i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$	5.59808	−	3.69615i	0.243165	−	0.160551i
$531$		0			0
$532$			5.00000i			0.216777i
$533$	−34.6410	+	10.0000i	−1.50047	+	0.433148i
$534$	1.00000			0.0432742
$535$	14.7846	+	22.3923i	0.639194	+	0.968104i
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$		−	8.00000i		−	0.344904i
$539$	27.0000	+	46.7654i	1.16297	+	2.01433i
$540$	2.23205	−	0.133975i	0.0960522	−	0.00576535i
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	1.73205	−	1.00000i	0.0743980	−	0.0429537i
$543$	5.19615	+	3.00000i	0.222988	+	0.128742i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−20.0000	−	10.0000i	−0.856706	−	0.428353i
$546$	5.00000	+	17.3205i	0.213980	+	0.741249i
$547$		−	6.00000i		−	0.256541i	−0.991739	−	0.128271i	$-0.959057\pi$
$547$		−	6.00000i		−	0.256541i	0.991739	−	0.128271i	$-0.0409426\pi$
$548$	−8.66025	−	5.00000i	−0.369948	−	0.213589i
$549$		0			0
$550$	−13.7942	−	5.89230i	−0.588188	−	0.251249i
$551$	−2.00000			−0.0852029
$552$		0			0
$553$	−60.6218	+	35.0000i	−2.57790	+	1.48835i
$554$	17.0000			0.722261
$555$	1.20577	+	20.0885i	0.0511821	+	0.852708i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.997204	−	0.0747252i	$-0.0238080\pi$
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.433888	+	0.900967i	$0.357141\pi$
$558$			4.00000i			0.169334i
$559$	42.0000	+	10.3923i	1.77641	+	0.439548i
$560$	5.00000	−	10.0000i	0.211289	−	0.422577i
$561$	6.00000	−	10.3923i	0.253320	−	0.438763i
$562$	25.9808	+	15.0000i	1.09593	+	0.632737i
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	−0.791123	−	0.611656i	$-0.790503\pi$
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	0.134148	+	0.990961i	$0.457170\pi$
$564$	7.00000			0.294753
$565$	−8.92820	+	0.535898i	−0.375612	+	0.0225454i
$566$	−3.00000	−	5.19615i	−0.126099	−	0.218411i
$567$		−	5.00000i		−	0.209980i
$568$	10.3923	−	6.00000i	0.436051	−	0.251754i
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$	−1.86603	+	1.23205i	−0.0781592	+	0.0516049i
$571$	15.0000			0.627730			0.313865	−	0.949468i	$-0.398376\pi$
$571$	15.0000			0.627730			0.313865	+	0.949468i	$0.398376\pi$
$572$	−7.79423	−	7.50000i	−0.325893	−	0.313591i
$573$			12.0000i			0.501307i
$574$	25.0000	−	43.3013i	1.04348	−	1.80736i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$	4.00000	+	2.00000i	0.166091	+	0.0830455i
$581$	25.0000	+	43.3013i	1.03717	+	1.79644i
$582$	−8.66025	−	5.00000i	−0.358979	−	0.207257i
$583$	7.79423	+	4.50000i	0.322804	+	0.186371i
$584$	16.0000			0.662085
$585$	−5.23205	+	6.13397i	−0.216319	+	0.253609i
$586$	3.00000			0.123929
$587$	−29.4449	−	17.0000i	−1.21532	−	0.701665i	−0.251406	−	0.967882i	$-0.580893\pi$
$587$	−29.4449	−	17.0000i	−1.21532	−	0.701665i	−0.963913	+	0.266217i	$0.914226\pi$
$588$	−15.5885	−	9.00000i	−0.642857	−	0.371154i
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$	−7.50000	−	12.9904i	−0.308509	−	0.534353i
$592$	7.79423	−	4.50000i	0.320341	−	0.184949i
$593$			20.0000i			0.821302i	0.911793	+	0.410651i	$0.134698\pi$
$593$			20.0000i			0.821302i	−0.911793	+	0.410651i	$0.865302\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$	−37.3205	+	24.6410i	−1.52999	+	1.01018i
$596$	−8.00000	+	13.8564i	−0.327693	+	0.567581i
$597$			14.0000i			0.572982i
$598$		0			0
$599$	−10.0000			−0.408589			−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000			−0.408589			−0.204294	+	0.978909i	$0.565490\pi$
$600$	4.96410	−	0.598076i	0.202659	−	0.0244164i
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$	−51.9615	+	30.0000i	−2.11779	+	1.22271i
