LMFDB - Embedded newform 546.2.bd.b.361.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.9
Root			$-1.91536i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.65875 - 0.957680i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.36927 - 2.26387i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.65875 - 0.957680i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.36927 - 2.26387i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.91536 q^{10} -6.08926i q^{11} +(0.500000 + 0.866025i) q^{12} +(3.13511 + 1.78076i) q^{13} +(-0.0538842 - 2.64520i) q^{14} +(1.65875 - 0.957680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.494789 + 0.857000i) q^{17} +(0.866025 + 0.500000i) q^{18} +1.50132i q^{19} +(1.65875 + 0.957680i) q^{20} +(-1.36927 - 2.26387i) q^{21} +(3.04463 - 5.27345i) q^{22} +(-2.74595 + 4.75613i) q^{23} +1.00000i q^{24} +(-0.665698 + 1.15302i) q^{25} +(1.82470 + 3.10974i) q^{26} +1.00000 q^{27} +(1.27594 - 2.31775i) q^{28} +(4.70363 + 8.14693i) q^{29} +1.91536 q^{30} +(-5.08892 - 2.93809i) q^{31} +(-0.866025 + 0.500000i) q^{32} -6.08926i q^{33} +0.989578i q^{34} +(-4.43933 - 2.44388i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.03838 - 1.17686i) q^{37} +(-0.750659 + 1.30018i) q^{38} +(3.13511 + 1.78076i) q^{39} +(0.957680 + 1.65875i) q^{40} +(-7.45751 + 4.30560i) q^{41} +(-0.0538842 - 2.64520i) q^{42} +(-0.281787 + 0.488069i) q^{43} +(5.27345 - 3.04463i) q^{44} +(1.65875 - 0.957680i) q^{45} +(-4.75613 + 2.74595i) q^{46} +(-0.0319090 + 0.0184227i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.25022 + 6.19968i) q^{49} +(-1.15302 + 0.665698i) q^{50} +(0.494789 + 0.857000i) q^{51} +(0.0253706 + 3.60546i) q^{52} +(4.17024 - 7.22306i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.83156 - 10.1006i) q^{55} +(2.26387 - 1.36927i) q^{56} +1.50132i q^{57} +9.40727i q^{58} +(6.52765 - 3.76874i) q^{59} +(1.65875 + 0.957680i) q^{60} -1.29963 q^{61} +(-2.93809 - 5.08892i) q^{62} +(-1.36927 - 2.26387i) q^{63} -1.00000 q^{64} +(6.90576 - 0.0485938i) q^{65} +(3.04463 - 5.27345i) q^{66} +11.1287i q^{67} +(-0.494789 + 0.857000i) q^{68} +(-2.74595 + 4.75613i) q^{69} +(-2.62264 - 4.33613i) q^{70} +(9.53931 + 5.50752i) q^{71} +1.00000i q^{72} +(-5.99988 - 3.46403i) q^{73} +(-1.17686 - 2.03838i) q^{74} +(-0.665698 + 1.15302i) q^{75} +(-1.30018 + 0.750659i) q^{76} +(-13.7853 + 8.33782i) q^{77} +(1.82470 + 3.10974i) q^{78} +(0.389363 + 0.674397i) q^{79} +1.91536i q^{80} +1.00000 q^{81} -8.61119 q^{82} -14.6405i q^{83} +(1.27594 - 2.31775i) q^{84} +(1.64146 + 0.947699i) q^{85} +(-0.488069 + 0.281787i) q^{86} +(4.70363 + 8.14693i) q^{87} +6.08926 q^{88} +(4.65842 + 2.68954i) q^{89} +1.91536 q^{90} +(-0.261388 - 9.53581i) q^{91} -5.49191 q^{92} +(-5.08892 - 2.93809i) q^{93} -0.0368454 q^{94} +(1.43778 + 2.49031i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-15.8848 - 9.17111i) q^{97} +(-5.91461 + 3.74397i) q^{98} -6.08926i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.65875	−	0.957680i	0.741816	−	0.428287i	−0.0809134	−	0.996721i	$-0.525784\pi$
$5$	1.65875	−	0.957680i	0.741816	−	0.428287i	0.822729	+	0.568434i	$0.192450\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.36927	−	2.26387i	−0.517534	−	0.855663i
$7$	−1.36927	−	2.26387i	−0.517534	−	0.855663i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	1.91536			0.605690
$11$		−	6.08926i		−	1.83598i	−0.396602	−	0.917990i	$-0.629811\pi$
$11$		−	6.08926i		−	1.83598i	0.396602	−	0.917990i	$-0.370189\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.13511	+	1.78076i	0.869522	+	0.493894i
$13$	3.13511	+	1.78076i	0.869522	+	0.493894i
$14$	−0.0538842	−	2.64520i	−0.0144011	−	0.706960i
$15$	1.65875	−	0.957680i	0.428287	−	0.247272i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.494789	+	0.857000i	0.120004	+	0.207853i	0.919769	−	0.392460i	$-0.128376\pi$
$17$	0.494789	+	0.857000i	0.120004	+	0.207853i	−0.799765	+	0.600313i	$0.795043\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$			1.50132i			0.344426i	0.985060	+	0.172213i	$0.0550917\pi$
$19$			1.50132i			0.344426i	−0.985060	+	0.172213i	$0.944908\pi$
$20$	1.65875	+	0.957680i	0.370908	+	0.214144i
$21$	−1.36927	−	2.26387i	−0.298798	−	0.494017i
$22$	3.04463	−	5.27345i	0.649117	−	1.12430i
$23$	−2.74595	+	4.75613i	−0.572571	+	0.991722i	0.423730	+	0.905789i	$0.360721\pi$
$23$	−2.74595	+	4.75613i	−0.572571	+	0.991722i	−0.996301	+	0.0859335i	$0.972613\pi$
$24$			1.00000i			0.204124i
$25$	−0.665698	+	1.15302i	−0.133140	+	0.230605i
$26$	1.82470	+	3.10974i	0.357854	+	0.609869i
$27$	1.00000			0.192450
$28$	1.27594	−	2.31775i	0.241129	−	0.438014i
$29$	4.70363	+	8.14693i	0.873443	+	1.51285i	0.858412	+	0.512961i	$0.171451\pi$
$29$	4.70363	+	8.14693i	0.873443	+	1.51285i	0.0150308	+	0.999887i	$0.495215\pi$
$30$	1.91536			0.349695
$31$	−5.08892	−	2.93809i	−0.913997	−	0.527696i	−0.0322818	−	0.999479i	$-0.510277\pi$
$31$	−5.08892	−	2.93809i	−0.913997	−	0.527696i	−0.881715	+	0.471783i	$0.843611\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		−	6.08926i		−	1.06000i
$34$			0.989578i			0.169711i
$35$	−4.43933	−	2.44388i	−0.750384	−	0.413091i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−2.03838	−	1.17686i	−0.335108	−	0.193475i	0.322999	−	0.946399i	$-0.395309\pi$
$37$	−2.03838	−	1.17686i	−0.335108	−	0.193475i	−0.658107	+	0.752925i	$0.728642\pi$
$38$	−0.750659	+	1.30018i	−0.121773	+	0.210917i
$39$	3.13511	+	1.78076i	0.502019	+	0.285150i
$40$	0.957680	+	1.65875i	0.151422	+	0.262271i
$41$	−7.45751	+	4.30560i	−1.16467	+	0.672421i	−0.952418	−	0.304794i	$-0.901412\pi$
$41$	−7.45751	+	4.30560i	−1.16467	+	0.672421i	−0.212249	+	0.977216i	$0.568079\pi$
$42$	−0.0538842	−	2.64520i	−0.00831451	−	0.408164i
$43$	−0.281787	+	0.488069i	−0.0429721	+	0.0744298i	−0.886711	−	0.462323i	$-0.847016\pi$
$43$	−0.281787	+	0.488069i	−0.0429721	+	0.0744298i	0.843739	+	0.536753i	$0.180349\pi$
$44$	5.27345	−	3.04463i	0.795003	−	0.458995i
$45$	1.65875	−	0.957680i	0.247272	−	0.142762i
$46$	−4.75613	+	2.74595i	−0.701253	+	0.404869i
$47$	−0.0319090	+	0.0184227i	−0.00465441	+	0.00268722i	−0.502325	−	0.864679i	$-0.667522\pi$
$47$	−0.0319090	+	0.0184227i	−0.00465441	+	0.00268722i	0.497671	+	0.867366i	$0.334189\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.25022	+	6.19968i	−0.464317	+	0.885669i
$50$	−1.15302	+	0.665698i	−0.163062	+	0.0941439i
$51$	0.494789	+	0.857000i	0.0692843	+	0.120004i
$52$	0.0253706	+	3.60546i	0.00351827	+	0.499988i
$53$	4.17024	−	7.22306i	0.572826	−	0.992163i	−0.423448	−	0.905920i	$-0.639180\pi$
$53$	4.17024	−	7.22306i	0.572826	−	0.992163i	0.996274	−	0.0862432i	$-0.0274862\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−5.83156	−	10.1006i	−0.786328	−	1.36196i
$56$	2.26387	−	1.36927i	0.302522	−	0.182976i
$57$			1.50132i			0.198854i
$58$			9.40727i			1.23523i
$59$	6.52765	−	3.76874i	0.849828	−	0.490648i	−0.0107650	−	0.999942i	$-0.503427\pi$
$59$	6.52765	−	3.76874i	0.849828	−	0.490648i	0.860593	+	0.509294i	$0.170093\pi$
$60$	1.65875	+	0.957680i	0.214144	+	0.123636i
$61$	−1.29963			−0.166400			−0.0832001	−	0.996533i	$-0.526514\pi$
$61$	−1.29963			−0.166400			−0.0832001	+	0.996533i	$0.526514\pi$
$62$	−2.93809	−	5.08892i	−0.373138	−	0.646293i
$63$	−1.36927	−	2.26387i	−0.172511	−	0.285221i
$64$	−1.00000			−0.125000
$65$	6.90576	−	0.0485938i	0.856554	−	0.00602732i
$66$	3.04463	−	5.27345i	0.374768	−	0.649117i
$67$			11.1287i			1.35959i	0.733401	+	0.679796i	$0.237932\pi$
$67$			11.1287i			1.35959i	−0.733401	+	0.679796i	$0.762068\pi$
$68$	−0.494789	+	0.857000i	−0.0600020	+	0.103926i
$69$	−2.74595	+	4.75613i	−0.330574	+	0.572571i
$70$	−2.62264	−	4.33613i	−0.313465	−	0.518266i
$71$	9.53931	+	5.50752i	1.13211	+	0.653622i	0.944464	−	0.328615i	$-0.106582\pi$
$71$	9.53931	+	5.50752i	1.13211	+	0.653622i	0.187643	+	0.982237i	$0.439915\pi$
$72$			1.00000i			0.117851i
$73$	−5.99988	−	3.46403i	−0.702233	−	0.405434i	0.105946	−	0.994372i	$-0.466213\pi$
$73$	−5.99988	−	3.46403i	−0.702233	−	0.405434i	−0.808179	+	0.588938i	$0.799546\pi$
$74$	−1.17686	−	2.03838i	−0.136807	−	0.236957i
$75$	−0.665698	+	1.15302i	−0.0768682	+	0.133140i
$76$	−1.30018	+	0.750659i	−0.149141	+	0.0861065i
$77$	−13.7853	+	8.33782i	−1.57098	+	0.950183i
$78$	1.82470	+	3.10974i	0.206607	+	0.352108i
$79$	0.389363	+	0.674397i	0.0438068	+	0.0758756i	0.887097	−	0.461582i	$-0.152718\pi$
$79$	0.389363	+	0.674397i	0.0438068	+	0.0758756i	−0.843291	+	0.537458i	$0.819385\pi$
$80$			1.91536i			0.214144i
$81$	1.00000			0.111111
$82$	−8.61119			−0.950947
$83$		−	14.6405i		−	1.60700i	−0.595305	−	0.803500i	$-0.702969\pi$
