LMFDB - Embedded newform 462.2.k.g.89.10

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			89.10
Root			$-0.0733649 - 1.73050i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.53534 + 0.801712i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79481 + 3.10870i) q^{5} +(0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} +1.00000i q^{8} +(1.71451 + 2.46180i) q^{9} +O(q^{10})$	\(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}+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
$3$	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	0.115194	+	0.993343i	$0.463251\pi$
$5$	−1.79481	+	3.10870i	−0.802663	+	1.39025i	−0.917857	+	0.396910i	$0.870082\pi$
$6$	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	$-0.983848\pi$
$13$		−	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	0.710336	−	0.703863i	$-0.248543\pi$
$17$	−1.04890	−	1.81675i	−0.254396	−	0.440626i	−0.964731	+	0.263237i	$0.915210\pi$
$18$	0.253915	+	2.98924i	0.0598484	+	0.704569i
$19$	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
$21$	3.29344	−	3.18642i	0.718687	−	0.695334i
$22$	−1.00000			−0.213201
$23$	−1.78784	−	1.03221i	−0.372790	−	0.215230i	0.301887	−	0.953344i	$-0.402384\pi$
$23$	−1.78784	−	1.03221i	−0.372790	−	0.215230i	−0.674677	+	0.738113i	$0.735717\pi$
$24$	−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	$-0.886752\pi$
$29$		−	3.75152i		−	0.696639i	0.937376	−	0.348319i	$-0.113248\pi$
$30$	−6.21182	+	0.263352i	−1.13412	+	0.0480813i
$31$	−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
$33$	−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	0.0189151	−	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
$39$	0.293226	−	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	0.154674	−	0.987965i	$-0.450567\pi$
$47$	6.39592	−	11.0781i	0.932940	−	1.61590i	0.778266	−	0.627935i	$-0.216100\pi$
$48$	−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	−0.269064	−	0.963122i	$-0.586714\pi$
$53$	3.13404	−	1.80944i	0.430493	−	0.248545i	0.699557	+	0.714577i	$0.253381\pi$
$54$	−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	0.999998	+	0.00182804i	$0.000581885\pi$
$59$	3.85273	+	6.67312i	0.501582	+	0.868766i	−0.498416	+	0.866938i	$0.666085\pi$
$60$	−5.51127	−	2.87784i	−0.711502	−	0.371528i
$61$	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
$63$	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	0.624104	−	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	$-0.915312\pi$
$71$		−	4.43092i		−	0.525853i	0.964816	−	0.262927i	$-0.0846878\pi$
$72$	−2.46180	+	1.71451i	−0.290125	+	0.202058i
$73$	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
$75$	−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	−0.989882	−	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
$81$	−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	0.203820	+	0.979008i	$0.434664\pi$
$89$	−7.03715	+	12.1887i	−0.745936	+	1.29200i	−0.949756	+	0.312991i	$0.898669\pi$
$90$	−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	$-0.989466\pi$
$97$		−	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	0.718825	−	0.695191i	$-0.244680\pi$
$101$	−2.43851	−	4.22363i	−0.242641	−	0.420267i	−0.961466	+	0.274925i	$0.911347\pi$
$102$	1.68183	−	3.22083i	0.166526	−	0.318910i
$103$	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
$105$	3.99453	+	15.9573i	0.389827	+	1.55728i
$106$	3.61887			0.351496
$107$	−15.6111	−	9.01307i	−1.50918	−	0.871327i	−0.999943	−	0.0107015i	$-0.996594\pi$
$107$	−15.6111	−	9.01307i	−1.50918	−	0.871327i	−0.509239	−	0.860625i	$-0.670073\pi$
$108$	−4.13434	+	3.14757i	−0.397827	+	0.302875i
$109$	−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	$0.0574512\pi$
$113$			3.81643i			0.359020i	−0.983756	+	0.179510i	$0.942549\pi$
$114$	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	−0.197860	−	0.980230i	$-0.563399\pi$
$131$	8.58385	−	14.8677i	0.749975	−	1.29899i	0.947834	−	0.318764i	$-0.103268\pi$
$132$	−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	−0.613498	−	0.789696i	$-0.710238\pi$
$137$	−2.76642	+	1.59719i	−0.236351	+	0.136457i	0.377148	+	0.926153i	$0.376905\pi$
$138$	−0.151456	−	3.57247i	−0.0128928	−	0.304109i
$139$			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
$144$	−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	0.816567	−	0.577251i	$-0.195875\pi$
$149$	8.84896	+	5.10895i	0.724935	+	0.418542i	−0.0916311	+	0.995793i	$0.529208\pi$
$150$	6.32179	−	12.1067i	0.516172	−	0.988507i