$603$			6.00000i			0.244339i
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	0.267949	+	4.46410i	0.0108937	+	0.181492i
$606$	10.0000			0.406222
$607$	2.59808	−	1.50000i	0.105453	−	0.0608831i	−0.446346	−	0.894860i	$-0.647275\pi$
$607$	2.59808	−	1.50000i	0.105453	−	0.0608831i	0.551799	+	0.833977i	$0.313942\pi$
$608$	0.866025	+	0.500000i	0.0351220	+	0.0202777i
$609$	5.00000	−	8.66025i	0.202610	−	0.350931i
$610$		0			0
$611$	−17.5000	+	18.1865i	−0.707974	+	0.735748i
$612$			4.00000i			0.161690i
$613$	25.1147	+	14.5000i	1.01437	+	0.585649i	0.912470	−	0.409145i	$-0.134173\pi$
$613$	25.1147	+	14.5000i	1.01437	+	0.585649i	0.101905	+	0.994794i	$0.467506\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$	22.3205	−	1.33975i	0.900050	−	0.0540238i
$616$	15.0000			0.604367
$617$	−41.5692	+	24.0000i	−1.67351	+	0.966204i	−0.707867	+	0.706346i	$0.750342\pi$
$617$	−41.5692	+	24.0000i	−1.67351	+	0.966204i	−0.965647	+	0.259858i	$0.916324\pi$
$618$	6.06218	−	3.50000i	0.243857	−	0.140791i
$619$	−5.00000			−0.200967			−0.100483	−	0.994939i	$-0.532039\pi$
$619$	−5.00000			−0.200967			−0.100483	+	0.994939i	$0.532039\pi$
$620$	0.535898	+	8.92820i	0.0215222	+	0.358565i
$621$		0			0
$622$	−17.3205	−	10.0000i	−0.694489	−	0.400963i
$623$		−	5.00000i		−	0.200321i
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$	−2.59808	−	1.50000i	−0.103757	−	0.0599042i
$628$	−2.59808	+	1.50000i	−0.103675	+	0.0598565i
$629$	−36.0000			−1.43541
$630$	−0.669873	−	11.1603i	−0.0266884	−	0.444635i
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	−0.997718	−	0.0675178i	$-0.978492\pi$
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	0.440387	−	0.897808i	$-0.354841\pi$
$632$			14.0000i			0.556890i
$633$	11.2583	−	6.50000i	0.447478	−	0.258352i
$634$	−3.50000	+	6.06218i	−0.139003	+	0.240760i
$635$	20.9449	+	31.7224i	0.831172	+	1.25887i
$636$	−3.00000			−0.118958
$637$	62.3538	−	18.0000i	2.47055	−	0.713186i
$638$			6.00000i			0.237542i
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−1.23205	−	1.86603i	−0.0487011	−	0.0737611i
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$		−	12.0000i		−	0.473602i
$643$	13.8564	−	8.00000i	0.546443	−	0.315489i	−0.201243	−	0.979541i	$-0.564498\pi$
$643$	13.8564	−	8.00000i	0.546443	−	0.315489i	0.747686	+	0.664052i	$0.231165\pi$
$644$		0			0
$645$	−24.0000	−	12.0000i	−0.944999	−	0.472500i
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	−28.5788	−	16.5000i	−1.12355	−	0.648682i	−0.181245	−	0.983438i	$-0.558013\pi$
$647$	−28.5788	−	16.5000i	−1.12355	−	0.648682i	−0.942305	+	0.334756i	$0.891346\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$		0			0
$650$	−10.8564	+	14.3923i	−0.425823	+	0.564513i
$651$	20.0000			0.783862
$652$	6.92820	+	4.00000i	0.271329	+	0.156652i
$653$	11.2583	+	6.50000i	0.440573	+	0.254365i	0.703840	−	0.710358i	$-0.251467\pi$
$653$	11.2583	+	6.50000i	0.440573	+	0.254365i	−0.263268	+	0.964723i	$0.584800\pi$
$654$	5.00000	+	8.66025i	0.195515	+	0.338643i
$655$	14.0000	+	7.00000i	0.547025	+	0.273513i
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$	13.8564	−	8.00000i	0.540590	−	0.312110i
$658$		−	35.0000i		−	1.36444i
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$	3.69615	+	5.59808i	0.143873	+	0.217905i
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$			4.00000i			0.155464i
$663$	−10.3923	−	10.0000i	−0.403604	−	0.388368i
$664$	10.0000			0.388075
$665$	6.16025	+	9.33013i	0.238884	+	0.361807i
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$		0			0
