LMFDB - Embedded newform 462.2.k.g.353.10

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			353.10
Root			$-0.0733649 + 1.73050i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.g.89.10

$q$-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} +(1.53534 - 0.801712i) 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} +(1.71451 - 2.46180i) q^{9} +(-3.10870 - 1.79481i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(0.0733649 - 1.73050i) 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} +(0.253915 - 2.98924i) q^{18} +(5.84896 - 3.37690i) q^{19} -3.58962 q^{20} +(3.29344 + 3.18642i) q^{21} -1.00000 q^{22} +(-1.78784 + 1.03221i) q^{23} +(-0.801712 - 1.53534i) 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} +(-6.21182 - 0.263352i) q^{30} +(-8.04779 - 4.64639i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.73050 - 0.0733649i) 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} +(0.293226 + 0.561549i) q^{39} +(-3.10870 + 1.79481i) q^{40} +3.58962 q^{41} +(4.44541 + 1.11280i) q^{42} +4.30096 q^{43} +(-0.866025 + 0.500000i) q^{44} +(-10.7302 - 0.911459i) 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} +(-0.153905 + 3.63024i) q^{51} +(0.316749 + 0.182875i) q^{52} +(3.13404 + 1.80944i) q^{53} +(-2.00666 - 4.79305i) 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} +(-5.51127 + 2.87784i) q^{60} +(7.48792 - 4.32316i) q^{61} -9.29278 q^{62} +(7.61113 + 2.25184i) q^{63} -1.00000 q^{64} +(1.13701 - 0.656451i) q^{65} +(-1.53534 + 0.801712i) 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} +(-2.46180 - 1.71451i) q^{72} +(4.69142 + 2.70859i) q^{73} +(9.22215 + 5.32441i) q^{74} +(-0.578509 + 13.6456i) 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} +(-3.12088 - 8.44157i) q^{81} +(3.10870 - 1.79481i) q^{82} -7.62475 q^{83} +(4.40624 - 1.25899i) q^{84} +7.53030 q^{85} +(3.72474 - 2.15048i) q^{86} +(3.00764 + 5.75984i) 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} +(-16.0811 - 0.681764i) q^{93} +(11.0781 + 6.39592i) q^{94} +(-20.9955 - 12.1218i) q^{95} +(-1.73050 - 0.0733649i) 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} - 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}+ \cdots - 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

Character values

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

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

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
$3$	1.53534	−	0.801712i	0.886427	−	0.462869i
$3$	1.53534	−	0.801712i	0.886427	−	0.462869i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.79481	−	3.10870i	−0.802663	−	1.39025i	−0.917857	−	0.396910i	$-0.870082\pi$
$5$	−1.79481	−	3.10870i	−0.802663	−	1.39025i	0.115194	−	0.993343i	$-0.463251\pi$
$6$	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
$9$	1.71451	−	2.46180i	0.571505	−	0.820599i
$10$	−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
$12$	0.0733649	−	1.73050i	0.0211786	−	0.499551i
$13$			0.365750i			0.101441i	0.998713	+	0.0507204i	$0.0161517\pi$
$13$			0.365750i			0.101441i	−0.998713	+	0.0507204i	$0.983848\pi$
$14$	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	$-0.915210\pi$
$17$	−1.04890	+	1.81675i	−0.254396	+	0.440626i	0.710336	+	0.703863i	$0.248543\pi$
$18$	0.253915	−	2.98924i	0.0598484	−	0.704569i
$19$	5.84896	−	3.37690i	1.34184	−	0.774713i	0.354765	−	0.934955i	$-0.384561\pi$
$19$	5.84896	−	3.37690i	1.34184	−	0.774713i	0.987078	+	0.160242i	$0.0512275\pi$
$20$	−3.58962			−0.802663
$21$	3.29344	+	3.18642i	0.718687	+	0.695334i
$22$	−1.00000			−0.213201
$23$	−1.78784	+	1.03221i	−0.372790	+	0.215230i	−0.674677	−	0.738113i	$-0.735717\pi$
$23$	−1.78784	+	1.03221i	−0.372790	+	0.215230i	0.301887	+	0.953344i	$0.402384\pi$
$24$	−0.801712	−	1.53534i	−0.163649	−	0.313399i
$25$	−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	$0.886752\pi$
$30$	−6.21182	−	0.263352i	−1.13412	−	0.0480813i
$31$	−8.04779	−	4.64639i	−1.44543	−	0.834517i	−0.447221	−	0.894423i	$-0.647586\pi$
$31$	−8.04779	−	4.64639i	−1.44543	−	0.834517i	−0.998204	+	0.0599066i	$0.980920\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.73050	−	0.0733649i	−0.301241	−	0.0127712i
$34$			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	0.856413	+	0.516291i	$0.172688\pi$
$37$	5.32441	+	9.22215i	0.875328	+	1.51611i	0.0189151	+	0.999821i	$0.493979\pi$
$38$	3.37690	−	5.84896i	0.547805	−	0.948826i
$39$	0.293226	+	0.561549i	0.0469537	+	0.0899198i
$40$	−3.10870	+	1.79481i	−0.491529	+	0.283784i
$41$	3.58962			0.560604			0.280302	−	0.959912i	$-0.409565\pi$
$41$	3.58962			0.560604			0.280302	+	0.959912i	$0.409565\pi$
$42$	4.44541	+	1.11280i	0.685942	+	0.171709i
$43$	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
$45$	−10.7302	−	0.911459i	−1.59957	−	0.135872i
$46$	−1.03221	+	1.78784i	−0.152191	+	0.263602i
$47$	6.39592	+	11.0781i	0.932940	+	1.61590i	0.778266	+	0.627935i	$0.216100\pi$
$47$	6.39592	+	11.0781i	0.932940	+	1.61590i	0.154674	+	0.987965i	$0.450567\pi$
$48$	−1.46197	−	0.928784i	−0.211017	−	0.134058i
$49$	−5.60895	+	4.18804i	−0.801279	+	0.598291i
$50$			7.88536i			1.11516i
$51$	−0.153905	+	3.63024i	−0.0215510	+	0.508335i
$52$	0.316749	+	0.182875i	0.0439251	+	0.0253602i
$53$	3.13404	+	1.80944i	0.430493	+	0.248545i	0.699557	−	0.714577i	$-0.253381\pi$
$53$	3.13404	+	1.80944i	0.430493	+	0.248545i	−0.269064	+	0.963122i	$0.586714\pi$
$54$	−2.00666	−	4.79305i	−0.273072	−	0.652251i
$55$			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	−0.498416	−	0.866938i	$-0.666085\pi$
$59$	3.85273	−	6.67312i	0.501582	−	0.868766i	0.999998	−	0.00182804i	$-0.000581885\pi$
$60$	−5.51127	+	2.87784i	−0.711502	+	0.371528i
$61$	7.48792	−	4.32316i	0.958731	−	0.553523i	0.0629484	−	0.998017i	$-0.479950\pi$
$61$	7.48792	−	4.32316i	0.958731	−	0.553523i	0.895782	+	0.444493i	$0.146616\pi$
$62$	−9.29278			−1.18018
$63$	7.61113	+	2.25184i	0.958912	+	0.283705i
$64$	−1.00000			−0.125000
$65$	1.13701	−	0.656451i	0.141028	−	0.0814227i
$66$	−1.53534	+	0.801712i	−0.188987	+	0.0986840i
$67$	−2.98446	+	5.16923i	−0.364610	+	0.631522i	−0.988713	−	0.149819i	$-0.952131\pi$
$67$	−2.98446	+	5.16923i	−0.364610	+	0.631522i	0.624104	+	0.781341i	$0.285464\pi$
$68$	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	$0.915312\pi$
$72$	−2.46180	−	1.71451i	−0.290125	−	0.202058i
$73$	4.69142	+	2.70859i	0.549089	+	0.317017i	0.748754	−	0.662847i	$-0.230652\pi$
$73$	4.69142	+	2.70859i	0.549089	+	0.317017i	−0.199666	+	0.979864i	$0.563986\pi$
$74$	9.22215	+	5.32441i	1.07205	+	0.618950i
$75$	−0.578509	+	13.6456i	−0.0668005	+	1.57566i
$76$		−	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	0.617823	−	0.786317i	$-0.288015\pi$
$79$	−3.30693	−	5.72777i	−0.372059	−	0.644424i	−0.989882	+	0.141892i	$0.954681\pi$