$151$	−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
$156$	0.632929	−	0.0268332i	0.0506748	−	0.00214837i
$157$	−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
$159$	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	−0.983790	−	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
$165$	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	0.490824	+	0.871259i	$0.336696\pi$
$173$	−6.69644	+	11.5986i	−0.509121	+	0.881823i	−0.999944	+	0.0105638i	$0.996637\pi$
$174$	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	−0.895647	−	0.444766i	$-0.853287\pi$
$179$	−12.8211	+	7.40224i	−0.958291	+	0.553270i	−0.0626446	+	0.998036i	$0.519953\pi$
$180$	−6.15445	−	8.83691i	−0.458726	−	0.658664i
$181$		−	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
$186$	−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	0.284649	−	0.958632i	$-0.408123\pi$
$191$	−5.57270	−	3.21740i	−0.403227	−	0.232803i	−0.687875	+	0.725829i	$0.741456\pi$
$192$	−1.53534	−	0.801712i	−0.110803	−	0.0578586i
$193$	−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	$-0.834802\pi$
$197$		−	13.9234i		−	0.992000i	0.868323	−	0.496000i	$-0.165198\pi$
$198$	−1.71451	−	2.46180i	−0.121845	−	0.174952i
$199$	−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
$201$	−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	$-0.697026\pi$
$223$		−	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	$0.0239744\pi$
$227$	8.49372	+	14.7116i	0.563748	+	0.976440i	−0.433417	+	0.901193i	$0.642692\pi$
$228$	−5.41460	+	10.3693i	−0.358591	+	0.686727i
$229$	−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
$231$	−1.25899	+	4.40624i	−0.0828355	+	0.289909i
$232$	3.75152			0.246299
$233$	3.07054	+	1.77278i	0.201158	+	0.116139i	0.597195	−	0.802096i	$-0.296282\pi$
$233$	3.07054	+	1.77278i	0.201158	+	0.116139i	−0.396038	+	0.918234i	$0.629615\pi$
$234$	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	$0.334141\pi$
$239$			26.8160i			1.73458i	−0.497800	+	0.867292i	$0.665859\pi$
$240$	−0.263352	−	6.21182i	−0.0169993	−	0.400971i
$241$	−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
$243$	−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	−0.884798	−	0.465975i	$-0.845704\pi$
$257$	−0.622864	+	1.07883i	−0.0388532	+	0.0672957i	0.845945	+	0.533270i	$0.179037\pi$
$258$	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	−0.495302	−	0.868721i	$-0.664943\pi$
$263$	0.152136	−	0.0878358i	0.00938111	−	0.00541619i	0.504683	+	0.863305i	$0.331609\pi$
$264$	−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	0.668878	−	0.743373i	$-0.266775\pi$
$269$	−5.07356	−	8.78767i	−0.309341	−	0.535794i	−0.978218	+	0.207579i	$0.933442\pi$
$270$	−11.2986	−	14.8407i	−0.687610	−	0.903177i
$271$	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
$273$	−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	0.965828	+	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	$0.0843274\pi$
$281$			8.77829i			0.523669i	−0.965113	+	0.261834i	$0.915673\pi$
$282$	22.1362	−	0.938472i	1.31819	−	0.0558852i
$283$	−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
$285$	−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	$0.159122\pi$
$307$			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	$-0.993638\pi$
$311$	−9.12108	−	15.7982i	−0.517209	−	0.895832i	0.482591	−	0.875846i	$-0.339696\pi$
$312$	0.561549	+	0.293226i	0.0317914	+	0.0166007i
$313$	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
$315$	−6.66023	+	27.7023i	−0.375262	+	1.56085i
$316$	−6.61386			−0.372059
$317$	−5.24858	−	3.03027i	−0.294789	−	0.170197i	0.345310	−	0.938489i	$-0.387774\pi$
$317$	−5.24858	−	3.03027i	−0.294789	−	0.170197i	−0.640100	+	0.768292i	$0.721107\pi$
$318$	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	−0.859662	−	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
$333$	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	−0.106221	−	0.994343i	$-0.533875\pi$
$347$	13.0730	−	7.54769i	0.701794	−	0.405181i	0.808015	+	0.589161i	$0.200542\pi$
$348$	6.49198	−	0.275230i	0.348007	−	0.0147539i
$349$		−	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	0.711616	−	0.702568i	$-0.247964\pi$
$353$	−4.74656	−	8.22129i	−0.252634	−	0.437575i	−0.964250	+	0.264993i	$0.914630\pi$
$354$	−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	0.340709	−	0.940169i	$-0.389333\pi$
$359$	−5.74380	−	3.31618i	−0.303146	−	0.175021i	−0.643855	+	0.765147i	$0.722666\pi$