$83$		−	14.6405i		−	1.60700i	0.595305	−	0.803500i	$-0.297031\pi$
$84$	1.27594	−	2.31775i	0.139216	−	0.252888i
$85$	1.64146	+	0.947699i	0.178042	+	0.102792i
$86$	−0.488069	+	0.281787i	−0.0526298	+	0.0303858i
$87$	4.70363	+	8.14693i	0.504283	+	0.873443i
$88$	6.08926			0.649117
$89$	4.65842	+	2.68954i	0.493791	+	0.285090i	0.726146	−	0.687541i	$-0.241310\pi$
$89$	4.65842	+	2.68954i	0.493791	+	0.285090i	−0.232355	+	0.972631i	$0.574643\pi$
$90$	1.91536			0.201897
$91$	−0.261388	−	9.53581i	−0.0274009	−	0.999625i
$92$	−5.49191			−0.572571
$93$	−5.08892	−	2.93809i	−0.527696	−	0.304666i
$94$	−0.0368454			−0.00380031
$95$	1.43778	+	2.49031i	0.147513	+	0.255501i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−15.8848	−	9.17111i	−1.61286	−	0.931185i	−0.988703	−	0.149885i	$-0.952110\pi$
$97$	−15.8848	−	9.17111i	−1.61286	−	0.931185i	−0.624156	−	0.781300i	$-0.714557\pi$
$98$	−5.91461	+	3.74397i	−0.597466	+	0.378198i
$99$		−	6.08926i		−	0.611994i
$100$	−1.33140			−0.133140
$101$	11.5238			1.14666			0.573331	−	0.819324i	$-0.305651\pi$
$101$	11.5238			1.14666			0.573331	+	0.819324i	$0.305651\pi$
$102$			0.989578i			0.0979828i
$103$	−4.74114	−	8.21190i	−0.467159	−	0.809143i	0.532137	−	0.846658i	$-0.321389\pi$
$103$	−4.74114	−	8.21190i	−0.467159	−	0.809143i	−0.999296	+	0.0375154i	$0.988056\pi$
$104$	−1.78076	+	3.13511i	−0.174618	+	0.307423i
$105$	−4.43933	−	2.44388i	−0.433235	−	0.238498i
$106$	7.22306	−	4.17024i	0.701566	−	0.405049i
$107$	−3.39785	+	5.88524i	−0.328482	+	0.568948i	−0.982211	−	0.187781i	$-0.939870\pi$
$107$	−3.39785	+	5.88524i	−0.328482	+	0.568948i	0.653729	+	0.756729i	$0.273204\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−8.53194	−	4.92592i	−0.817212	−	0.471818i	0.0322421	−	0.999480i	$-0.489735\pi$
$109$	−8.53194	−	4.92592i	−0.817212	−	0.471818i	−0.849454	+	0.527662i	$0.823069\pi$
$110$		−	11.6631i		−	1.11204i
$111$	−2.03838	−	1.17686i	−0.193475	−	0.111703i
$112$	2.64520	−	0.0538842i	0.249948	−	0.00509157i
$113$	−2.78542	+	4.82449i	−0.262030	+	0.453850i	−0.966781	−	0.255605i	$-0.917725\pi$
$113$	−2.78542	+	4.82449i	−0.262030	+	0.453850i	0.704751	+	0.709455i	$0.251059\pi$
$114$	−0.750659	+	1.30018i	−0.0703056	+	0.121773i
$115$			10.5190i			0.980900i
$116$	−4.70363	+	8.14693i	−0.436721	+	0.756424i
$117$	3.13511	+	1.78076i	0.289841	+	0.164631i
$118$	7.53748			0.693881
$119$	1.26264	−	2.29360i	0.115746	−	0.210254i
$120$	0.957680	+	1.65875i	0.0874238	+	0.151422i
$121$	−26.0791			−2.37083
$122$	−1.12551	−	0.649814i	−0.101899	−	0.0588314i
$123$	−7.45751	+	4.30560i	−0.672421	+	0.388222i
$124$		−	5.87618i		−	0.527696i
$125$			12.1269i			1.08466i
$126$	−0.0538842	−	2.64520i	−0.00480038	−	0.235653i
$127$	−1.10698	−	1.91734i	−0.0982282	−	0.170136i	0.812723	−	0.582650i	$-0.197984\pi$
$127$	−1.10698	−	1.91734i	−0.0982282	−	0.170136i	−0.910951	+	0.412514i	$0.864651\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.281787	+	0.488069i	−0.0248099	+	0.0429721i
$130$	6.00486	+	3.41080i	0.526661	+	0.299147i
$131$	4.50445	+	7.80194i	0.393556	+	0.681659i	0.992916	−	0.118821i	$-0.0379115\pi$
$131$	4.50445	+	7.80194i	0.393556	+	0.681659i	−0.599360	+	0.800480i	$0.704578\pi$
$132$	5.27345	−	3.04463i	0.458995	−	0.265001i
$133$	3.39879	−	2.05570i	0.294712	−	0.178252i
$134$	−5.56437	+	9.63777i	−0.480688	+	0.832577i
$135$	1.65875	−	0.957680i	0.142762	−	0.0824240i
$136$	−0.857000	+	0.494789i	−0.0734871	+	0.0424278i
$137$	2.79910	−	1.61606i	0.239143	−	0.138069i	−0.375640	−	0.926766i	$-0.622577\pi$
$137$	2.79910	−	1.61606i	0.239143	−	0.138069i	0.614783	+	0.788696i	$0.289244\pi$
$138$	−4.75613	+	2.74595i	−0.404869	+	0.233751i
$139$	2.02098	−	3.50044i	0.171417	−	0.296903i	−0.767498	−	0.641051i	$-0.778499\pi$
$139$	2.02098	−	3.50044i	0.171417	−	0.296903i	0.938916	+	0.344148i	$0.111832\pi$
$140$	−0.103208	−	5.06651i	−0.00872263	−	0.428199i
$141$	−0.0319090	+	0.0184227i	−0.00268722	+	0.00155147i
$142$	5.50752	+	9.53931i	0.462181	+	0.800521i
$143$	10.8435	−	19.0905i	0.906780	−	1.59643i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	15.6043	+	9.00915i	1.29587	+	0.748169i
$146$	−3.46403	−	5.99988i	−0.286685	−	0.496554i
$147$	−3.25022	+	6.19968i	−0.268074	+	0.511341i
$148$		−	2.35372i		−	0.193475i
$149$		−	5.52778i		−	0.452854i	−0.974028	−	0.226427i	$-0.927296\pi$
$149$		−	5.52778i		−	0.452854i	0.974028	−	0.226427i	$-0.0727044\pi$
$150$	−1.15302	+	0.665698i	−0.0941439	+	0.0543540i
$151$	−3.27744	−	1.89223i	−0.266714	−	0.153988i	0.360679	−	0.932690i	$-0.382545\pi$
$151$	−3.27744	−	1.89223i	−0.266714	−	0.153988i	−0.627394	+	0.778702i	$0.715878\pi$
$152$	−1.50132			−0.121773
$153$	0.494789	+	0.857000i	0.0400013	+	0.0692843i
$154$	−16.1073	+	0.328115i	−1.29797	+	0.0264402i
$155$	−11.2550			−0.904023
$156$	0.0253706	+	3.60546i	0.00203127	+	0.288668i
$157$	8.41478	−	14.5748i	0.671573	−	1.16320i	−0.305885	−	0.952068i	$-0.598952\pi$
$157$	8.41478	−	14.5748i	0.671573	−	1.16320i	0.977458	−	0.211130i	$-0.0677142\pi$
$158$			0.778727i			0.0619522i
$159$	4.17024	−	7.22306i	0.330721	−	0.572826i
$160$	−0.957680	+	1.65875i	−0.0757112	+	0.131136i
$161$	14.5272	−	0.295927i	1.14490	−	0.0233223i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			19.2685i			1.50923i	0.656168	+	0.754615i	$0.272176\pi$
$163$			19.2685i			1.50923i	−0.656168	+	0.754615i	$0.727824\pi$
$164$	−7.45751	−	4.30560i	−0.582334	−	0.336211i
$165$	−5.83156	−	10.1006i	−0.453986	−	0.786328i
$166$	7.32023	−	12.6790i	0.568160	−	0.984082i
$167$	−14.7661	+	8.52518i	−1.14263	+	0.659699i	−0.947081	−	0.320995i	$-0.895983\pi$
$167$	−14.7661	+	8.52518i	−1.14263	+	0.659699i	−0.195551	+	0.980694i	$0.562649\pi$
$168$	2.26387	−	1.36927i	0.174661	−	0.105641i
$169$	6.65779	+	11.1657i	0.512138	+	0.858903i
$170$	0.947699	+	1.64146i	0.0726852	+	0.125894i
$171$			1.50132i			0.114809i
$172$	−0.563573			−0.0429721
$173$	−3.42412			−0.260331			−0.130166	−	0.991492i	$-0.541551\pi$
$173$	−3.42412			−0.260331			−0.130166	+	0.991492i	$0.541551\pi$
$174$			9.40727i			0.713163i
$175$	3.52181	−	0.0717412i	0.266224	−	0.00542312i
$176$	5.27345	+	3.04463i	0.397502	+	0.229498i
$177$	6.52765	−	3.76874i	0.490648	−	0.283276i
$178$	2.68954	+	4.65842i	0.201589	+	0.349163i
$179$	4.15211			0.310343			0.155172	−	0.987888i	$-0.450407\pi$
$179$	4.15211			0.310343			0.155172	+	0.987888i	$0.450407\pi$
$180$	1.65875	+	0.957680i	0.123636	+	0.0713812i
$181$	−9.58691			−0.712589			−0.356295	−	0.934374i	$-0.615960\pi$
$181$	−9.58691			−0.712589			−0.356295	+	0.934374i	$0.615960\pi$
$182$	4.54154	−	8.38895i	0.336641	−	0.621830i
$183$	−1.29963			−0.0960712
$184$	−4.75613	−	2.74595i	−0.350627	−	0.202434i
$185$	−4.50822			−0.331451
$186$	−2.93809	−	5.08892i	−0.215431	−	0.373138i
$187$	5.21849	−	3.01290i	0.381614	−	0.220325i
$188$	−0.0319090	−	0.0184227i	−0.00232721	−	0.00134361i
$189$	−1.36927	−	2.26387i	−0.0995995	−	0.164672i
$190$			2.87556i			0.208615i
$191$	−4.62026			−0.334310			−0.167155	−	0.985931i	$-0.553458\pi$
$191$	−4.62026			−0.334310			−0.167155	+	0.985931i	$0.553458\pi$
$192$	−1.00000			−0.0721688
$193$			21.3252i			1.53502i	0.641038	+	0.767509i	$0.278504\pi$
$193$			21.3252i			1.53502i	−0.641038	+	0.767509i	$0.721496\pi$
$194$	−9.17111	−	15.8848i	−0.658447	−	1.14046i
$195$	6.90576	−	0.0485938i	0.494532	−	0.00347987i
$196$	−6.99419	+	0.285069i	−0.499585	+	0.0203621i
$197$	23.0573	−	13.3121i	1.64277	−	0.948451i	0.662922	−	0.748689i	$-0.269316\pi$
$197$	23.0573	−	13.3121i	1.64277	−	0.948451i	0.979844	−	0.199763i	$-0.0640171\pi$
$198$	3.04463	−	5.27345i	0.216372	−	0.374768i
$199$	−10.4959	−	18.1794i	−0.744034	−	1.28871i	−0.950645	−	0.310282i	$-0.899576\pi$
$199$	−10.4959	−	18.1794i	−0.744034	−	1.28871i	0.206610	−	0.978423i	$-0.433757\pi$
$200$	−1.15302	−	0.665698i	−0.0815310	−	0.0470720i
$201$			11.1287i			0.784961i
$202$	9.97991	+	5.76191i	0.702184	+	0.405406i
$203$	12.0031	−	21.8037i	0.842451	−	1.53032i
$204$	−0.494789	+	0.857000i	−0.0346422	+	0.0600020i
$205$	−8.24677	+	14.2838i	−0.575979	+	0.997625i
$206$		−	9.48229i		−	0.660662i
$207$	−2.74595	+	4.75613i	−0.190857	+	0.330574i
$208$	−3.10974	+	1.82470i	−0.215621	+	0.126520i
$209$	9.14191			0.632359
$210$	−2.62264	−	4.33613i	−0.180979	−	0.299221i
$211$	−7.55416	−	13.0842i	−0.520050	−	0.900753i	−0.999728	−	0.0233084i	$-0.992580\pi$
$211$	−7.55416	−	13.0842i	−0.520050	−	0.900753i	0.479678	−	0.877444i	$-0.340753\pi$
$212$	8.34047			0.572826
$213$	9.53931	+	5.50752i	0.653622	+	0.377369i
$214$	−5.88524	+	3.39785i	−0.402307	+	0.232272i
$215$			1.07945i			0.0736176i
$216$			1.00000i			0.0680414i
$217$	0.316633	+	15.5437i	0.0214944	+	1.05517i