$80$	−1.79481	+	3.10870i	−0.200666	+	0.347563i
$81$	−3.12088	−	8.44157i	−0.346764	−	0.937952i
$82$	3.10870	−	1.79481i	0.343299	−	0.198204i
$83$	−7.62475			−0.836925			−0.418463	−	0.908234i	$-0.637431\pi$
$83$	−7.62475			−0.836925			−0.418463	+	0.908234i	$0.637431\pi$
$84$	4.40624	−	1.25899i	0.480760	−	0.137367i
$85$	7.53030			0.816776
$86$	3.72474	−	2.15048i	0.401649	−	0.231892i
$87$	3.00764	+	5.75984i	0.322452	+	0.617519i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−7.03715	−	12.1887i	−0.745936	−	1.29200i	−0.949756	−	0.312991i	$-0.898669\pi$
$89$	−7.03715	−	12.1887i	−0.745936	−	1.29200i	0.203820	−	0.979008i	$-0.434664\pi$
$90$	−9.74837	+	4.57576i	−1.02757	+	0.482328i
$91$	−0.918351	+	0.305028i	−0.0962693	+	0.0319756i
$92$			2.06442i			0.215230i
$93$	−16.0811	−	0.681764i	−1.66754	−	0.0706957i
$94$	11.0781	+	6.39592i	1.14261	+	0.659689i
$95$	−20.9955	−	12.1218i	−2.15410	−	1.24367i
$96$	−1.73050	−	0.0733649i	−0.176618	−	0.00748777i
$97$			0.651733i			0.0661735i	0.999452	+	0.0330867i	$0.0105338\pi$
$97$			0.651733i			0.0661735i	−0.999452	+	0.0330867i	$0.989466\pi$
$98$	−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	$-0.911347\pi$
$101$	−2.43851	+	4.22363i	−0.242641	+	0.420267i	0.718825	+	0.695191i	$0.244680\pi$
$102$	1.68183	+	3.22083i	0.166526	+	0.318910i
$103$	8.19883	−	4.73360i	0.807855	−	0.466415i	−0.0383556	−	0.999264i	$-0.512212\pi$
$103$	8.19883	−	4.73360i	0.807855	−	0.466415i	0.846210	+	0.532849i	$0.178879\pi$
$104$	0.365750			0.0358647
$105$	3.99453	−	15.9573i	0.389827	−	1.55728i
$106$	3.61887			0.351496
$107$	−15.6111	+	9.01307i	−1.50918	+	0.871327i	−0.509239	+	0.860625i	$0.670073\pi$
$107$	−15.6111	+	9.01307i	−1.50918	+	0.871327i	−0.999943	+	0.0107015i	$0.996594\pi$
$108$	−4.13434	−	3.14757i	−0.397827	−	0.302875i
$109$	−7.24061	+	12.5411i	−0.693524	+	1.20122i	0.277151	+	0.960826i	$0.410610\pi$
$109$	−7.24061	+	12.5411i	−0.693524	+	1.20122i	−0.970676	+	0.240393i	$0.922724\pi$
$110$	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	$-0.0574512\pi$
$114$	0.495491	−	11.6874i	0.0464070	−	1.09463i
$115$	6.41766	+	3.70524i	0.598450	+	0.345515i
$116$	3.24891	+	1.87576i	0.301653	+	0.174160i
$117$	0.900401	+	0.627083i	0.0832421	+	0.0579739i
$118$		−	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
$123$	5.51127	−	2.87784i	0.496935	−	0.259486i
$124$	−8.04779	+	4.64639i	−0.722713	+	0.417258i
$125$	10.3574			0.926390
$126$	7.71735	−	1.85542i	0.687516	−	0.165294i
$127$	−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
$129$	6.60341	−	3.44813i	0.581398	−	0.303591i
$130$	0.656451	−	1.13701i	0.0575746	−	0.0997221i
$131$	8.58385	+	14.8677i	0.749975	+	1.29899i	0.947834	+	0.318764i	$0.103268\pi$
$131$	8.58385	+	14.8677i	0.749975	+	1.29899i	−0.197860	+	0.980230i	$0.563399\pi$
$132$	−0.928784	+	1.46197i	−0.0808403	+	0.127248i
$133$	13.3569	+	11.8697i	1.15819	+	1.02923i
$134$			5.96892i			0.515636i
$135$	−17.2052	+	7.20315i	−1.48079	+	0.619948i
$136$	1.81675	+	1.04890i	0.155785	+	0.0899425i
$137$	−2.76642	−	1.59719i	−0.236351	−	0.136457i	0.377148	−	0.926153i	$-0.376905\pi$
$137$	−2.76642	−	1.59719i	−0.236351	−	0.136457i	−0.613498	+	0.789696i	$0.710238\pi$
$138$	−0.151456	+	3.57247i	−0.0128928	+	0.304109i
$139$		−	4.54442i		−	0.385453i	−0.981253	−	0.192726i	$-0.938267\pi$
$139$		−	4.54442i		−	0.385453i	0.981253	−	0.192726i	$-0.0617330\pi$
$140$	−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
$144$	−2.98924	−	0.253915i	−0.249103	−	0.0211596i
$145$	11.6623	−	6.73326i	0.968505	−	0.559166i
$146$	5.41718			0.448329
$147$	−5.25403	+	10.9268i	−0.433345	+	0.901228i
$148$	10.6488			0.875328
$149$	8.84896	−	5.10895i	0.724935	−	0.418542i	−0.0916311	−	0.995793i	$-0.529208\pi$
$149$	8.84896	−	5.10895i	0.724935	−	0.418542i	0.816567	+	0.577251i	$0.195875\pi$
$150$	6.32179	+	12.1067i	0.516172	+	0.988507i
$151$	−2.89840	+	5.02017i	−0.235868	+	0.408536i	−0.959525	−	0.281625i	$-0.909127\pi$
$151$	−2.89840	+	5.02017i	−0.235868	+	0.408536i	0.723656	+	0.690160i	$0.242460\pi$
$152$	−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
$156$	0.632929	+	0.0268332i	0.0506748	+	0.00214837i
$157$	−14.8987	−	8.60176i	−1.18904	−	0.686495i	−0.230955	−	0.972964i	$-0.574185\pi$
$157$	−14.8987	−	8.60176i	−1.18904	−	0.686495i	−0.958089	+	0.286469i	$0.907518\pi$
$158$	−5.72777	−	3.30693i	−0.455677	−	0.263085i
$159$	6.26244	+	0.265498i	0.496644	+	0.0210554i
$160$			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	0.647195	−	0.762325i	$-0.275942\pi$
$163$	−4.29736	−	7.44325i	−0.336595	−	0.583000i	−0.983790	+	0.179325i	$0.942609\pi$
$164$	1.79481	−	3.10870i	0.140151	−	0.242749i
$165$	2.87784	+	5.51127i	0.224040	+	0.429052i
$166$	−6.60323	+	3.81238i	−0.512510	+	0.295898i
$167$	−16.0018			−1.23825			−0.619127	−	0.785291i	$-0.712513\pi$
$167$	−16.0018			−1.23825			−0.619127	+	0.785291i	$0.712513\pi$
$168$	3.18642	−	3.29344i	0.245838	−	0.254094i
$169$	12.8662			0.989710
$170$	6.52143	−	3.76515i	0.500171	−	0.288774i
$171$	1.71489	−	20.1887i	0.131141	−	1.54387i
$172$	2.15048	−	3.72474i	0.163972	−	0.284009i
$173$	−6.69644	−	11.5986i	−0.509121	−	0.881823i	−0.999944	−	0.0105638i	$-0.996637\pi$
$173$	−6.69644	−	11.5986i	−0.509121	−	0.881823i	0.490824	−	0.871259i	$-0.336696\pi$
$174$	5.48461	+	3.48435i	0.415787	+	0.264148i
$175$	−20.4347	−	4.20438i	−1.54472	−	0.317821i
$176$			1.00000i			0.0753778i
$177$	0.565310	−	13.3343i	0.0424913	−	1.00226i
$178$	−12.1887	−	7.03715i	−0.913581	−	0.527457i
$179$	−12.8211	−	7.40224i	−0.958291	−	0.553270i	−0.0626446	−	0.998036i	$-0.519953\pi$
$179$	−12.8211	−	7.40224i	−0.958291	−	0.553270i	−0.895647	+	0.444766i	$0.853287\pi$
$180$	−6.15445	+	8.83691i	−0.458726	+	0.658664i
$181$			3.50491i			0.260518i	0.991480	+	0.130259i	$0.0415808\pi$
$181$			3.50491i			0.260518i	−0.991480	+	0.130259i	$0.958419\pi$
$182$	−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
$186$	−14.2675	+	7.45014i	−1.04615	+	0.546271i
$187$	1.81675	−	1.04890i	0.132854	−	0.0767032i
$188$	12.7918			0.932940
$189$	13.4910	−	2.64461i	0.981323	−	0.192367i
$190$	−24.2435			−1.75881
$191$	−5.57270	+	3.21740i	−0.403227	+	0.232803i	−0.687875	−	0.725829i	$-0.741456\pi$
$191$	−5.57270	+	3.21740i	−0.403227	+	0.232803i	0.284649	+	0.958632i	$0.408123\pi$
$192$	−1.53534	+	0.801712i	−0.110803	+	0.0578586i
$193$	−3.28995	+	5.69836i	−0.236816	+	0.410177i	−0.959799	−	0.280689i	$-0.909437\pi$
$193$	−3.28995	+	5.69836i	−0.236816	+	0.410177i	0.722983	+	0.690866i	$0.242770\pi$
$194$	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	$0.834802\pi$
$198$	−1.71451	+	2.46180i	−0.121845	+	0.174952i
$199$	−22.8967	−	13.2194i	−1.62311	−	0.937101i	−0.986082	−	0.166258i	$-0.946831\pi$