$360$	−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	−0.976476	−	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
$369$	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	−0.751816	−	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
$375$	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	−0.795828	−	0.605522i	$-0.792964\pi$
$383$	2.47533	−	4.28740i	0.126483	−	0.219076i	0.922312	+	0.386446i	$0.126298\pi$
$384$	−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	−0.569807	−	0.821779i	$-0.692982\pi$
$389$	−2.82098	+	1.62869i	−0.143029	+	0.0825779i	0.426778	+	0.904357i	$0.359649\pi$
$390$	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	0.687056	−	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
$399$	30.0234	−	7.51563i	1.50305	−	0.376252i
$400$	7.88536			0.394268
$401$	6.64897	+	3.83879i	0.332034	+	0.191700i	0.656744	−	0.754114i	$-0.271933\pi$
$401$	6.64897	+	3.83879i	0.332034	+	0.191700i	−0.324710	+	0.945814i	$0.605267\pi$
$402$	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	−0.217625	−	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
$411$	−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	−0.0926100	−	0.995702i	$-0.529521\pi$
$431$	15.0179	−	8.67061i	0.723389	−	0.417649i	0.815999	+	0.578054i	$0.196188\pi$
$432$	−4.79305	−	2.00666i	−0.230606	−	0.0965455i
$433$			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
$438$	8.31720	+	4.34302i	0.397411	+	0.207518i
$439$	−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
$441$	0.693461	−	20.9885i	0.0330219	−	0.999455i
$442$	−0.767270			−0.0364953
$443$	−12.5406	−	7.24029i	−0.595820	−	0.343997i	0.171576	−	0.985171i	$-0.445114\pi$
$443$	−12.5406	−	7.24029i	−0.595820	−	0.343997i	−0.767395	+	0.641174i	$0.778448\pi$
$444$	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	$0.138967\pi$
$449$			17.9197i			0.845683i	−0.906204	+	0.422842i	$0.861033\pi$
$450$	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	−0.677065	−	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
$459$	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	0.387544	+	0.921851i	$0.373324\pi$
$467$	−13.0650	+	22.6292i	−0.604575	+	1.04715i	−0.992119	+	0.125303i	$0.960010\pi$
$468$	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	−0.957770	−	0.287535i	$-0.907164\pi$
$479$	−15.9308	−	27.5930i	−0.727898	−	1.26076i	0.229872	−	0.973221i	$-0.426169\pi$
$480$	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	−0.625132	−	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	$-0.815902\pi$
$491$		−	24.2260i		−	1.09331i	0.837359	−	0.546653i	$-0.184098\pi$
$492$	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	−0.660074	−	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
$501$	−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	−0.582271	−	0.812995i	$-0.697836\pi$
$509$	9.31633	−	16.1364i	0.412939	−	0.715231i	0.995210	+	0.0977636i	$0.0311689\pi$
$510$	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	0.586798	−	0.809733i	$-0.300388\pi$
$521$	−9.30936	−	16.1243i	−0.407850	−	0.706418i	−0.994649	+	0.103316i	$0.967055\pi$
$522$	11.2142	−	0.952567i	0.490831	−	0.0416927i
$523$	−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
$525$	−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	0.432093	+	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
$543$	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	0.204936	−	0.978775i	$-0.434301\pi$
$557$	27.2601	−	15.7386i	1.15505	−	0.666868i	0.950112	+	0.311908i	$0.100968\pi$
$558$	−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	0.614924	−	0.788587i	$-0.289187\pi$
$563$	−8.90911	−	15.4310i	−0.375474	−	0.650340i	−0.990398	+	0.138246i	$0.955853\pi$
$564$	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	0.398155	−	0.917318i	$-0.369651\pi$
$569$	−4.70368	−	2.71567i	−0.197189	−	0.113847i	−0.595344	+	0.803471i	$0.702984\pi$
$570$	−37.2220	−	19.4363i	−1.55906	−	0.814099i
$571$	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
$576$	−1.71451	−	2.46180i	−0.0714381	−	0.102575i
$577$	−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
$579$	−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	−0.144709	−	0.989474i	$-0.546225\pi$
$593$	19.1052	−	33.0911i	0.784555	−	1.35889i	0.929264	−	0.369416i	$-0.120442\pi$
$594$	−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	−0.376867	−	0.926267i	$-0.622999\pi$
$599$	5.79727	−	3.34705i	0.236870	−	0.136757i	0.613737	+	0.789510i	$0.289665\pi$
$600$	13.6456	−	0.578509i	0.557079	−	0.0236175i