$218$	−4.92592	−	8.53194i	−0.333625	−	0.577856i
$219$	−5.99988	−	3.46403i	−0.405434	−	0.234078i
$220$	5.83156	−	10.1006i	0.393164	−	0.680980i
$221$	0.0251062	+	3.56789i	0.00168882	+	0.240002i
$222$	−1.17686	−	2.03838i	−0.0789857	−	0.136807i
$223$	−5.98759	+	3.45693i	−0.400958	+	0.231493i	−0.686897	−	0.726754i	$-0.741028\pi$
$223$	−5.98759	+	3.45693i	−0.400958	+	0.231493i	0.285939	+	0.958248i	$0.407695\pi$
$224$	2.31775	+	1.27594i	0.154861	+	0.0852521i
$225$	−0.665698	+	1.15302i	−0.0443799	+	0.0768682i
$226$	−4.82449	+	2.78542i	−0.320920	+	0.185283i
$227$	−12.1029	+	6.98762i	−0.803298	+	0.463784i	−0.844623	−	0.535361i	$-0.820175\pi$
$227$	−12.1029	+	6.98762i	−0.803298	+	0.463784i	0.0413250	+	0.999146i	$0.486842\pi$
$228$	−1.30018	+	0.750659i	−0.0861065	+	0.0497136i
$229$	8.91770	−	5.14864i	0.589298	−	0.340232i	−0.175522	−	0.984476i	$-0.556161\pi$
$229$	8.91770	−	5.14864i	0.589298	−	0.340232i	0.764820	+	0.644244i	$0.222828\pi$
$230$	−5.25949	+	9.10971i	−0.346801	+	0.600676i
$231$	−13.7853	+	8.33782i	−0.907006	+	0.548588i
$232$	−8.14693	+	4.70363i	−0.534872	+	0.308809i
$233$	9.12977	+	15.8132i	0.598111	+	1.03596i	0.993100	+	0.117273i	$0.0374153\pi$
$233$	9.12977	+	15.8132i	0.598111	+	1.03596i	−0.394988	+	0.918686i	$0.629251\pi$
$234$	1.82470	+	3.10974i	0.119285	+	0.203290i
$235$	−0.0352861	+	0.0611173i	−0.00230181	+	0.00398685i
$236$	6.52765	+	3.76874i	0.424914	+	0.245324i
$237$	0.389363	+	0.674397i	0.0252919	+	0.0438068i
$238$	2.24028	−	1.35500i	0.145216	−	0.0878313i
$239$		−	15.5912i		−	1.00851i	−0.863554	−	0.504256i	$-0.831767\pi$
$239$		−	15.5912i		−	1.00851i	0.863554	−	0.504256i	$-0.168233\pi$
$240$			1.91536i			0.123636i
$241$	13.0640	−	7.54249i	0.841524	−	0.485854i	−0.0162577	−	0.999868i	$-0.505175\pi$
$241$	13.0640	−	7.54249i	0.841524	−	0.485854i	0.857782	+	0.514014i	$0.171842\pi$
$242$	−22.5852	−	13.0395i	−1.45183	−	0.838214i
$243$	1.00000			0.0641500
$244$	−0.649814	−	1.12551i	−0.0416001	−	0.0720534i
$245$	0.546010	+	13.3964i	0.0348833	+	0.855864i
$246$	−8.61119			−0.549030
$247$	−2.67349	+	4.70679i	−0.170110	+	0.299486i
$248$	2.93809	−	5.08892i	0.186569	−	0.323147i
$249$		−	14.6405i		−	0.927801i
$250$	−6.06345	+	10.5022i	−0.383486	+	0.664218i
$251$	8.84418	−	15.3186i	0.558240	−	0.966900i	−0.439404	−	0.898290i	$-0.644810\pi$
$251$	8.84418	−	15.3186i	0.558240	−	0.966900i	0.997644	−	0.0686100i	$-0.0218564\pi$
$252$	1.27594	−	2.31775i	0.0803764	−	0.146005i
$253$	28.9613	+	16.7208i	1.82078	+	1.05123i
$254$		−	2.21395i		−	0.138916i
$255$	1.64146	+	0.947699i	0.102792	+	0.0593472i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.3659	+	23.1505i	−0.833743	+	1.44409i	0.0613064	+	0.998119i	$0.480473\pi$
$257$	−13.3659	+	23.1505i	−0.833743	+	1.44409i	−0.895050	+	0.445967i	$0.852860\pi$
$258$	−0.488069	+	0.281787i	−0.0303858	+	0.0175433i
$259$	0.126828	+	6.22607i	0.00788072	+	0.386869i
$260$	3.49496	+	5.95626i	0.216748	+	0.369392i
$261$	4.70363	+	8.14693i	0.291148	+	0.504283i
$262$			9.00890i			0.556572i
$263$	6.48217			0.399708			0.199854	−	0.979826i	$-0.435953\pi$
$263$	6.48217			0.399708			0.199854	+	0.979826i	$0.435953\pi$
$264$	6.08926			0.374768
$265$		−	15.9750i		−	0.981337i
$266$	3.97129	−	0.0808972i	0.243495	−	0.00496013i
$267$	4.65842	+	2.68954i	0.285090	+	0.164597i
$268$	−9.63777	+	5.56437i	−0.588721	+	0.339898i
$269$	−4.11359	−	7.12495i	−0.250810	−	0.434416i	0.712939	−	0.701226i	$-0.247364\pi$
$269$	−4.11359	−	7.12495i	−0.250810	−	0.434416i	−0.963749	+	0.266810i	$0.914030\pi$
$270$	1.91536			0.116565
$271$	17.9814	+	10.3816i	1.09229	+	0.630636i	0.934186	−	0.356786i	$-0.116128\pi$
$271$	17.9814	+	10.3816i	1.09229	+	0.630636i	0.158107	+	0.987422i	$0.449461\pi$
$272$	−0.989578			−0.0600020
$273$	−0.261388	−	9.53581i	−0.0158199	−	0.577133i
$274$	3.23212			0.195260
$275$	7.02106	+	4.05361i	0.423386	+	0.244442i
$276$	−5.49191			−0.330574
$277$	5.52750	+	9.57391i	0.332115	+	0.575241i	0.982926	−	0.183999i	$-0.0589044\pi$
$277$	5.52750	+	9.57391i	0.332115	+	0.575241i	−0.650811	+	0.759240i	$0.725571\pi$
$278$	3.50044	−	2.02098i	0.209942	−	0.121210i
$279$	−5.08892	−	2.93809i	−0.304666	−	0.175899i
$280$	2.44388	−	4.43933i	0.146050	−	0.265301i
$281$			25.6128i			1.52793i	0.645256	+	0.763966i	$0.276751\pi$
$281$			25.6128i			1.52793i	−0.645256	+	0.763966i	$0.723249\pi$
$282$	−0.0368454			−0.00219411
$283$	28.2872			1.68150			0.840750	−	0.541424i	$-0.182115\pi$
$283$	28.2872			1.68150			0.840750	+	0.541424i	$0.182115\pi$
$284$			11.0150i			0.653622i
$285$	1.43778	+	2.49031i	0.0851669	+	0.147513i
$286$	18.9360	−	11.1111i	1.11971	−	0.657012i
$287$	19.9586	+	10.9873i	1.17812	+	0.648562i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	8.01037	−	13.8744i	0.471198	−	0.816139i
$290$	9.00915	+	15.6043i	0.529036	+	0.916317i
$291$	−15.8848	−	9.17111i	−0.931185	−	0.537620i
$292$		−	6.92807i		−	0.405434i
$293$	−11.6542	−	6.72853i	−0.680843	−	0.393085i	0.119330	−	0.992855i	$-0.461926\pi$
$293$	−11.6542	−	6.72853i	−0.680843	−	0.393085i	−0.800173	+	0.599770i	$0.795259\pi$
$294$	−5.91461	+	3.74397i	−0.344947	+	0.218353i
$295$	7.21849	−	12.5028i	0.420277	−	0.727941i
$296$	1.17686	−	2.03838i	0.0684036	−	0.118479i
$297$		−	6.08926i		−	0.353335i
$298$	2.76389	−	4.78720i	0.160108	−	0.277315i
$299$	−17.0784	+	10.0211i	−0.987669	+	0.579535i
$300$	−1.33140			−0.0768682
$301$	1.49077	−	0.0303677i	0.0859263	−	0.00175036i
$302$	−1.89223	−	3.27744i	−0.108886	−	0.188596i
$303$	11.5238			0.662026
$304$	−1.30018	−	0.750659i	−0.0745704	−	0.0430532i
$305$	−2.15576	+	1.24463i	−0.123438	+	0.0712672i
$306$			0.989578i			0.0565704i
$307$		−	14.6943i		−	0.838645i	−0.907837	−	0.419323i	$-0.862268\pi$
$307$		−	14.6943i		−	0.838645i	0.907837	−	0.419323i	$-0.137732\pi$
$308$	−14.1134	−	7.76951i	−0.804186	−	0.442709i
$309$	−4.74114	−	8.21190i	−0.269714	−	0.467159i
$310$	−9.74711	−	5.62750i	−0.553599	−	0.319620i
$311$	2.95573	−	5.11947i	0.167604	−	0.290298i	−0.769973	−	0.638076i	$-0.779730\pi$
$311$	2.95573	−	5.11947i	0.167604	−	0.290298i	0.937577	+	0.347778i	$0.113064\pi$
$312$	−1.78076	+	3.13511i	−0.100816	+	0.177490i
$313$	−8.30358	−	14.3822i	−0.469346	−	0.812932i	0.530040	−	0.847973i	$-0.322177\pi$
$313$	−8.30358	−	14.3822i	−0.469346	−	0.812932i	−0.999386	+	0.0350413i	$0.988844\pi$
$314$	14.5748	−	8.41478i	0.822505	−	0.474874i
$315$	−4.43933	−	2.44388i	−0.250128	−	0.137697i
$316$	−0.389363	+	0.674397i	−0.0219034	+	0.0379378i
$317$	28.7686	−	16.6095i	1.61580	−	0.932885i	0.627815	−	0.778363i	$-0.283950\pi$
$317$	28.7686	−	16.6095i	1.61580	−	0.932885i	0.987989	−	0.154522i	$-0.0493838\pi$
$318$	7.22306	−	4.17024i	0.405049	−	0.233855i
$319$	49.6088	−	28.6417i	2.77756	−	1.60362i
$320$	−1.65875	+	0.957680i	−0.0927270	+	0.0535359i
$321$	−3.39785	+	5.88524i	−0.189649	+	0.328482i
$322$	12.7289	+	7.00733i	0.709354	+	0.390503i
$323$	−1.28663	+	0.742835i	−0.0715899	+	0.0413325i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−4.14029	+	2.42940i	−0.229662	+	0.134759i
$326$	−9.63427	+	16.6871i	−0.533593	+	0.924210i
$327$	−8.53194	−	4.92592i	−0.471818	−	0.272404i
$328$	−4.30560	−	7.45751i	−0.237737	−	0.411772i
$329$	0.0853985	+	0.0470123i	0.00470817	+	0.00259187i
$330$		−	11.6631i		−	0.642034i
$331$			20.0514i			1.10213i	0.834463	+	0.551064i	$0.185778\pi$
$331$			20.0514i			1.10213i	−0.834463	+	0.551064i	$0.814222\pi$
$332$	12.6790	−	7.32023i	0.695851	−	0.401750i
$333$	−2.03838	−	1.17686i	−0.111703	−	0.0644915i
$334$	−17.0504			−0.932955
$335$	10.6578	+	18.4598i	0.582296	+	1.00857i
$336$	2.64520	−	0.0538842i	0.144308	−	0.00293962i
$337$	−13.8383			−0.753823			−0.376911	−	0.926249i	$-0.623014\pi$
$337$	−13.8383			−0.753823			−0.376911	+	0.926249i	$0.623014\pi$
$338$	0.182945	+	12.9987i	0.00995091	+	0.707037i
$339$	−2.78542	+	4.82449i	−0.151283	+	0.262030i
$340$			1.89540i			0.102792i
$341$	−17.8908	+	30.9877i	−0.968840	+	1.67808i
$342$	−0.750659	+	1.30018i	−0.0405910	+	0.0703056i
$343$	18.4857	−	1.13094i	0.998134	−	0.0610651i
$344$	−0.488069	−	0.281787i	−0.0263149	−	0.0151929i
$345$			10.5190i			0.566323i
$346$	−2.96538	−	1.71206i	−0.159420	−	0.0920409i
$347$	−8.13096	−	14.0832i	−0.436493	−	0.756028i	0.560923	−	0.827868i	$-0.310446\pi$
$347$	−8.13096	−	14.0832i	−0.436493	−	0.756028i	−0.997416	+	0.0718397i	$0.977113\pi$
$348$	−4.70363	+	8.14693i	−0.252141	+	0.436721i
$349$	−4.35089	+	2.51199i	−0.232898	+	0.134464i	−0.611908	−	0.790929i	$-0.709598\pi$
$349$	−4.35089	+	2.51199i	−0.232898	+	0.134464i	0.379010	+	0.925392i	$0.376264\pi$
$350$	3.08585	+	1.69878i	0.164946	+	0.0908034i
$351$	3.13511	+	1.78076i	0.167340	+	0.0950499i