$199$	−22.8967	−	13.2194i	−1.62311	−	0.937101i	−0.637025	−	0.770843i	$-0.719835\pi$
$200$	6.82893	+	3.94268i	0.482878	+	0.278790i
$201$	−0.437909	+	10.3292i	−0.0308877	+	0.728565i
$202$			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
$207$	−0.524187	+	6.17103i	−0.0364335	+	0.428916i
$208$	0.316749	−	0.182875i	0.0219626	−	0.0126801i
$209$	−6.75379			−0.467170
$210$	−4.51930	−	15.8167i	−0.311861	−	1.09146i
$211$	−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
$213$	3.55232	+	6.80295i	0.243401	+	0.466131i
$214$	−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
$219$	9.37441	+	0.397431i	0.633464	+	0.0268559i
$220$	3.10870	+	1.79481i	0.209589	+	0.121006i
$221$	−0.664475	−	0.383635i	−0.0446974	−	0.0258061i
$222$	18.4278	+	0.781250i	1.23679	+	0.0524341i
$223$			24.3253i			1.62895i	0.580202	+	0.814473i	$0.302974\pi$
$223$			24.3253i			1.62895i	−0.580202	+	0.814473i	$0.697026\pi$
$224$	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	−0.433417	−	0.901193i	$-0.642692\pi$
$227$	8.49372	−	14.7116i	0.563748	−	0.976440i	0.997165	−	0.0752465i	$-0.0239744\pi$
$228$	−5.41460	−	10.3693i	−0.358591	−	0.686727i
$229$	−17.9426	+	10.3592i	−1.18568	+	0.684553i	−0.957322	−	0.289025i	$-0.906669\pi$
$229$	−17.9426	+	10.3592i	−1.18568	+	0.684553i	−0.228358	+	0.973577i	$0.573336\pi$
$230$	7.41047			0.488632
$231$	−1.25899	−	4.40624i	−0.0828355	−	0.289909i
$232$	3.75152			0.246299
$233$	3.07054	−	1.77278i	0.201158	−	0.116139i	−0.396038	−	0.918234i	$-0.629615\pi$
$233$	3.07054	−	1.77278i	0.201158	−	0.116139i	0.597195	+	0.802096i	$0.296282\pi$
$234$	1.09331	+	0.0928695i	0.0714720	+	0.00607107i
$235$	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	$-0.334141\pi$
$240$	−0.263352	+	6.21182i	−0.0169993	+	0.400971i
$241$	−4.29195	−	2.47796i	−0.276469	−	0.159619i	0.355355	−	0.934731i	$-0.384360\pi$
$241$	−4.29195	−	2.47796i	−0.276469	−	0.159619i	−0.631824	+	0.775112i	$0.717693\pi$
$242$	0.866025	+	0.500000i	0.0556702	+	0.0321412i
$243$	−11.5593	−	10.4586i	−0.741530	−	0.670920i
$244$		−	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
$249$	−11.7066	+	6.11286i	−0.741873	+	0.387387i
$250$	8.96973	−	5.17868i	0.567296	−	0.327528i
$251$	16.6823			1.05297			0.526487	−	0.850183i	$-0.323509\pi$
$251$	16.6823			1.05297			0.526487	+	0.850183i	$0.323509\pi$
$252$	5.75571	−	5.46551i	0.362576	−	0.344295i
$253$	2.06442			0.129789
$254$	−3.88414	+	2.24251i	−0.243713	+	0.140708i
$255$	11.5615	−	6.03714i	0.724012	−	0.378060i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.622864	−	1.07883i	−0.0388532	−	0.0672957i	0.845945	−	0.533270i	$-0.179037\pi$
$257$	−0.622864	−	1.07883i	−0.0388532	−	0.0672957i	−0.884798	+	0.465975i	$0.845704\pi$
$258$	3.99466	−	6.28787i	0.248697	−	0.391466i
$259$	−18.7152	+	21.0600i	−1.16290	+	1.30861i
$260$		−	1.31290i		−	0.0814227i
$261$	9.23547	+	6.43203i	0.571661	+	0.398133i
$262$	14.8677	+	8.58385i	0.918528	+	0.530312i
$263$	0.152136	+	0.0878358i	0.00938111	+	0.00541619i	0.504683	−	0.863305i	$-0.331609\pi$
$263$	0.152136	+	0.0878358i	0.00938111	+	0.00541619i	−0.495302	+	0.868721i	$0.664943\pi$
$264$	−0.0733649	+	1.73050i	−0.00451530	+	0.106505i
$265$		−	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	$-0.933442\pi$
$269$	−5.07356	+	8.78767i	−0.309341	+	0.535794i	0.668878	+	0.743373i	$0.266775\pi$
$270$	−11.2986	+	14.8407i	−0.687610	+	0.903177i
$271$	25.5195	−	14.7337i	1.55020	−	0.895007i	0.552072	−	0.833796i	$-0.313837\pi$
$271$	25.5195	−	14.7337i	1.55020	−	0.895007i	0.998125	−	0.0612103i	$-0.0194960\pi$
$272$	2.09780			0.127198
$273$	−1.16543	+	1.20457i	−0.0705352	+	0.0729041i
$274$	−3.19438			−0.192980
$275$	6.82893	−	3.94268i	0.411800	−	0.237753i
$276$	1.65507	+	3.16957i	0.0996234	+	0.190786i
$277$	11.7731	−	20.3916i	0.707375	−	1.22521i	−0.258452	−	0.966024i	$-0.583213\pi$
$277$	11.7731	−	20.3916i	0.707375	−	1.22521i	0.965828	−	0.259186i	$-0.0834541\pi$
$278$	−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	$-0.0843274\pi$
$282$	22.1362	+	0.938472i	1.31819	+	0.0558852i
$283$	−7.65207	−	4.41792i	−0.454868	−	0.262618i	0.255016	−	0.966937i	$-0.417919\pi$
$283$	−7.65207	−	4.41792i	−0.454868	−	0.262618i	−0.709884	+	0.704319i	$0.751253\pi$
$284$	3.83729	+	2.21546i	0.227701	+	0.131463i
$285$	−41.9534	−	1.77863i	−2.48510	−	0.105357i
$286$		−	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
$291$	0.522502	+	1.00063i	0.0306296	+	0.0586579i
$292$	4.69142	−	2.70859i	0.274544	−	0.158508i
$293$	30.3145			1.77099			0.885496	−	0.464648i	$-0.153819\pi$
$293$	30.3145			1.77099			0.885496	+	0.464648i	$0.153819\pi$
$294$	0.913285	+	12.0899i	0.0532638	+	0.705098i
$295$	−27.6596			−1.61041
$296$	9.22215	−	5.32441i	0.536027	−	0.309475i
$297$	−3.14757	+	4.13434i	−0.182641	+	0.239899i
$298$	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
$303$	−0.357802	+	8.43967i	−0.0205552	+	0.484846i
$304$	−5.84896	−	3.37690i	−0.335461	−	0.193678i
$305$	−26.8788	−	15.5185i	−1.53908	−	0.888586i
$306$	5.16436	+	3.59671i	0.295227	+	0.205610i
$307$		−	16.7973i		−	0.958671i	−0.877632	−	0.479336i	$-0.840878\pi$
$307$		−	16.7973i		−	0.958671i	0.877632	−	0.479336i	$-0.159122\pi$
$308$	−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	0.482591	+	0.875846i	$0.339696\pi$
$311$	−9.12108	+	15.7982i	−0.517209	+	0.895832i	−0.999800	+	0.0199867i	$0.993638\pi$
$312$	0.561549	−	0.293226i	0.0317914	−	0.0166007i
$313$	7.15808	−	4.13272i	0.404598	−	0.233595i	−0.283868	−	0.958863i	$-0.591618\pi$
$313$	7.15808	−	4.13272i	0.404598	−	0.233595i	0.688466	+	0.725268i	$0.258284\pi$
$314$	−17.2035			−0.970851
$315$	−6.66023	−	27.7023i	−0.375262	−	1.56085i
$316$	−6.61386			−0.372059
$317$	−5.24858	+	3.03027i	−0.294789	+	0.170197i	−0.640100	−	0.768292i	$-0.721107\pi$
$317$	−5.24858	+	3.03027i	−0.294789	+	0.170197i	0.345310	+	0.938489i	$0.387774\pi$
$318$	5.55619	−	2.90129i	0.311575	−	0.162696i
$319$	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
$324$	−8.87105	−	1.51803i	−0.492836	−	0.0843348i
$325$	−2.49768	−	1.44203i	−0.138546	−	0.0799897i
$326$	−7.44325	−	4.29736i	−0.412243	−	0.238009i
$327$	−1.06241	+	25.0597i	−0.0587516	+	1.38580i
$328$		−	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	0.872252	−	0.489057i	$-0.162659\pi$
$331$	0.229059	+	0.396742i	0.0125902	+	0.0218069i	−0.859662	+	0.510864i	$0.829326\pi$
$332$	−3.81238	+	6.60323i	−0.209231	+	0.362399i
$333$	31.8318	+	2.70390i	1.74437	+	0.148173i
$334$	−13.8579	+	8.00088i	−0.758272	+	0.437789i
$335$	21.4261			1.17064
$336$	1.11280	−	4.44541i	0.0607083	−	0.242517i
$337$	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
$339$	−3.05968	−	5.85951i	−0.166179	−	0.318245i
$340$	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
$345$	12.8238	+	0.543668i	0.690410	+	0.0292701i
