LMFDB - Embedded newform 462.2.k.g.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
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} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 $ x^20 - 6x^19 + 19x^18 - 42x^17 + 62x^16 - 42x^15 - 25x^14 + 6x^13 + 445x^12 - 1764x^11 + 3864x^10 - 5292x^9 + 4005x^8 + 162x^7 - 2025x^6 - 10206x^5 + 45198x^4 - 91854x^3 + 124659x^2 - 118098*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Root			$-1.53534 + 0.801712i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.0733649 - 1.73050i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.79481 - 3.10870i) q^{5} +(-0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} -1.00000i q^{8} +(-2.98924 - 0.253915i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.0733649 - 1.73050i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.79481 - 3.10870i) q^{5} +(-0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} -1.00000i q^{8} +(-2.98924 - 0.253915i) q^{9} +(-3.10870 + 1.79481i) q^{10} +(0.866025 - 0.500000i) q^{11} +(1.53534 - 0.801712i) q^{12} -0.365750i q^{13} +(-1.97768 + 1.75749i) q^{14} +(-5.24792 - 3.33398i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.04890 + 1.81675i) q^{17} +(2.46180 + 1.71451i) q^{18} +(5.84896 + 3.37690i) q^{19} +3.58962 q^{20} +(-4.28387 - 1.62741i) q^{21} -1.00000 q^{22} +(1.78784 + 1.03221i) q^{23} +(-1.73050 - 0.0733649i) q^{24} +(-3.94268 - 6.82893i) q^{25} +(-0.182875 + 0.316749i) q^{26} +(-0.658705 + 5.15423i) q^{27} +(2.59147 - 0.533187i) q^{28} +3.75152i q^{29} +(2.87784 + 5.51127i) q^{30} +(-8.04779 + 4.64639i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.801712 - 1.53534i) q^{33} -2.09780i q^{34} +(-6.30871 - 7.09913i) q^{35} +(-1.27472 - 2.71571i) q^{36} +(5.32441 - 9.22215i) q^{37} +(-3.37690 - 5.84896i) q^{38} +(-0.632929 - 0.0268332i) q^{39} +(-3.10870 - 1.79481i) q^{40} -3.58962 q^{41} +(2.89623 + 3.55131i) q^{42} +4.30096 q^{43} +(0.866025 + 0.500000i) q^{44} +(-6.15445 + 8.83691i) q^{45} +(-1.03221 - 1.78784i) q^{46} +(-6.39592 + 11.0781i) q^{47} +(1.46197 + 0.928784i) q^{48} +(-5.60895 - 4.18804i) q^{49} +7.88536i q^{50} +(3.22083 - 1.68183i) q^{51} +(0.316749 - 0.182875i) q^{52} +(-3.13404 + 1.80944i) q^{53} +(3.14757 - 4.13434i) q^{54} -3.58962i q^{55} +(-2.51087 - 0.833981i) q^{56} +(6.27282 - 9.87385i) q^{57} +(1.87576 - 3.24891i) q^{58} +(-3.85273 - 6.67312i) q^{59} +(0.263352 - 6.21182i) q^{60} +(7.48792 + 4.32316i) q^{61} +9.29278 q^{62} +(-3.13051 + 7.29383i) q^{63} -1.00000 q^{64} +(-1.13701 - 0.656451i) q^{65} +(-0.0733649 + 1.73050i) q^{66} +(-2.98446 - 5.16923i) q^{67} +(-1.04890 + 1.81675i) q^{68} +(1.91740 - 3.01812i) q^{69} +(1.91394 + 9.30239i) q^{70} +4.43092i q^{71} +(-0.253915 + 2.98924i) q^{72} +(4.69142 - 2.70859i) q^{73} +(-9.22215 + 5.32441i) q^{74} +(-12.1067 + 6.32179i) q^{75} +6.75379i q^{76} +(-0.533187 - 2.59147i) q^{77} +(0.534716 + 0.339702i) q^{78} +(-3.30693 + 5.72777i) q^{79} +(1.79481 + 3.10870i) q^{80} +(8.87105 + 1.51803i) q^{81} +(3.10870 + 1.79481i) q^{82} +7.62475 q^{83} +(-0.732556 - 4.52364i) q^{84} +7.53030 q^{85} +(-3.72474 - 2.15048i) q^{86} +(6.49198 + 0.275230i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(7.03715 - 12.1887i) q^{89} +(9.74837 - 4.57576i) q^{90} +(-0.918351 - 0.305028i) q^{91} +2.06442i q^{92} +(7.45014 + 14.2675i) q^{93} +(11.0781 - 6.39592i) q^{94} +(20.9955 - 12.1218i) q^{95} +(-0.801712 - 1.53534i) q^{96} -0.651733i q^{97} +(2.76348 + 6.43142i) q^{98} +(-2.71571 + 1.27472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.0733649	−	1.73050i	0.0423572	−	0.999103i
$3$	0.0733649	−	1.73050i	0.0423572	−	0.999103i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.79481	−	3.10870i	0.802663	−	1.39025i	−0.115194	−	0.993343i	$-0.536749\pi$
$5$	1.79481	−	3.10870i	0.802663	−	1.39025i	0.917857	−	0.396910i	$-0.129918\pi$
$6$	−0.928784	+	1.46197i	−0.379174	+	0.596847i
$7$	0.833981	−	2.51087i	0.315215	−	0.949020i
$7$	0.833981	−	2.51087i	0.315215	−	0.949020i
$8$		−	1.00000i		−	0.353553i
$9$	−2.98924	−	0.253915i	−0.996412	−	0.0846385i
$10$	−3.10870	+	1.79481i	−0.983058	+	0.567569i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	1.53534	−	0.801712i	0.443213	−	0.231434i
$13$		−	0.365750i		−	0.101441i	−0.998713	−	0.0507204i	$-0.983848\pi$
$13$		−	0.365750i		−	0.101441i	0.998713	−	0.0507204i	$-0.0161517\pi$
$14$	−1.97768	+	1.75749i	−0.528558	+	0.469708i
$15$	−5.24792	−	3.33398i	−1.35501	−	0.860830i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.04890	+	1.81675i	0.254396	+	0.440626i	0.964731	−	0.263237i	$-0.0847901\pi$
$17$	1.04890	+	1.81675i	0.254396	+	0.440626i	−0.710336	+	0.703863i	$0.751457\pi$
$18$	2.46180	+	1.71451i	0.580251	+	0.404115i
$19$	5.84896	+	3.37690i	1.34184	+	0.774713i	0.987078	−	0.160242i	$-0.0512275\pi$
$19$	5.84896	+	3.37690i	1.34184	+	0.774713i	0.354765	+	0.934955i	$0.384561\pi$
$20$	3.58962			0.802663
$21$	−4.28387	−	1.62741i	−0.934817	−	0.355130i
$22$	−1.00000			−0.213201
$23$	1.78784	+	1.03221i	0.372790	+	0.215230i	0.674677	−	0.738113i	$-0.264283\pi$
$23$	1.78784	+	1.03221i	0.372790	+	0.215230i	−0.301887	+	0.953344i	$0.597616\pi$
$24$	−1.73050	−	0.0733649i	−0.353236	−	0.0149755i
$25$	−3.94268	−	6.82893i	−0.788536	−	1.36579i
$26$	−0.182875	+	0.316749i	−0.0358647	+	0.0621195i
$27$	−0.658705	+	5.15423i	−0.126768	+	0.991932i
$28$	2.59147	−	0.533187i	0.489742	−	0.100763i
$29$			3.75152i			0.696639i	0.937376	+	0.348319i	$0.113248\pi$
$29$			3.75152i			0.696639i	−0.937376	+	0.348319i	$0.886752\pi$
$30$	2.87784	+	5.51127i	0.525420	+	1.00622i
$31$	−8.04779	+	4.64639i	−1.44543	+	0.834517i	−0.998204	−	0.0599066i	$-0.980920\pi$
$31$	−8.04779	+	4.64639i	−1.44543	+	0.834517i	−0.447221	+	0.894423i	$0.647586\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.801712	−	1.53534i	−0.139560	−	0.267268i
$34$		−	2.09780i		−	0.359770i
$35$	−6.30871	−	7.09913i	−1.06637	−	1.19997i
$36$	−1.27472	−	2.71571i	−0.212453	−	0.452619i
$37$	5.32441	−	9.22215i	0.875328	−	1.51611i	0.0189151	−	0.999821i	$-0.493979\pi$
$37$	5.32441	−	9.22215i	0.875328	−	1.51611i	0.856413	−	0.516291i	$-0.172688\pi$
$38$	−3.37690	−	5.84896i	−0.547805	−	0.948826i
$39$	−0.632929	−	0.0268332i	−0.101350	−	0.00429675i
$40$	−3.10870	−	1.79481i	−0.491529	−	0.283784i
$41$	−3.58962			−0.560604			−0.280302	−	0.959912i	$-0.590435\pi$
$41$	−3.58962			−0.560604			−0.280302	+	0.959912i	$0.590435\pi$
$42$	2.89623	+	3.55131i	0.446899	+	0.547980i
$43$	4.30096			0.655890			0.327945	−	0.944697i	$-0.393644\pi$
$43$	4.30096			0.655890			0.327945	+	0.944697i	$0.393644\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$	−6.15445	+	8.83691i	−0.917452	+	1.31733i
$46$	−1.03221	−	1.78784i	−0.152191	−	0.263602i
$47$	−6.39592	+	11.0781i	−0.932940	+	1.61590i	−0.154674	+	0.987965i	$0.549433\pi$
$47$	−6.39592	+	11.0781i	−0.932940	+	1.61590i	−0.778266	+	0.627935i	$0.783900\pi$
$48$	1.46197	+	0.928784i	0.211017	+	0.134058i
$49$	−5.60895	−	4.18804i	−0.801279	−	0.598291i
$50$			7.88536i			1.11516i
$51$	3.22083	−	1.68183i	0.451006	−	0.235504i
$52$	0.316749	−	0.182875i	0.0439251	−	0.0253602i
$53$	−3.13404	+	1.80944i	−0.430493	+	0.248545i	−0.699557	−	0.714577i	$-0.746619\pi$
$53$	−3.13404	+	1.80944i	−0.430493	+	0.248545i	0.269064	+	0.963122i	$0.413286\pi$
$54$	3.14757	−	4.13434i	0.428330	−	0.562613i
$55$		−	3.58962i		−	0.484024i
$56$	−2.51087	−	0.833981i	−0.335529	−	0.111445i
$57$	6.27282	−	9.87385i	0.830855	−	1.30782i
$58$	1.87576	−	3.24891i	0.246299	−	0.426602i
$59$	−3.85273	−	6.67312i	−0.501582	−	0.868766i	−0.999998	−	0.00182804i	$-0.999418\pi$
$59$	−3.85273	−	6.67312i	−0.501582	−	0.868766i	0.498416	−	0.866938i	$-0.333915\pi$
$60$	0.263352	−	6.21182i	0.0339986	−	0.801943i
$61$	7.48792	+	4.32316i	0.958731	+	0.553523i	0.895782	−	0.444493i	$-0.146616\pi$
$61$	7.48792	+	4.32316i	0.958731	+	0.553523i	0.0629484	+	0.998017i	$0.479950\pi$
$62$	9.29278			1.18018
$63$	−3.13051	+	7.29383i	−0.394408	+	0.918936i
$64$	−1.00000			−0.125000
$65$	−1.13701	−	0.656451i	−0.141028	−	0.0814227i
$66$	−0.0733649	+	1.73050i	−0.00903059	+	0.213009i
$67$	−2.98446	−	5.16923i	−0.364610	−	0.631522i	0.624104	−	0.781341i	$-0.285464\pi$
$67$	−2.98446	−	5.16923i	−0.364610	−	0.631522i	−0.988713	+	0.149819i	$0.952131\pi$
$68$	−1.04890	+	1.81675i	−0.127198	+	0.220313i
$69$	1.91740	−	3.01812i	0.230828	−	0.363339i
$70$	1.91394	+	9.30239i	0.228759	+	1.11185i
$71$			4.43092i			0.525853i	0.964816	+	0.262927i	$0.0846878\pi$
$71$			4.43092i			0.525853i	−0.964816	+	0.262927i	$0.915312\pi$
$72$	−0.253915	+	2.98924i	−0.0299242	+	0.352285i
$73$	4.69142	−	2.70859i	0.549089	−	0.317017i	−0.199666	−	0.979864i	$-0.563986\pi$
$73$	4.69142	−	2.70859i	0.549089	−	0.317017i	0.748754	+	0.662847i	$0.230652\pi$
$74$	−9.22215	+	5.32441i	−1.07205	+	0.618950i