$352$	3.04463	+	5.27345i	0.162279	+	0.281076i
$353$		−	15.7290i		−	0.837172i	−0.908177	−	0.418586i	$-0.862526\pi$
$353$		−	15.7290i		−	0.837172i	0.908177	−	0.418586i	$-0.137474\pi$
$354$	7.53748			0.400613
$355$	21.0978			1.11975
$356$			5.37907i			0.285090i
$357$	1.26264	−	2.29360i	0.0668259	−	0.121390i
$358$	3.59583	+	2.07605i	0.190046	+	0.109723i
$359$	12.7639	−	7.36925i	0.673654	−	0.388934i	−0.123806	−	0.992306i	$-0.539510\pi$
$359$	12.7639	−	7.36925i	0.673654	−	0.388934i	0.797460	+	0.603372i	$0.206177\pi$
$360$	0.957680	+	1.65875i	0.0504742	+	0.0874238i
$361$	16.7460			0.881371
$362$	−8.30251	−	4.79345i	−0.436370	−	0.251938i
$363$	−26.0791			−1.36880
$364$	8.12756	−	4.99427i	0.426000	−	0.261771i
$365$	−13.2697			−0.694570
$366$	−1.12551	−	0.649814i	−0.0588314	−	0.0339663i
$367$	−3.70974			−0.193647			−0.0968233	−	0.995302i	$-0.530868\pi$
$367$	−3.70974			−0.193647			−0.0968233	+	0.995302i	$0.530868\pi$
$368$	−2.74595	−	4.75613i	−0.143143	−	0.247931i
$369$	−7.45751	+	4.30560i	−0.388222	+	0.224140i
$370$	−3.90423	−	2.25411i	−0.202971	−	0.117186i
$371$	−22.0622	+	0.449419i	−1.14541	+	0.0233327i
$372$		−	5.87618i		−	0.304666i
$373$	2.89011			0.149644			0.0748220	−	0.997197i	$-0.476161\pi$
$373$	2.89011			0.149644			0.0748220	+	0.997197i	$0.476161\pi$
$374$	6.02580			0.311587
$375$			12.1269i			0.626231i
$376$	−0.0184227	−	0.0319090i	−0.000950078	−	0.00164558i
$377$	0.238668	+	33.9175i	0.0122920	+	1.74684i
$378$	−0.0538842	−	2.64520i	−0.00277150	−	0.136055i
$379$	−15.6860	+	9.05631i	−0.805735	+	0.465191i	−0.845473	−	0.534019i	$-0.820681\pi$
$379$	−15.6860	+	9.05631i	−0.805735	+	0.465191i	0.0397375	+	0.999210i	$0.487348\pi$
$380$	−1.43778	+	2.49031i	−0.0737567	+	0.127750i
$381$	−1.10698	−	1.91734i	−0.0567121	−	0.0982282i
$382$	−4.00126	−	2.31013i	−0.204722	−	0.118196i
$383$		−	12.8927i		−	0.658788i	−0.944193	−	0.329394i	$-0.893156\pi$
$383$		−	12.8927i		−	0.658788i	0.944193	−	0.329394i	$-0.106844\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	−14.8814	+	27.0323i	−0.758427	+	1.37769i
$386$	−10.6626	+	18.4681i	−0.542711	+	0.940003i
$387$	−0.281787	+	0.488069i	−0.0143240	+	0.0248099i
$388$		−	18.3422i		−	0.931185i
$389$	−4.10597	+	7.11174i	−0.208181	+	0.360580i	−0.951141	−	0.308755i	$-0.900088\pi$
$389$	−4.10597	+	7.11174i	−0.208181	+	0.360580i	0.742961	+	0.669335i	$0.233421\pi$
$390$	6.00486	+	3.41080i	0.304068	+	0.172712i
$391$	−5.43467			−0.274843
$392$	−6.19968	−	3.25022i	−0.313131	−	0.164161i
$393$	4.50445	+	7.80194i	0.227220	+	0.393556i
$394$	26.6243			1.34131
$395$	1.29171	+	0.745771i	0.0649932	+	0.0375238i
$396$	5.27345	−	3.04463i	0.265001	−	0.152998i
$397$			13.4926i			0.677176i	0.940935	+	0.338588i	$0.109949\pi$
$397$			13.4926i			0.677176i	−0.940935	+	0.338588i	$0.890051\pi$
$398$		−	20.9918i		−	1.05222i
$399$	3.39879	−	2.05570i	0.170152	−	0.102914i
$400$	−0.665698	−	1.15302i	−0.0332849	−	0.0576512i
$401$	5.68607	+	3.28286i	0.283949	+	0.163938i	0.635210	−	0.772340i	$-0.280914\pi$
$401$	5.68607	+	3.28286i	0.283949	+	0.163938i	−0.351261	+	0.936278i	$0.614247\pi$
$402$	−5.56437	+	9.63777i	−0.277526	+	0.480688i
$403$	−10.7223	−	18.2734i	−0.534115	−	0.910261i
$404$	5.76191	+	9.97991i	0.286666	+	0.496519i
$405$	1.65875	−	0.957680i	0.0824240	−	0.0475875i
$406$	21.2968	−	12.8811i	1.05694	−	0.639276i
$407$	−7.16621	+	12.4122i	−0.355216	+	0.615252i
$408$	−0.857000	+	0.494789i	−0.0424278	+	0.0244957i
$409$	17.6924	−	10.2147i	0.874831	−	0.505084i	0.00588036	−	0.999983i	$-0.498128\pi$
$409$	17.6924	−	10.2147i	0.874831	−	0.505084i	0.868951	+	0.494899i	$0.164795\pi$
$410$	−14.2838	+	8.24677i	−0.705427	+	0.407279i
$411$	2.79910	−	1.61606i	0.138069	−	0.0797145i
$412$	4.74114	−	8.21190i	0.233579	−	0.404571i
$413$	−17.4700	−	9.61735i	−0.859644	−	0.473239i
$414$	−4.75613	+	2.74595i	−0.233751	+	0.134956i
$415$	−14.0209	−	24.2849i	−0.688258	−	1.19210i
$416$	−3.60546	+	0.0253706i	−0.176772	+	0.00124389i
$417$	2.02098	−	3.50044i	0.0989678	−	0.171417i
$418$	7.91713	+	4.57096i	0.387239	+	0.223573i
$419$	−14.0822	−	24.3910i	−0.687959	−	1.19158i	−0.972497	−	0.232915i	$-0.925173\pi$
$419$	−14.0822	−	24.3910i	−0.687959	−	1.19158i	0.284538	−	0.958665i	$-0.408160\pi$
$420$	−0.103208	−	5.06651i	−0.00503601	−	0.247221i
$421$		−	37.1296i		−	1.80959i	−0.425852	−	0.904793i	$-0.640026\pi$
$421$		−	37.1296i		−	1.80959i	0.425852	−	0.904793i	$-0.359974\pi$
$422$		−	15.1083i		−	0.735462i
$423$	−0.0319090	+	0.0184227i	−0.00155147	+	0.000895742i
$424$	7.22306	+	4.17024i	0.350783	+	0.202525i
$425$	−1.31752			−0.0639091
$426$	5.50752	+	9.53931i	0.266840	+	0.462181i
$427$	1.77954	+	2.94219i	0.0861178	+	0.142382i
$428$	−6.79569			−0.328482
$429$	10.8435	−	19.0905i	0.523529	−	0.921697i
$430$	−0.539723	+	0.934828i	−0.0260278	+	0.0450814i
$431$		−	37.6140i		−	1.81180i	−0.423490	−	0.905901i	$-0.639195\pi$
$431$		−	37.6140i		−	1.81180i	0.423490	−	0.905901i	$-0.360805\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−8.53304	+	14.7797i	−0.410072	+	0.710265i	−0.994897	−	0.100894i	$-0.967830\pi$
$433$	−8.53304	+	14.7797i	−0.410072	+	0.710265i	0.584825	+	0.811159i	$0.301163\pi$
$434$	−7.49763	+	13.6195i	−0.359898	+	0.653759i
$435$	15.6043	+	9.00915i	0.748169	+	0.431956i
$436$		−	9.85184i		−	0.471818i
$437$	−7.14047	−	4.12255i	−0.341575	−	0.197208i
$438$	−3.46403	−	5.99988i	−0.165518	−	0.286685i
$439$	−6.04302	+	10.4668i	−0.288417	+	0.499554i	−0.973432	−	0.228976i	$-0.926462\pi$
$439$	−6.04302	+	10.4668i	−0.288417	+	0.499554i	0.685015	+	0.728529i	$0.259796\pi$
$440$	10.1006	−	5.83156i	0.481525	−	0.278009i
$441$	−3.25022	+	6.19968i	−0.154772	+	0.295223i
$442$	−1.76220	+	3.10243i	−0.0838193	+	0.147568i
$443$	−4.02276	−	6.96763i	−0.191127	−	0.331042i	0.754497	−	0.656304i	$-0.227881\pi$
$443$	−4.02276	−	6.96763i	−0.191127	−	0.331042i	−0.945624	+	0.325262i	$0.894548\pi$
$444$		−	2.35372i		−	0.111703i
$445$	10.3029			0.488403
$446$	−6.91387			−0.327381
$447$		−	5.52778i		−	0.261455i
$448$	1.36927	+	2.26387i	0.0646918	+	0.106958i
$449$	−13.6786	−	7.89736i	−0.645535	−	0.372700i	0.141209	−	0.989980i	$-0.454901\pi$
$449$	−13.6786	−	7.89736i	−0.645535	−	0.372700i	−0.786743	+	0.617280i	$0.788234\pi$
$450$	−1.15302	+	0.665698i	−0.0543540	+	0.0313813i
$451$	26.2179	+	45.4107i	1.23455	+	2.13831i
$452$	−5.57084			−0.262030
$453$	−3.27744	−	1.89223i	−0.153988	−	0.0889048i
$454$	−13.9752			−0.655890
$455$	−9.56583	−	15.5672i	−0.448453	−	0.729802i
$456$	−1.50132			−0.0703056
$457$	−4.00978	−	2.31505i	−0.187570	−	0.108293i	0.403275	−	0.915079i	$-0.367872\pi$
$457$	−4.00978	−	2.31505i	−0.187570	−	0.108293i	−0.590844	+	0.806786i	$0.701205\pi$
$458$	10.2973			0.481160
$459$	0.494789	+	0.857000i	0.0230948	+	0.0400013i
$460$	−9.10971	+	5.25949i	−0.424742	+	0.245225i
$461$	25.9440	+	14.9788i	1.20833	+	0.697631i	0.962395	−	0.271655i	$-0.0875711\pi$
$461$	25.9440	+	14.9788i	1.20833	+	0.697631i	0.245937	+	0.969286i	$0.420904\pi$
$462$	−16.1073	+	0.328115i	−0.749381	+	0.0152653i
$463$		−	3.42058i		−	0.158968i	−0.996836	−	0.0794840i	$-0.974673\pi$
$463$		−	3.42058i		−	0.158968i	0.996836	−	0.0794840i	$-0.0253273\pi$
$464$	−9.40727			−0.436721
$465$	−11.2550			−0.521938
$466$			18.2595i			0.845857i
$467$	−12.4308	−	21.5308i	−0.575230	−	0.996327i	−0.996017	−	0.0891677i	$-0.971579\pi$
$467$	−12.4308	−	21.5308i	−0.575230	−	0.996327i	0.420787	−	0.907160i	$-0.361754\pi$
$468$	0.0253706	+	3.60546i	0.00117276	+	0.166663i
$469$	25.1940	−	15.2382i	1.16335	−	0.703635i
$470$	−0.0611173	+	0.0352861i	−0.00281913	+	0.00162763i
$471$	8.41478	−	14.5748i	0.387733	−	0.671573i
$472$	3.76874	+	6.52765i	0.173470	+	0.300459i
$473$	2.97198	+	1.71587i	0.136652	+	0.0788959i
$474$			0.778727i			0.0357681i
$475$	−1.73105	−	0.999425i	−0.0794262	−	0.0458567i
$476$	2.61763	−	0.0533226i	0.119979	−	0.00244404i
$477$	4.17024	−	7.22306i	0.190942	−	0.330721i
$478$	7.79561	−	13.5024i	0.356563	−	0.617585i
$479$		−	3.80312i		−	0.173769i	−0.996218	−	0.0868846i	$-0.972309\pi$
$479$		−	3.80312i		−	0.173769i	0.996218	−	0.0868846i	$-0.0276911\pi$
$480$	−0.957680	+	1.65875i	−0.0437119	+	0.0757112i
$481$	−4.29484	−	7.31945i	−0.195828	−	0.333738i
$482$	15.0850			0.687102
$483$	14.5272	−	0.295927i	0.661011	−	0.0134651i
$484$	−13.0395	−	22.5852i	−0.592707	−	1.02660i
$485$	−35.1319			−1.59526
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−16.1813	+	9.34228i	−0.733245	+	0.423339i	−0.819608	−	0.572925i	$-0.805809\pi$
$487$	−16.1813	+	9.34228i	−0.733245	+	0.423339i	0.0863631	+	0.996264i	$0.472475\pi$
$488$		−	1.29963i		−	0.0588314i
$489$			19.2685i			0.871354i
$490$	−6.22534	+	11.8746i	−0.281232	+	0.536441i