$668$		−	19.0000i		−	0.735132i
$669$	−0.500000	−	0.866025i	−0.0193311	−	0.0334825i
$670$	0.803848	+	13.3923i	0.0310553	+	0.517390i
$671$		0			0
$672$	−4.33013	+	2.50000i	−0.167038	+	0.0964396i
$673$	−6.92820	−	4.00000i	−0.267063	−	0.154189i	0.360489	−	0.932763i	$-0.382610\pi$
$673$	−6.92820	−	4.00000i	−0.267063	−	0.154189i	−0.627552	+	0.778575i	$0.715943\pi$
$674$	5.00000	−	8.66025i	0.192593	−	0.333581i
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$	3.46410	+	2.00000i	0.133038	+	0.0768095i
$679$	−25.0000	+	43.3013i	−0.959412	+	1.66175i
$680$	0.535898	+	8.92820i	0.0205508	+	0.342381i
$681$	2.00000			0.0766402
$682$	−10.3923	+	6.00000i	−0.397942	+	0.229752i
$683$	13.8564	−	8.00000i	0.530201	−	0.306111i	−0.210898	−	0.977508i	$-0.567639\pi$
$683$	13.8564	−	8.00000i	0.530201	−	0.306111i	0.741098	+	0.671397i	$0.234305\pi$
$684$	1.00000			0.0382360
$685$	−22.3205	+	1.33975i	−0.852823	+	0.0511891i
$686$	−27.5000	+	47.6314i	−1.04995	+	1.81858i
$687$	−19.0526	−	11.0000i	−0.726900	−	0.419676i
$688$			12.0000i			0.457496i
$689$	7.50000	−	7.79423i	0.285727	−	0.296936i
$690$		0			0
$691$	−4.50000	+	7.79423i	−0.171188	+	0.296506i	−0.938835	−	0.344366i	$-0.888094\pi$
$691$	−4.50000	+	7.79423i	−0.171188	+	0.296506i	0.767647	+	0.640872i	$0.221427\pi$
$692$	−6.06218	−	3.50000i	−0.230449	−	0.133050i
$693$	12.9904	−	7.50000i	0.493464	−	0.284901i
$694$	−22.0000			−0.835109
$695$	−0.669873	−	11.1603i	−0.0254097	−	0.423333i
$696$	−1.00000	−	1.73205i	−0.0379049	−	0.0656532i
$697$			40.0000i			1.51511i
$698$	−8.66025	+	5.00000i	−0.327795	+	0.189253i
$699$		0			0
$700$	−2.99038	−	24.8205i	−0.113026	−	0.938127i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	3.46410	−	1.00000i	0.130744	−	0.0377426i
$703$			9.00000i			0.339441i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	13.0622	−	8.62436i	0.491950	−	0.324812i
$706$	−17.0000	−	29.4449i	−0.639803	−	1.10817i
$707$		−	50.0000i		−	1.88044i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	12.0000	−	24.0000i	0.450352	−	0.900704i
$711$	7.00000	+	12.1244i	0.262521	+	0.454699i
$712$	−0.866025	−	0.500000i	−0.0324557	−	0.0187383i
$713$		0			0
$714$	20.0000			0.748481
$715$	−23.7846	−	4.39230i	−0.889494	−	0.164263i
$716$	12.0000			0.448461
$717$	12.1244	+	7.00000i	0.452792	+	0.261420i
$718$	17.3205	+	10.0000i	0.646396	+	0.373197i
$719$	16.0000	+	27.7128i	0.596699	+	1.03351i	0.993305	+	0.115524i	$0.0368548\pi$
$719$	16.0000	+	27.7128i	0.596699	+	1.03351i	−0.396605	+	0.917989i	$0.629812\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	−17.5000	−	30.3109i	−0.651734	−	1.12884i
$722$	15.5885	−	9.00000i	0.580142	−	0.334945i
$723$			3.00000i			0.111571i
$724$	−3.00000	−	5.19615i	−0.111494	−	0.193113i
$725$	9.92820	−	1.19615i	0.368724	−	0.0444240i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$			37.0000i			1.37225i	0.727482	+	0.686127i	$0.240691\pi$
$727$			37.0000i			1.37225i	−0.727482	+	0.686127i	$0.759309\pi$
$728$	4.33013	−	17.5000i	0.160485	−	0.648593i
$729$	−1.00000			−0.0370370
$730$	29.8564	−	19.7128i	1.10504	−	0.729604i
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$		0			0
$733$		−	45.0000i		−	1.66211i	−0.556188	−	0.831056i	$-0.687737\pi$
$733$		−	45.0000i		−	1.66211i	0.556188	−	0.831056i	$-0.312263\pi$
$734$	−12.0000	−	20.7846i	−0.442928	−	0.767174i
$735$	−40.1769	+	2.41154i	−1.48195	+	0.0889511i
$736$		0			0
$737$	−15.5885	+	9.00000i	−0.574208	+	0.331519i
$738$	−8.66025	−	5.00000i	−0.318788	−	0.184053i