$75$	−12.1067	+	6.32179i	−1.39796	+	0.729978i
$76$			6.75379i			0.774713i
$77$	−0.533187	−	2.59147i	−0.0607623	−	0.295325i
$78$	0.534716	+	0.339702i	0.0605446	+	0.0384637i
$79$	−3.30693	+	5.72777i	−0.372059	+	0.644424i	−0.989882	−	0.141892i	$-0.954681\pi$
$79$	−3.30693	+	5.72777i	−0.372059	+	0.644424i	0.617823	+	0.786317i	$0.288015\pi$
$80$	1.79481	+	3.10870i	0.200666	+	0.347563i
$81$	8.87105	+	1.51803i	0.985673	+	0.168670i
$82$	3.10870	+	1.79481i	0.343299	+	0.198204i
$83$	7.62475			0.836925			0.418463	−	0.908234i	$-0.362569\pi$
$83$	7.62475			0.836925			0.418463	+	0.908234i	$0.362569\pi$
$84$	−0.732556	−	4.52364i	−0.0799284	−	0.493570i
$85$	7.53030			0.816776
$86$	−3.72474	−	2.15048i	−0.401649	−	0.231892i
$87$	6.49198	+	0.275230i	0.696014	+	0.0295077i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	7.03715	−	12.1887i	0.745936	−	1.29200i	−0.203820	−	0.979008i	$-0.565336\pi$
$89$	7.03715	−	12.1887i	0.745936	−	1.29200i	0.949756	−	0.312991i	$-0.101331\pi$
$90$	9.74837	−	4.57576i	1.02757	−	0.482328i
$91$	−0.918351	−	0.305028i	−0.0962693	−	0.0319756i
$92$			2.06442i			0.215230i
$93$	7.45014	+	14.2675i	0.772544	+	1.47948i
$94$	11.0781	−	6.39592i	1.14261	−	0.659689i
$95$	20.9955	−	12.1218i	2.15410	−	1.24367i
$96$	−0.801712	−	1.53534i	−0.0818244	−	0.156700i
$97$		−	0.651733i		−	0.0661735i	−0.999452	−	0.0330867i	$-0.989466\pi$
$97$		−	0.651733i		−	0.0661735i	0.999452	−	0.0330867i	$-0.0105338\pi$
$98$	2.76348	+	6.43142i	0.279153	+	0.649672i
$99$	−2.71571	+	1.27472i	−0.272939	+	0.128114i
$100$	3.94268	−	6.82893i	0.394268	−	0.682893i
$101$	2.43851	+	4.22363i	0.242641	+	0.420267i	0.961466	−	0.274925i	$-0.0886530\pi$
$101$	2.43851	+	4.22363i	0.242641	+	0.420267i	−0.718825	+	0.695191i	$0.755320\pi$
$102$	−3.63024	−	0.153905i	−0.359447	−	0.0152389i
$103$	8.19883	+	4.73360i	0.807855	+	0.466415i	0.846210	−	0.532849i	$-0.178879\pi$
$103$	8.19883	+	4.73360i	0.807855	+	0.466415i	−0.0383556	+	0.999264i	$0.512212\pi$
$104$	−0.365750			−0.0358647
$105$	−12.7479	+	10.3964i	−1.24406	+	1.01458i
$106$	3.61887			0.351496
$107$	15.6111	+	9.01307i	1.50918	+	0.871327i	0.999943	+	0.0107015i	$0.00340646\pi$
$107$	15.6111	+	9.01307i	1.50918	+	0.871327i	0.509239	+	0.860625i	$0.329927\pi$
$108$	−4.79305	+	2.00666i	−0.461211	+	0.193091i
$109$	−7.24061	−	12.5411i	−0.693524	−	1.20122i	−0.970676	−	0.240393i	$-0.922724\pi$
$109$	−7.24061	−	12.5411i	−0.693524	−	1.20122i	0.277151	−	0.960826i	$-0.410610\pi$
$110$	−1.79481	+	3.10870i	−0.171128	+	0.296403i
$111$	−15.5683	−	9.89046i	−1.47768	−	0.938761i
$112$	1.75749	+	1.97768i	0.166067	+	0.186874i
$113$		−	3.81643i		−	0.359020i	−0.983756	−	0.179510i	$-0.942549\pi$
$113$		−	3.81643i		−	0.359020i	0.983756	−	0.179510i	$-0.0574512\pi$
$114$	−10.3693	+	5.41460i	−0.971178	+	0.507124i
$115$	6.41766	−	3.70524i	0.598450	−	0.345515i
$116$	−3.24891	+	1.87576i	−0.301653	+	0.174160i
$117$	−0.0928695	+	1.09331i	−0.00858579	+	0.101077i
$118$			7.70545i			0.709344i
$119$	5.43638	−	1.11852i	0.498353	−	0.102535i
$120$	−3.33398	+	5.24792i	−0.304349	+	0.479067i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−4.32316	−	7.48792i	−0.391400	−	0.677925i
$123$	−0.263352	+	6.21182i	−0.0237457	+	0.560101i
$124$	−8.04779	−	4.64639i	−0.722713	−	0.417258i
$125$	−10.3574			−0.926390
$126$	6.35802	−	4.75138i	0.566417	−	0.423287i
$127$	−4.48502			−0.397981			−0.198991	−	0.980001i	$-0.563766\pi$
$127$	−4.48502			−0.397981			−0.198991	+	0.980001i	$0.563766\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.315539	−	7.44279i	0.0277817	−	0.655301i
$130$	0.656451	+	1.13701i	0.0575746	+	0.0997221i
$131$	−8.58385	+	14.8677i	−0.749975	+	1.29899i	0.197860	+	0.980230i	$0.436601\pi$
$131$	−8.58385	+	14.8677i	−0.749975	+	1.29899i	−0.947834	+	0.318764i	$0.896732\pi$
$132$	0.928784	−	1.46197i	0.0808403	−	0.127248i
$133$	13.3569	−	11.8697i	1.15819	−	1.02923i
$134$			5.96892i			0.515636i
$135$	14.8407	+	11.2986i	1.27729	+	0.972427i
$136$	1.81675	−	1.04890i	0.155785	−	0.0899425i
$137$	2.76642	−	1.59719i	0.236351	−	0.136457i	−0.377148	−	0.926153i	$-0.623095\pi$
$137$	2.76642	−	1.59719i	0.236351	−	0.136457i	0.613498	+	0.789696i	$0.289762\pi$
$138$	−3.16957	+	1.65507i	−0.269812	+	0.140889i
$139$			4.54442i			0.385453i	0.981253	+	0.192726i	$0.0617330\pi$
$139$			4.54442i			0.385453i	−0.981253	+	0.192726i	$0.938267\pi$
$140$	2.99367	−	9.01307i	0.253012	−	0.761744i
$141$	18.7013	+	11.8809i	1.57493	+	1.00055i
$142$	2.21546	−	3.83729i	0.185917	−	0.322018i
$143$	−0.182875	−	0.316749i	−0.0152928	−	0.0264878i
$144$	1.71451	−	2.46180i	0.142876	−	0.205150i
$145$	11.6623	+	6.73326i	0.968505	+	0.559166i
$146$	−5.41718			−0.448329
$147$	−7.65888	+	9.39902i	−0.631694	+	0.775218i
$148$	10.6488			0.875328
$149$	−8.84896	−	5.10895i	−0.724935	−	0.418542i	0.0916311	−	0.995793i	$-0.470792\pi$
$149$	−8.84896	−	5.10895i	−0.724935	−	0.418542i	−0.816567	+	0.577251i	$0.804125\pi$
$150$	13.6456	+	0.578509i	1.11416	+	0.0472351i
$151$	−2.89840	−	5.02017i	−0.235868	−	0.408536i	0.723656	−	0.690160i	$-0.242460\pi$
$151$	−2.89840	−	5.02017i	−0.235868	−	0.408536i	−0.959525	+	0.281625i	$0.909127\pi$
$152$	3.37690	−	5.84896i	0.273903	−	0.474413i
$153$	−2.67411	−	5.69702i	−0.216189	−	0.460577i
$154$	−0.833981	+	2.51087i	−0.0672041	+	0.202332i
$155$			33.3576i			2.67934i
$156$	−0.293226	−	0.561549i	−0.0234769	−	0.0449599i
$157$	−14.8987	+	8.60176i	−1.18904	+	0.686495i	−0.958089	−	0.286469i	$-0.907518\pi$
$157$	−14.8987	+	8.60176i	−1.18904	+	0.686495i	−0.230955	+	0.972964i	$0.574185\pi$
$158$	5.72777	−	3.30693i	0.455677	−	0.263085i
$159$	2.90129	+	5.55619i	0.230088	+	0.440634i
$160$		−	3.58962i		−	0.283784i
$161$	4.08277	−	3.62819i	0.321767	−	0.285941i
$162$	−6.92355	−	5.75018i	−0.543965	−	0.451776i
$163$	−4.29736	+	7.44325i	−0.336595	+	0.583000i	−0.983790	−	0.179325i	$-0.942609\pi$
$163$	−4.29736	+	7.44325i	−0.336595	+	0.583000i	0.647195	+	0.762325i	$0.275942\pi$
$164$	−1.79481	−	3.10870i	−0.140151	−	0.242749i
$165$	−6.21182	−	0.263352i	−0.483590	−	0.0205019i
$166$	−6.60323	−	3.81238i	−0.512510	−	0.295898i
$167$	16.0018			1.23825			0.619127	−	0.785291i	$-0.287487\pi$
$167$	16.0018			1.23825			0.619127	+	0.785291i	$0.287487\pi$
$168$	−1.62741	+	4.28387i	−0.125557	+	0.330508i
$169$	12.8662			0.989710
$170$	−6.52143	−	3.76515i	−0.500171	−	0.288774i
$171$	−16.6265	−	11.5795i	−1.27146	−	0.885505i
$172$	2.15048	+	3.72474i	0.163972	+	0.284009i
$173$	6.69644	−	11.5986i	0.509121	−	0.881823i	−0.490824	−	0.871259i	$-0.663304\pi$
$173$	6.69644	−	11.5986i	0.509121	−	0.881823i	0.999944	−	0.0105638i	$-0.00336263\pi$
$174$	−5.48461	−	3.48435i	−0.415787	−	0.264148i
$175$	−20.4347	+	4.20438i	−1.54472	+	0.317821i
$176$			1.00000i			0.0753778i
$177$	−11.8305	+	6.17756i	−0.889232	+	0.464334i
$178$	−12.1887	+	7.03715i	−0.913581	+	0.527457i
$179$	12.8211	−	7.40224i	0.958291	−	0.553270i	0.0626446	−	0.998036i	$-0.480047\pi$
$179$	12.8211	−	7.40224i	0.958291	−	0.553270i	0.895647	+	0.444766i	$0.146713\pi$
$180$	−10.7302	−	0.911459i	−0.799783	−	0.0679362i
$181$		−	3.50491i		−	0.260518i	−0.991480	−	0.130259i	$-0.958419\pi$
$181$		−	3.50491i		−	0.260518i	0.991480	−	0.130259i	$-0.0415808\pi$
$182$	0.642801	+	0.723337i	0.0476476	+	0.0536173i
$183$	8.03056	−	12.6407i	0.593636	−	0.934424i
$184$	1.03221	−	1.78784i	0.0760954	−	0.131801i
$185$	−19.1126	−	33.1040i	−1.40519	−	2.43386i
$186$	0.681764	−	16.0811i	0.0499894	−	1.17913i
$187$	1.81675	+	1.04890i	0.132854	+	0.0767032i
$188$	−12.7918			−0.932940
$189$	12.3923	+	5.95245i	0.901405	+	0.432977i
$190$	−24.2435			−1.75881
$191$	5.57270	+	3.21740i	0.403227	+	0.232803i	0.687875	−	0.725829i	$-0.258544\pi$
$191$	5.57270	+	3.21740i	0.403227	+	0.232803i	−0.284649	+	0.958632i	$0.591877\pi$
$192$	−0.0733649	+	1.73050i	−0.00529466	+	0.124888i
$193$	−3.28995	−	5.69836i	−0.236816	−	0.410177i	0.722983	−	0.690866i	$-0.242770\pi$
$193$	−3.28995	−	5.69836i	−0.236816	−	0.410177i	−0.959799	+	0.280689i	$0.909437\pi$
$194$	−0.325866	+	0.564417i	−0.0233958	+	0.0405228i
$195$	−1.21940	+	1.91943i	−0.0873232	+	0.137453i
$196$	0.822470	−	6.95151i	0.0587479	−	0.496537i
$197$			13.9234i			0.992000i	0.868323	+	0.496000i	$0.165198\pi$
$197$			13.9234i			0.992000i	−0.868323	+	0.496000i	$0.834802\pi$
$198$	2.98924	+	0.253915i	0.212436	+	0.0180450i
$199$	−22.8967	+	13.2194i	−1.62311	+	0.937101i	−0.637025	+	0.770843i	$0.719835\pi$
$199$	−22.8967	+	13.2194i	−1.62311	+	0.937101i	−0.986082	+	0.166258i	$0.946831\pi$
$200$	−6.82893	+	3.94268i	−0.482878	+	0.278790i
$201$	−9.16430	+	4.78535i	−0.646400	+	0.337533i
$202$		−	4.87702i		−	0.343146i
$203$	9.41957	+	3.12869i	0.661124	+	0.219591i
$204$	3.06692	+	1.94840i	0.214728	+	0.136416i
$205$	−6.44268	+	11.1591i	−0.449976	+	0.779382i
$206$	−4.73360	−	8.19883i	−0.329805	−	0.571240i
$207$	−5.08217	−	3.53947i	−0.353236	−	0.246010i