$491$	1.72582	+	2.98921i	0.0778852	+	0.134901i	0.902337	−	0.431031i	$-0.141850\pi$
$491$	1.72582	+	2.98921i	0.0778852	+	0.134901i	−0.824452	+	0.565932i	$0.808517\pi$
$492$	−7.45751	−	4.30560i	−0.336211	−	0.194111i
$493$	−4.65461	+	8.06203i	−0.209633	+	0.363095i
$494$	−4.66870	+	2.73946i	−0.210055	+	0.123254i
$495$	−5.83156	−	10.1006i	−0.262109	−	0.453986i
$496$	5.08892	−	2.93809i	0.228499	−	0.131924i
$497$	−0.593536	−	29.1370i	−0.0266237	−	1.30697i
$498$	7.32023	−	12.6790i	0.328027	−	0.568160i
$499$	−37.0020	+	21.3631i	−1.65644	+	0.956345i	−0.682099	+	0.731260i	$0.738933\pi$
$499$	−37.0020	+	21.3631i	−1.65644	+	0.956345i	−0.974339	+	0.225085i	$0.927734\pi$
$500$	−10.5022	+	6.06345i	−0.469673	+	0.271166i
$501$	−14.7661	+	8.52518i	−0.659699	+	0.380877i
$502$	15.3186	−	8.84418i	0.683701	−	0.394735i
$503$	3.67137	−	6.35900i	0.163698	−	0.283534i	−0.772494	−	0.635022i	$-0.780991\pi$
$503$	3.67137	−	6.35900i	0.163698	−	0.283534i	0.936192	+	0.351488i	$0.114324\pi$
$504$	2.26387	−	1.36927i	0.100841	−	0.0609920i
$505$	19.1151	−	11.0361i	0.850612	−	0.491101i
$506$	16.7208	+	28.9613i	0.743332	+	1.28749i
$507$	6.65779	+	11.1657i	0.295683	+	0.495888i
$508$	1.10698	−	1.91734i	0.0491141	−	0.0850682i
$509$	−10.0408	−	5.79707i	−0.445052	−	0.256951i	0.260686	−	0.965424i	$-0.416051\pi$
$509$	−10.0408	−	5.79707i	−0.445052	−	0.256951i	−0.705738	+	0.708473i	$0.749384\pi$
$510$	0.947699	+	1.64146i	0.0419648	+	0.0726852i
$511$	0.373313	+	18.3261i	0.0165144	+	0.810701i
$512$		−	1.00000i		−	0.0441942i
$513$			1.50132i			0.0662848i
$514$	−23.1505	+	13.3659i	−1.02112	+	0.589545i
$515$	−15.7287	−	9.08100i	−0.693091	−	0.400156i
$516$	−0.563573			−0.0248099
$517$	0.112181	+	0.194302i	0.00493369	+	0.00854541i
$518$	−3.00320	+	5.45535i	−0.131953	+	0.239694i
$519$	−3.42412			−0.150302
$520$	0.0485938	+	6.90576i	0.00213098	+	0.302837i
$521$	−18.5153	+	32.0694i	−0.811169	+	1.40499i	0.100877	+	0.994899i	$0.467835\pi$
$521$	−18.5153	+	32.0694i	−0.811169	+	1.40499i	−0.912046	+	0.410087i	$0.865498\pi$
$522$			9.40727i			0.411745i
$523$	−10.3547	+	17.9349i	−0.452780	+	0.784238i	−0.998558	−	0.0536924i	$-0.982901\pi$
$523$	−10.3547	+	17.9349i	−0.452780	+	0.784238i	0.545778	+	0.837930i	$0.316234\pi$
$524$	−4.50445	+	7.80194i	−0.196778	+	0.340829i
$525$	3.52181	−	0.0717412i	0.153705	−	0.00313104i
$526$	5.61372	+	3.24108i	0.244770	+	0.141318i
$527$		−	5.81493i		−	0.253303i
$528$	5.27345	+	3.04463i	0.229498	+	0.132501i
$529$	−3.58053	−	6.20166i	−0.155675	−	0.269637i
$530$	7.98750	−	13.8348i	0.346955	−	0.600943i
$531$	6.52765	−	3.76874i	0.283276	−	0.163549i
$532$	3.47969	+	1.91559i	0.150864	+	0.0830512i
$533$	−31.0473	+	0.218471i	−1.34481	+	0.00946303i
$534$	2.68954	+	4.65842i	0.116388	+	0.201589i
$535$			13.0162i			0.562739i
$536$	−11.1287			−0.480688
$537$	4.15211			0.179177
$538$		−	8.22718i		−	0.354699i
$539$	37.7515	+	19.7914i	1.62607	+	0.852477i
$540$	1.65875	+	0.957680i	0.0713812	+	0.0412120i
$541$	38.1431	−	22.0219i	1.63990	−	0.946796i	0.659031	−	0.752116i	$-0.270967\pi$
$541$	38.1431	−	22.0219i	1.63990	−	0.946796i	0.980867	−	0.194680i	$-0.0623668\pi$
$542$	10.3816	+	17.9814i	0.445927	+	0.772368i
$543$	−9.58691			−0.411414
$544$	−0.857000	−	0.494789i	−0.0367436	−	0.0212139i
$545$	−18.8698			−0.808294
$546$	4.54154	−	8.38895i	0.194360	−	0.359014i
$547$	−37.3765			−1.59810			−0.799052	−	0.601262i	$-0.794665\pi$
$547$	−37.3765			−1.59810			−0.799052	+	0.601262i	$0.794665\pi$
$548$	2.79910	+	1.61606i	0.119572	+	0.0690347i
$549$	−1.29963			−0.0554668
$550$	4.05361	+	7.02106i	0.172846	+	0.299379i
$551$	−12.2311	+	7.06165i	−0.521064	+	0.300836i
$552$	−4.75613	−	2.74595i	−0.202434	−	0.116876i
$553$	0.993606	−	1.80490i	0.0422524	−	0.0767521i
$554$			11.0550i			0.469682i
$555$	−4.50822			−0.191363
$556$	4.04196			0.171417
$557$			39.3719i			1.66824i	0.551583	+	0.834120i	$0.314024\pi$
$557$			39.3719i			1.66824i	−0.551583	+	0.834120i	$0.685976\pi$
$558$	−2.93809	−	5.08892i	−0.124379	−	0.215431i
$559$	−1.75256	+	1.02835i	−0.0741256	+	0.0434947i
$560$	4.33613	−	2.62264i	0.183235	−	0.110827i
$561$	5.21849	−	3.01290i	0.220325	−	0.127205i
$562$	−12.8064	+	22.1813i	−0.540206	+	0.935664i
$563$	13.7545	+	23.8235i	0.579683	+	1.00404i	0.995515	+	0.0945993i	$0.0301570\pi$
$563$	13.7545	+	23.8235i	0.579683	+	1.00404i	−0.415832	+	0.909441i	$0.636510\pi$
$564$	−0.0319090	−	0.0184227i	−0.00134361	−	0.000775735i
$565$			10.6702i			0.448897i
$566$	24.4974	+	14.1436i	1.02970	+	0.594500i
$567$	−1.36927	−	2.26387i	−0.0575038	−	0.0950736i
$568$	−5.50752	+	9.53931i	−0.231090	+	0.400260i
$569$	13.6283	−	23.6048i	0.571326	−	0.989566i	−0.425104	−	0.905145i	$-0.639762\pi$
$569$	13.6283	−	23.6048i	0.571326	−	0.989566i	0.996430	−	0.0844215i	$-0.0269042\pi$
$570$			2.87556i			0.120444i
$571$	−3.18353	+	5.51404i	−0.133227	+	0.230755i	−0.924919	−	0.380165i	$-0.875867\pi$
$571$	−3.18353	+	5.51404i	−0.133227	+	0.230755i	0.791692	+	0.610920i	$0.209200\pi$
$572$	21.9546	−	0.154488i	0.917968	−	0.00645947i
$573$	−4.62026			−0.193014
$574$	11.7910	+	19.4946i	0.492147	+	0.813690i
$575$	−3.65595	−	6.33230i	−0.152464	−	0.264075i
$576$	−1.00000			−0.0416667
$577$	−34.1845	−	19.7364i	−1.42312	−	0.821638i	−0.426554	−	0.904462i	$-0.640273\pi$
$577$	−34.1845	−	19.7364i	−1.42312	−	0.821638i	−0.996564	+	0.0828247i	$0.973606\pi$
$578$	13.8744	−	8.01037i	0.577097	−	0.333187i
$579$			21.3252i			0.886244i
$580$			18.0183i			0.748169i
$581$	−33.1441	+	20.0467i	−1.37505	+	0.831677i
$582$	−9.17111	−	15.8848i	−0.380155	−	0.658447i
$583$	−43.9831	−	25.3936i	−1.82159	−	1.05170i
$584$	3.46403	−	5.99988i	0.143343	−	0.248277i
$585$	6.90576	−	0.0485938i	0.285518	−	0.00200911i
$586$	−6.72853	−	11.6542i	−0.277953	−	0.481429i
$587$	−30.6873	+	17.7173i	−1.26660	+	0.731273i	−0.974344	−	0.225066i	$-0.927740\pi$
$587$	−30.6873	+	17.7173i	−1.26660	+	0.731273i	−0.292259	+	0.956339i	$0.594407\pi$
$588$	−6.99419	+	0.285069i	−0.288436	+	0.0117560i
$589$	4.41100	−	7.64008i	0.181752	−	0.314804i
$590$	12.5028	−	7.21849i	0.514732	−	0.297181i
$591$	23.0573	−	13.3121i	0.948451	−	0.547589i
$592$	2.03838	−	1.17686i	0.0837770	−	0.0483686i
$593$	20.1290	−	11.6215i	0.826600	−	0.477238i	−0.0260872	−	0.999660i	$-0.508305\pi$
$593$	20.1290	−	11.6215i	0.826600	−	0.477238i	0.852687	+	0.522422i	$0.174971\pi$
$594$	3.04463	−	5.27345i	0.124923	−	0.216372i
$595$	−0.102132	−	5.01371i	−0.00418700	−	0.205542i
$596$	4.78720	−	2.76389i	0.196091	−	0.113213i
$597$	−10.4959	−	18.1794i	−0.429568	−	0.744034i
$598$	−19.8009	+	0.139333i	−0.809718	+	0.00569775i
$599$	3.67815	−	6.37074i	0.150285	−	0.260301i	−0.781047	−	0.624472i	$-0.785314\pi$
$599$	3.67815	−	6.37074i	0.150285	−	0.260301i	0.931332	+	0.364171i	$0.118648\pi$
$600$	−1.15302	−	0.665698i	−0.0470720	−	0.0271770i
$601$	−20.1141	−	34.8387i	−0.820473	−	1.42110i	−0.905331	−	0.424708i	$-0.860377\pi$
$601$	−20.1141	−	34.8387i	−0.820473	−	1.42110i	0.0848578	−	0.996393i	$-0.472956\pi$
$602$	1.30622	+	0.719084i	0.0532377	+	0.0293077i
$603$			11.1287i			0.453197i
$604$		−	3.78446i		−	0.153988i
$605$	−43.2587	+	24.9754i	−1.75872	+	1.01540i
$606$	9.97991	+	5.76191i	0.405406	+	0.234061i
$607$	30.6548			1.24424			0.622120	−	0.782922i	$-0.286272\pi$
$607$	30.6548			1.24424			0.622120	+	0.782922i	$0.286272\pi$
$608$	−0.750659	−	1.30018i	−0.0304432	−	0.0527292i
$609$	12.0031	−	21.8037i	0.486389	−	0.883532i
$610$	−2.48925			−0.100787
$611$	−0.132845		0.000934788i	−0.00537432		3.78175e-5i
$612$	−0.494789	+	0.857000i	−0.0200007	+	0.0346422i
$613$			23.7787i			0.960413i	0.877156	+	0.480206i	$0.159438\pi$
$613$			23.7787i			0.960413i	−0.877156	+	0.480206i	$0.840562\pi$
$614$	7.34713	−	12.7256i	0.296506	−	0.513563i
$615$	−8.24677	+	14.2838i	−0.332542	+	0.575979i
$616$	−8.33782	−	13.7853i	−0.335940	−	0.555425i
$617$	−29.2131	−	16.8662i	−1.17608	−	0.679008i	−0.220973	−	0.975280i	$-0.570923\pi$
$617$	−29.2131	−	16.8662i	−1.17608	−	0.679008i	−0.955104	+	0.296271i	$0.904257\pi$
$618$		−	9.48229i		−	0.381433i
$619$	−24.7897	−	14.3123i	−0.996382	−	0.575262i	−0.0892065	−	0.996013i	$-0.528433\pi$
$619$	−24.7897	−	14.3123i	−0.996382	−	0.575262i	−0.907176	+	0.420751i	$0.861766\pi$
$620$	−5.62750	−	9.74711i	−0.226006	−	0.391453i
$621$	−2.74595	+	4.75613i	−0.110191	+	0.190857i
$622$	5.11947	−	2.95573i	0.205272	−	0.118514i
$623$	−0.289847	−	14.2287i	−0.0116125	−	0.570063i
$624$	−3.10974	+	1.82470i	−0.124489	+	0.0730466i
$625$	8.28520	+	14.3504i	0.331408	+	0.574016i
$626$		−	16.6072i		−	0.663756i
$627$	9.14191			0.365093
$628$	16.8296			0.671573
$629$		−	2.32919i		−	0.0928709i
$630$	−2.62264	−	4.33613i	−0.104488	−	0.172755i