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	0.465848	+	0.884865i	$0.345749\pi$
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	−0.999239	+	0.0389959i	$0.987584\pi$
$740$	9.00000	−	18.0000i	0.330847	−	0.661693i
$741$	−2.50000	+	2.59808i	−0.0918398	+	0.0954427i
$742$			15.0000i			0.550667i
$743$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$743$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	2.14359	+	35.7128i	0.0785352	+	1.30842i
$746$	6.00000			0.219676
$747$	8.66025	−	5.00000i	0.316862	−	0.182940i
$748$	−10.3923	+	6.00000i	−0.379980	+	0.219382i
$749$	−60.0000			−2.19235
$750$	8.52628	−	7.23205i	0.311336	−	0.264077i
$751$	15.0000	−	25.9808i	0.547358	−	0.948051i	−0.451097	−	0.892475i	$-0.648967\pi$
$751$	15.0000	−	25.9808i	0.547358	−	0.948051i	0.998454	−	0.0555764i	$-0.0176996\pi$
$752$	−6.06218	−	3.50000i	−0.221065	−	0.127632i
$753$			13.0000i			0.473746i
$754$	7.00000	+	1.73205i	0.254925	+	0.0630776i
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	−21.6506	−	12.5000i	−0.786906	−	0.454320i	0.0519664	−	0.998649i	$-0.483451\pi$
$757$	−21.6506	−	12.5000i	−0.786906	−	0.454320i	−0.838872	+	0.544329i	$0.816784\pi$
$758$	16.4545	−	9.50000i	0.597654	−	0.345056i
$759$		0			0
$760$	2.23205	−	0.133975i	0.0809650	−	0.00485977i
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$		−	17.0000i		−	0.615845i
$763$	43.3013	−	25.0000i	1.56761	−	0.905061i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$	4.92820	+	7.46410i	0.178180	+	0.269865i
$766$	−16.0000			−0.578103
$767$		0			0
$768$			1.00000i			0.0360844i
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	27.9904	−	18.4808i	1.00870	−	0.666000i
$771$	−5.00000	−	8.66025i	−0.180071	−	0.311891i
$772$		−	4.00000i		−	0.143963i
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	−0.135910	−	0.990721i	$-0.543396\pi$
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	0.790034	+	0.613062i	$0.210063\pi$
$774$	6.00000	+	10.3923i	0.215666	+	0.373544i
$775$	12.0000	+	16.0000i	0.431053	+	0.574737i
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$	−38.9711	−	22.5000i	−1.39808	−	0.807183i
$778$	−20.7846	−	12.0000i	−0.745164	−	0.430221i
$779$	10.0000			0.358287
$780$	7.59808	−	2.69615i	0.272055	−	0.0965377i
$781$	36.0000			1.28818
$782$		0			0
$783$	−1.73205	−	1.00000i	−0.0618984	−	0.0357371i
$784$	9.00000	+	15.5885i	0.321429	+	0.556731i
$785$	−3.00000	+	6.00000i	−0.107075	+	0.214149i
$786$	−3.50000	−	6.06218i	−0.124841	−	0.216231i
$787$	36.3731	−	21.0000i	1.29656	−	0.748569i	0.316752	−	0.948509i	$-0.397408\pi$
$787$	36.3731	−	21.0000i	1.29656	−	0.748569i	0.979808	+	0.199939i	$0.0640745\pi$
$788$			15.0000i			0.534353i
$789$	−3.50000	−	6.06218i	−0.124603	−	0.215819i
$790$	17.2487	+	26.1244i	0.613682	+	0.929463i
$791$	10.0000	−	17.3205i	0.355559	−	0.615846i
$792$		−	3.00000i		−	0.106600i
$793$		0			0
$794$	−23.0000			−0.816239
$795$	−5.59808	+	3.69615i	−0.198543	+	0.131089i
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	−0.197826	−	0.980237i	$-0.563388\pi$
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	0.749997	+	0.661441i	$0.230055\pi$
$798$		−	5.00000i		−	0.176998i
$799$	14.0000	+	24.2487i	0.495284	+	0.857858i
$800$	−4.59808	−	1.96410i	−0.162567	−	0.0694415i
$801$	−1.00000			−0.0353333
$802$	18.1865	−	10.5000i	0.642189	−	0.370768i
$803$	41.5692	+	24.0000i	1.46695	+	0.846942i
$804$	3.00000	−	5.19615i	0.105802	−	0.183254i
$805$		0			0
$806$	4.00000	+	13.8564i	0.140894	+	0.488071i
$807$			8.00000i			0.281613i