$208$	0.316749	+	0.182875i	0.0219626	+	0.0126801i
$209$	6.75379			0.467170
$210$	16.2382	−	2.62960i	1.12054	−	0.181459i
$211$	−13.4659			−0.927030			−0.463515	−	0.886089i	$-0.653412\pi$
$211$	−13.4659			−0.927030			−0.463515	+	0.886089i	$0.653412\pi$
$212$	−3.13404	−	1.80944i	−0.215246	−	0.124273i
$213$	7.66769	+	0.325074i	0.525382	+	0.0222737i
$214$	−9.01307	−	15.6111i	−0.616121	−	1.06715i
$215$	7.71940	−	13.3704i	0.526458	−	0.911853i
$216$	5.15423	+	0.658705i	0.350701	+	0.0448192i
$217$	4.95479	+	24.0820i	0.336353	+	1.63479i
$218$			14.4812i			0.980792i
$219$	−4.34302	−	8.31720i	−0.293474	−	0.562024i
$220$	3.10870	−	1.79481i	0.209589	−	0.121006i
$221$	0.664475	−	0.383635i	0.0446974	−	0.0258061i
$222$	8.53729	+	16.3495i	0.572986	+	1.09731i
$223$		−	24.3253i		−	1.62895i	−0.580202	−	0.814473i	$-0.697026\pi$
$223$		−	24.3253i		−	1.62895i	0.580202	−	0.814473i	$-0.302974\pi$
$224$	−0.533187	−	2.59147i	−0.0356251	−	0.173150i
$225$	10.0516	+	21.4144i	0.670109	+	1.42762i
$226$	−1.90822	+	3.30513i	−0.126933	+	0.219854i
$227$	−8.49372	−	14.7116i	−0.563748	−	0.976440i	−0.997165	−	0.0752465i	$-0.976026\pi$
$227$	−8.49372	−	14.7116i	−0.563748	−	0.976440i	0.433417	−	0.901193i	$-0.357308\pi$
$228$	11.6874	+	0.495491i	0.774018	+	0.0328147i
$229$	−17.9426	−	10.3592i	−1.18568	−	0.684553i	−0.228358	−	0.973577i	$-0.573336\pi$
$229$	−17.9426	−	10.3592i	−1.18568	−	0.684553i	−0.957322	+	0.289025i	$0.906669\pi$
$230$	−7.41047			−0.488632
$231$	−4.52364	+	0.732556i	−0.297634	+	0.0481986i
$232$	3.75152			0.246299
$233$	−3.07054	−	1.77278i	−0.201158	−	0.116139i	0.396038	−	0.918234i	$-0.370385\pi$
$233$	−3.07054	−	1.77278i	−0.201158	−	0.116139i	−0.597195	+	0.802096i	$0.703718\pi$
$234$	0.627083	−	0.900401i	0.0409937	−	0.0588611i
$235$	22.9589	+	39.7660i	1.49767	+	2.59405i
$236$	3.85273	−	6.67312i	0.250791	−	0.434383i
$237$	9.66927	+	6.14285i	0.628087	+	0.399021i
$238$	−5.26731	−	1.74953i	−0.341429	−	0.113405i
$239$		−	26.8160i		−	1.73458i	−0.497800	−	0.867292i	$-0.665859\pi$
$239$		−	26.8160i		−	1.73458i	0.497800	−	0.867292i	$-0.334141\pi$
$240$	5.51127	−	2.87784i	0.355751	−	0.185764i
$241$	−4.29195	+	2.47796i	−0.276469	+	0.159619i	−0.631824	−	0.775112i	$-0.717693\pi$
$241$	−4.29195	+	2.47796i	−0.276469	+	0.159619i	0.355355	+	0.934731i	$0.384360\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	3.27776	−	15.2400i	0.210269	−	0.977644i
$244$			8.64631i			0.553523i
$245$	−23.0864	+	9.91983i	−1.47493	+	0.633755i
$246$	3.33398	−	5.24792i	0.212567	−	0.334595i
$247$	1.23510	−	2.13925i	0.0785875	−	0.136117i
$248$	4.64639	+	8.04779i	0.295046	+	0.511035i
$249$	0.559389	−	13.1946i	0.0354499	−	0.836174i
$250$	8.96973	+	5.17868i	0.567296	+	0.327528i
$251$	−16.6823			−1.05297			−0.526487	−	0.850183i	$-0.676491\pi$
$251$	−16.6823			−1.05297			−0.526487	+	0.850183i	$0.676491\pi$
$252$	−7.88189	+	0.935808i	−0.496513	+	0.0589504i
$253$	2.06442			0.129789
$254$	3.88414	+	2.24251i	0.243713	+	0.140708i
$255$	0.552460	−	13.0312i	0.0345964	−	0.816043i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.622864	−	1.07883i	0.0388532	−	0.0672957i	−0.845945	−	0.533270i	$-0.820963\pi$
$257$	0.622864	−	1.07883i	0.0388532	−	0.0672957i	0.884798	+	0.465975i	$0.154296\pi$
$258$	−3.99466	+	6.28787i	−0.248697	+	0.391466i
$259$	−18.7152	−	21.0600i	−1.16290	−	1.30861i
$260$		−	1.31290i		−	0.0814227i
$261$	0.952567	−	11.2142i	0.0589624	−	0.694139i
$262$	14.8677	−	8.58385i	0.918528	−	0.530312i
$263$	−0.152136	+	0.0878358i	−0.00938111	+	0.00541619i	−0.504683	−	0.863305i	$-0.668391\pi$
$263$	−0.152136	+	0.0878358i	−0.00938111	+	0.00541619i	0.495302	+	0.868721i	$0.335057\pi$
$264$	−1.53534	+	0.801712i	−0.0944934	+	0.0493420i
$265$			12.9904i			0.797992i
$266$	−17.5022	+	3.60104i	−1.07313	+	0.220794i
$267$	−20.5762	−	13.0720i	−1.25924	−	0.799992i
$268$	2.98446	−	5.16923i	0.182305	−	0.315761i
$269$	5.07356	+	8.78767i	0.309341	+	0.535794i	0.978218	−	0.207579i	$-0.0665583\pi$
$269$	5.07356	+	8.78767i	0.309341	+	0.535794i	−0.668878	+	0.743373i	$0.733225\pi$
$270$	−7.20315	−	17.2052i	−0.438370	−	1.04708i
$271$	25.5195	+	14.7337i	1.55020	+	0.895007i	0.998125	+	0.0612103i	$0.0194960\pi$
$271$	25.5195	+	14.7337i	1.55020	+	0.895007i	0.552072	+	0.833796i	$0.313837\pi$
$272$	−2.09780			−0.127198
$273$	−0.595225	+	1.56682i	−0.0360246	+	0.0948285i
$274$	−3.19438			−0.192980
$275$	−6.82893	−	3.94268i	−0.411800	−	0.237753i
$276$	3.57247	+	0.151456i	0.215037	+	0.00911657i
$277$	11.7731	+	20.3916i	0.707375	+	1.22521i	0.965828	+	0.259186i	$0.0834541\pi$
$277$	11.7731	+	20.3916i	0.707375	+	1.22521i	−0.258452	+	0.966024i	$0.583213\pi$
$278$	2.27221	−	3.93558i	0.136278	−	0.236041i
$279$	25.2365	−	11.8457i	1.51087	−	0.709184i
$280$	−7.09913	+	6.30871i	−0.424254	+	0.377018i
$281$		−	8.77829i		−	0.523669i	−0.965113	−	0.261834i	$-0.915673\pi$
$281$		−	8.77829i		−	0.523669i	0.965113	−	0.261834i	$-0.0843274\pi$
$282$	−10.2554	−	19.6398i	−0.610698	−	1.16953i
$283$	−7.65207	+	4.41792i	−0.454868	+	0.262618i	−0.709884	−	0.704319i	$-0.751253\pi$
$283$	−7.65207	+	4.41792i	−0.454868	+	0.262618i	0.255016	+	0.966937i	$0.417919\pi$
$284$	−3.83729	+	2.21546i	−0.227701	+	0.131463i
$285$	−19.4363	−	37.2220i	−1.15131	−	2.20484i
$286$			0.365750i			0.0216272i
$287$	−2.99367	+	9.01307i	−0.176711	+	0.532025i
$288$	−2.71571	+	1.27472i	−0.160025	+	0.0751136i
$289$	6.29962	−	10.9113i	0.370566	−	0.641839i
$290$	−6.73326	−	11.6623i	−0.395390	−	0.684836i
$291$	−1.12782	−	0.0478143i	−0.0661141	−	0.00280293i
$292$	4.69142	+	2.70859i	0.274544	+	0.158508i
$293$	−30.3145			−1.77099			−0.885496	−	0.464648i	$-0.846181\pi$
$293$	−30.3145			−1.77099			−0.885496	+	0.464648i	$0.846181\pi$
$294$	11.3323	−	4.31035i	0.660913	−	0.251384i
$295$	−27.6596			−1.61041
$296$	−9.22215	−	5.32441i	−0.536027	−	0.309475i
$297$	2.00666	+	4.79305i	0.116438	+	0.278121i
$298$	5.10895	+	8.84896i	0.295954	+	0.512607i
$299$	0.377530	−	0.653901i	0.0218331	−	0.0378161i
$300$	−11.5282	−	7.32380i	−0.665580	−	0.422840i
$301$	3.58691	−	10.7991i	0.206746	−	0.622453i
$302$			5.79680i			0.333568i
$303$	7.48787	−	3.90997i	0.430167	−	0.224622i
$304$	−5.84896	+	3.37690i	−0.335461	+	0.193678i
$305$	26.8788	−	15.5185i	1.53908	−	0.888586i
$306$	−0.532664	+	6.27082i	−0.0304504	+	0.358479i
$307$			16.7973i			0.958671i	0.877632	+	0.479336i	$0.159122\pi$
$307$			16.7973i			0.958671i	−0.877632	+	0.479336i	$0.840878\pi$
$308$	1.97768	−	1.75749i	0.112689	−	0.100142i
$309$	8.79298	−	13.8408i	0.500215	−	0.787374i
$310$	16.6788	−	28.8885i	0.947291	−	1.64076i
$311$	9.12108	+	15.7982i	0.517209	+	0.895832i	0.999800	+	0.0199867i	$0.00636238\pi$
$311$	9.12108	+	15.7982i	0.517209	+	0.895832i	−0.482591	+	0.875846i	$0.660304\pi$
$312$	−0.0268332	+	0.632929i	−0.00151913	+	0.0358325i
$313$	7.15808	+	4.13272i	0.404598	+	0.233595i	0.688466	−	0.725268i	$-0.258284\pi$
$313$	7.15808	+	4.13272i	0.404598	+	0.233595i	−0.283868	+	0.958863i	$0.591618\pi$
$314$	17.2035			0.970851
$315$	17.0556	+	22.8229i	0.960977	+	1.28592i
$316$	−6.61386			−0.372059
$317$	5.24858	+	3.03027i	0.294789	+	0.170197i	0.640100	−	0.768292i	$-0.278893\pi$
$317$	5.24858	+	3.03027i	0.294789	+	0.170197i	−0.345310	+	0.938489i	$0.612226\pi$
$318$	0.265498	−	6.26244i	0.0148884	−	0.351180i
$319$	1.87576	+	3.24891i	0.105022	+	0.181904i
$320$	−1.79481	+	3.10870i	−0.100333	+	0.173782i
$321$	16.7424	−	26.3537i	0.934469	−	1.47092i
$322$	−5.34987	+	1.10072i	−0.298137	+	0.0613408i
$323$			14.1681i			0.788335i
$324$	3.12088	+	8.44157i	0.173382	+	0.468976i
$325$	−2.49768	+	1.44203i	−0.138546	+	0.0799897i
$326$	7.44325	−	4.29736i	0.412243	−	0.238009i
$327$	−22.2335	+	11.6098i	−1.22952	+	0.642022i
$328$			3.58962i			0.198204i
$329$	22.4815	+	25.2982i	1.23945	+	1.39474i
$330$	5.24792	+	3.33398i	0.288888	+	0.183530i
$331$	0.229059	−	0.396742i	0.0125902	−	0.0218069i	−0.859662	−	0.510864i	$-0.829326\pi$
$331$	0.229059	−	0.396742i	0.0125902	−	0.0218069i	0.872252	+	0.489057i	$0.162659\pi$
$332$	3.81238	+	6.60323i	0.209231	+	0.362399i
$333$	−18.2576	+	26.2152i	−1.00051	+	1.43659i
$334$	−13.8579	−	8.00088i	−0.758272	−	0.437789i
$335$	−21.4261			−1.17064
$336$	3.55131	−	2.89623i	0.193740	−	0.158003i
$337$	6.14509			0.334744			0.167372	−	0.985894i	$-0.446472\pi$
$337$	6.14509			0.334744			0.167372	+	0.985894i	$0.446472\pi$
$338$	−11.1425	−	6.43311i	−0.606071	−	0.349915i
$339$	−6.60433	−	0.279992i	−0.358698	−	0.0152071i
$340$	3.76515	+	6.52143i	0.204194	+	0.353674i
$341$	−4.64639	+	8.04779i	−0.251616	+	0.435812i
$342$	8.60920	+	18.3414i	0.465532	+	0.991787i
$343$	−15.1934	+	10.5906i	−0.820365	+	0.571840i
$344$		−	4.30096i		−	0.231892i
$345$	−5.94107	−	11.3776i	−0.319856	−	0.612548i
$346$	−11.5986	+	6.69644i	−0.623543	+	0.360003i
$347$	−13.0730	+	7.54769i	−0.701794	+	0.405181i	−0.808015	−	0.589161i	$-0.799458\pi$