$631$	29.1600	+	16.8356i	1.16084	+	0.670213i	0.951506	−	0.307631i	$-0.0995361\pi$
$631$	29.1600	+	16.8356i	1.16084	+	0.670213i	0.209337	+	0.977844i	$0.432869\pi$
$632$	−0.674397	+	0.389363i	−0.0268261	+	0.0154880i
$633$	−7.55416	−	13.0842i	−0.300251	−	0.520050i
$634$	33.2191			1.31930
$635$	−3.67239	−	2.12026i	−0.145735	−	0.0841399i
$636$	8.34047			0.330721
$637$	−21.2299	+	13.6488i	−0.841160	+	0.540786i
$638$	57.2833			2.26787
$639$	9.53931	+	5.50752i	0.377369	+	0.217874i
$640$	−1.91536			−0.0757112
$641$	−4.23584	−	7.33669i	−0.167306	−	0.289782i	0.770166	−	0.637843i	$-0.220173\pi$
$641$	−4.23584	−	7.33669i	−0.167306	−	0.289782i	−0.937472	+	0.348062i	$0.886840\pi$
$642$	−5.88524	+	3.39785i	−0.232272	+	0.134102i
$643$	−4.62113	−	2.66801i	−0.182239	−	0.105216i	0.406105	−	0.913826i	$-0.366887\pi$
$643$	−4.62113	−	2.66801i	−0.182239	−	0.105216i	−0.588344	+	0.808610i	$0.700220\pi$
$644$	7.51989	+	12.4330i	0.296325	+	0.489928i
$645$			1.07945i			0.0425031i
$646$	−1.48567			−0.0584529
$647$	−14.8494			−0.583792			−0.291896	−	0.956450i	$-0.594286\pi$
$647$	−14.8494			−0.583792			−0.291896	+	0.956450i	$0.594286\pi$
$648$			1.00000i			0.0392837i
$649$	−22.9488	−	39.7486i	−0.900821	−	1.56027i
$650$	−4.80030	+	0.0337783i	−0.188283	+	0.00132489i
$651$	0.316633	+	15.5437i	0.0124098	+	0.609205i
$652$	−16.6871	+	9.63427i	−0.653515	+	0.377307i
$653$	3.50021	−	6.06254i	0.136974	−	0.237246i	−0.789376	−	0.613910i	$-0.789596\pi$
$653$	3.50021	−	6.06254i	0.136974	−	0.237246i	0.926350	+	0.376664i	$0.122929\pi$
$654$	−4.92592	−	8.53194i	−0.192619	−	0.333625i
$655$	14.9435	+	8.62765i	0.583892	+	0.337110i
$656$		−	8.61119i		−	0.336211i
$657$	−5.99988	−	3.46403i	−0.234078	−	0.135145i
$658$	0.0504511	+	0.0834132i	0.00196679	+	0.00325178i
$659$	8.85693	−	15.3406i	0.345017	−	0.597587i	−0.640340	−	0.768092i	$-0.721207\pi$
$659$	8.85693	−	15.3406i	0.345017	−	0.597587i	0.985357	+	0.170505i	$0.0545398\pi$
$660$	5.83156	−	10.1006i	0.226993	−	0.393164i
$661$		−	9.36410i		−	0.364221i	−0.983278	−	0.182111i	$-0.941707\pi$
$661$		−	9.36410i		−	0.364221i	0.983278	−	0.182111i	$-0.0582929\pi$
$662$	−10.0257	+	17.3651i	−0.389661	+	0.674912i
$663$	0.0251062	+	3.56789i	0.000975043	+	0.138565i
$664$	14.6405			0.568160
$665$	3.66904	−	6.66485i	0.142279	−	0.258452i
$666$	−1.17686	−	2.03838i	−0.0456024	−	0.0789857i
$667$	−51.6639			−2.00043
$668$	−14.7661	−	8.52518i	−0.571316	−	0.329849i
$669$	−5.98759	+	3.45693i	−0.231493	+	0.133653i
$670$			21.3155i			0.823491i
$671$			7.91377i			0.305508i
$672$	2.31775	+	1.27594i	0.0894093	+	0.0492203i
$673$	8.78701	+	15.2195i	0.338714	+	0.586670i	0.984191	−	0.177109i	$-0.0566747\pi$
$673$	8.78701	+	15.2195i	0.338714	+	0.586670i	−0.645477	+	0.763780i	$0.723341\pi$
$674$	−11.9844	−	6.91917i	−0.461620	−	0.266517i
$675$	−0.665698	+	1.15302i	−0.0256227	+	0.0443799i
$676$	−6.34092	+	11.3487i	−0.243882	+	0.436488i
$677$	16.2994	+	28.2313i	0.626436	+	1.08502i	0.988261	+	0.152773i	$0.0488202\pi$
$677$	16.2994	+	28.2313i	0.626436	+	1.08502i	−0.361826	+	0.932246i	$0.617846\pi$
$678$	−4.82449	+	2.78542i	−0.185283	+	0.106973i
$679$	0.988355	+	48.5189i	0.0379296	+	1.86198i
$680$	−0.947699	+	1.64146i	−0.0363426	+	0.0629472i
$681$	−12.1029	+	6.98762i	−0.463784	+	0.267766i
$682$	−30.9877	+	17.8908i	−1.18658	+	0.685073i
$683$	1.18045	−	0.681534i	0.0451687	−	0.0260782i	−0.477246	−	0.878770i	$-0.658365\pi$
$683$	1.18045	−	0.681534i	0.0451687	−	0.0260782i	0.522414	+	0.852692i	$0.325031\pi$
$684$	−1.30018	+	0.750659i	−0.0497136	+	0.0287022i
$685$	3.09534	−	5.36129i	0.118267	−	0.204844i
$686$	16.5746	+	8.26342i	0.632819	+	0.315499i
$687$	8.91770	−	5.14864i	0.340232	−	0.196433i
$688$	−0.281787	−	0.488069i	−0.0107430	−	0.0186075i
$689$	25.9367	−	15.2189i	0.988108	−	0.579793i
$690$	−5.25949	+	9.10971i	−0.200225	+	0.346801i
$691$	−7.84753	−	4.53078i	−0.298534	−	0.172359i	0.343250	−	0.939244i	$-0.388472\pi$
$691$	−7.84753	−	4.53078i	−0.298534	−	0.172359i	−0.641784	+	0.766885i	$0.721806\pi$
$692$	−1.71206	−	2.96538i	−0.0650828	−	0.112727i
$693$	−13.7853	+	8.33782i	−0.523660	+	0.316728i
$694$		−	16.2619i		−	0.617294i
$695$		−	7.74180i		−	0.293663i
$696$	−8.14693	+	4.70363i	−0.308809	+	0.178291i
$697$	−7.37979	−	4.26072i	−0.279529	−	0.161386i
$698$	−5.02397			−0.190160
$699$	9.12977	+	15.8132i	0.345320	+	0.598111i
$700$	1.82304	+	3.01411i	0.0689043	+	0.113923i
$701$	33.3533			1.25974			0.629869	−	0.776702i	$-0.283109\pi$
$701$	33.3533			1.25974			0.629869	+	0.776702i	$0.283109\pi$
$702$	1.82470	+	3.10974i	0.0688690	+	0.117369i
$703$	1.76684	−	3.06026i	0.0666377	−	0.115420i
$704$			6.08926i			0.229498i
$705$	−0.0352861	+	0.0611173i	−0.00132895	+	0.00230181i
$706$	7.86452	−	13.6217i	0.295985	−	0.512661i
$707$	−15.7792	−	26.0884i	−0.593437	−	0.981156i
$708$	6.52765	+	3.76874i	0.245324	+	0.141638i
$709$		−	40.7866i		−	1.53177i	−0.642976	−	0.765886i	$-0.722301\pi$
$709$		−	40.7866i		−	1.53177i	0.642976	−	0.765886i	$-0.277699\pi$
$710$	18.2712	+	10.5489i	0.685706	+	0.395893i
$711$	0.389363	+	0.674397i	0.0146023	+	0.0252919i
$712$	−2.68954	+	4.65842i	−0.100795	+	0.174581i
$713$	27.9479	−	16.1357i	1.04666	−	0.604287i
$714$	2.24028	−	1.35500i	0.0838402	−	0.0507094i
$715$	−0.295900	−	42.0510i	−0.0110660	−	1.57262i
$716$	2.07605	+	3.59583i	0.0775858	+	0.134383i
$717$		−	15.5912i		−	0.582265i
$718$	14.7385			0.550036
$719$	21.8463			0.814730			0.407365	−	0.913265i	$-0.366448\pi$
$719$	21.8463			0.814730			0.407365	+	0.913265i	$0.366448\pi$
$720$			1.91536i			0.0713812i
$721$	−12.0988	+	21.9776i	−0.450583	+	0.818489i
$722$	14.5025	+	8.37302i	0.539727	+	0.311612i
$723$	13.0640	−	7.54249i	0.485854	−	0.280508i
$724$	−4.79345	−	8.30251i	−0.178147	−	0.308560i
$725$	−12.5248			−0.465160
$726$	−22.5852	−	13.0395i	−0.838214	−	0.483943i
$727$	32.9006			1.22021			0.610107	−	0.792319i	$-0.291126\pi$
$727$	32.9006			1.22021			0.610107	+	0.792319i	$0.291126\pi$
$728$	9.53581	−	0.261388i	0.353421	−	0.00968767i
$729$	1.00000			0.0370370
$730$	−11.4919	−	6.63487i	−0.425335	−	0.245568i
$731$	−0.557700			−0.0206273
$732$	−0.649814	−	1.12551i	−0.0240178	−	0.0416001i
$733$	13.9722	−	8.06685i	0.516075	−	0.297956i	−0.219252	−	0.975668i	$-0.570362\pi$
$733$	13.9722	−	8.06685i	0.516075	−	0.297956i	0.735327	+	0.677712i	$0.237028\pi$
$734$	−3.21273	−	1.85487i	−0.118584	−	0.0684644i
$735$	0.546010	+	13.3964i	0.0201399	+	0.494134i
$736$		−	5.49191i		−	0.202434i
$737$	67.7658			2.49619
$738$	−8.61119			−0.316982
$739$		−	7.11710i		−	0.261807i	−0.991395	−	0.130903i	$-0.958212\pi$
$739$		−	7.11710i		−	0.261807i	0.991395	−	0.130903i	$-0.0417878\pi$
$740$	−2.25411	−	3.90423i	−0.0828627	−	0.143522i
$741$	−2.67349	+	4.70679i	−0.0982130	+	0.172908i
$742$	−19.3312	−	10.6419i	−0.709669	−	0.390677i
$743$	−1.46525	+	0.845960i	−0.0537546	+	0.0310353i	−0.526636	−	0.850091i	$-0.676547\pi$
$743$	−1.46525	+	0.845960i	−0.0537546	+	0.0310353i	0.472882	+	0.881126i	$0.343214\pi$
$744$	2.93809	−	5.08892i	0.107716	−	0.186569i
$745$	−5.29385	−	9.16921i	−0.193952	−	0.335934i
$746$	2.50290	+	1.44505i	0.0916378	+	0.0529071i
$747$		−	14.6405i		−	0.535666i
$748$	5.21849	+	3.01290i	0.190807	+	0.110162i
$749$	17.9760	−	0.366180i	0.656828	−	0.0133799i
$750$	−6.06345	+	10.5022i	−0.221406	+	0.383486i
$751$	−2.89853	+	5.02039i	−0.105769	+	0.183197i	−0.914052	−	0.405597i	$-0.867064\pi$
$751$	−2.89853	+	5.02039i	−0.105769	+	0.183197i	0.808283	+	0.588794i	$0.200397\pi$
$752$		−	0.0368454i		−	0.00134361i
$753$	8.84418	−	15.3186i	0.322300	−	0.558240i
$754$	−16.7521	+	29.4928i	−0.610075	+	1.07406i
$755$	−7.24861			−0.263804
$756$	1.27594	−	2.31775i	0.0464054	−	0.0842959i
$757$	1.06884	+	1.85128i	0.0388476	+	0.0672860i	0.884795	−	0.465980i	$-0.154298\pi$
$757$	1.06884	+	1.85128i	0.0388476	+	0.0672860i	−0.845948	+	0.533266i	$0.820965\pi$
$758$	−18.1126			−0.657880
$759$	28.9613	+	16.7208i	1.05123	+	0.606928i
$760$	−2.49031	+	1.43778i	−0.0903331	+	0.0521538i
$761$		−	27.7976i		−	1.00766i	−0.863802	−	0.503831i	$-0.831923\pi$
$761$		−	27.7976i		−	1.00766i	0.863802	−	0.503831i	$-0.168077\pi$
$762$		−	2.21395i		−	0.0802030i
$763$	0.530858	+	26.0601i	0.0192184	+	0.943439i
$764$	−2.31013	−	4.00126i	−0.0835775	−	0.144761i
$765$	1.64146	+	0.947699i	0.0593472	+	0.0342641i
$766$	6.44637	−	11.1654i	0.232917	−	0.403424i
$767$	27.1761	−	0.191230i	0.981272	−	0.00690492i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	32.1326	−	18.5518i	1.15873	−	0.668994i	0.207733	−	0.978186i	$-0.433392\pi$
$769$	32.1326	−	18.5518i	1.15873	−	0.668994i	0.951000	+	0.309191i	$0.100058\pi$
$770$	−26.4038	+	15.9699i	−0.951527	+	0.575516i