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$	−2.23205	+	0.133975i	−0.0784263	+	0.00470739i
$811$	13.0000			0.456492			0.228246	−	0.973604i	$-0.426701\pi$
$811$	13.0000			0.456492			0.228246	+	0.973604i	$0.426701\pi$
$812$	−8.66025	+	5.00000i	−0.303915	+	0.175466i
$813$	−1.73205	+	1.00000i	−0.0607457	+	0.0350715i
$814$	27.0000			0.946350
$815$	17.8564	−	1.07180i	0.625483	−	0.0375434i
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	−10.3923	−	6.00000i	−0.363581	−	0.209913i
$818$		−	19.0000i		−	0.664319i
$819$	−5.00000	−	17.3205i	−0.174714	−	0.605228i
$820$	−20.0000	−	10.0000i	−0.698430	−	0.349215i
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$	8.66025	+	5.00000i	0.302061	+	0.174395i
$823$	−35.5070	+	20.5000i	−1.23770	+	0.714585i	−0.968623	−	0.248534i	$-0.920051\pi$
$823$	−35.5070	+	20.5000i	−1.23770	+	0.714585i	−0.269075	+	0.963119i	$0.586718\pi$
$824$	−7.00000			−0.243857
$825$	13.7942	+	5.89230i	0.480253	+	0.205144i
$826$		0			0
$827$			2.00000i			0.0695468i	0.999395	+	0.0347734i	$0.0110710\pi$
$827$			2.00000i			0.0695468i	−0.999395	+	0.0347734i	$0.988929\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$	18.6603	−	12.3205i	0.647707	−	0.427651i
$831$	−17.0000			−0.589723
$832$	−2.59808	−	2.50000i	−0.0900721	−	0.0866719i
$833$		−	72.0000i		−	2.49465i
$834$	−2.50000	+	4.33013i	−0.0865679	+	0.149940i
$835$	−23.4090	−	35.4545i	−0.810101	−	1.22695i
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$		−	4.00000i		−	0.138260i
$838$	−24.2487	+	14.0000i	−0.837658	+	0.483622i
$839$	23.0000	+	39.8372i	0.794048	+	1.37533i	0.923442	+	0.383738i	$0.125364\pi$
$839$	23.0000	+	39.8372i	0.794048	+	1.37533i	−0.129394	+	0.991593i	$0.541303\pi$
$840$	−5.00000	+	10.0000i	−0.172516	+	0.345033i
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	13.8564	+	8.00000i	0.477523	+	0.275698i
$843$	−25.9808	−	15.0000i	−0.894825	−	0.516627i
$844$	−13.0000			−0.447478
$845$	−11.9904	+	26.4808i	−0.412482	+	0.910966i
$846$	−7.00000			−0.240665
$847$	−8.66025	−	5.00000i	−0.297570	−	0.171802i
$848$	2.59808	+	1.50000i	0.0892183	+	0.0515102i
$849$	3.00000	+	5.19615i	0.102960	+	0.178331i
$850$	12.0000	+	16.0000i	0.411597	+	0.548795i
$851$		0			0
$852$	−10.3923	+	6.00000i	−0.356034	+	0.205557i
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	1.86603	−	1.23205i	0.0638167	−	0.0421352i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$	7.79423	+	7.50000i	0.266091	+	0.256046i
$859$	−55.0000			−1.87658			−0.938288	−	0.345855i	$-0.887589\pi$
$859$	−55.0000			−1.87658			−0.938288	+	0.345855i	$0.887589\pi$
$860$	14.7846	+	22.3923i	0.504151	+	0.763571i
$861$	−25.0000	+	43.3013i	−0.851998	+	1.47570i
$862$	34.6410	−	20.0000i	1.17988	−	0.681203i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−15.6244	+	0.937822i	−0.531244	+	0.0318869i
$866$	−8.00000			−0.271851
$867$	0.866025	−	0.500000i	0.0294118	−	0.0169809i
$868$	−17.3205	−	10.0000i	−0.587896	−	0.339422i
$869$	−21.0000	+	36.3731i	−0.712376	+	1.23387i
$870$	−4.00000	−	2.00000i	−0.135613	−	0.0678064i
$871$	6.00000	+	20.7846i	0.203302	+	0.704260i
$872$		−	10.0000i		−	0.338643i
$873$	8.66025	+	5.00000i	0.293105	+	0.169224i
$874$		0			0
$875$	−36.1603	−	42.6314i	−1.22244	−	1.44120i
$876$	−16.0000			−0.540590
$877$	15.5885	−	9.00000i	0.526385	−	0.303908i	−0.213158	−	0.977018i	$-0.568375\pi$
$877$	15.5885	−	9.00000i	0.526385	−	0.303908i	0.739543	+	0.673109i	$0.235042\pi$
$878$	13.8564	−	8.00000i	0.467631	−	0.269987i
$879$	−3.00000			−0.101187
$880$	−0.401924	−	6.69615i	−0.0135488	−	0.225727i