$346$	−11.5986	−	6.69644i	−0.623543	−	0.360003i
$347$	13.0730	+	7.54769i	0.701794	+	0.405181i	0.808015	−	0.589161i	$-0.200542\pi$
$347$	13.0730	+	7.54769i	0.701794	+	0.405181i	−0.106221	+	0.994343i	$0.533875\pi$
$348$	6.49198	+	0.275230i	0.348007	+	0.0147539i
$349$			7.70859i			0.412632i	0.978485	+	0.206316i	$0.0661474\pi$
$349$			7.70859i			0.412632i	−0.978485	+	0.206316i	$0.933853\pi$
$350$	−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	$-0.914630\pi$
$353$	−4.74656	+	8.22129i	−0.252634	+	0.437575i	0.711616	+	0.702568i	$0.247964\pi$
$354$	−6.17756	−	11.8305i	−0.328333	−	0.628782i
$355$	13.7744	−	7.95266i	0.731070	−	0.422083i
$356$	−14.0743			−0.745936
$357$	−9.24341	+	2.64111i	−0.489213	+	0.139782i
$358$	−14.8045			−0.782442
$359$	−5.74380	+	3.31618i	−0.303146	+	0.175021i	−0.643855	−	0.765147i	$-0.722666\pi$
$359$	−5.74380	+	3.31618i	−0.303146	+	0.175021i	0.340709	+	0.940169i	$0.389333\pi$
$360$	−0.911459	+	10.7302i	−0.0480381	+	0.565532i
$361$	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
$366$	0.634336	−	14.9624i	0.0331573	−	0.782098i
$367$	−24.4825	−	14.1350i	−1.27797	−	0.737838i	−0.301498	−	0.953467i	$-0.597487\pi$
$367$	−24.4825	−	14.1350i	−1.27797	−	0.737838i	−0.976476	+	0.215628i	$0.930820\pi$
$368$	1.78784	+	1.03221i	0.0931975	+	0.0538076i
$369$	6.15445	−	8.83691i	0.320388	−	0.460031i
$370$		−	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	0.946942	−	0.321406i	$-0.104155\pi$
$373$	3.76850	+	6.52723i	0.195125	+	0.337967i	−0.751816	+	0.659373i	$0.770822\pi$
$374$	1.04890	−	1.81675i	0.0542373	−	0.0939418i
$375$	15.9020	−	8.30362i	0.821177	−	0.428797i
$376$	11.0781	−	6.39592i	0.571307	−	0.329844i
$377$	−1.37212			−0.0706675
$378$	10.3612	−	9.03578i	0.532923	−	0.464750i
$379$	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
$381$	−6.88602	+	3.59570i	−0.352781	+	0.184213i
$382$	−3.21740	+	5.57270i	−0.164617	+	0.285124i
$383$	2.47533	+	4.28740i	0.126483	+	0.219076i	0.922312	−	0.386446i	$-0.126298\pi$
$383$	2.47533	+	4.28740i	0.126483	+	0.219076i	−0.795828	+	0.605522i	$0.792964\pi$
$384$	−0.928784	+	1.46197i	−0.0473968	+	0.0746059i
$385$	−9.01307	+	2.99367i	−0.459349	+	0.152572i
$386$			6.57990i			0.334908i
$387$	7.37405	−	10.5881i	0.374844	−	0.538222i
$388$	0.564417	+	0.325866i	0.0286539	+	0.0165434i
$389$	−2.82098	−	1.62869i	−0.143029	−	0.0825779i	0.426778	−	0.904357i	$-0.359649\pi$
$389$	−2.82098	−	1.62869i	−0.143029	−	0.0825779i	−0.569807	+	0.821779i	$0.692982\pi$
$390$	0.0963209	−	2.27197i	0.00487740	−	0.115046i
$391$		−	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
$396$	−0.253915	+	2.98924i	−0.0127597	+	0.150215i
$397$	7.99636	−	4.61670i	0.401326	−	0.231706i	−0.285730	−	0.958310i	$-0.592236\pi$
$397$	7.99636	−	4.61670i	0.401326	−	0.231706i	0.687056	+	0.726605i	$0.258903\pi$
$398$	−26.4389			−1.32526
$399$	30.0234	+	7.51563i	1.50305	+	0.376252i
$400$	7.88536			0.394268
$401$	6.64897	−	3.83879i	0.332034	−	0.191700i	−0.324710	−	0.945814i	$-0.605267\pi$
$401$	6.64897	−	3.83879i	0.332034	−	0.191700i	0.656744	+	0.754114i	$0.271933\pi$
$402$	4.78535	+	9.16430i	0.238672	+	0.457074i
$403$	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
$408$	3.63024	+	0.153905i	0.179723	+	0.00761943i
$409$	10.4927	+	6.05798i	0.518832	+	0.299548i	0.736457	−	0.676485i	$-0.236498\pi$
$409$	10.4927	+	6.05798i	0.518832	+	0.299548i	−0.217625	+	0.976033i	$0.569831\pi$
$410$	−11.1591	−	6.44268i	−0.551106	−	0.318181i
$411$	−5.52787	−	0.234355i	−0.272669	−	0.0115599i
$412$		−	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
$417$	−3.64332	−	6.97721i	−0.178414	−	0.341676i
$418$	−5.84896	+	3.37690i	−0.286082	+	0.165169i
$419$	6.64928			0.324839			0.162419	−	0.986722i	$-0.448070\pi$
$419$	6.64928			0.324839			0.162419	+	0.986722i	$0.448070\pi$
$420$	−11.8222	−	11.4380i	−0.576864	−	0.558119i
$421$	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
$423$	38.2378	+	3.24804i	1.85919	+	0.157925i
$424$	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
$429$	0.0268332	−	0.632929i	0.00129552	−	0.0305581i
$430$	−13.3704	−	7.71940i	−0.644777	−	0.372262i
$431$	15.0179	+	8.67061i	0.723389	+	0.417649i	0.815999	−	0.578054i	$-0.196188\pi$
$431$	15.0179	+	8.67061i	0.723389	+	0.417649i	−0.0926100	+	0.995702i	$0.529521\pi$
$432$	−4.79305	+	2.00666i	−0.230606	+	0.0965455i
$433$		−	24.1020i		−	1.15827i	−0.815232	−	0.579135i	$-0.803390\pi$
$433$		−	24.1020i		−	1.15827i	0.815232	−	0.579135i	$-0.196610\pi$
$434$	−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
$438$	8.31720	−	4.34302i	0.397411	−	0.207518i
$439$	−22.7596	+	13.1403i	−1.08626	+	0.627151i	−0.932577	−	0.360970i	$-0.882446\pi$
$439$	−22.7596	+	13.1403i	−1.08626	+	0.627151i	−0.153680	+	0.988121i	$0.549112\pi$
$440$	3.58962			0.171128
$441$	0.693461	+	20.9885i	0.0330219	+	0.999455i
$442$	−0.767270			−0.0364953
$443$	−12.5406	+	7.24029i	−0.595820	+	0.343997i	−0.767395	−	0.641174i	$-0.778448\pi$
$443$	−12.5406	+	7.24029i	−0.595820	+	0.343997i	0.171576	+	0.985171i	$0.445114\pi$
$444$	16.3495	−	8.53729i	0.775914	−	0.405162i
$445$	−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	$-0.138967\pi$
$450$	19.4122	+	13.5196i	0.915098	+	0.637319i
$451$	−3.10870	−	1.79481i	−0.146383	−	0.0845143i
$452$	−3.30513	−	1.90822i	−0.155460	−	0.0897550i
$453$	−0.425281	+	10.0313i	−0.0199815	+	0.471313i
$454$		−	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	0.975861	−	0.218394i	$-0.0700818\pi$
$457$	6.38752	+	11.0635i	0.298796	+	0.517529i	−0.677065	+	0.735923i	$0.736748\pi$
$458$	−10.3592	+	17.9426i	−0.484052	+	0.838402i
$459$	8.67303	+	6.60298i	0.404822	+	0.308201i
$460$	6.41766	−	3.70524i	0.299225	−	0.172758i
$461$	20.6420			0.961394			0.480697	−	0.876887i	$-0.340384\pi$
$461$	20.6420			0.961394			0.480697	+	0.876887i	$0.340384\pi$
$462$	−3.29344	−	3.18642i	−0.153225	−	0.148246i
$463$	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
$465$	26.7432	+	51.2151i	1.24018	+	2.37504i
$466$	1.77278	−	3.07054i	0.0821224	−	0.142240i
$467$	−13.0650	−	22.6292i	−0.604575	−	1.04715i	−0.992119	−	0.125303i	$-0.960010\pi$
$467$	−13.0650	−	22.6292i	−0.604575	−	1.04715i	0.387544	−	0.921851i	$-0.373324\pi$
$468$	0.993271	−	0.466229i	0.0459139	−	0.0215514i
$469$	−15.4683	−	3.18255i	−0.714258	−	0.146957i
$470$		−	45.9178i		−	2.11803i
$471$	−29.7706	−	1.26213i	−1.37176	−	0.0581561i
$472$	−6.67312	−	3.85273i	−0.307155	−	0.177336i
$473$	−3.72474	−	2.15048i	−0.171264	−	0.0988791i
$474$	−11.4453	−	0.485225i	−0.525698	−	0.0222871i
$475$			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	0.229872	+	0.973221i	$0.426169\pi$
$479$	−15.9308	+	27.5930i	−0.727898	+	1.26076i	−0.957770	+	0.287535i	$0.907164\pi$
$480$	2.87784	+	5.51127i	0.131355	+	0.251554i