$771$	−13.3659	+	23.1505i	−0.481362	+	0.833743i
$772$	−18.4681	+	10.6626i	−0.664683	+	0.383755i
$773$	1.86505	−	1.07679i	0.0670814	−	0.0387294i	−0.466084	−	0.884740i	$-0.654336\pi$
$773$	1.86505	−	1.07679i	0.0670814	−	0.0387294i	0.533166	+	0.846011i	$0.321002\pi$
$774$	−0.488069	+	0.281787i	−0.0175433	+	0.0101286i
$775$	6.77537	−	3.91176i	0.243378	−	0.140515i
$776$	9.17111	−	15.8848i	0.329224	−	0.570232i
$777$	0.126828	+	6.22607i	0.00454994	+	0.223359i
$778$	−7.11174	+	4.10597i	−0.254968	+	0.147206i
$779$	−6.46407	−	11.1961i	−0.231599	−	0.401142i
$780$	3.49496	+	5.95626i	0.125140	+	0.213268i
$781$	33.5367	−	58.0873i	1.20004	−	2.07853i
$782$	−4.70656	−	2.71734i	−0.168306	−	0.0971717i
$783$	4.70363	+	8.14693i	0.168094	+	0.291148i
$784$	−3.74397	−	5.91461i	−0.133713	−	0.211236i
$785$		−	32.2347i		−	1.15050i
$786$			9.00890i			0.321337i
$787$	−10.6865	+	6.16986i	−0.380933	+	0.219932i	−0.678224	−	0.734855i	$-0.737250\pi$
$787$	−10.6865	+	6.16986i	−0.380933	+	0.219932i	0.297291	+	0.954787i	$0.403917\pi$
$788$	23.0573	+	13.3121i	0.821383	+	0.474226i
$789$	6.48217			0.230771
$790$	0.745771	+	1.29171i	0.0265333	+	0.0459571i
$791$	14.7360	−	0.300180i	0.523952	−	0.0106732i
$792$	6.08926			0.216372
$793$	−4.07447	−	2.31432i	−0.144689	−	0.0821841i
$794$	−6.74631	+	11.6850i	−0.239418	+	0.414684i
$795$		−	15.9750i		−	0.566575i
$796$	10.4959	−	18.1794i	0.372017	−	0.644353i
$797$	−8.16003	+	14.1336i	−0.289043	+	0.500637i	−0.973582	−	0.228339i	$-0.926670\pi$
$797$	−8.16003	+	14.1336i	−0.289043	+	0.500637i	0.684539	+	0.728977i	$0.260004\pi$
$798$	3.97129	−	0.0808972i	0.140582	−	0.00286373i
$799$	−0.0315765	−	0.0182307i	−0.00111710	−	0.000644955i
$800$		−	1.33140i		−	0.0470720i
$801$	4.65842	+	2.68954i	0.164597	+	0.0950301i
$802$	3.28286	+	5.68607i	0.115922	+	0.200782i
$803$	−21.0934	+	36.5348i	−0.744370	+	1.28929i
$804$	−9.63777	+	5.56437i	−0.339898	+	0.196240i
$805$	23.8136	−	14.4033i	0.839320	−	0.507649i
$806$	−0.149082	−	21.1863i	−0.00525119	−	0.746257i
$807$	−4.11359	−	7.12495i	−0.144805	−	0.250810i
$808$			11.5238i			0.405406i
$809$	56.4487			1.98463			0.992315	−	0.123737i	$-0.0394878\pi$
$809$	56.4487			1.98463			0.992315	+	0.123737i	$0.0394878\pi$
$810$	1.91536			0.0672989
$811$			19.5621i			0.686920i	0.939167	+	0.343460i	$0.111599\pi$
$811$			19.5621i			0.686920i	−0.939167	+	0.343460i	$0.888401\pi$
$812$	24.8841	−	0.506903i	0.873262	−	0.0177888i
$813$	17.9814	+	10.3816i	0.630636	+	0.364098i
$814$	−12.4122	+	7.16621i	−0.435049	+	0.251175i
$815$	18.4531	+	31.9617i	0.646384	+	1.11957i
$816$	−0.989578			−0.0346422
$817$	−0.732746	−	0.423051i	−0.0256356	−	0.0148007i
$818$	20.4294			0.714296
$819$	−0.261388	−	9.53581i	−0.00913362	−	0.333208i
$820$	−16.4935			−0.575979
$821$	−37.4132	−	21.6005i	−1.30573	−	0.753863i	−0.324348	−	0.945938i	$-0.605145\pi$
$821$	−37.4132	−	21.6005i	−1.30573	−	0.753863i	−0.981380	+	0.192075i	$0.938478\pi$
$822$	3.23212			0.112733
$823$	3.02412	+	5.23793i	0.105414	+	0.182583i	0.913907	−	0.405923i	$-0.133050\pi$
$823$	3.02412	+	5.23793i	0.105414	+	0.182583i	−0.808493	+	0.588506i	$0.799716\pi$
$824$	8.21190	−	4.74114i	0.286075	−	0.165166i
$825$	7.02106	+	4.05361i	0.244442	+	0.141129i
$826$	−10.3208	−	17.0639i	−0.359107	−	0.593728i
$827$			47.9436i			1.66716i	0.552397	+	0.833581i	$0.313713\pi$
$827$			47.9436i			1.66716i	−0.552397	+	0.833581i	$0.686287\pi$
$828$	−5.49191			−0.190857
$829$	−22.7469			−0.790032			−0.395016	−	0.918674i	$-0.629261\pi$
$829$	−22.7469			−0.790032			−0.395016	+	0.918674i	$0.629261\pi$
$830$		−	28.0418i		−	0.973343i
$831$	5.52750	+	9.57391i	0.191747	+	0.332115i
$832$	−3.13511	−	1.78076i	−0.108690	−	0.0617367i
$833$	−6.92130	+	0.282098i	−0.239809	+	0.00977412i
$834$	3.50044	−	2.02098i	0.121210	−	0.0699808i
$835$	−16.3288	+	28.2823i	−0.565081	+	0.978750i
$836$	4.57096	+	7.91713i	0.158090	+	0.273820i
$837$	−5.08892	−	2.93809i	−0.175899	−	0.101555i
$838$		−	28.1643i		−	0.972921i
$839$	18.1058	+	10.4534i	0.625082	+	0.360891i	0.778845	−	0.627217i	$-0.215806\pi$
$839$	18.1058	+	10.4534i	0.625082	+	0.360891i	−0.153763	+	0.988108i	$0.549139\pi$
$840$	2.44388	−	4.43933i	0.0843218	−	0.153172i
$841$	−29.7484	+	51.5257i	−1.02581	+	1.77675i
$842$	18.5648	−	32.1552i	0.639785	−	1.10814i
$843$			25.6128i			0.882152i
$844$	7.55416	−	13.0842i	0.260025	−	0.450376i
$845$	21.7368	+	12.1451i	0.747769	+	0.417806i
$846$	−0.0368454			−0.00126677
$847$	35.7092	+	59.0397i	1.22698	+	2.02863i
$848$	4.17024	+	7.22306i	0.143206	+	0.248041i
$849$	28.2872			0.970814
$850$	−1.14101	−	0.658760i	−0.0391362	−	0.0225953i
$851$	11.1946	−	6.46321i	0.383746	−	0.221556i
$852$			11.0150i			0.377369i
$853$		−	13.3998i		−	0.458799i	−0.973332	−	0.229399i	$-0.926324\pi$
$853$		−	13.3998i		−	0.458799i	0.973332	−	0.229399i	$-0.0736762\pi$
$854$	0.0700293	+	3.43778i	0.00239635	+	0.117638i
$855$	1.43778	+	2.49031i	0.0491711	+	0.0851669i
$856$	−5.88524	−	3.39785i	−0.201153	−	0.116136i
$857$	−2.69063	+	4.66032i	−0.0919103	+	0.159193i	−0.908315	−	0.418287i	$-0.862631\pi$
$857$	−2.69063	+	4.66032i	−0.0919103	+	0.159193i	0.816405	+	0.577480i	$0.195964\pi$
$858$	18.9360	−	11.1111i	0.646464	−	0.379326i
$859$	21.1551	+	36.6418i	0.721804	+	1.25020i	0.960276	+	0.279052i	$0.0900202\pi$
$859$	21.1551	+	36.6418i	0.721804	+	1.25020i	−0.238472	+	0.971149i	$0.576646\pi$
$860$	−0.934828	+	0.539723i	−0.0318774	+	0.0184044i
$861$	19.9586	+	10.9873i	0.680188	+	0.374447i
$862$	18.8070	−	32.5747i	0.640569	−	1.10950i
$863$	7.71830	−	4.45616i	0.262734	−	0.151690i	−0.362847	−	0.931849i	$-0.618195\pi$
$863$	7.71830	−	4.45616i	0.262734	−	0.151690i	0.625581	+	0.780159i	$0.284862\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−5.67976	+	3.27921i	−0.193118	+	0.111497i
$866$	−14.7797	+	8.53304i	−0.502234	+	0.289965i
$867$	8.01037	−	13.8744i	0.272046	−	0.471198i
$868$	−13.3029	+	8.04605i	−0.451530	+	0.273101i
$869$	4.10658	−	2.37094i	0.139306	−	0.0804285i
$870$	9.00915	+	15.6043i	0.305439	+	0.529036i
$871$	−19.8176	+	34.8898i	−0.671494	+	1.18220i
$872$	4.92592	−	8.53194i	0.166813	−	0.288928i
$873$	−15.8848	−	9.17111i	−0.537620	−	0.310395i
$874$	−4.12255	−	7.14047i	−0.139447	−	0.241530i
$875$	27.4537	−	16.6050i	0.928106	−	0.561350i
$876$		−	6.92807i		−	0.234078i
$877$			56.8187i			1.91863i	0.282334	+	0.959316i	$0.408891\pi$
$877$			56.8187i			1.91863i	−0.282334	+	0.959316i	$0.591109\pi$
$878$	−10.4668	+	6.04302i	−0.353238	+	0.203942i
$879$	−11.6542	−	6.72853i	−0.393085	−	0.226948i
$880$	11.6631			0.393164
$881$	−11.2124	−	19.4205i	−0.377757	−	0.654294i	0.612979	−	0.790099i	$-0.289971\pi$
$881$	−11.2124	−	19.4205i	−0.377757	−	0.654294i	−0.990736	+	0.135806i	$0.956638\pi$
$882$	−5.91461	+	3.74397i	−0.199155	+	0.126066i
$883$	35.8658			1.20698			0.603491	−	0.797370i	$-0.293776\pi$
$883$	35.8658			1.20698			0.603491	+	0.797370i	$0.293776\pi$
$884$	−3.07733	+	1.80569i	−0.103502	+	0.0607318i
$885$	7.21849	−	12.5028i	0.242647	−	0.420277i
$886$		−	8.04553i		−	0.270295i
$887$	12.5904	−	21.8072i	0.422744	−	0.732214i	−0.573463	−	0.819232i	$-0.694400\pi$
$887$	12.5904	−	21.8072i	0.422744	−	0.732214i	0.996207	+	0.0870173i	$0.0277335\pi$
$888$	1.17686	−	2.03838i	0.0394928	−	0.0684036i
$889$	−2.82486	+	5.13140i	−0.0947428	+	0.172102i
$890$	8.92254	+	5.15143i	0.299084	+	0.172676i
$891$		−	6.08926i		−	0.203998i
$892$	−5.98759	−	3.45693i	−0.200479	−	0.115747i
$893$	−0.0276583	−	0.0479056i	−0.000925550	−	0.00160310i
$894$	2.76389	−	4.78720i	0.0924384	−	0.160108i
$895$	6.88731	−	3.97639i	0.230217	−	0.132916i
$896$	0.0538842	+	2.64520i	0.00180014	+	0.0883700i
$897$	−17.0784	+	10.0211i	−0.570231	+	0.334595i
$898$	−7.89736	−	13.6786i	−0.263538	−	0.456462i
$899$		−	55.2788i		−	1.84365i
$900$	−1.33140			−0.0443799
$901$	8.25354			0.274965
$902$			52.4358i			1.74592i
$903$	1.49077	−	0.0303677i	0.0496096	−	0.00101057i
$904$	−4.82449	−	2.78542i	−0.160460	−	0.0926417i
$905$	−15.9023	+	9.18119i	−0.528610	+	0.305193i
$906$	−1.89223	−	3.27744i	−0.0628652	−	0.108886i
$907$	−43.0830			−1.43055			−0.715273	−	0.698845i	$-0.753698\pi$
$907$	−43.0830			−1.43055			−0.715273	+	0.698845i	$0.753698\pi$
$908$	−12.1029	−	6.98762i	−0.401649	−	0.231892i
$909$	11.5238			0.382221
$910$	−0.500651	−	18.2645i	−0.0165964	−	0.605463i
$911$	−18.1704			−0.602012			−0.301006	−	0.953622i	$-0.597322\pi$
$911$	−18.1704			−0.602012			−0.301006	+	0.953622i	$0.597322\pi$
$912$	−1.30018	−	0.750659i	−0.0430532	−	0.0248568i
$913$	−89.1496			−2.95042
$914$	−2.31505	−	4.00978i	−0.0765750	−	0.132632i
$915$	−2.15576	+	1.24463i	−0.0712672	+	0.0411461i