$347$	−13.0730	+	7.54769i	−0.701794	+	0.405181i	0.106221	+	0.994343i	$0.466125\pi$
$348$	3.00764	+	5.75984i	0.161226	+	0.308760i
$349$		−	7.70859i		−	0.412632i	−0.978485	−	0.206316i	$-0.933853\pi$
$349$		−	7.70859i		−	0.412632i	0.978485	−	0.206316i	$-0.0661474\pi$
$350$	19.7991	+	6.57624i	1.05831	+	0.351515i
$351$	1.88516	+	0.240921i	0.100622	+	0.0128594i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	4.74656	+	8.22129i	0.252634	+	0.437575i	0.964250	−	0.264993i	$-0.0853698\pi$
$353$	4.74656	+	8.22129i	0.252634	+	0.437575i	−0.711616	+	0.702568i	$0.752036\pi$
$354$	13.3343	+	0.565310i	0.708708	+	0.0300459i
$355$	13.7744	+	7.95266i	0.731070	+	0.422083i
$356$	14.0743			0.745936
$357$	−1.53676	−	9.48970i	−0.0813338	−	0.502248i
$358$	−14.8045			−0.782442
$359$	5.74380	+	3.31618i	0.303146	+	0.175021i	0.643855	−	0.765147i	$-0.277334\pi$
$359$	5.74380	+	3.31618i	0.303146	+	0.175021i	−0.340709	+	0.940169i	$0.610667\pi$
$360$	8.83691	+	6.15445i	0.465746	+	0.324368i
$361$	13.3069	+	23.0482i	0.700361	+	1.21306i
$362$	−1.75245	+	3.03534i	−0.0921069	+	0.159534i
$363$	−1.46197	−	0.928784i	−0.0767336	−	0.0487485i
$364$	−0.195013	−	0.947829i	−0.0102215	−	0.0496797i
$365$		−	19.4456i		−	1.01783i
$366$	−13.2750	+	6.93185i	−0.693895	+	0.362334i
$367$	−24.4825	+	14.1350i	−1.27797	+	0.737838i	−0.976476	−	0.215628i	$-0.930820\pi$
$367$	−24.4825	+	14.1350i	−1.27797	+	0.737838i	−0.301498	+	0.953467i	$0.597487\pi$
$368$	−1.78784	+	1.03221i	−0.0931975	+	0.0538076i
$369$	10.7302	+	0.911459i	0.558593	+	0.0474487i
$370$			38.2252i			1.98723i
$371$	1.92954	+	9.37819i	0.100177	+	0.486892i
$372$	−8.63099	+	13.5858i	−0.447496	+	0.704390i
$373$	3.76850	−	6.52723i	0.195125	−	0.337967i	−0.751816	−	0.659373i	$-0.770822\pi$
$373$	3.76850	−	6.52723i	0.195125	−	0.337967i	0.946942	+	0.321406i	$0.104155\pi$
$374$	−1.04890	−	1.81675i	−0.0542373	−	0.0939418i
$375$	−0.759866	+	17.9234i	−0.0392393	+	0.925559i
$376$	11.0781	+	6.39592i	0.571307	+	0.329844i
$377$	1.37212			0.0706675
$378$	−7.75579	−	11.3511i	−0.398915	−	0.583838i
$379$	23.4885			1.20652			0.603261	−	0.797544i	$-0.293868\pi$
$379$	23.4885			1.20652			0.603261	+	0.797544i	$0.293868\pi$
$380$	20.9955	+	12.1218i	1.07705	+	0.621834i
$381$	−0.329043	+	7.76132i	−0.0168574	+	0.397624i
$382$	−3.21740	−	5.57270i	−0.164617	−	0.285124i
$383$	−2.47533	+	4.28740i	−0.126483	+	0.219076i	−0.922312	−	0.386446i	$-0.873702\pi$
$383$	−2.47533	+	4.28740i	−0.126483	+	0.219076i	0.795828	+	0.605522i	$0.207036\pi$
$384$	0.928784	−	1.46197i	0.0473968	−	0.0746059i
$385$	−9.01307	−	2.99367i	−0.459349	−	0.152572i
$386$			6.57990i			0.334908i
$387$	−12.8566	−	1.09208i	−0.653536	−	0.0555135i
$388$	0.564417	−	0.325866i	0.0286539	−	0.0165434i
$389$	2.82098	−	1.62869i	0.143029	−	0.0825779i	−0.426778	−	0.904357i	$-0.640351\pi$
$389$	2.82098	−	1.62869i	0.143029	−	0.0825779i	0.569807	+	0.821779i	$0.307018\pi$
$390$	2.01575	−	1.05257i	0.102071	−	0.0532989i
$391$			4.33074i			0.219015i
$392$	−4.18804	+	5.60895i	−0.211528	+	0.283295i
$393$	25.0987	+	15.9451i	1.26606	+	0.804323i
$394$	6.96169	−	12.0580i	0.350725	−	0.607473i
$395$	11.8706	+	20.5605i	0.597275	+	1.03451i
$396$	−2.46180	−	1.71451i	−0.123710	−	0.0861576i
$397$	7.99636	+	4.61670i	0.401326	+	0.231706i	0.687056	−	0.726605i	$-0.258903\pi$
$397$	7.99636	+	4.61670i	0.401326	+	0.231706i	−0.285730	+	0.958310i	$0.592236\pi$
$398$	26.4389			1.32526
$399$	−19.5606	−	23.9848i	−0.979253	−	1.20074i
$400$	7.88536			0.394268
$401$	−6.64897	−	3.83879i	−0.332034	−	0.191700i	0.324710	−	0.945814i	$-0.394733\pi$
$401$	−6.64897	−	3.83879i	−0.332034	−	0.191700i	−0.656744	+	0.754114i	$0.728067\pi$
$402$	10.3292	+	0.437909i	0.515173	+	0.0218409i
$403$	1.69942	+	2.94348i	0.0846540	+	0.146625i
$404$	−2.43851	+	4.22363i	−0.121320	+	0.210133i
$405$	20.6409	−	24.8529i	1.02566	−	1.23495i
$406$	−6.59324	−	7.41931i	−0.327217	−	0.368214i
$407$		−	10.6488i		−	0.527843i
$408$	−1.68183	−	3.22083i	−0.0832631	−	0.159455i
$409$	10.4927	−	6.05798i	0.518832	−	0.299548i	−0.217625	−	0.976033i	$-0.569831\pi$
$409$	10.4927	−	6.05798i	0.518832	−	0.299548i	0.736457	+	0.676485i	$0.236498\pi$
$410$	11.1591	−	6.44268i	0.551106	−	0.318181i
$411$	−2.56097	−	4.90445i	−0.126324	−	0.241919i
$412$			9.46719i			0.466415i
$413$	−19.9684	+	4.10845i	−0.982583	+	0.202164i
$414$	2.63155	+	5.60636i	0.129334	+	0.275538i
$415$	13.6850	−	23.7031i	0.671769	−	1.16354i
$416$	−0.182875	−	0.316749i	−0.00896618	−	0.0155299i
$417$	7.86410	+	0.333401i	0.385107	+	0.0163267i
$418$	−5.84896	−	3.37690i	−0.286082	−	0.165169i
$419$	−6.64928			−0.324839			−0.162419	−	0.986722i	$-0.551930\pi$
$419$	−6.64928			−0.324839			−0.162419	+	0.986722i	$0.551930\pi$
$420$	−15.3775	−	5.84178i	−0.750343	−	0.285050i
$421$	1.35380			0.0659800			0.0329900	−	0.999456i	$-0.489497\pi$
$421$	1.35380			0.0659800			0.0329900	+	0.999456i	$0.489497\pi$
$422$	11.6618	+	6.73294i	0.567688	+	0.327755i
$423$	21.9318	−	31.4909i	1.06636	−	1.53114i
$424$	1.80944	+	3.13404i	0.0878740	+	0.152202i
$425$	8.27096	−	14.3257i	0.401200	−	0.694900i
$426$	−6.47788	−	4.11537i	−0.313854	−	0.199390i
$427$	17.0997	−	15.1958i	0.827511	−	0.735376i
$428$			18.0261i			0.871327i
$429$	−0.561549	+	0.293226i	−0.0271118	+	0.0141571i
$430$	−13.3704	+	7.71940i	−0.644777	+	0.372262i
$431$	−15.0179	+	8.67061i	−0.723389	+	0.417649i	−0.815999	−	0.578054i	$-0.803812\pi$
$431$	−15.0179	+	8.67061i	−0.723389	+	0.417649i	0.0926100	+	0.995702i	$0.470479\pi$
$432$	−4.13434	−	3.14757i	−0.198914	−	0.151438i
$433$			24.1020i			1.15827i	0.815232	+	0.579135i	$0.196610\pi$
$433$			24.1020i			1.15827i	−0.815232	+	0.579135i	$0.803390\pi$
$434$	7.75000	−	23.3330i	0.372012	−	1.12002i
$435$	12.5075	−	19.6877i	0.599688	−	0.943951i
$436$	7.24061	−	12.5411i	0.346762	−	0.600610i
$437$	6.97132	+	12.0747i	0.333484	+	0.577611i
$438$	−0.397431	+	9.37441i	−0.0189900	+	0.447927i
$439$	−22.7596	−	13.1403i	−1.08626	−	0.627151i	−0.153680	−	0.988121i	$-0.549112\pi$
$439$	−22.7596	−	13.1403i	−1.08626	−	0.627151i	−0.932577	+	0.360970i	$0.882446\pi$
$440$	−3.58962			−0.171128
$441$	15.7031	+	13.9432i	0.747765	+	0.663963i
$442$	−0.767270			−0.0364953
$443$	12.5406	+	7.24029i	0.595820	+	0.343997i	0.767395	−	0.641174i	$-0.221552\pi$
$443$	12.5406	+	7.24029i	0.595820	+	0.343997i	−0.171576	+	0.985171i	$0.554886\pi$
$444$	0.781250	−	18.4278i	0.0370765	−	0.874542i
$445$	−25.2607	−	43.7528i	−1.19747	−	2.07408i
$446$	−12.1627	+	21.0664i	−0.575919	+	0.997521i
$447$	−9.49023	+	14.9383i	−0.448872	+	0.706557i
$448$	−0.833981	+	2.51087i	−0.0394019	+	0.118628i
$449$		−	17.9197i		−	0.845683i	−0.906204	−	0.422842i	$-0.861033\pi$
$449$		−	17.9197i		−	0.845683i	0.906204	−	0.422842i	$-0.138967\pi$
$450$	2.00222	−	23.5712i	0.0943853	−	1.11116i
$451$	−3.10870	+	1.79481i	−0.146383	+	0.0845143i
$452$	3.30513	−	1.90822i	0.155460	−	0.0897550i
$453$	−8.90003	+	4.64736i	−0.418160	+	0.218352i
$454$			16.9874i			0.797260i
$455$	−2.59651	+	2.30741i	−0.121726	+	0.108173i
$456$	−9.87385	−	6.27282i	−0.462386	−	0.293752i
$457$	6.38752	−	11.0635i	0.298796	−	0.517529i	−0.677065	−	0.735923i	$-0.736748\pi$
$457$	6.38752	−	11.0635i	0.298796	−	0.517529i	0.975861	+	0.218394i	$0.0700818\pi$
$458$	10.3592	+	17.9426i	0.484052	+	0.838402i
$459$	−10.0549	+	4.20957i	−0.469321	+	0.196486i
$460$	6.41766	+	3.70524i	0.299225	+	0.172758i
$461$	−20.6420			−0.961394			−0.480697	−	0.876887i	$-0.659616\pi$
$461$	−20.6420			−0.961394			−0.480697	+	0.876887i	$0.659616\pi$
$462$	4.28387	+	1.62741i	0.199304	+	0.0757140i
$463$	6.73301			0.312909			0.156455	−	0.987685i	$-0.449993\pi$
$463$	6.73301			0.312909			0.156455	+	0.987685i	$0.449993\pi$
$464$	−3.24891	−	1.87576i	−0.150827	−	0.0870799i
$465$	57.7251	+	2.44727i	2.67694	+	0.113490i
$466$	1.77278	+	3.07054i	0.0821224	+	0.142240i
$467$	13.0650	−	22.6292i	0.604575	−	1.04715i	−0.387544	−	0.921851i	$-0.626676\pi$
$467$	13.0650	−	22.6292i	0.604575	−	1.04715i	0.992119	−	0.125303i	$-0.0399902\pi$
$468$	−0.993271	+	0.466229i	−0.0459139	+	0.0215514i
$469$	−15.4683	+	3.18255i	−0.714258	+	0.146957i
$470$		−	45.9178i		−	2.11803i
$471$	13.7923	+	26.4132i	0.635514	+	1.21706i
$472$	−6.67312	+	3.85273i	−0.307155	+	0.177336i
$473$	3.72474	−	2.15048i	0.171264	−	0.0988791i
$474$	−5.30241	−	10.1545i	−0.243548	−	0.466411i
$475$		−	53.2561i		−	2.44356i
$476$	3.68686	+	4.14879i	0.168987	+	0.190159i
$477$	9.82781	−	4.61305i	0.449985	−	0.211217i
$478$	−13.4080	+	23.2233i	−0.613268	+	1.06221i
$479$	15.9308	+	27.5930i	0.727898	+	1.26076i	0.957770	+	0.287535i	$0.0928358\pi$
$479$	15.9308	+	27.5930i	0.727898	+	1.26076i	−0.229872	+	0.973221i	$0.573831\pi$
$480$	−6.21182	−	0.263352i	−0.283530	−	0.0120203i
$481$	−3.37300	−	1.94740i	−0.153796	−	0.0887939i
$482$	4.95592			0.225736
$483$	−5.97904	−	7.33139i	−0.272056	−	0.333590i
$484$	1.00000			0.0454545
$485$	−2.02604	−	1.16974i	−0.0919979	−	0.0531150i