$481$	−3.37300	+	1.94740i	−0.153796	+	0.0887939i
$482$	−4.95592			−0.225736
$483$	−9.17718	−	2.29729i	−0.417576	−	0.104530i
$484$	1.00000			0.0454545
$485$	2.02604	−	1.16974i	0.0919979	−	0.0531150i
$486$	−15.2400	−	3.27776i	−0.691298	−	0.148682i
$487$	−21.8146	+	37.7840i	−0.988515	+	1.71216i	−0.363383	+	0.931640i	$0.618378\pi$
$487$	−21.8146	+	37.7840i	−0.988515	+	1.71216i	−0.625132	+	0.780519i	$0.714955\pi$
$488$	−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	$0.815902\pi$
$492$	0.263352	−	6.21182i	0.0118728	−	0.280051i
$493$	−6.81556	−	3.93497i	−0.306957	−	0.177222i
$494$	2.13925	+	1.23510i	0.0962496	+	0.0555697i
$495$	8.83691	+	6.15445i	0.397190	+	0.276622i
$496$			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	0.980596	−	0.196040i	$-0.0628084\pi$
$499$	7.15992	+	12.4013i	0.320522	+	0.555160i	−0.660074	+	0.751201i	$0.729475\pi$
$500$	5.17868	−	8.96973i	0.231598	−	0.401139i
$501$	−24.5681	+	12.8288i	−1.09762	+	0.573149i
$502$	14.4473	−	8.34113i	0.644812	−	0.372283i
$503$	4.44169			0.198045			0.0990226	−	0.995085i	$-0.468428\pi$
$503$	4.44169			0.198045			0.0990226	+	0.995085i	$0.468428\pi$
$504$	2.25184	−	7.61113i	0.100305	−	0.339026i
$505$	17.5067			0.779036
$506$	1.78784	−	1.03221i	0.0794791	−	0.0458873i
$507$	19.7540	−	10.3150i	0.877305	−	0.458106i
$508$	−2.24251	+	3.88414i	−0.0994954	+	0.172331i
$509$	9.31633	+	16.1364i	0.412939	+	0.715231i	0.995210	−	0.0977636i	$-0.0311689\pi$
$509$	9.31633	+	16.1364i	0.412939	+	0.715231i	−0.582271	+	0.812995i	$0.697836\pi$
$510$	6.99403	−	11.0091i	0.309701	−	0.487491i
$511$	−2.88837	+	14.0385i	−0.127774	+	0.621025i
$512$			1.00000i			0.0441942i
$513$	−13.5526	−	32.3713i	−0.598361	−	1.42923i
$514$	−1.07883	−	0.622864i	−0.0475853	−	0.0274734i
$515$	−29.4307	−	16.9918i	−1.29687	−	0.748749i
$516$	0.315539	−	7.44279i	0.0138908	−	0.327651i
$517$		−	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	$-0.967055\pi$
$521$	−9.30936	+	16.1243i	−0.407850	+	0.706418i	0.586798	+	0.809733i	$0.300388\pi$
$522$	11.2142	+	0.952567i	0.490831	+	0.0416927i
$523$	−11.3315	+	6.54227i	−0.495494	+	0.286074i	−0.726851	−	0.686795i	$-0.759017\pi$
$523$	−11.3315	+	6.54227i	−0.495494	+	0.286074i	0.231357	+	0.972869i	$0.425684\pi$
$524$	17.1677			0.749975
$525$	−34.7448	+	9.92760i	−1.51639	+	0.433276i
$526$	0.175672			0.00765965
$527$	16.8827	−	9.74720i	0.735420	−	0.424595i
$528$	0.801712	+	1.53534i	0.0348900	+	0.0668169i
$529$	−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
$534$	−24.3555	−	1.03256i	−1.05397	−	0.0446832i
$535$	56.0379	+	32.3535i	2.42273	+	1.39876i
$536$	5.16923	+	2.98446i	0.223277	+	0.128909i
$537$	−25.6191	−	1.08613i	−1.10555	−	0.0468700i
$538$			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	−0.997053	−	0.0767105i	$-0.975558\pi$
$541$	−13.1406	−	22.7602i	−0.564960	−	0.978539i	0.432093	−	0.901829i	$-0.357775\pi$
$542$	14.7337	−	25.5195i	0.632865	−	1.09615i
$543$	2.80993	+	5.38121i	0.120586	+	0.230930i
$544$	1.81675	−	1.04890i	0.0778925	−	0.0449712i
$545$	51.9820			2.22667
$546$	−0.407007	+	1.62591i	−0.0174183	+	0.0695824i
$547$	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
$549$	2.19543	−	25.8459i	0.0936987	−	1.10307i
$550$	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
$555$	2.80439	−	66.1486i	0.119040	−	2.80785i
$556$	−3.93558	−	2.27221i	−0.166906	−	0.0963632i
$557$	27.2601	+	15.7386i	1.15505	+	0.666868i	0.950112	−	0.311908i	$-0.100968\pi$
$557$	27.2601	+	15.7386i	1.15505	+	0.666868i	0.204936	+	0.978775i	$0.434301\pi$
$558$	−15.9326	+	22.8769i	−0.674481	+	0.968458i
$559$			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	$-0.955853\pi$
$563$	−8.90911	+	15.4310i	−0.375474	+	0.650340i	0.614924	+	0.788587i	$0.289187\pi$
$564$	19.6398	−	10.2554i	0.826983	−	0.431829i
$565$	−11.8642	+	6.84977i	−0.499129	+	0.288172i
$566$	−8.83585			−0.371398
$567$	18.5929	−	14.8762i	0.780830	−	0.624743i
$568$	4.43092			0.185917
$569$	−4.70368	+	2.71567i	−0.197189	+	0.113847i	−0.595344	−	0.803471i	$-0.702984\pi$
$569$	−4.70368	+	2.71567i	−0.197189	+	0.113847i	0.398155	+	0.917318i	$0.369651\pi$
$570$	−37.2220	+	19.4363i	−1.55906	+	0.814099i
$571$	19.0251	−	32.9524i	0.796175	−	1.37902i	−0.125916	−	0.992041i	$-0.540187\pi$
$571$	19.0251	−	32.9524i	0.796175	−	1.37902i	0.922091	−	0.386974i	$-0.126480\pi$
$572$	−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
$576$	−1.71451	+	2.46180i	−0.0714381	+	0.102575i
$577$	−22.1072	−	12.7636i	−0.920334	−	0.531355i	−0.0365921	−	0.999330i	$-0.511650\pi$
$577$	−22.1072	−	12.7636i	−0.920334	−	0.531355i	−0.883741	+	0.467975i	$0.844984\pi$
$578$	10.9113	+	6.29962i	0.453848	+	0.262030i
$579$	−0.482733	+	11.3865i	−0.0200617	+	0.473206i
$580$		−	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
$585$	0.333366	−	3.92457i	0.0137830	−	0.162261i
$586$	26.2531	−	15.1572i	1.08451	−	0.626140i
$587$	−25.8408			−1.06656			−0.533282	−	0.845937i	$-0.679042\pi$
$587$	−25.8408			−1.06656			−0.533282	+	0.845937i	$0.679042\pi$
$588$	6.83588	+	10.0135i	0.281907	+	0.412951i
$589$	−62.7616			−2.58604
$590$	−23.9540	+	13.8298i	−0.986169	+	0.569365i
$591$	11.1625	+	21.3771i	0.459166	+	0.879335i
$592$	5.32441	−	9.22215i	0.218832	−	0.379028i
$593$	19.1052	+	33.0911i	0.784555	+	1.35889i	0.929264	+	0.369416i	$0.120442\pi$
$593$	19.1052	+	33.0911i	0.784555	+	1.35889i	−0.144709	+	0.989474i	$0.546225\pi$
$594$	−0.658705	+	5.15423i	−0.0270270	+	0.211481i
$595$	6.28013	+	18.9076i	0.257460	+	0.775137i
$596$		−	10.2179i		−	0.418542i
$597$	−45.7524	−	1.93969i	−1.87252	−	0.0793861i
$598$	−0.653901	−	0.377530i	−0.0267400	−	0.0154383i
$599$	5.79727	+	3.34705i	0.236870	+	0.136757i	0.613737	−	0.789510i	$-0.289665\pi$
$599$	5.79727	+	3.34705i	0.236870	+	0.136757i	−0.376867	+	0.926267i	$0.622999\pi$
$600$	13.6456	+	0.578509i	0.557079	+	0.0236175i
$601$		−	8.82221i		−	0.359865i	−0.983679	−	0.179933i	$-0.942412\pi$
$601$		−	8.82221i		−	0.359865i	0.983679	−	0.179933i	$-0.0575880\pi$
$602$	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
$606$	3.90997	+	7.48787i	0.158832	+	0.304174i
$607$	−7.12129	+	4.11148i	−0.289044	+	0.166880i	−0.637511	−	0.770442i	$-0.720036\pi$
$607$	−7.12129	+	4.11148i	−0.289044	+	0.166880i	0.348467	+	0.937321i	$0.386702\pi$
$608$	−6.75379			−0.273903
$609$	−11.9539	+	12.3554i	−0.484397	+	0.500665i
$610$	−31.0370			−1.25665
$611$	−4.05179	+	2.33930i	−0.163918	+	0.0946381i
$612$	6.27082	+	0.532664i	0.253483	+	0.0215317i
$613$	10.7116	−	18.5530i	0.432635	−	0.749347i	−0.564464	−	0.825458i	$-0.690917\pi$
$613$	10.7116	−	18.5530i	0.432635	−	0.749347i	0.997099	+	0.0761112i	$0.0242504\pi$
$614$	−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	$-0.339840\pi$
$618$	0.694560	−	16.3829i	0.0279393	−	0.659019i