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	−0.964263	−	0.264946i	$-0.914646\pi$
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	0.711582	+	0.702603i	$0.247979\pi$
$882$	15.5885	+	9.00000i	0.524891	+	0.303046i
$883$		−	50.0000i		−	1.68263i	−0.540542	−	0.841317i	$-0.681781\pi$
$883$		−	50.0000i		−	1.68263i	0.540542	−	0.841317i	$-0.318219\pi$
$884$	4.00000	+	13.8564i	0.134535	+	0.466041i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	28.5788	+	16.5000i	0.959583	+	0.554016i	0.896045	−	0.443964i	$-0.146428\pi$
$887$	28.5788	+	16.5000i	0.959583	+	0.554016i	0.0635387	+	0.997979i	$0.479761\pi$
$888$	−7.79423	+	4.50000i	−0.261557	+	0.151010i
$889$	−85.0000			−2.85081
$890$	−2.23205	+	0.133975i	−0.0748185	+	0.00449084i
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$			1.00000i			0.0334825i
$893$	6.06218	−	3.50000i	0.202863	−	0.117123i
$894$	8.00000	−	13.8564i	0.267560	−	0.463428i
$895$	22.3923	−	14.7846i	0.748492	−	0.494195i
$896$	5.00000			0.167038
$897$		0			0
$898$		−	13.0000i		−	0.433816i
$899$	4.00000	−	6.92820i	0.133407	−	0.231069i
$900$	−4.96410	+	0.598076i	−0.165470	+	0.0199359i
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		−	30.0000i		−	0.998891i
$903$	51.9615	−	30.0000i	1.72917	−	0.998337i
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$	−12.0000	−	6.00000i	−0.398893	−	0.199447i
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	0.712084	−	0.702094i	$-0.247752\pi$
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	−0.251990	+	0.967730i	$0.581085\pi$
$908$	−1.73205	−	1.00000i	−0.0574801	−	0.0331862i
$909$	−10.0000			−0.331679
$910$	−13.4808	−	37.9904i	−0.446883	−	1.25937i
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−0.866025	−	0.500000i	−0.0286770	−	0.0165567i
$913$	25.9808	+	15.0000i	0.859838	+	0.496428i
$914$	−14.0000	−	24.2487i	−0.463079	−	0.802076i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	−30.3109	+	17.5000i	−1.00095	+	0.577901i
$918$		−	4.00000i		−	0.132020i
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$			22.0000i			0.724531i
$923$	10.3923	−	42.0000i	0.342067	−	1.38245i
$924$	−15.0000			−0.493464
$925$	−5.38269	−	44.6769i	−0.176982	−	1.46897i
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	−6.06218	+	3.50000i	−0.199108	+	0.114955i
$928$			2.00000i			0.0656532i
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	0.997684	+	0.0680235i	$0.0216693\pi$
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	−0.439932	+	0.898031i	$0.644997\pi$
$930$	−0.535898	−	8.92820i	−0.0175728	−	0.292767i
$931$	−18.0000			−0.589926
$932$		0			0
$933$	17.3205	+	10.0000i	0.567048	+	0.327385i
$934$	−17.0000	+	29.4449i	−0.556257	+	0.963465i
$935$	−12.0000	+	24.0000i	−0.392442	+	0.784884i
$936$	−3.50000	−	0.866025i	−0.114401	−	0.0283069i
$937$		−	36.0000i		−	1.17607i	−0.808836	−	0.588034i	$-0.799902\pi$
$937$		−	36.0000i		−	1.17607i	0.808836	−	0.588034i	$-0.200098\pi$
$938$	−25.9808	−	15.0000i	−0.848302	−	0.489767i
$939$	−7.00000	+	12.1244i	−0.228436	+	0.395663i
$940$	−15.6244	+	0.937822i	−0.509610	+	0.0305884i
$941$	52.0000			1.69515			0.847576	−	0.530674i	$-0.178061\pi$
$941$	52.0000			1.69515			0.847576	+	0.530674i	$0.178061\pi$
$942$	2.59808	−	1.50000i	0.0846499	−	0.0488726i
$943$		0			0
$944$		0			0
$945$	0.669873	+	11.1603i	0.0217910	+	0.363043i
$946$	−18.0000	+	31.1769i	−0.585230	+	1.01365i
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$		−	14.0000i		−	0.454699i
$949$	40.0000	−	41.5692i	1.29845	−	1.34939i
$950$	4.00000	−	3.00000i	0.129777	−	0.0973329i