$486$	−10.4586	+	11.5593i	−0.474412	+	0.524341i
$487$	−21.8146	−	37.7840i	−0.988515	−	1.71216i	−0.625132	−	0.780519i	$-0.714955\pi$
$487$	−21.8146	−	37.7840i	−0.988515	−	1.71216i	−0.363383	−	0.931640i	$-0.618378\pi$
$488$	4.32316	−	7.48792i	0.195700	−	0.338962i
$489$	12.5652	+	7.98264i	0.568220	+	0.360987i
$490$	24.9533	+	2.95235i	1.12727	+	0.133374i
$491$			24.2260i			1.09331i	0.837359	+	0.546653i	$0.184098\pi$
$491$			24.2260i			1.09331i	−0.837359	+	0.546653i	$0.815902\pi$
$492$	−5.51127	+	2.87784i	−0.248467	+	0.129743i
$493$	−6.81556	+	3.93497i	−0.306957	+	0.177222i
$494$	−2.13925	+	1.23510i	−0.0962496	+	0.0555697i
$495$	−0.911459	+	10.7302i	−0.0409671	+	0.482287i
$496$		−	9.29278i		−	0.417258i
$497$	11.1255	+	3.69530i	0.499046	+	0.165757i
$498$	−7.08175	+	11.1472i	−0.317341	+	0.499517i
$499$	7.15992	−	12.4013i	0.320522	−	0.555160i	−0.660074	−	0.751201i	$-0.729475\pi$
$499$	7.15992	−	12.4013i	0.320522	−	0.555160i	0.980596	+	0.196040i	$0.0628084\pi$
$500$	−5.17868	−	8.96973i	−0.231598	−	0.401139i
$501$	1.17397	−	27.6910i	0.0524490	−	1.23714i
$502$	14.4473	+	8.34113i	0.644812	+	0.372283i
$503$	−4.44169			−0.198045			−0.0990226	−	0.995085i	$-0.531572\pi$
$503$	−4.44169			−0.198045			−0.0990226	+	0.995085i	$0.531572\pi$
$504$	7.29383	+	3.13051i	0.324893	+	0.139444i
$505$	17.5067			0.779036
$506$	−1.78784	−	1.03221i	−0.0794791	−	0.0458873i
$507$	0.943929	−	22.2650i	0.0419214	−	0.988822i
$508$	−2.24251	−	3.88414i	−0.0994954	−	0.172331i
$509$	−9.31633	+	16.1364i	−0.412939	+	0.715231i	−0.995210	−	0.0977636i	$-0.968831\pi$
$509$	−9.31633	+	16.1364i	−0.412939	+	0.715231i	0.582271	+	0.812995i	$0.302164\pi$
$510$	−6.99403	+	11.0091i	−0.309701	+	0.487491i
$511$	−2.88837	−	14.0385i	−0.127774	−	0.621025i
$512$			1.00000i			0.0441942i
$513$	−21.2580	+	27.9225i	−0.938566	+	1.23281i
$514$	−1.07883	+	0.622864i	−0.0475853	+	0.0274734i
$515$	29.4307	−	16.9918i	1.29687	−	0.748749i
$516$	6.60341	−	3.44813i	0.290699	−	0.151795i
$517$			12.7918i			0.562584i
$518$	5.67782	+	27.5961i	0.249469	+	1.21250i
$519$	−19.5800	−	12.4391i	−0.859466	−	0.546015i
$520$	−0.656451	+	1.13701i	−0.0287873	+	0.0498610i
$521$	9.30936	+	16.1243i	0.407850	+	0.706418i	0.994649	−	0.103316i	$-0.0329452\pi$
$521$	9.30936	+	16.1243i	0.407850	+	0.706418i	−0.586798	+	0.809733i	$0.699612\pi$
$522$	−6.43203	+	9.23547i	−0.281522	+	0.404225i
$523$	−11.3315	−	6.54227i	−0.495494	−	0.286074i	0.231357	−	0.972869i	$-0.425684\pi$
$523$	−11.3315	−	6.54227i	−0.495494	−	0.286074i	−0.726851	+	0.686795i	$0.759017\pi$
$524$	−17.1677			−0.749975
$525$	5.77647	+	35.6706i	0.252106	+	1.55679i
$526$	0.175672			0.00765965
$527$	−16.8827	−	9.74720i	−0.735420	−	0.424595i
$528$	1.73050	+	0.0733649i	0.0753102	+	0.00319280i
$529$	−9.36909	−	16.2277i	−0.407352	−	0.705554i
$530$	6.49519	−	11.2500i	0.282133	−	0.488668i
$531$	9.82230	+	20.9258i	0.426251	+	0.908102i
$532$	16.9579	+	5.63253i	0.735219	+	0.244201i
$533$			1.31290i			0.0568681i
$534$	11.2835	+	21.6088i	0.488286	+	0.935103i
$535$	56.0379	−	32.3535i	2.42273	−	1.39876i
$536$	−5.16923	+	2.98446i	−0.223277	+	0.128909i
$537$	−11.8689	−	22.7299i	−0.512183	−	0.980866i
$538$		−	10.1471i		−	0.437474i
$539$	−6.95151	−	0.822470i	−0.299423	−	0.0354263i
$540$	−2.36450	+	18.5017i	−0.101752	+	0.796188i
$541$	−13.1406	+	22.7602i	−0.564960	+	0.978539i	0.432093	+	0.901829i	$0.357775\pi$
$541$	−13.1406	+	22.7602i	−0.564960	+	0.978539i	−0.997053	+	0.0767105i	$0.975558\pi$
$542$	−14.7337	−	25.5195i	−0.632865	−	1.09615i
$543$	−6.06523	−	0.257137i	−0.260284	−	0.0110348i
$544$	1.81675	+	1.04890i	0.0778925	+	0.0449712i
$545$	−51.9820			−2.22667
$546$	1.29889	−	1.05930i	0.0555874	−	0.0453337i
$547$	16.4908			0.705097			0.352548	−	0.935794i	$-0.385315\pi$
$547$	16.4908			0.705097			0.352548	+	0.935794i	$0.385315\pi$
$548$	2.76642	+	1.59719i	0.118175	+	0.0682286i
$549$	−21.2855	−	14.8242i	−0.908441	−	0.632683i
$550$	3.94268	+	6.82893i	0.168117	+	0.291186i
$551$	−12.6685	+	21.9425i	−0.539695	+	0.934780i
$552$	−3.01812	−	1.91740i	−0.128460	−	0.0816099i
$553$	11.6238	+	13.0801i	0.494293	+	0.556223i
$554$		−	23.5461i		−	1.00038i
$555$	−58.6886	+	30.6456i	−2.49119	+	1.30083i
$556$	−3.93558	+	2.27221i	−0.166906	+	0.0963632i
$557$	−27.2601	+	15.7386i	−1.15505	+	0.666868i	−0.950112	−	0.311908i	$-0.899032\pi$
$557$	−27.2601	+	15.7386i	−1.15505	+	0.666868i	−0.204936	+	0.978775i	$0.565699\pi$
$558$	−27.7783	−	2.35958i	−1.17595	−	0.0998890i
$559$		−	1.57307i		−	0.0665339i
$560$	9.30239	−	1.91394i	0.393098	−	0.0808787i
$561$	1.94840	−	3.06692i	0.0822617	−	0.129486i
$562$	−4.38914	+	7.60222i	−0.185145	+	0.320680i
$563$	8.90911	+	15.4310i	0.375474	+	0.650340i	0.990398	−	0.138246i	$-0.0441465\pi$
$563$	8.90911	+	15.4310i	0.375474	+	0.650340i	−0.614924	+	0.788587i	$0.710813\pi$
$564$	−0.938472	+	22.1362i	−0.0395168	+	0.932103i
$565$	−11.8642	−	6.84977i	−0.499129	−	0.288172i
$566$	8.83585			0.371398
$567$	11.2099	−	21.0081i	0.470770	−	0.882256i
$568$	4.43092			0.185917
$569$	4.70368	+	2.71567i	0.197189	+	0.113847i	0.595344	−	0.803471i	$-0.297016\pi$
$569$	4.70368	+	2.71567i	0.197189	+	0.113847i	−0.398155	+	0.917318i	$0.630349\pi$
$570$	−1.77863	+	41.9534i	−0.0744984	+	1.75723i
$571$	19.0251	+	32.9524i	0.796175	+	1.37902i	0.922091	+	0.386974i	$0.126480\pi$
$571$	19.0251	+	32.9524i	0.796175	+	1.37902i	−0.125916	+	0.992041i	$0.540187\pi$
$572$	0.182875	−	0.316749i	0.00764638	−	0.0132439i
$573$	5.97654	−	9.40750i	0.249674	−	0.393004i
$574$	7.09913	−	6.30871i	0.296312	−	0.263321i
$575$		−	16.2787i		−	0.678868i
$576$	2.98924	+	0.253915i	0.124551	+	0.0105798i
$577$	−22.1072	+	12.7636i	−0.920334	+	0.531355i	−0.883741	−	0.467975i	$-0.844984\pi$
$577$	−22.1072	+	12.7636i	−0.920334	+	0.531355i	−0.0365921	+	0.999330i	$0.511650\pi$
$578$	−10.9113	+	6.29962i	−0.453848	+	0.262030i
$579$	−10.1024	+	5.27518i	−0.419839	+	0.219229i
$580$			13.4665i			0.559166i
$581$	6.35890	−	19.1448i	0.263812	−	0.794259i
$582$	0.952815	+	0.605319i	0.0394954	+	0.0250913i
$583$	−1.80944	+	3.13404i	−0.0749392	+	0.129798i
$584$	−2.70859	−	4.69142i	−0.112082	−	0.194132i
$585$	3.23210	+	2.25099i	0.133631	+	0.0930670i
$586$	26.2531	+	15.1572i	1.08451	+	0.626140i
$587$	25.8408			1.06656			0.533282	−	0.845937i	$-0.320958\pi$
$587$	25.8408			1.06656			0.533282	+	0.845937i	$0.320958\pi$
$588$	−11.9692	−	1.93328i	−0.493603	−	0.0797271i
$589$	−62.7616			−2.58604
$590$	23.9540	+	13.8298i	0.986169	+	0.569365i
$591$	24.0944	+	1.02149i	0.991109	+	0.0420184i
$592$	5.32441	+	9.22215i	0.218832	+	0.379028i
$593$	−19.1052	+	33.0911i	−0.784555	+	1.35889i	0.144709	+	0.989474i	$0.453775\pi$
$593$	−19.1052	+	33.0911i	−0.784555	+	1.35889i	−0.929264	+	0.369416i	$0.879558\pi$
$594$	0.658705	−	5.15423i	0.0270270	−	0.211481i
$595$	6.28013	−	18.9076i	0.257460	−	0.775137i
$596$		−	10.2179i		−	0.418542i
$597$	21.1964	+	40.5926i	0.867510	+	1.66134i
$598$	−0.653901	+	0.377530i	−0.0267400	+	0.0154383i
$599$	−5.79727	+	3.34705i	−0.236870	+	0.136757i	−0.613737	−	0.789510i	$-0.710335\pi$
$599$	−5.79727	+	3.34705i	−0.236870	+	0.136757i	0.376867	+	0.926267i	$0.377001\pi$
$600$	6.32179	+	12.1067i	0.258086	+	0.494253i
$601$			8.82221i			0.359865i	0.983679	+	0.179933i	$0.0575880\pi$
$601$			8.82221i			0.359865i	−0.983679	+	0.179933i	$0.942412\pi$
$602$	−8.50593	+	7.55888i	−0.346676	+	0.308077i
$603$	7.60870	+	16.2099i	0.309850	+	0.660116i
$604$	2.89840	−	5.02017i	0.117934	−	0.204268i
$605$	−1.79481	−	3.10870i	−0.0729694	−	0.126387i
$606$	−8.43967	−	0.357802i	−0.342838	−	0.0145347i
$607$	−7.12129	−	4.11148i	−0.289044	−	0.166880i	0.348467	−	0.937321i	$-0.386702\pi$
$607$	−7.12129	−	4.11148i	−0.289044	−	0.166880i	−0.637511	+	0.770442i	$0.720036\pi$
$608$	6.75379			0.273903
$609$	6.10526	−	16.0710i	0.247397	−	0.651230i
$610$	−31.0370			−1.25665
$611$	4.05179	+	2.33930i	0.163918	+	0.0946381i
$612$	3.59671	−	5.16436i	0.145388	−	0.208757i
$613$	10.7116	+	18.5530i	0.432635	+	0.749347i	0.997099	−	0.0761112i	$-0.0242504\pi$
$613$	10.7116	+	18.5530i	0.432635	+	0.749347i	−0.564464	+	0.825458i	$0.690917\pi$
$614$	8.39864	−	14.5469i	0.338942	−	0.587064i
$615$	18.8380	+	11.9677i	0.759623	+	0.482585i
$616$	−2.59147	+	0.533187i	−0.104413	+	0.0214827i
$617$		−	43.5220i		−	1.75213i	−0.482194	−	0.876065i	$-0.660160\pi$
$617$		−	43.5220i		−	1.75213i	0.482194	−	0.876065i	$-0.339840\pi$
$618$	−14.5353	+	7.58997i	−0.584697	+	0.305313i
$619$	6.97855	−	4.02906i	0.280491	−	0.161942i	−0.353154	−	0.935565i	$-0.614891\pi$
$619$	6.97855	−	4.02906i	0.280491	−	0.161942i	0.633646	+	0.773623i	$0.281558\pi$
$620$	−28.8885	+	16.6788i	−1.16019	+	0.669836i
$621$	−6.49790	+	8.53501i	−0.260752	+	0.342498i
$622$		−	18.2422i		−	0.731444i
$623$	−24.7354	−	27.8345i	−0.991003	−	1.11517i
$624$	0.339702	−	0.534716i	0.0135990	−	0.0214058i