$619$	6.97855	+	4.02906i	0.280491	+	0.161942i	0.633646	−	0.773623i	$-0.281558\pi$
$619$	6.97855	+	4.02906i	0.280491	+	0.161942i	−0.353154	+	0.935565i	$0.614891\pi$
$620$	28.8885	+	16.6788i	1.16019	+	0.669836i
$621$	4.14259	+	9.89485i	0.166236	+	0.397067i
$622$			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
$627$	−10.3693	+	5.41460i	−0.414112	+	0.216238i
$628$	−14.8987	+	8.60176i	−0.594522	+	0.343248i
$629$	−22.3391			−0.890719
$630$	−19.6191	−	20.6608i	−0.781644	−	0.823146i
$631$	−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
$633$	−20.6747	+	10.7958i	−0.821744	+	0.429093i
$634$	−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
$639$	10.9080	+	7.59688i	0.431515	+	0.300528i
$640$	3.10870	+	1.79481i	0.122882	+	0.0709461i
$641$	30.5777	+	17.6540i	1.20775	+	0.697293i	0.962267	−	0.272109i	$-0.0877210\pi$
$641$	30.5777	+	17.6540i	1.20775	+	0.697293i	0.245480	+	0.969402i	$0.421054\pi$
$642$	−1.32249	+	31.1942i	−0.0521944	+	1.23114i
$643$			22.4466i			0.885208i	0.896717	+	0.442604i	$0.145945\pi$
$643$			22.4466i			0.885208i	−0.896717	+	0.442604i	$0.854055\pi$
$644$	−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	$-0.677074\pi$
$647$	11.9912	−	20.7693i	0.471422	−	0.816527i	0.999466	+	0.0326902i	$0.0104075\pi$
$648$	−8.44157	+	3.12088i	−0.331616	+	0.122600i
$649$	−6.67312	+	3.85273i	−0.261943	+	0.151233i
$650$	−2.88407			−0.113123
$651$	−11.6995	−	40.9462i	−0.458541	−	1.60481i
$652$	−8.59472			−0.336595
$653$	32.7520	−	18.9094i	1.28169	−	0.739981i	0.304529	−	0.952503i	$-0.401501\pi$
$653$	32.7520	−	18.9094i	1.28169	−	0.739981i	0.977156	+	0.212522i	$0.0681677\pi$
$654$	11.6098	+	22.2335i	0.453978	+	0.869400i
$655$	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	$-0.254829\pi$
$660$	6.21182	+	0.263352i	0.241795	+	0.0102510i
$661$	−7.15403	−	4.13038i	−0.278259	−	0.160653i	0.354376	−	0.935103i	$-0.384693\pi$
$661$	−7.15403	−	4.13038i	−0.278259	−	0.160653i	−0.632635	+	0.774450i	$0.718027\pi$
$662$	0.396742	+	0.229059i	0.0154198	+	0.00890264i
$663$	−1.32776	−	0.0562907i	−0.0515658	−	0.00218615i
$664$			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
$669$	19.5019	+	37.3476i	0.753988	+	1.44394i
$670$	18.5556	−	10.7131i	0.716865	−	0.413882i
$671$	−8.64631			−0.333787
$672$	−1.25899	−	4.40624i	−0.0485666	−	0.169974i
$673$	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
$675$	32.6008	+	24.8197i	1.25481	+	0.955312i
$676$	6.43311	−	11.1425i	0.247427	−	0.428557i
$677$	−2.71109	−	4.69574i	−0.104195	−	0.180472i	0.809214	−	0.587514i	$-0.199893\pi$
$677$	−2.71109	−	4.69574i	−0.104195	−	0.180472i	−0.913409	+	0.407042i	$0.866560\pi$
$678$	−5.57952	−	3.54464i	−0.214280	−	0.136131i
$679$	−1.63642	+	0.543533i	−0.0627999	+	0.0208589i
$680$		−	7.53030i		−	0.288774i
$681$	1.24628	−	29.3967i	0.0477576	−	1.12648i
$682$	8.04779	+	4.64639i	0.308166	+	0.177920i
$683$	20.3425	+	11.7447i	0.778383	+	0.449399i	0.835857	−	0.548948i	$-0.184971\pi$
$683$	20.3425	+	11.7447i	0.778383	+	0.449399i	−0.0574741	+	0.998347i	$0.518305\pi$
$684$	−16.6265	−	11.5795i	−0.635729	−	0.442752i
$685$			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
$690$	11.3776	−	5.94107i	0.433137	−	0.226173i
$691$	−16.9265	+	9.77251i	−0.643913	+	0.371764i	−0.786120	−	0.618073i	$-0.787913\pi$
$691$	−16.9265	+	9.77251i	−0.643913	+	0.371764i	0.142207	+	0.989837i	$0.454580\pi$
$692$	−13.3929			−0.509121
$693$	−5.46551	−	5.75571i	−0.207618	−	0.218641i
$694$	15.0954			0.573013
$695$	−14.1272	+	8.15637i	−0.535877	+	0.309389i
$696$	5.75984	−	3.00764i	0.218326	−	0.114004i
$697$	−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	$-0.0371419\pi$
$702$	1.75306	−	0.733936i	0.0661648	−	0.0277006i
$703$	62.2845	+	35.9600i	2.34911	+	1.35626i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$	3.36876	−	79.4606i	0.126875	−	2.99266i
$706$			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	0.918739	−	0.394866i	$-0.129209\pi$
$709$	3.12615	+	5.41464i	0.117405	+	0.203351i	−0.801334	+	0.598218i	$0.795876\pi$
$710$	7.95266	−	13.7744i	0.298458	−	0.516944i
$711$	−19.7704	−	1.67936i	−0.741447	−	0.0629809i
$712$	−12.1887	+	7.03715i	−0.456791	+	0.263728i
$713$	19.1842			0.718453
$714$	−6.68447	+	6.90897i	−0.250160	+	0.258562i
$715$	−1.31290			−0.0490998
$716$	−12.8211	+	7.40224i	−0.479146	+	0.276635i
$717$	−21.4987	−	41.1716i	−0.802885	−	1.53758i
$718$	−3.31618	+	5.74380i	−0.123759	+	0.214357i
$719$	−14.3651	−	24.8812i	−0.535730	−	0.927911i	−0.999128	−	0.0417607i	$-0.986703\pi$
$719$	−14.3651	−	24.8812i	−0.535730	−	0.927911i	0.463398	−	0.886150i	$-0.346630\pi$
$720$	4.57576	+	9.74837i	0.170529	+	0.363300i
$721$	18.7231	+	16.6385i	0.697285	+	0.619649i
$722$		−	26.6137i		−	0.990461i
$723$	−8.57620	−	0.363591i	−0.318952	−	0.0135221i
$724$	3.03534	+	1.75245i	0.112808	+	0.0651294i
$725$	−25.6188	−	14.7910i	−0.951459	−	0.549325i
$726$	1.73050	+	0.0733649i	0.0642247	+	0.00272283i
$727$			0.429770i			0.0159393i	0.999968	+	0.00796964i	$0.00253684\pi$
$727$			0.429770i			0.0159393i	−0.999968	+	0.00796964i	$0.997463\pi$
$728$	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
$732$	−6.93185	−	13.2750i	−0.256209	−	0.490658i
$733$	−26.9259	+	15.5457i	−0.994532	+	0.574194i	−0.906626	−	0.421935i	$-0.861351\pi$
$733$	−26.9259	+	15.5457i	−0.994532	+	0.574194i	−0.0879064	+	0.996129i	$0.528018\pi$
$734$	−28.2699			−1.04346
$735$	43.3982	−	3.27834i	1.60077	−	0.120924i
$736$	2.06442			0.0760954
$737$	5.16923	−	2.98446i	0.190411	−	0.109934i
$738$	0.911459	−	10.7302i	0.0335513	−	0.394985i
$739$	1.15436	−	1.99941i	0.0424639	−	0.0735496i	−0.844012	−	0.536324i	$-0.819813\pi$
$739$	1.15436	−	1.99941i	0.0424639	−	0.0735496i	0.886476	+	0.462774i	$0.153146\pi$
$740$	−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	$-0.243444\pi$
$744$	−0.681764	+	16.0811i	−0.0249947	+	0.589563i
$745$	−31.7644	−	18.3392i	−1.16376	−	0.671896i
$746$	6.52723	+	3.76850i	0.238979	+	0.137974i
$747$	−13.0728	+	18.7706i	−0.478307	+	0.686780i
$748$		−	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	−0.925805	−	0.378002i	$-0.876611\pi$
$751$	−21.6566	−	37.5104i	−0.790262	−	1.36877i	0.135543	−	0.990771i	$-0.456722\pi$
$752$	6.39592	−	11.0781i	0.233235	−	0.403975i
$753$	25.6129	−	13.3744i	0.933385	−	0.487389i
$754$	−1.18829	+	0.686058i	−0.0432749	+	0.0249848i
$755$	20.8083			0.757291
$756$	4.45518	−	13.0058i	0.162033	−	0.473017i
$757$	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
$759$	3.16957	−	1.65507i	0.115048	−	0.0600752i
$760$	−12.1218	+	20.9955i	−0.439703	+	0.761588i
$761$	25.3900	+	43.9767i	0.920386	+	1.59416i	0.798818	+	0.601573i	$0.205459\pi$
$761$	25.3900	+	43.9767i	0.920386	+	1.59416i	0.121568	+	0.992583i	$0.461208\pi$
$762$	−4.16562	+	6.55698i	−0.150904	+	0.237534i