$951$	3.50000	−	6.06218i	0.113495	−	0.196580i
$952$	−17.3205	−	10.0000i	−0.561361	−	0.324102i
$953$	25.9808	−	15.0000i	0.841599	−	0.485898i	−0.0162081	−	0.999869i	$-0.505159\pi$
$953$	25.9808	−	15.0000i	0.841599	−	0.485898i	0.857808	+	0.513971i	$0.171826\pi$
$954$	3.00000			0.0971286
$955$	−1.60770	−	26.7846i	−0.0520238	−	0.866730i
$956$	−7.00000	−	12.1244i	−0.226396	−	0.392130i
$957$		−	6.00000i		−	0.193952i
$958$	8.66025	−	5.00000i	0.279800	−	0.161543i
$959$	25.0000	−	43.3013i	0.807292	−	1.39827i
$960$	1.23205	+	1.86603i	0.0397643	+	0.0602257i
$961$	−15.0000			−0.483871
$962$	7.79423	−	31.5000i	0.251296	−	1.01560i
$963$			12.0000i			0.386695i
$964$	1.50000	−	2.59808i	0.0483117	−	0.0836784i
$965$	−4.92820	−	7.46410i	−0.158644	−	0.240278i
$966$		0			0
$967$			37.0000i			1.18984i	0.803785	+	0.594920i	$0.202816\pi$
$967$			37.0000i			1.18984i	−0.803785	+	0.594920i	$0.797184\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$	20.0000	+	10.0000i	0.642161	+	0.321081i
$971$	25.5000	+	44.1673i	0.818334	+	1.41740i	0.906909	+	0.421326i	$0.138435\pi$
$971$	25.5000	+	44.1673i	0.818334	+	1.41740i	−0.0885751	+	0.996070i	$0.528231\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	21.6506	+	12.5000i	0.694087	+	0.400732i
$974$	1.00000			0.0320421
$975$	10.8564	−	14.3923i	0.347683	−	0.460923i
$976$		0			0
$977$	−32.9090	−	19.0000i	−1.05285	−	0.607864i	−0.129405	−	0.991592i	$-0.541307\pi$
$977$	−32.9090	−	19.0000i	−1.05285	−	0.607864i	−0.923446	+	0.383728i	$0.874640\pi$
$978$	−6.92820	−	4.00000i	−0.221540	−	0.127906i
$979$	−1.50000	−	2.59808i	−0.0479402	−	0.0830349i
$980$	36.0000	+	18.0000i	1.14998	+	0.574989i
$981$	−5.00000	−	8.66025i	−0.159638	−	0.276501i
$982$	−12.9904	+	7.50000i	−0.414540	+	0.239335i
$983$			23.0000i			0.733586i	0.930303	+	0.366793i	$0.119544\pi$
$983$			23.0000i			0.733586i	−0.930303	+	0.366793i	$0.880456\pi$
$984$	5.00000	+	8.66025i	0.159394	+	0.276079i
$985$	18.4808	+	27.9904i	0.588846	+	0.891848i
$986$	4.00000	−	6.92820i	0.127386	−	0.220639i
$987$			35.0000i			1.11406i
$988$	3.46410	−	1.00000i	0.110208	−	0.0318142i
$989$		0			0
$990$	−3.69615	−	5.59808i	−0.117471	−	0.177919i
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		−	4.00000i		−	0.126936i
$994$	30.0000	+	51.9615i	0.951542	+	1.64812i
$995$	−1.87564	−	31.2487i	−0.0594619	−	0.990651i
$996$	−10.0000			−0.316862
$997$	−45.8993	+	26.5000i	−1.45365	+	0.839263i	−0.998686	−	0.0512480i	$-0.983680\pi$
$997$	−45.8993	+	26.5000i	−1.45365	+	0.839263i	−0.454961	+	0.890511i	$0.650347\pi$
$998$	20.7846	+	12.0000i	0.657925	+	0.379853i
$999$	−4.50000	+	7.79423i	−0.142374	+	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.y.e.139.2	yes	4
3.2	odd	2		1170.2.bp.b.919.1		4
5.2	odd	4		1950.2.i.a.451.1		2
5.3	odd	4		1950.2.i.x.451.1		2
5.4	even	2	inner	390.2.y.e.139.1	✓	4
13.3	even	3	inner	390.2.y.e.289.1	yes	4
15.14	odd	2		1170.2.bp.b.919.2		4
39.29	odd	6		1170.2.bp.b.289.2		4
65.3	odd	12		1950.2.i.x.601.1		2
65.29	even	6	inner	390.2.y.e.289.2	yes	4
65.42	odd	12		1950.2.i.a.601.1		2
195.29	odd	6		1170.2.bp.b.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.e.139.1	✓	4	5.4	even	2	inner
390.2.y.e.139.2	yes	4	1.1	even	1	trivial
390.2.y.e.289.1	yes	4	13.3	even	3	inner
390.2.y.e.289.2	yes	4	65.29	even	6	inner
1170.2.bp.b.289.1		4	195.29	odd	6
1170.2.bp.b.289.2		4	39.29	odd	6
1170.2.bp.b.919.1		4	3.2	odd	2
1170.2.bp.b.919.2		4	15.14	odd	2
1950.2.i.a.451.1		2	5.2	odd	4
1950.2.i.a.601.1		2	65.42	odd	12
1950.2.i.x.451.1		2	5.3	odd	4