$625$	1.12393	−	1.94670i	0.0449572	−	0.0778681i
$626$	−4.13272	−	7.15808i	−0.165177	−	0.286094i
$627$	0.495491	−	11.6874i	0.0197880	−	0.466750i
$628$	−14.8987	−	8.60176i	−0.594522	−	0.343248i
$629$	22.3391			0.890719
$630$	−3.35920	−	28.2930i	−0.133834	−	1.12722i
$631$	−15.6519			−0.623091			−0.311546	−	0.950231i	$-0.600847\pi$
$631$	−15.6519			−0.623091			−0.311546	+	0.950231i	$0.600847\pi$
$632$	5.72777	+	3.30693i	0.227838	+	0.131543i
$633$	−0.987923	+	23.3027i	−0.0392664	+	0.926198i
$634$	−3.03027	−	5.24858i	−0.120347	−	0.208448i
$635$	−8.04976	+	13.9426i	−0.319445	+	0.553295i
$636$	−3.36115	+	5.29069i	−0.133278	+	0.209789i
$637$	−1.53177	+	2.05147i	−0.0606911	+	0.0812823i
$638$		−	3.75152i		−	0.148524i
$639$	1.12508	−	13.2451i	0.0445074	−	0.523967i
$640$	3.10870	−	1.79481i	0.122882	−	0.0709461i
$641$	−30.5777	+	17.6540i	−1.20775	+	0.697293i	−0.962267	−	0.272109i	$-0.912279\pi$
$641$	−30.5777	+	17.6540i	−1.20775	+	0.697293i	−0.245480	+	0.969402i	$0.578946\pi$
$642$	−27.6762	+	14.4518i	−1.09229	+	0.570366i
$643$		−	22.4466i		−	0.885208i	−0.896717	−	0.442604i	$-0.854055\pi$
$643$		−	22.4466i		−	0.885208i	0.896717	−	0.442604i	$-0.145945\pi$
$644$	5.18349	+	1.72168i	0.204258	+	0.0678439i
$645$	−22.5711	−	14.3393i	−0.888735	−	0.564610i
$646$	7.08406	−	12.2699i	0.278718	−	0.482755i
$647$	−11.9912	−	20.7693i	−0.471422	−	0.816527i	0.528043	−	0.849217i	$-0.322926\pi$
$647$	−11.9912	−	20.7693i	−0.471422	−	0.816527i	−0.999466	+	0.0326902i	$0.989593\pi$
$648$	1.51803	−	8.87105i	0.0596337	−	0.348488i
$649$	−6.67312	−	3.85273i	−0.261943	−	0.151233i
$650$	2.88407			0.113123
$651$	42.0373	−	6.80748i	1.64757	−	0.266806i
$652$	−8.59472			−0.336595
$653$	−32.7520	−	18.9094i	−1.28169	−	0.739981i	−0.304529	−	0.952503i	$-0.598499\pi$
$653$	−32.7520	−	18.9094i	−1.28169	−	0.739981i	−0.977156	+	0.212522i	$0.931832\pi$
$654$	25.0597	+	1.06241i	0.979911	+	0.0415436i
$655$	30.8128	+	53.3693i	1.20395	+	2.08531i
$656$	1.79481	−	3.10870i	0.0700755	−	0.121374i
$657$	−14.7115	+	6.90539i	−0.573950	+	0.269405i
$658$	−6.82044	−	33.1496i	−0.265889	−	1.29231i
$659$		−	36.8508i		−	1.43550i	−0.696298	−	0.717752i	$-0.745171\pi$
$659$		−	36.8508i		−	1.43550i	0.696298	−	0.717752i	$-0.254829\pi$
$660$	−2.87784	−	5.51127i	−0.112020	−	0.214526i
$661$	−7.15403	+	4.13038i	−0.278259	+	0.160653i	−0.632635	−	0.774450i	$-0.718027\pi$
$661$	−7.15403	+	4.13038i	−0.278259	+	0.160653i	0.354376	+	0.935103i	$0.384693\pi$
$662$	−0.396742	+	0.229059i	−0.0154198	+	0.00890264i
$663$	−0.615130	−	1.17802i	−0.0238897	−	0.0457504i
$664$		−	7.62475i		−	0.295898i
$665$	−12.9264	−	62.8264i	−0.501262	−	2.43630i
$666$	28.9191	−	13.5743i	1.12059	−	0.525992i
$667$	−3.87235	+	6.70710i	−0.149938	+	0.259700i
$668$	8.00088	+	13.8579i	0.309563	+	0.536179i
$669$	−42.0949	−	1.78463i	−1.62748	−	0.0689976i
$670$	18.5556	+	10.7131i	0.716865	+	0.413882i
$671$	8.64631			0.333787
$672$	−4.52364	+	0.732556i	−0.174503	+	0.0282590i
$673$	38.7394			1.49329			0.746647	−	0.665221i	$-0.231663\pi$
$673$	38.7394			1.49329			0.746647	+	0.665221i	$0.231663\pi$
$674$	−5.32181	−	3.07255i	−0.204988	−	0.118350i
$675$	37.7949	−	15.8233i	1.45473	−	0.609037i
$676$	6.43311	+	11.1425i	0.247427	+	0.428557i
$677$	2.71109	−	4.69574i	0.104195	−	0.180472i	−0.809214	−	0.587514i	$-0.800107\pi$
$677$	2.71109	−	4.69574i	0.104195	−	0.180472i	0.913409	+	0.407042i	$0.133440\pi$
$678$	5.57952	+	3.54464i	0.214280	+	0.136131i
$679$	−1.63642	−	0.543533i	−0.0627999	−	0.0208589i
$680$		−	7.53030i		−	0.288774i
$681$	−26.0814	+	13.6190i	−0.999442	+	0.521883i
$682$	8.04779	−	4.64639i	0.308166	−	0.177920i
$683$	−20.3425	+	11.7447i	−0.778383	+	0.449399i	−0.835857	−	0.548948i	$-0.815029\pi$
$683$	−20.3425	+	11.7447i	−0.778383	+	0.449399i	0.0574741	+	0.998347i	$0.481695\pi$
$684$	1.71489	−	20.1887i	0.0655705	−	0.771933i
$685$		−	11.4666i		−	0.438117i
$686$	18.4532	−	1.57505i	0.704545	−	0.0601358i
$687$	−19.2428	+	30.2896i	−0.734160	+	1.15562i
$688$	−2.15048	+	3.72474i	−0.0819862	+	0.142004i
$689$	0.661801	+	1.14627i	0.0252126	+	0.0436695i
$690$	−0.543668	+	12.8238i	−0.0206971	+	0.488193i
$691$	−16.9265	−	9.77251i	−0.643913	−	0.371764i	0.142207	−	0.989837i	$-0.454580\pi$
$691$	−16.9265	−	9.77251i	−0.643913	−	0.371764i	−0.786120	+	0.618073i	$0.787913\pi$
$692$	13.3929			0.509121
$693$	0.935808	+	7.88189i	0.0355484	+	0.299408i
$694$	15.0954			0.573013
$695$	14.1272	+	8.15637i	0.535877	+	0.309389i
$696$	0.275230	−	6.49198i	0.0104325	−	0.246078i
$697$	−3.76515	−	6.52143i	−0.142615	−	0.247017i
$698$	−3.85430	+	6.67584i	−0.145887	+	0.252684i
$699$	−3.29306	+	5.18350i	−0.124555	+	0.196058i
$700$	−13.8584	−	15.5948i	−0.523800	−	0.589427i
$701$		−	6.16477i		−	0.232840i	−0.993200	−	0.116420i	$-0.962858\pi$
$701$		−	6.16477i		−	0.232840i	0.993200	−	0.116420i	$-0.0371419\pi$
$702$	−1.51213	−	1.15122i	−0.0570719	−	0.0434501i
$703$	62.2845	−	35.9600i	2.34911	−	1.35626i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	70.4993	−	36.8129i	2.65516	−	1.38645i
$706$		−	9.49312i		−	0.357278i
$707$	12.6387	−	2.60037i	0.475326	−	0.0977969i
$708$	−11.2652	−	7.15670i	−0.423370	−	0.268965i
$709$	3.12615	−	5.41464i	0.117405	−	0.203351i	−0.801334	−	0.598218i	$-0.795876\pi$
$709$	3.12615	−	5.41464i	0.117405	−	0.203351i	0.918739	+	0.394866i	$0.129209\pi$
$710$	−7.95266	−	13.7744i	−0.298458	−	0.516944i
$711$	11.3396	−	16.2820i	0.425267	−	0.610622i
$712$	−12.1887	−	7.03715i	−0.456791	−	0.263728i
$713$	−19.1842			−0.718453
$714$	−3.41398	+	8.98670i	−0.127765	+	0.336319i
$715$	−1.31290			−0.0490998
$716$	12.8211	+	7.40224i	0.479146	+	0.276635i
$717$	−46.4050	−	1.96735i	−1.73303	−	0.0734722i
$718$	−3.31618	−	5.74380i	−0.123759	−	0.214357i
$719$	14.3651	−	24.8812i	0.535730	−	0.927911i	−0.463398	−	0.886150i	$-0.653370\pi$
$719$	14.3651	−	24.8812i	0.535730	−	0.927911i	0.999128	−	0.0417607i	$-0.0132967\pi$
$720$	−4.57576	−	9.74837i	−0.170529	−	0.363300i
$721$	18.7231	−	16.6385i	0.697285	−	0.619649i
$722$		−	26.6137i		−	0.990461i
$723$	3.97322	+	7.60900i	0.147766	+	0.282982i
$724$	3.03534	−	1.75245i	0.112808	−	0.0651294i
$725$	25.6188	−	14.7910i	0.951459	−	0.549325i
$726$	0.801712	+	1.53534i	0.0297543	+	0.0569817i
$727$		−	0.429770i		−	0.0159393i	−0.999968	−	0.00796964i	$-0.997463\pi$
$727$		−	0.429770i		−	0.0159393i	0.999968	−	0.00796964i	$-0.00253684\pi$
$728$	−0.305028	+	0.918351i	−0.0113051	+	0.0340363i
$729$	−26.1322	−	6.79023i	−0.967860	−	0.251490i
$730$	−9.72281	+	16.8404i	−0.359857	+	0.623291i
$731$	4.51127	+	7.81376i	0.166855	+	0.289002i
$732$	14.9624	+	0.634336i	0.553027	+	0.0234457i
$733$	−26.9259	−	15.5457i	−0.994532	−	0.574194i	−0.0879064	−	0.996129i	$-0.528018\pi$
$733$	−26.9259	−	15.5457i	−0.994532	−	0.574194i	−0.906626	+	0.421935i	$0.861351\pi$
$734$	28.2699			1.04346
$735$	15.4725	+	40.6786i	0.570712	+	1.50045i
$736$	2.06442			0.0760954
$737$	−5.16923	−	2.98446i	−0.190411	−	0.109934i
$738$	−8.83691	−	6.15445i	−0.325291	−	0.226549i
$739$	1.15436	+	1.99941i	0.0424639	+	0.0735496i	0.886476	−	0.462774i	$-0.153146\pi$
$739$	1.15436	+	1.99941i	0.0424639	+	0.0735496i	−0.844012	+	0.536324i	$0.819813\pi$
$740$	19.1126	−	33.1040i	0.702594	−	1.21693i
$741$	−3.61136	−	2.29428i	−0.132667	−	0.0842825i
$742$	3.01807	−	9.08652i	0.110797	−	0.333577i
$743$		−	37.7466i		−	1.38479i	−0.721520	−	0.692394i	$-0.756556\pi$
$743$		−	37.7466i		−	1.38479i	0.721520	−	0.692394i	$-0.243444\pi$
$744$	14.2675	−	7.45014i	0.523074	−	0.273135i
$745$	−31.7644	+	18.3392i	−1.16376	+	0.671896i
$746$	−6.52723	+	3.76850i	−0.238979	+	0.137974i
$747$	−22.7922	−	1.93604i	−0.833922	−	0.0708361i
$748$			2.09780i			0.0767032i
$749$	35.6500	−	31.6807i	1.30262	−	1.15759i
$750$	9.61975	−	15.1422i	0.351263	−	0.552913i
$751$	−21.6566	+	37.5104i	−0.790262	+	1.36877i	0.135543	+	0.990771i	$0.456722\pi$
$751$	−21.6566	+	37.5104i	−0.790262	+	1.36877i	−0.925805	+	0.378002i	$0.876611\pi$
$752$	−6.39592	−	11.0781i	−0.233235	−	0.403975i
$753$	−1.22389	+	28.8686i	−0.0446011	+	1.05203i
$754$	−1.18829	−	0.686058i	−0.0432749	−	0.0249848i
$755$	−20.8083			−0.757291
$756$	1.04116	+	13.7082i	0.0378666	+	0.498564i
$757$	21.8956			0.795807			0.397904	−	0.917427i	$-0.369738\pi$
$757$	21.8956			0.795807			0.397904	+	0.917427i	$0.369738\pi$
$758$	−20.3416	−	11.7442i	−0.738841	−	0.426570i
$759$	0.151456	−	3.57247i	0.00549750	−	0.129672i
$760$	−12.1218	−	20.9955i	−0.439703	−	0.761588i
$761$	−25.3900	+	43.9767i	−0.920386	+	1.59416i	−0.121568	+	0.992583i	$0.538792\pi$
$761$	−25.3900	+	43.9767i	−0.920386	+	1.59416i	−0.798818	+	0.601573i	$0.794541\pi$
$762$	4.16562	−	6.55698i	0.150904	−	0.237534i
$763$	−37.5276	+	7.72120i	−1.35859	+	0.279526i
$764$			6.43480i			0.232803i
$765$	−22.5099	−	1.91206i	−0.813845	−	0.0691307i
$766$	4.28740	−	2.47533i	0.154910	−	0.0894373i
$767$	−2.44069	+	1.40913i	−0.0881282	+	0.0508809i