$916$	8.91770	+	5.14864i	0.294649	+	0.170116i
$917$	11.4948	−	20.8804i	0.379591	−	0.689533i
$918$			0.989578i			0.0326609i
$919$	58.8706			1.94196			0.970981	−	0.239156i	$-0.0768708\pi$
$919$	58.8706			1.94196			0.970981	+	0.239156i	$0.0768708\pi$
$920$	−10.5190			−0.346801
$921$		−	14.6943i		−	0.484192i
$922$	14.9788	+	25.9440i	0.493299	+	0.854419i
$923$	20.0992	+	34.2539i	0.661572	+	1.12748i
$924$	−14.1134	−	7.76951i	−0.464297	−	0.255598i
$925$	2.71389	−	1.56687i	0.0892323	−	0.0515183i
$926$	1.71029	−	2.96231i	0.0562037	−	0.0973476i
$927$	−4.74114	−	8.21190i	−0.155720	−	0.269714i
$928$	−8.14693	−	4.70363i	−0.267436	−	0.154404i
$929$		−	2.47815i		−	0.0813053i	−0.999173	−	0.0406527i	$-0.987056\pi$
$929$		−	2.47815i		−	0.0813053i	0.999173	−	0.0406527i	$-0.0129437\pi$
$930$	−9.74711	−	5.62750i	−0.319620	−	0.184533i
$931$	−9.30769	−	4.87961i	−0.305047	−	0.159923i
$932$	−9.12977	+	15.8132i	−0.299056	+	0.517980i
$933$	2.95573	−	5.11947i	0.0967661	−	0.167604i
$934$		−	24.8616i		−	0.813498i
$935$	5.77078	−	9.99529i	0.188725	−	0.326881i
$936$	−1.78076	+	3.13511i	−0.0582059	+	0.102474i
$937$	45.6501			1.49132			0.745662	−	0.666325i	$-0.232133\pi$
$937$	45.6501			1.49132			0.745662	+	0.666325i	$0.232133\pi$
$938$	29.4378	−	0.599663i	0.961177	−	0.0195797i
$939$	−8.30358	−	14.3822i	−0.270977	−	0.469346i
$940$	−0.0705721			−0.00230181
$941$	7.38444	+	4.26341i	0.240726	+	0.138983i	0.615510	−	0.788129i	$-0.288950\pi$
$941$	7.38444	+	4.26341i	0.240726	+	0.138983i	−0.374784	+	0.927112i	$0.622283\pi$
$942$	14.5748	−	8.41478i	0.474874	−	0.274168i
$943$		−	47.2919i		−	1.54004i
$944$			7.53748i			0.245324i
$945$	−4.43933	−	2.44388i	−0.144412	−	0.0794993i
$946$	1.71587	+	2.97198i	0.0557878	+	0.0966273i
$947$	−0.498831	−	0.288000i	−0.0162098	−	0.00935875i	0.491873	−	0.870667i	$-0.336312\pi$
$947$	−0.498831	−	0.288000i	−0.0162098	−	0.00935875i	−0.508083	+	0.861308i	$0.669646\pi$
$948$	−0.389363	+	0.674397i	−0.0126459	+	0.0219034i
$949$	−12.6417	−	21.5445i	−0.410366	−	0.699363i
$950$	−0.999425	−	1.73105i	−0.0324256	−	0.0561628i
$951$	28.7686	−	16.6095i	0.932885	−	0.538601i
$952$	2.29360	+	1.26264i	0.0743360	+	0.0409223i
$953$	29.2214	−	50.6129i	0.946573	−	1.63951i	0.194002	−	0.981001i	$-0.437853\pi$
$953$	29.2214	−	50.6129i	0.946573	−	1.63951i	0.752571	−	0.658511i	$-0.228813\pi$
$954$	7.22306	−	4.17024i	0.233855	−	0.135016i
$955$	−7.66385	+	4.42473i	−0.247996	+	0.143181i
$956$	13.5024	−	7.79561i	0.436699	−	0.252128i
$957$	49.6088	−	28.6417i	1.60362	−	0.925853i
$958$	1.90156	−	3.29360i	0.0614367	−	0.106411i
$959$	−7.49127	−	4.12398i	−0.241906	−	0.133170i
$960$	−1.65875	+	0.957680i	−0.0535359	+	0.0309090i
$961$	1.76472	+	3.05659i	0.0569266	+	0.0985998i
$962$	−0.0597152	−	8.48625i	−0.00192530	−	0.273608i
$963$	−3.39785	+	5.88524i	−0.109494	+	0.189649i
$964$	13.0640	+	7.54249i	0.420762	+	0.242927i
$965$	20.4227	+	35.3731i	0.657429	+	1.13870i
$966$	12.7289	+	7.00733i	0.409546	+	0.225457i
$967$			38.1619i			1.22720i	0.789615	+	0.613602i	$0.210280\pi$
$967$			38.1619i			1.22720i	−0.789615	+	0.613602i	$0.789720\pi$
$968$		−	26.0791i		−	0.838214i
$969$	−1.28663	+	0.742835i	−0.0413325	+	0.0238633i
$970$	−30.4252	−	17.5660i	−0.976893	−	0.564009i
$971$	−9.78685			−0.314075			−0.157038	−	0.987593i	$-0.550194\pi$
$971$	−9.78685			−0.314075			−0.157038	+	0.987593i	$0.550194\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−10.6918	+	0.217797i	−0.342763	+	0.00698227i
$974$	−18.6846			−0.598692
$975$	−4.14029	+	2.42940i	−0.132595	+	0.0778031i
$976$	0.649814	−	1.12551i	0.0208000	−	0.0360267i
$977$			36.0987i			1.15490i	0.816427	+	0.577449i	$0.195952\pi$
$977$			36.0987i			1.15490i	−0.816427	+	0.577449i	$0.804048\pi$
$978$	−9.63427	+	16.6871i	−0.308070	+	0.533593i
$979$	16.3773	−	28.3663i	0.523421	−	0.906591i
$980$	−11.3286	+	7.17106i	−0.361879	+	0.229071i
$981$	−8.53194	−	4.92592i	−0.272404	−	0.157273i
$982$			3.45164i			0.110146i
$983$	4.14325	+	2.39211i	0.132149	+	0.0762963i	0.564617	−	0.825353i	$-0.309024\pi$
$983$	4.14325	+	2.39211i	0.132149	+	0.0762963i	−0.432468	+	0.901649i	$0.642357\pi$
$984$	−4.30560	−	7.45751i	−0.137257	−	0.237737i
$985$	25.4976	−	44.1631i	0.812420	−	1.40715i
$986$	−8.06203	+	4.65461i	−0.256747	+	0.148233i
$987$	0.0853985	+	0.0470123i	0.00271827	+	0.00149642i
$988$	−5.41294	+	0.0380893i	−0.172209	+	0.00121178i
$989$	−1.54755	−	2.68043i	−0.0492091	−	0.0852327i
$990$		−	11.6631i		−	0.370678i
$991$	−12.5659			−0.399168			−0.199584	−	0.979881i	$-0.563959\pi$
$991$	−12.5659			−0.399168			−0.199584	+	0.979881i	$0.563959\pi$
$992$	5.87618			0.186569
$993$			20.0514i			0.636313i
$994$	14.0545	−	25.5302i	0.445781	−	0.809768i
$995$	−34.8201	−	20.1034i	−1.10387	−	0.637321i
$996$	12.6790	−	7.32023i	0.401750	−	0.231950i
$997$	−0.698972	−	1.21065i	−0.0221367	−	0.0383418i	0.854745	−	0.519048i	$-0.173714\pi$
$997$	−0.698972	−	1.21065i	−0.0221367	−	0.0383418i	−0.876882	+	0.480707i	$0.840380\pi$
$998$	−42.7263			−1.35248
$999$	−2.03838	−	1.17686i	−0.0644915	−	0.0372342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.361.9	yes	20
3.2	odd	2		1638.2.cr.b.361.2		20
7.2	even	3		546.2.bm.b.205.2	yes	20
13.4	even	6		546.2.bm.b.277.7	yes	20
21.2	odd	6		1638.2.dt.b.1297.9		20
39.17	odd	6		1638.2.dt.b.1369.4		20
91.30	even	6	inner	546.2.bd.b.121.9	✓	20
273.212	odd	6		1638.2.cr.b.667.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.9	✓	20	91.30	even	6	inner
546.2.bd.b.361.9	yes	20	1.1	even	1	trivial
546.2.bm.b.205.2	yes	20	7.2	even	3
546.2.bm.b.277.7	yes	20	13.4	even	6
1638.2.cr.b.361.2		20	3.2	odd	2
1638.2.cr.b.667.2		20	273.212	odd	6
1638.2.dt.b.1297.9		20	21.2	odd	6
1638.2.dt.b.1369.4		20	39.17	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.65875 - 0.957680i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.36927 - 2.26387i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.65875 - 0.957680i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.36927 - 2.26387i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.91536 q^{10} -6.08926i q^{11} +(0.500000 + 0.866025i) q^{12} +(3.13511 + 1.78076i) q^{13} +(-0.0538842 - 2.64520i) q^{14} +(1.65875 - 0.957680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.494789 + 0.857000i) q^{17} +(0.866025 + 0.500000i) q^{18} +1.50132i q^{19} +(1.65875 + 0.957680i) q^{20} +(-1.36927 - 2.26387i) q^{21} +(3.04463 - 5.27345i) q^{22} +(-2.74595 + 4.75613i) q^{23} +1.00000i q^{24} +(-0.665698 + 1.15302i) q^{25} +(1.82470 + 3.10974i) q^{26} +1.00000 q^{27} +(1.27594 - 2.31775i) q^{28} +(4.70363 + 8.14693i) q^{29} +1.91536 q^{30} +(-5.08892 - 2.93809i) q^{31} +(-0.866025 + 0.500000i) q^{32} -6.08926i q^{33} +0.989578i q^{34} +(-4.43933 - 2.44388i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.03838 - 1.17686i) q^{37} +(-0.750659 + 1.30018i) q^{38} +(3.13511 + 1.78076i) q^{39} +(0.957680 + 1.65875i) q^{40} +(-7.45751 + 4.30560i) q^{41} +(-0.0538842 - 2.64520i) q^{42} +(-0.281787 + 0.488069i) q^{43} +(5.27345 - 3.04463i) q^{44} +(1.65875 - 0.957680i) q^{45} +(-4.75613 + 2.74595i) q^{46} +(-0.0319090 + 0.0184227i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.25022 + 6.19968i) q^{49} +(-1.15302 + 0.665698i) q^{50} +(0.494789 + 0.857000i) q^{51} +(0.0253706 + 3.60546i) q^{52} +(4.17024 - 7.22306i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.83156 - 10.1006i) q^{55} +(2.26387 - 1.36927i) q^{56} +1.50132i q^{57} +9.40727i q^{58} +(6.52765 - 3.76874i) q^{59} +(1.65875 + 0.957680i) q^{60} -1.29963 q^{61} +(-2.93809 - 5.08892i) q^{62} +(-1.36927 - 2.26387i) q^{63} -1.00000 q^{64} +(6.90576 - 0.0485938i) q^{65} +(3.04463 - 5.27345i) q^{66} +11.1287i q^{67} +(-0.494789 + 0.857000i) q^{68} +(-2.74595 + 4.75613i) q^{69} +(-2.62264 - 4.33613i) q^{70} +(9.53931 + 5.50752i) q^{71} +1.00000i q^{72} +(-5.99988 - 3.46403i) q^{73} +(-1.17686 - 2.03838i) q^{74} +(-0.665698 + 1.15302i) q^{75} +(-1.30018 + 0.750659i) q^{76} +(-13.7853 + 8.33782i) q^{77} +(1.82470 + 3.10974i) q^{78} +(0.389363 + 0.674397i) q^{79} +1.91536i q^{80} +1.00000 q^{81} -8.61119 q^{82} -14.6405i q^{83} +(1.27594 - 2.31775i) q^{84} +(1.64146 + 0.947699i) q^{85} +(-0.488069 + 0.281787i) q^{86} +(4.70363 + 8.14693i) q^{87} +6.08926 q^{88} +(4.65842 + 2.68954i) q^{89} +1.91536 q^{90} +(-0.261388 - 9.53581i) q^{91} -5.49191 q^{92} +(-5.08892 - 2.93809i) q^{93} -0.0368454 q^{94} +(1.43778 + 2.49031i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-15.8848 - 9.17111i) q^{97} +(-5.91461 + 3.74397i) q^{98} -6.08926i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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