1950.2.i.x.601.1		2	65.3	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.23205 + 1.86603i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(2.59808 + 2.50000i) q^{13} -5.00000 q^{14} +(-1.23205 - 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +1.00000i q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.133975 + 2.23205i) q^{20} +5.00000 q^{21} +(-2.59808 + 1.50000i) q^{22} +(0.500000 - 0.866025i) q^{24} +(3.00000 + 4.00000i) q^{25} +(1.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-4.33013 - 2.50000i) q^{28} +(1.00000 - 1.73205i) q^{29} +(-0.133975 - 2.23205i) q^{30} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +4.00000 q^{34} +(-11.1603 + 0.669873i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-7.79423 - 4.50000i) q^{37} -1.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(-1.00000 + 2.00000i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(4.33013 + 2.50000i) q^{42} +(10.3923 - 6.00000i) q^{43} -3.00000 q^{44} +(0.133975 + 2.23205i) q^{45} +7.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(9.00000 - 15.5885i) q^{49} +(0.598076 + 4.96410i) q^{50} -4.00000 q^{51} +(-0.866025 + 3.50000i) q^{52} -3.00000i q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.59808 + 3.69615i) q^{55} +(-2.50000 - 4.33013i) q^{56} +1.00000i q^{57} +(1.73205 - 1.00000i) q^{58} +(1.00000 - 2.00000i) q^{60} +(3.46410 + 2.00000i) q^{62} +(-4.33013 - 2.50000i) q^{63} -1.00000 q^{64} +(2.69615 + 7.59808i) q^{65} +3.00000 q^{66} +(5.19615 + 3.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-10.0000 - 5.00000i) q^{70} +(-6.00000 - 10.3923i) q^{71} +(-0.866025 + 0.500000i) q^{72} -16.0000i q^{73} +(-4.50000 - 7.79423i) q^{74} +(-0.598076 - 4.96410i) q^{75} +(0.500000 - 0.866025i) q^{76} -15.0000i q^{77} +(0.866025 - 3.50000i) q^{78} +14.0000 q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -10.0000i q^{83} +(2.50000 + 4.33013i) q^{84} +(8.92820 - 0.535898i) q^{85} +12.0000 q^{86} +(-1.73205 + 1.00000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-1.00000 + 2.00000i) q^{90} +(-17.5000 - 4.33013i) q^{91} +(-3.46410 - 2.00000i) q^{93} +(-3.50000 + 6.06218i) q^{94} +(-0.133975 - 2.23205i) q^{95} +1.00000 q^{96} +(8.66025 - 5.00000i) q^{97} +(15.5885 - 9.00000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{19} + 4 q^{20} + 20 q^{21} + 2 q^{24} + 12 q^{25} + 4 q^{26} + 4 q^{29} - 4 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} - 2 q^{36} - 4 q^{39} - 4 q^{40} - 20 q^{41} - 12 q^{44} + 4 q^{45} + 36 q^{49} - 8 q^{50} - 16 q^{51} + 2 q^{54} - 12 q^{55} - 10 q^{56} + 4 q^{60} - 4 q^{64} - 10 q^{65} + 12 q^{66} - 40 q^{70} - 24 q^{71} - 18 q^{74} + 8 q^{75} + 2 q^{76} + 56 q^{79} - 4 q^{80} - 2 q^{81} + 10 q^{84} + 8 q^{85} + 48 q^{86} - 2 q^{89} - 4 q^{90} - 70 q^{91} - 14 q^{94} - 4 q^{95} + 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^19 + 4 * q^20 + 20 * q^21 + 2 * q^24 + 12 * q^25 + 4 * q^26 + 4 * q^29 - 4 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 - 2 * q^36 - 4 * q^39 - 4 * q^40 - 20 * q^41 - 12 * q^44 + 4 * q^45 + 36 * q^49 - 8 * q^50 - 16 * q^51 + 2 * q^54 - 12 * q^55 - 10 * q^56 + 4 * q^60 - 4 * q^64 - 10 * q^65 + 12 * q^66 - 40 * q^70 - 24 * q^71 - 18 * q^74 + 8 * q^75 + 2 * q^76 + 56 * q^79 - 4 * q^80 - 2 * q^81 + 10 * q^84 + 8 * q^85 + 48 * q^86 - 2 * q^89 - 4 * q^90 - 70 * q^91 - 14 * q^94 - 4 * q^95 + 4 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

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Database

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