$763$	−37.5276	−	7.72120i	−1.35859	−	0.279526i
$764$			6.43480i			0.232803i
$765$	12.9108	−	18.5381i	0.466792	−	0.670245i
$766$	4.28740	+	2.47533i	0.154910	+	0.0894373i
$767$	2.44069	+	1.40913i	0.0881282	+	0.0508809i
$768$	−0.0733649	+	1.73050i	−0.00264733	+	0.0624439i
$769$		−	50.9343i		−	1.83674i	−0.395725	−	0.918369i	$-0.629507\pi$
$769$		−	50.9343i		−	1.83674i	0.395725	−	0.918369i	$-0.370493\pi$
$770$	−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	$-0.902351\pi$
$773$	−5.98128	+	10.3599i	−0.215132	+	0.372619i	0.738182	+	0.674602i	$0.235685\pi$
$774$	1.09208	−	12.8566i	0.0392540	−	0.462120i
$775$	63.4597	−	36.6385i	2.27954	−	1.31609i
$776$	0.651733			0.0233958
$777$	−11.8500	+	47.3384i	−0.425117	+	1.69826i
$778$	−3.25738			−0.116783
$779$	20.9955	−	12.1218i	0.752243	−	0.434308i
$780$	−1.05257	−	2.01575i	−0.0376880	−	0.0721753i
$781$	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
$786$	29.7086	+	1.25951i	1.05967	+	0.0449251i
$787$	10.0726	+	5.81543i	0.359050	+	0.207298i	0.668664	−	0.743565i	$-0.266866\pi$
$787$	10.0726	+	5.81543i	0.359050	+	0.207298i	−0.309614	+	0.950862i	$0.600200\pi$
$788$	12.0580	+	6.96169i	0.429548	+	0.248000i
$789$	0.303999	+	0.0128881i	0.0108227	+	0.000458830i
$790$			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
$795$	−10.4145	−	19.9446i	−0.369366	−	0.707362i
$796$	−22.8967	+	13.2194i	−0.811554	+	0.468551i
$797$	−18.0276			−0.638570			−0.319285	−	0.947659i	$-0.603443\pi$
$797$	−18.0276			−0.638570			−0.319285	+	0.947659i	$0.603443\pi$
$798$	29.7588	−	8.50296i	1.05345	−	0.301002i
$799$	−26.8347			−0.949344
$800$	6.82893	−	3.94268i	0.241439	−	0.139395i
$801$	−42.0714	−	3.57368i	−1.48652	−	0.126270i
$802$	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
$807$	−0.744443	+	17.5596i	−0.0262056	+	0.618126i
$808$	4.22363	+	2.43851i	0.148587	+	0.0857865i
$809$	−10.4831	−	6.05241i	−0.368566	−	0.212791i	0.304266	−	0.952587i	$-0.401589\pi$
$809$	−10.4831	−	6.05241i	−0.368566	−	0.212791i	−0.672832	+	0.739796i	$0.734922\pi$
$810$	−5.44913	+	31.8437i	−0.191463	+	1.11887i
$811$		−	20.3659i		−	0.715143i	−0.933886	−	0.357572i	$-0.883605\pi$
$811$		−	20.3659i		−	0.715143i	0.933886	−	0.357572i	$-0.116395\pi$
$812$	−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
$816$	3.22083	−	1.68183i	0.112752	−	0.0588759i
$817$	25.1561	−	14.5239i	0.880101	−	0.508126i
$818$	12.1160			0.423624
$819$	−0.823608	+	2.78377i	−0.0287792	+	0.0972727i
$820$	−12.8854			−0.449976
$821$	10.5624	−	6.09822i	0.368631	−	0.212829i	−0.304229	−	0.952599i	$-0.598399\pi$
$821$	10.5624	−	6.09822i	0.368631	−	0.212829i	0.672860	+	0.739770i	$0.265066\pi$
$822$	−4.90445	+	2.56097i	−0.171062	+	0.0893243i
$823$	16.2161	−	28.0871i	0.565258	−	0.979055i	−0.431768	−	0.901985i	$-0.642110\pi$
$823$	16.2161	−	28.0871i	0.565258	−	0.979055i	0.997026	−	0.0770704i	$-0.0245566\pi$
$824$	−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	$0.605419\pi$
$828$	5.08217	+	3.53947i	0.176618	+	0.123005i
$829$	−43.5306	−	25.1324i	−1.51188	−	0.872885i	−0.999904	−	0.0138857i	$-0.995580\pi$
$829$	−43.5306	−	25.1324i	−1.51188	−	0.872885i	−0.511977	−	0.858999i	$-0.671087\pi$
$830$	23.7031	+	13.6850i	0.822746	+	0.475013i
$831$	1.72746	−	40.7465i	0.0599249	−	1.41348i
$832$		−	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
$837$	−29.2497	+	38.4196i	−1.01102	+	1.32797i
$838$	5.75845	−	3.32464i	0.198922	−	0.114848i
$839$	−36.9731			−1.27645			−0.638226	−	0.769849i	$-0.720331\pi$
$839$	−36.9731			−1.27645			−0.638226	+	0.769849i	$0.720331\pi$
$840$	−15.9573	−	3.99453i	−0.550580	−	0.137824i
$841$	14.9261			0.514694
$842$	1.17242	−	0.676898i	0.0404043	−	0.0233274i
$843$	−7.03766	−	13.4776i	−0.242390	−	0.464194i
$844$	−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
$849$	−15.2904	−	0.648241i	−0.524765	−	0.0222476i
$850$	−14.3257	−	8.27096i	−0.491368	−	0.283692i
$851$	−19.0384	−	10.9918i	−0.652627	−	0.376794i
$852$	7.66769	+	0.325074i	0.262691	+	0.0111369i
$853$			4.92939i			0.168779i	0.996433	+	0.0843896i	$0.0268940\pi$
$853$			4.92939i			0.168779i	−0.996433	+	0.0843896i	$0.973106\pi$
$854$	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	0.300854	+	0.953670i	$0.402728\pi$
$857$	−19.7742	+	34.2500i	−0.675475	+	1.16996i	−0.976330	+	0.216288i	$0.930605\pi$
$858$	−0.293226	−	0.561549i	−0.0100106	−	0.0191710i
$859$	18.4240	−	10.6371i	0.628619	−	0.362934i	−0.151598	−	0.988442i	$-0.548442\pi$
$859$	18.4240	−	10.6371i	0.628619	−	0.362934i	0.780217	+	0.625509i	$0.215109\pi$
$860$	−15.4388			−0.526458
$861$	11.8222	+	11.4380i	0.402899	+	0.389807i
$862$	17.3412			0.590644
$863$	−29.0704	+	16.7838i	−0.989568	+	0.571327i	−0.905145	−	0.425103i	$-0.860238\pi$
$863$	−29.0704	+	16.7838i	−0.989568	+	0.571327i	−0.0844227	+	0.996430i	$0.526905\pi$
$864$	−3.14757	+	4.13434i	−0.107083	+	0.140653i
$865$	−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
$870$	0.987969	−	23.3037i	0.0334953	−	0.790071i
$871$	−1.89065	−	1.09156i	−0.0640621	−	0.0369863i
$872$	12.5411	+	7.24061i	0.424695	+	0.245198i
$873$	1.60443	+	1.11741i	0.0543018	+	0.0378185i
$874$			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	0.993279	+	0.115748i	$0.0369266\pi$
$877$	17.6761	+	30.6159i	0.596880	+	1.03383i	−0.396398	+	0.918079i	$0.629740\pi$
$878$	−13.1403	+	22.7596i	−0.443463	+	0.768100i
$879$	46.5429	−	24.3035i	1.56985	−	0.819737i
$880$	3.10870	−	1.79481i	0.104794	−	0.0605030i
$881$	−37.4261			−1.26092			−0.630459	−	0.776223i	$-0.717133\pi$
$881$	−37.4261			−1.26092			−0.630459	+	0.776223i	$0.717133\pi$
$882$	11.0948	+	17.8299i	0.373582	+	0.600363i
$883$	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
$885$	−42.4668	+	22.1751i	−1.42751	+	0.745407i
$886$	−7.24029	+	12.5406i	−0.243242	+	0.421308i
$887$	−12.7745	−	22.1261i	−0.428925	−	0.742920i	0.567853	−	0.823130i	$-0.307774\pi$
$887$	−12.7745	−	22.1261i	−0.428925	−	0.742920i	−0.996778	+	0.0802098i	$0.974441\pi$
$888$	9.89046	−	15.5683i	0.331902	−	0.522437i
$889$	−3.74042	−	11.2613i	−0.125450	−	0.377692i
$890$			50.5214i			1.69348i
$891$	−1.51803	+	8.87105i	−0.0508558	+	0.297191i
$892$	21.0664	+	12.1627i	0.705354	+	0.407236i
$893$	74.8189	+	43.1967i	2.50372	+	1.44552i
$894$	0.749636	−	17.6820i	0.0250716	−	0.591376i
$895$			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
$900$	23.5712	+	2.00222i	0.785707	+	0.0667405i
$901$	−6.57458	+	3.79584i	−0.219031	+	0.126458i
$902$	−3.58962			−0.119521
$903$	14.1649	+	13.7047i	0.471379	+	0.456062i
$904$	−3.81643			−0.126933
$905$	10.8957	−	6.29064i	0.362186	−	0.209108i
$906$	4.64736	+	8.90003i	0.154398	+	0.295684i
$907$	1.07480	−	1.86161i	0.0356882	−	0.0618138i	−0.847630	−	0.530588i	$-0.821971\pi$