$768$	−1.53534	+	0.801712i	−0.0554017	+	0.0289293i
$769$			50.9343i			1.83674i	0.395725	+	0.918369i	$0.370493\pi$
$769$			50.9343i			1.83674i	−0.395725	+	0.918369i	$0.629507\pi$
$770$	6.30871	+	7.09913i	0.227350	+	0.255835i
$771$	−1.82122	−	1.15701i	−0.0655896	−	0.0416688i
$772$	3.28995	−	5.69836i	0.118408	−	0.205088i
$773$	5.98128	+	10.3599i	0.215132	+	0.372619i	0.953313	−	0.301983i	$-0.0976486\pi$
$773$	5.98128	+	10.3599i	0.215132	+	0.372619i	−0.738182	+	0.674602i	$0.764315\pi$
$774$	10.5881	+	7.37405i	0.380581	+	0.265055i
$775$	63.4597	+	36.6385i	2.27954	+	1.31609i
$776$	−0.651733			−0.0233958
$777$	−37.8173	+	30.8415i	−1.35669	+	1.10643i
$778$	−3.25738			−0.116783
$779$	−20.9955	−	12.1218i	−0.752243	−	0.434308i
$780$	−2.27197	−	0.0963209i	−0.0813497	−	0.00344884i
$781$	2.21546	+	3.83729i	0.0792754	+	0.137309i
$782$	2.16537	−	3.75053i	0.0774334	−	0.134119i
$783$	−19.3362	−	2.47114i	−0.691019	−	0.0883113i
$784$	6.43142	−	2.76348i	0.229694	−	0.0986956i
$785$			61.7541i			2.20410i
$786$	−13.7636	−	26.3582i	−0.490930	−	0.940166i
$787$	10.0726	−	5.81543i	0.359050	−	0.207298i	−0.309614	−	0.950862i	$-0.600200\pi$
$787$	10.0726	−	5.81543i	0.359050	−	0.207298i	0.668664	+	0.743565i	$0.266866\pi$
$788$	−12.0580	+	6.96169i	−0.429548	+	0.248000i
$789$	0.140838	+	0.269715i	0.00501397	+	0.00960211i
$790$		−	23.7412i		−	0.844675i
$791$	−9.58258	−	3.18283i	−0.340717	−	0.113169i
$792$	1.27472	+	2.71571i	0.0452952	+	0.0964986i
$793$	1.58119	−	2.73871i	0.0561498	−	0.0972543i
$794$	−4.61670	−	7.99636i	−0.163841	−	0.283780i
$795$	22.4798	+	0.953037i	0.797276	+	0.0338007i
$796$	−22.8967	−	13.2194i	−0.811554	−	0.468551i
$797$	18.0276			0.638570			0.319285	−	0.947659i	$-0.396557\pi$
$797$	18.0276			0.638570			0.319285	+	0.947659i	$0.396557\pi$
$798$	4.94753	+	30.5518i	0.175141	+	1.08152i
$799$	−26.8347			−0.949344
$800$	−6.82893	−	3.94268i	−0.241439	−	0.139395i
$801$	−24.1306	+	34.6480i	−0.852612	+	1.22423i
$802$	3.83879	+	6.64897i	0.135552	+	0.234783i
$803$	2.70859	−	4.69142i	0.0955841	−	0.165557i
$804$	−8.72639	−	5.54384i	−0.307756	−	0.195516i
$805$	−3.95117	−	19.2040i	−0.139260	−	0.676852i
$806$		−	3.39883i		−	0.119719i
$807$	15.5793	−	8.13508i	0.548416	−	0.286368i
$808$	4.22363	−	2.43851i	0.148587	−	0.0857865i
$809$	10.4831	−	6.05241i	0.368566	−	0.212791i	−0.304266	−	0.952587i	$-0.598411\pi$
$809$	10.4831	−	6.05241i	0.368566	−	0.212791i	0.672832	+	0.739796i	$0.265078\pi$
$810$	−30.3020	+	11.2028i	−1.06470	+	0.393625i
$811$			20.3659i			0.715143i	0.933886	+	0.357572i	$0.116395\pi$
$811$			20.3659i			0.715143i	−0.933886	+	0.357572i	$0.883605\pi$
$812$	2.00026	+	9.72194i	0.0701954	+	0.341173i
$813$	27.3688	−	43.0804i	0.959865	−	1.51090i
$814$	−5.32441	+	9.22215i	−0.186621	+	0.323236i
$815$	15.4259	+	26.7184i	0.540345	+	0.935905i
$816$	−0.153905	+	3.63024i	−0.00538775	+	0.127084i
$817$	25.1561	+	14.5239i	0.880101	+	0.508126i
$818$	−12.1160			−0.423624
$819$	2.66771	+	1.14498i	0.0932175	+	0.0400090i
$820$	−12.8854			−0.449976
$821$	−10.5624	−	6.09822i	−0.368631	−	0.212829i	0.304229	−	0.952599i	$-0.401601\pi$
$821$	−10.5624	−	6.09822i	−0.368631	−	0.212829i	−0.672860	+	0.739770i	$0.734934\pi$
$822$	−0.234355	+	5.52787i	−0.00817409	+	0.192806i
$823$	16.2161	+	28.0871i	0.565258	+	0.979055i	0.997026	+	0.0770704i	$0.0245566\pi$
$823$	16.2161	+	28.0871i	0.565258	+	0.979055i	−0.431768	+	0.901985i	$0.642110\pi$
$824$	4.73360	−	8.19883i	0.164903	−	0.285620i
$825$	−7.32380	+	11.5282i	−0.254982	+	0.401360i
$826$	19.3474	+	6.42620i	0.673182	+	0.223596i
$827$			54.3898i			1.89132i	0.325161	+	0.945659i	$0.394581\pi$
$827$			54.3898i			1.89132i	−0.325161	+	0.945659i	$0.605419\pi$
$828$	0.524187	−	6.17103i	0.0182168	−	0.214458i
$829$	−43.5306	+	25.1324i	−1.51188	+	0.872885i	−0.511977	+	0.858999i	$0.671087\pi$
$829$	−43.5306	+	25.1324i	−1.51188	+	0.872885i	−0.999904	+	0.0138857i	$0.995580\pi$
$830$	−23.7031	+	13.6850i	−0.822746	+	0.475013i
$831$	36.1512	−	18.8772i	1.25407	−	0.654844i
$832$			0.365750i			0.0126801i
$833$	1.72538	−	14.5829i	0.0597808	−	0.505267i
$834$	−6.64381	−	4.22078i	−0.230056	−	0.146154i
$835$	28.7201	−	49.7447i	0.993900	−	1.72149i
$836$	3.37690	+	5.84896i	0.116792	+	0.202290i
$837$	−18.6475	−	44.5408i	−0.644551	−	1.53955i
$838$	5.75845	+	3.32464i	0.198922	+	0.114848i
$839$	36.9731			1.27645			0.638226	−	0.769849i	$-0.279669\pi$
$839$	36.9731			1.27645			0.638226	+	0.769849i	$0.279669\pi$
$840$	10.3964	+	12.7479i	0.358709	+	0.439843i
$841$	14.9261			0.514694
$842$	−1.17242	−	0.676898i	−0.0404043	−	0.0233274i
$843$	−15.1908	−	0.644018i	−0.523199	−	0.0221812i
$844$	−6.73294	−	11.6618i	−0.231757	−	0.401416i
$845$	23.0924	−	39.9973i	0.794404	−	1.37595i
$846$	−34.7389	+	16.3060i	−1.19435	+	0.560612i
$847$	−1.75749	−	1.97768i	−0.0603880	−	0.0679540i
$848$		−	3.61887i		−	0.124273i
$849$	7.08381	+	13.5660i	0.243116	+	0.465584i
$850$	−14.3257	+	8.27096i	−0.491368	+	0.283692i
$851$	19.0384	−	10.9918i	0.652627	−	0.376794i
$852$	3.55232	+	6.80295i	0.121701	+	0.233065i
$853$		−	4.92939i		−	0.168779i	−0.996433	−	0.0843896i	$-0.973106\pi$
$853$		−	4.92939i		−	0.168779i	0.996433	−	0.0843896i	$-0.0268940\pi$
$854$	−22.4066	+	4.61010i	−0.766740	+	0.157754i
$855$	−65.8385	+	30.9037i	−2.25163	+	1.05689i
$856$	9.01307	−	15.6111i	0.308060	−	0.533576i
$857$	19.7742	+	34.2500i	0.675475	+	1.16996i	0.976330	+	0.216288i	$0.0693949\pi$
$857$	19.7742	+	34.2500i	0.675475	+	1.16996i	−0.300854	+	0.953670i	$0.597272\pi$
$858$	0.632929	+	0.0268332i	0.0216078	+	0.000916070i
$859$	18.4240	+	10.6371i	0.628619	+	0.362934i	0.780217	−	0.625509i	$-0.215109\pi$
$859$	18.4240	+	10.6371i	0.628619	+	0.362934i	−0.151598	+	0.988442i	$0.548442\pi$
$860$	15.4388			0.526458
$861$	15.3775	+	5.84178i	0.524062	+	0.199087i
$862$	17.3412			0.590644
$863$	29.0704	+	16.7838i	0.989568	+	0.571327i	0.905145	−	0.425103i	$-0.139762\pi$
$863$	29.0704	+	16.7838i	0.989568	+	0.571327i	0.0844227	+	0.996430i	$0.473095\pi$
$864$	2.00666	+	4.79305i	0.0682680	+	0.163063i
$865$	−24.0377	−	41.6344i	−0.817305	−	1.41561i
$866$	12.0510	−	20.8730i	0.409510	−	0.709293i
$867$	−18.4197	−	11.7020i	−0.625566	−	0.397420i
$868$	−18.3782	+	16.3320i	−0.623797	+	0.554343i
$869$			6.61386i			0.224360i
$870$	−20.6756	+	10.7963i	−0.700969	+	0.366028i
$871$	−1.89065	+	1.09156i	−0.0640621	+	0.0369863i
$872$	−12.5411	+	7.24061i	−0.424695	+	0.245198i
$873$	−0.165485	+	1.94818i	−0.00560082	+	0.0659360i
$874$		−	13.9426i		−	0.471617i
$875$	−8.63784	+	26.0060i	−0.292012	+	0.879163i
$876$	5.03139	−	7.91977i	0.169995	−	0.267584i
$877$	17.6761	−	30.6159i	0.596880	−	1.03383i	−0.396398	−	0.918079i	$-0.629740\pi$
$877$	17.6761	−	30.6159i	0.596880	−	1.03383i	0.993279	−	0.115748i	$-0.0369266\pi$
$878$	13.1403	+	22.7596i	0.443463	+	0.768100i
$879$	−2.22402	+	52.4591i	−0.0750143	+	1.76940i
$880$	3.10870	+	1.79481i	0.104794	+	0.0605030i
$881$	37.4261			1.26092			0.630459	−	0.776223i	$-0.282867\pi$
$881$	37.4261			1.26092			0.630459	+	0.776223i	$0.282867\pi$
$882$	−6.62764	−	19.9267i	−0.223164	−	0.670968i
$883$	38.4595			1.29427			0.647133	−	0.762377i	$-0.275968\pi$
$883$	38.4595			1.29427			0.647133	+	0.762377i	$0.275968\pi$
$884$	0.664475	+	0.383635i	0.0223487	+	0.0129030i
$885$	−2.02925	+	47.8649i	−0.0682124	+	1.60896i
$886$	−7.24029	−	12.5406i	−0.243242	−	0.421308i
$887$	12.7745	−	22.1261i	0.428925	−	0.742920i	−0.567853	−	0.823130i	$-0.692226\pi$
$887$	12.7745	−	22.1261i	0.428925	−	0.742920i	0.996778	+	0.0802098i	$0.0255590\pi$
$888$	−9.89046	+	15.5683i	−0.331902	+	0.522437i
$889$	−3.74042	+	11.2613i	−0.125450	+	0.377692i
$890$			50.5214i			1.69348i
$891$	8.44157	−	3.12088i	0.282803	−	0.104553i
$892$	21.0664	−	12.1627i	0.705354	−	0.407236i
$893$	−74.8189	+	43.1967i	−2.50372	+	1.44552i
$894$	15.6879	−	8.19182i	0.524683	−	0.273975i
$895$		−	53.1425i		−	1.77636i
$896$	1.97768	−	1.75749i	0.0660698	−	0.0587136i
$897$	−1.10388	−	0.701288i	−0.0368573	−	0.0234153i
$898$	−8.95985	+	15.5189i	−0.298994	+	0.517873i
$899$	−17.4310	−	30.1914i	−0.581357	−	1.00694i
$900$	−13.5196	+	19.4122i	−0.450652	+	0.647072i
$901$	−6.57458	−	3.79584i	−0.219031	−	0.126458i
$902$	3.58962			0.119521
$903$	−18.4247	−	6.99942i	−0.613137	−	0.232926i
$904$	−3.81643			−0.126933
$905$	−10.8957	−	6.29064i	−0.362186	−	0.209108i
$906$	10.0313	+	0.425281i	0.333269	+	0.0141290i
$907$	1.07480	+	1.86161i	0.0356882	+	0.0618138i	0.883318	−	0.468775i	$-0.155304\pi$
$907$	1.07480	+	1.86161i	0.0356882	+	0.0618138i	−0.847630	+	0.530588i	$0.821971\pi$
$908$	8.49372	−	14.7116i	0.281874	−	0.488220i
$909$	−6.21684	−	13.2446i	−0.206200	−	0.439295i
$910$	3.40234	−	0.700023i	0.112787	−	0.0232055i
$911$		−	34.3652i		−	1.13857i	−0.822140	−	0.569286i	$-0.807220\pi$
$911$		−	34.3652i		−	1.13857i	0.822140	−	0.569286i	$-0.192780\pi$
$912$	5.41460	+	10.3693i	0.179295	+	0.343363i