$907$	1.07480	−	1.86161i	0.0356882	−	0.0618138i	0.883318	+	0.468775i	$0.155304\pi$
$908$	−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	$-0.192780\pi$
$912$	−11.6874	−	0.495491i	−0.387009	−	0.0164074i
$913$	6.60323	+	3.81238i	0.218535	+	0.126171i
$914$	11.0635	+	6.38752i	0.365948	+	0.211280i
$915$	−53.7093	−	2.27702i	−1.77558	−	0.0752761i
$916$			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	−0.862101	−	0.506737i	$-0.830852\pi$
$919$	−26.3709	−	45.6758i	−0.869897	−	1.50671i	−0.00779650	−	0.999970i	$-0.502482\pi$
$920$	3.70524	−	6.41766i	0.122158	−	0.211584i
$921$	−13.4666	−	25.7895i	−0.443739	−	0.849792i
$922$	17.8765	−	10.3210i	0.588731	−	0.339904i
$923$	−1.62061			−0.0533430
$924$	−4.44541	−	1.11280i	−0.146243	−	0.0366085i
$925$	−83.9699			−2.76091
$926$	5.83095	−	3.36650i	0.191617	−	0.110630i
$927$	2.40387	−	28.2997i	0.0789533	−	0.929483i
$928$	1.87576	−	3.24891i	0.0615748	−	0.106651i
$929$	15.7809	+	27.3334i	0.517756	+	0.896779i	0.999787	+	0.0206252i	$0.00656569\pi$
$929$	15.7809	+	27.3334i	0.517756	+	0.896779i	−0.482032	+	0.876154i	$0.660101\pi$
$930$	48.7678	+	30.9820i	1.59916	+	1.01594i
$931$	−18.6640	+	43.4365i	−0.611686	+	1.42357i
$932$		−	3.54556i		−	0.116139i
$933$	−1.33833	+	31.5680i	−0.0438151	+	1.03349i
$934$	−22.6292	−	13.0650i	−0.740450	−	0.427499i
$935$	−6.52143	−	3.76515i	−0.213274	−	0.123134i
$936$	0.627083	−	0.900401i	0.0204969	−	0.0294305i
$937$		−	31.4813i		−	1.02845i	−0.857655	−	0.514225i	$-0.828080\pi$
$937$		−	31.4813i		−	1.02845i	0.857655	−	0.514225i	$-0.171920\pi$
$938$	−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	$-0.940382\pi$
$941$	−10.1230	+	17.5335i	−0.329999	+	0.571575i	0.652512	+	0.757778i	$0.273715\pi$
$942$	−26.4132	+	13.7923i	−0.860588	+	0.449377i
$943$	−6.41766	+	3.70524i	−0.208988	+	0.120659i
$944$	−7.70545			−0.250791
$945$	−32.4350	−	37.1928i	−1.05511	−	1.20988i
$946$	−4.30096			−0.139836
$947$	−10.9410	+	6.31679i	−0.355535	+	0.205268i	−0.667120	−	0.744950i	$-0.732473\pi$
$947$	−10.9410	+	6.31679i	−0.355535	+	0.205268i	0.311586	+	0.950218i	$0.399140\pi$
$948$	−10.1545	+	5.30241i	−0.329803	+	0.172214i
$949$	−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	$-0.0158610\pi$
$954$	6.20461	−	8.90892i	0.200882	−	0.288437i
$955$	20.0039	+	11.5492i	0.647310	+	0.373725i
$956$	−23.2233	−	13.4080i	−0.751097	−	0.433646i
$957$	0.275230	−	6.49198i	0.00889691	−	0.209856i
$958$			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
$963$	−4.57712	+	53.8844i	−0.147495	+	1.73640i
$964$	−4.29195	+	2.47796i	−0.138234	+	0.0798097i
$965$	23.6193			0.760333
$966$	−9.09632	+	2.59908i	−0.292669	+	0.0836241i
$967$	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
$969$	11.3588	+	21.7528i	0.364896	+	0.698801i
$970$	1.16974	−	2.02604i	0.0375580	−	0.0650523i
$971$	−18.6107	−	32.2347i	−0.597246	−	1.03446i	−0.993226	−	0.116202i	$-0.962928\pi$
$971$	−18.6107	−	32.2347i	−0.597246	−	1.03446i	0.395979	−	0.918259i	$-0.370405\pi$
$972$	−14.8371	+	4.78135i	−0.475899	+	0.153362i
$973$	11.4105	−	3.78996i	0.365802	−	0.121500i
$974$			43.6293i			1.39797i
$975$	−4.99087	−	0.211589i	−0.159836	−	0.00677629i
$976$	−7.48792	−	4.32316i	−0.239683	−	0.138381i
$977$	−23.9340	−	13.8183i	−0.765717	−	0.442087i	0.0656276	−	0.997844i	$-0.479095\pi$
$977$	−23.9340	−	13.8183i	−0.765717	−	0.442087i	−0.831345	+	0.555757i	$0.812428\pi$
$978$	−14.8731	−	0.630551i	−0.475590	−	0.0201628i
$979$			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	$-0.825060\pi$
$983$	0.814813	−	1.41130i	0.0259885	−	0.0450134i	0.878727	+	0.477324i	$0.158393\pi$
$984$	−2.87784	−	5.51127i	−0.0917422	−	0.175693i
$985$	43.2836	−	24.9898i	1.37913	−	0.796242i
$986$	−7.86993			−0.250630
$987$	−14.2348	+	56.8650i	−0.453098	+	1.81003i
$988$	2.47020			0.0785875
$989$	−7.68941	+	4.43948i	−0.244509	+	0.141167i
$990$	10.7302	+	0.911459i	0.341029	+	0.0289681i
$991$	11.4482	−	19.8288i	0.363664	−	0.629884i	−0.624897	−	0.780707i	$-0.714859\pi$
$991$	11.4482	−	19.8288i	0.363664	−	0.629884i	0.988561	+	0.150823i	$0.0481924\pi$
$992$	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
$996$	−0.559389	+	13.1946i	−0.0177249	+	0.418087i
$997$	47.3773	+	27.3533i	1.50045	+	0.866287i	1.00000		0.000523534i	$0.000166646\pi$
$997$	47.3773	+	27.3533i	1.50045	+	0.866287i	0.500453	+	0.865764i	$0.333167\pi$
$998$	12.4013	+	7.15992i	0.392558	+	0.226643i
$999$	51.0403	−	21.3686i	1.61484	−	0.676072i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.4	✓	20	7.5	odd	6	inner
462.2.k.g.89.10	yes	20	21.5	even	6	inner
462.2.k.g.353.4	yes	20	3.2	odd	2	inner
462.2.k.g.353.10	yes	20	1.1	even	1	trivial

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} +(1.53534 - 0.801712i) 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} +(1.71451 - 2.46180i) q^{9} +(-3.10870 - 1.79481i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(0.0733649 - 1.73050i) 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} +(0.253915 - 2.98924i) q^{18} +(5.84896 - 3.37690i) q^{19} -3.58962 q^{20} +(3.29344 + 3.18642i) q^{21} -1.00000 q^{22} +(-1.78784 + 1.03221i) q^{23} +(-0.801712 - 1.53534i) 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} +(-6.21182 - 0.263352i) q^{30} +(-8.04779 - 4.64639i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.73050 - 0.0733649i) 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} +(0.293226 + 0.561549i) q^{39} +(-3.10870 + 1.79481i) q^{40} +3.58962 q^{41} +(4.44541 + 1.11280i) q^{42} +4.30096 q^{43} +(-0.866025 + 0.500000i) q^{44} +(-10.7302 - 0.911459i) 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} +(-0.153905 + 3.63024i) q^{51} +(0.316749 + 0.182875i) q^{52} +(3.13404 + 1.80944i) q^{53} +(-2.00666 - 4.79305i) 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} +(-5.51127 + 2.87784i) q^{60} +(7.48792 - 4.32316i) q^{61} -9.29278 q^{62} +(7.61113 + 2.25184i) q^{63} -1.00000 q^{64} +(1.13701 - 0.656451i) q^{65} +(-1.53534 + 0.801712i) 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} +(-2.46180 - 1.71451i) q^{72} +(4.69142 + 2.70859i) q^{73} +(9.22215 + 5.32441i) q^{74} +(-0.578509 + 13.6456i) 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} +(-3.12088 - 8.44157i) q^{81} +(3.10870 - 1.79481i) q^{82} -7.62475 q^{83} +(4.40624 - 1.25899i) q^{84} +7.53030 q^{85} +(3.72474 - 2.15048i) q^{86} +(3.00764 + 5.75984i) 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} +(-16.0811 - 0.681764i) q^{93} +(11.0781 + 6.39592i) q^{94} +(-20.9955 - 12.1218i) q^{95} +(-1.73050 - 0.0733649i) q^{96} +0.651733i q^{97} +(-2.76348 + 6.43142i) q^{98} +(-2.71571 + 1.27472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) 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

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