$913$	6.60323	−	3.81238i	0.218535	−	0.126171i
$914$	−11.0635	+	6.38752i	−0.365948	+	0.211280i
$915$	−24.8827	−	47.6522i	−0.822597	−	1.57533i
$916$		−	20.7183i		−	0.684553i
$917$	30.1720	+	33.9523i	0.996368	+	1.12120i
$918$	10.8126	+	1.38183i	0.356867	+	0.0456072i
$919$	−26.3709	+	45.6758i	−0.869897	+	1.50671i	−0.00779650	+	0.999970i	$0.502482\pi$
$919$	−26.3709	+	45.6758i	−0.869897	+	1.50671i	−0.862101	+	0.506737i	$0.830852\pi$
$920$	−3.70524	−	6.41766i	−0.122158	−	0.211584i
$921$	29.0676	+	1.23233i	0.957811	+	0.0406067i
$922$	17.8765	+	10.3210i	0.588731	+	0.339904i
$923$	1.62061			0.0533430
$924$	−2.89623	−	3.55131i	−0.0952791	−	0.116830i
$925$	−83.9699			−2.76091
$926$	−5.83095	−	3.36650i	−0.191617	−	0.110630i
$927$	−23.3063	−	16.2316i	−0.765479	−	0.533117i
$928$	1.87576	+	3.24891i	0.0615748	+	0.106651i
$929$	−15.7809	+	27.3334i	−0.517756	+	0.896779i	0.482032	+	0.876154i	$0.339899\pi$
$929$	−15.7809	+	27.3334i	−0.517756	+	0.896779i	−0.999787	+	0.0206252i	$0.993434\pi$
$930$	−48.7678	−	30.9820i	−1.59916	−	1.01594i
$931$	−18.6640	−	43.4365i	−0.611686	−	1.42357i
$932$		−	3.54556i		−	0.116139i
$933$	28.0079	−	14.6250i	0.916936	−	0.478800i
$934$	−22.6292	+	13.0650i	−0.740450	+	0.427499i
$935$	6.52143	−	3.76515i	0.213274	−	0.123134i
$936$	1.09331	+	0.0928695i	0.0357360	+	0.00303553i
$937$			31.4813i			1.02845i	0.857655	+	0.514225i	$0.171920\pi$
$937$			31.4813i			1.02845i	−0.857655	+	0.514225i	$0.828080\pi$
$938$	14.9872	+	4.97796i	0.489349	+	0.162536i
$939$	7.67680	−	12.0838i	0.250523	−	0.394341i
$940$	−22.9589	+	39.7660i	−0.748837	+	1.29702i
$941$	10.1230	+	17.5335i	0.329999	+	0.571575i	0.982511	−	0.186203i	$-0.0596182\pi$
$941$	10.1230	+	17.5335i	0.329999	+	0.571575i	−0.652512	+	0.757778i	$0.726285\pi$
$942$	1.26213	−	29.7706i	0.0411226	−	0.969980i
$943$	−6.41766	−	3.70524i	−0.208988	−	0.120659i
$944$	7.70545			0.250791
$945$	40.7462	−	27.8403i	1.32547	−	0.905646i
$946$	−4.30096			−0.139836
$947$	10.9410	+	6.31679i	0.355535	+	0.205268i	0.667120	−	0.744950i	$-0.267527\pi$
$947$	10.9410	+	6.31679i	0.355535	+	0.205268i	−0.311586	+	0.950218i	$0.600860\pi$
$948$	−0.485225	+	11.4453i	−0.0157594	+	0.371725i
$949$	−0.990666	−	1.71588i	−0.0321584	−	0.0557000i
$950$	−26.6281	+	46.1212i	−0.863928	+	1.49637i
$951$	5.62893	−	8.86033i	0.182530	−	0.287316i
$952$	−1.11852	−	5.43638i	−0.0362515	−	0.176194i
$953$		−	3.07523i		−	0.0996166i	−0.998759	−	0.0498083i	$-0.984139\pi$
$953$		−	3.07523i		−	0.0996166i	0.998759	−	0.0498083i	$-0.0158610\pi$
$954$	−10.8177	−	0.918887i	−0.350235	−	0.0297501i
$955$	20.0039	−	11.5492i	0.647310	−	0.373725i
$956$	23.2233	−	13.4080i	0.751097	−	0.433646i
$957$	5.75984	−	3.00764i	0.186189	−	0.0972231i
$958$		−	31.8616i		−	1.02940i
$959$	−1.70320	−	8.27814i	−0.0549993	−	0.267315i
$960$	5.24792	+	3.33398i	0.169376	+	0.107604i
$961$	27.6779	−	47.9396i	0.892836	−	1.54644i
$962$	1.94740	+	3.37300i	0.0627868	+	0.108750i
$963$	−44.3767	−	30.9061i	−1.43002	−	0.995935i
$964$	−4.29195	−	2.47796i	−0.138234	−	0.0798097i
$965$	−23.6193			−0.760333
$966$	1.51230	+	9.33869i	0.0486575	+	0.300467i
$967$	40.1868			1.29232			0.646160	−	0.763202i	$-0.276374\pi$
$967$	40.1868			1.29232			0.646160	+	0.763202i	$0.276374\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	24.5179	+	1.03944i	0.787627	+	0.0333917i
$970$	1.16974	+	2.02604i	0.0375580	+	0.0650523i
$971$	18.6107	−	32.2347i	0.597246	−	1.03446i	−0.395979	−	0.918259i	$-0.629595\pi$
$971$	18.6107	−	32.2347i	0.597246	−	1.03446i	0.993226	−	0.116202i	$-0.0370718\pi$
$972$	14.8371	−	4.78135i	0.475899	−	0.153362i
$973$	11.4105	+	3.78996i	0.365802	+	0.121500i
$974$			43.6293i			1.39797i
$975$	2.31219	+	4.42802i	0.0740495	+	0.141810i
$976$	−7.48792	+	4.32316i	−0.239683	+	0.138381i
$977$	23.9340	−	13.8183i	0.765717	−	0.442087i	−0.0656276	−	0.997844i	$-0.520905\pi$
$977$	23.9340	−	13.8183i	0.765717	−	0.442087i	0.831345	+	0.555757i	$0.187572\pi$
$978$	−6.89049	−	13.1958i	−0.220334	−	0.421955i
$979$		−	14.0743i		−	0.449816i
$980$	−20.1340	−	15.0335i	−0.643157	−	0.480226i
$981$	18.4595	+	39.3268i	0.589366	+	1.25561i
$982$	12.1130	−	20.9804i	0.386542	−	0.669510i
$983$	−0.814813	−	1.41130i	−0.0259885	−	0.0450134i	0.852739	−	0.522338i	$-0.174940\pi$
$983$	−0.814813	−	1.41130i	−0.0259885	−	0.0450134i	−0.878727	+	0.477324i	$0.841607\pi$
$984$	6.21182	+	0.263352i	0.198026	+	0.00839536i
$985$	43.2836	+	24.9898i	1.37913	+	0.796242i
$986$	7.86993			0.250630
$987$	45.4278	−	37.0482i	1.44598	−	1.17926i
$988$	2.47020			0.0785875
$989$	7.68941	+	4.43948i	0.244509	+	0.141167i
$990$	6.15445	−	8.83691i	0.195601	−	0.280855i
$991$	11.4482	+	19.8288i	0.363664	+	0.629884i	0.988561	−	0.150823i	$-0.0481924\pi$
$991$	11.4482	+	19.8288i	0.363664	+	0.629884i	−0.624897	+	0.780707i	$0.714859\pi$
$992$	−4.64639	+	8.04779i	−0.147523	+	0.255518i
$993$	−0.669756	−	0.425493i	−0.0212541	−	0.0135026i
$994$	−7.78729	−	8.76296i	−0.246998	−	0.277944i
$995$			94.9055i			3.00871i
$996$	11.7066	−	6.11286i	0.370937	−	0.193693i
$997$	47.3773	−	27.3533i	1.50045	−	0.866287i	0.500453	−	0.865764i	$-0.333167\pi$
$997$	47.3773	−	27.3533i	1.50045	−	0.866287i	1.00000		0.000523534i	$-0.000166646\pi$
$998$	−12.4013	+	7.15992i	−0.392558	+	0.226643i
$999$	44.0259	+	33.5179i	1.39292	+	1.06046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.g.89.4	✓	20
3.2	odd	2	inner	462.2.k.g.89.10	yes	20
7.3	odd	6	inner	462.2.k.g.353.10	yes	20
21.17	even	6	inner	462.2.k.g.353.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.4	✓	20	1.1	even	1	trivial
462.2.k.g.89.10	yes	20	3.2	odd	2	inner
462.2.k.g.353.4	yes	20	21.17	even	6	inner
462.2.k.g.353.10	yes	20	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.0733649 - 1.73050i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.79481 - 3.10870i) q^{5} +(-0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} -1.00000i q^{8} +(-2.98924 - 0.253915i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.0733649 - 1.73050i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.79481 - 3.10870i) q^{5} +(-0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} -1.00000i q^{8} +(-2.98924 - 0.253915i) q^{9} +(-3.10870 + 1.79481i) q^{10} +(0.866025 - 0.500000i) q^{11} +(1.53534 - 0.801712i) q^{12} -0.365750i q^{13} +(-1.97768 + 1.75749i) q^{14} +(-5.24792 - 3.33398i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.04890 + 1.81675i) q^{17} +(2.46180 + 1.71451i) q^{18} +(5.84896 + 3.37690i) q^{19} +3.58962 q^{20} +(-4.28387 - 1.62741i) q^{21} -1.00000 q^{22} +(1.78784 + 1.03221i) q^{23} +(-1.73050 - 0.0733649i) q^{24} +(-3.94268 - 6.82893i) q^{25} +(-0.182875 + 0.316749i) q^{26} +(-0.658705 + 5.15423i) q^{27} +(2.59147 - 0.533187i) q^{28} +3.75152i q^{29} +(2.87784 + 5.51127i) q^{30} +(-8.04779 + 4.64639i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.801712 - 1.53534i) q^{33} -2.09780i q^{34} +(-6.30871 - 7.09913i) q^{35} +(-1.27472 - 2.71571i) q^{36} +(5.32441 - 9.22215i) q^{37} +(-3.37690 - 5.84896i) q^{38} +(-0.632929 - 0.0268332i) q^{39} +(-3.10870 - 1.79481i) q^{40} -3.58962 q^{41} +(2.89623 + 3.55131i) q^{42} +4.30096 q^{43} +(0.866025 + 0.500000i) q^{44} +(-6.15445 + 8.83691i) q^{45} +(-1.03221 - 1.78784i) q^{46} +(-6.39592 + 11.0781i) q^{47} +(1.46197 + 0.928784i) q^{48} +(-5.60895 - 4.18804i) q^{49} +7.88536i q^{50} +(3.22083 - 1.68183i) q^{51} +(0.316749 - 0.182875i) q^{52} +(-3.13404 + 1.80944i) q^{53} +(3.14757 - 4.13434i) q^{54} -3.58962i q^{55} +(-2.51087 - 0.833981i) q^{56} +(6.27282 - 9.87385i) q^{57} +(1.87576 - 3.24891i) q^{58} +(-3.85273 - 6.67312i) q^{59} +(0.263352 - 6.21182i) q^{60} +(7.48792 + 4.32316i) q^{61} +9.29278 q^{62} +(-3.13051 + 7.29383i) q^{63} -1.00000 q^{64} +(-1.13701 - 0.656451i) q^{65} +(-0.0733649 + 1.73050i) q^{66} +(-2.98446 - 5.16923i) q^{67} +(-1.04890 + 1.81675i) q^{68} +(1.91740 - 3.01812i) q^{69} +(1.91394 + 9.30239i) q^{70} +4.43092i q^{71} +(-0.253915 + 2.98924i) q^{72} +(4.69142 - 2.70859i) q^{73} +(-9.22215 + 5.32441i) q^{74} +(-12.1067 + 6.32179i) q^{75} +6.75379i q^{76} +(-0.533187 - 2.59147i) q^{77} +(0.534716 + 0.339702i) q^{78} +(-3.30693 + 5.72777i) q^{79} +(1.79481 + 3.10870i) q^{80} +(8.87105 + 1.51803i) q^{81} +(3.10870 + 1.79481i) q^{82} +7.62475 q^{83} +(-0.732556 - 4.52364i) q^{84} +7.53030 q^{85} +(-3.72474 - 2.15048i) q^{86} +(6.49198 + 0.275230i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(7.03715 - 12.1887i) q^{89} +(9.74837 - 4.57576i) q^{90} +(-0.918351 - 0.305028i) q^{91} +2.06442i q^{92} +(7.45014 + 14.2675i) q^{93} +(11.0781 - 6.39592i) q^{94} +(20.9955 - 12.1218i) q^{95} +(-0.801712 - 1.53534i) q^{96} -0.651733i q^{97} +(2.76348 + 6.43142i) q^{98} +(-2.71571 + 1.27472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Introduction

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