$601$			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
$606$	3.90997	−	7.48787i	0.158832	−	0.304174i
$607$	−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
$609$	−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	0.997099	−	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	$0.339840\pi$
$617$			43.5220i			1.75213i	−0.482194	+	0.876065i	$0.660160\pi$
$618$	0.694560	+	16.3829i	0.0279393	+	0.659019i
$619$	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
$621$	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	0.245480	−	0.969402i	$-0.421054\pi$
$641$	30.5777	−	17.6540i	1.20775	−	0.697293i	0.962267	+	0.272109i	$0.0877210\pi$
$642$	−1.32249	−	31.1942i	−0.0521944	−	1.23114i
$643$		−	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	0.999466	−	0.0326902i	$-0.0104075\pi$
$647$	11.9912	+	20.7693i	0.471422	+	0.816527i	−0.528043	+	0.849217i	$0.677074\pi$
$648$	−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	0.977156	−	0.212522i	$-0.0681677\pi$
$653$	32.7520	+	18.9094i	1.28169	+	0.739981i	0.304529	+	0.952503i	$0.401501\pi$
$654$	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	$0.254829\pi$
$659$			36.8508i			1.43550i	−0.696298	+	0.717752i	$0.745171\pi$
$660$	6.21182	−	0.263352i	0.241795	−	0.0102510i
$661$	−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
$663$	−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	−0.913409	−	0.407042i	$-0.866560\pi$
$677$	−2.71109	+	4.69574i	−0.104195	+	0.180472i	0.809214	+	0.587514i	$0.199893\pi$
$678$	−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	−0.0574741	−	0.998347i	$-0.518305\pi$
$683$	20.3425	−	11.7447i	0.778383	−	0.449399i	0.835857	+	0.548948i	$0.184971\pi$
$684$	−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	0.142207	−	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
$693$	−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	$0.0371419\pi$
$701$			6.16477i			0.232840i	−0.993200	+	0.116420i	$0.962858\pi$
$702$	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	−0.801334	−	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
$711$	−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	0.463398	+	0.886150i	$0.346630\pi$
$719$	−14.3651	+	24.8812i	−0.535730	+	0.927911i	−0.999128	+	0.0417607i	$0.986703\pi$
$720$	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	$-0.997463\pi$
$727$		−	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
$732$	−6.93185	+	13.2750i	−0.256209	+	0.490658i
$733$	−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
$735$	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	0.886476	−	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	$0.243444\pi$
$743$			37.7466i			1.38479i	−0.721520	+	0.692394i	$0.756556\pi$
$744$	−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	0.135543	+	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
$753$	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	0.121568	−	0.992583i	$-0.461208\pi$
$761$	25.3900	−	43.9767i	0.920386	−	1.59416i	0.798818	−	0.601573i	$-0.205459\pi$
$762$	−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	$0.370493\pi$
$769$			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	0.738182	−	0.674602i	$-0.235685\pi$
$773$	−5.98128	−	10.3599i	−0.215132	−	0.372619i	−0.953313	+	0.301983i	$0.902351\pi$
$774$	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	−0.309614	−	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
$789$	0.303999	−	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	−0.672832	−	0.739796i	$-0.734922\pi$
$809$	−10.4831	+	6.05241i	−0.368566	+	0.212791i	0.304266	+	0.952587i	$0.401589\pi$
$810$	−5.44913	−	31.8437i	−0.191463	−	1.11887i
$811$			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
$816$	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	0.672860	−	0.739770i	$-0.265066\pi$
$821$	10.5624	+	6.09822i	0.368631	+	0.212829i	−0.304229	+	0.952599i	$0.598399\pi$
$822$	−4.90445	−	2.56097i	−0.171062	−	0.0893243i
$823$	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	$-0.605419\pi$
$827$		−	54.3898i		−	1.89132i	0.325161	−	0.945659i	$-0.394581\pi$
$828$	5.08217	−	3.53947i	0.176618	−	0.123005i
$829$	−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
$831$	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	$-0.973106\pi$
$853$		−	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	$-0.930605\pi$
$857$	−19.7742	−	34.2500i	−0.675475	−	1.16996i	0.300854	−	0.953670i	$-0.402728\pi$
$858$	−0.293226	+	0.561549i	−0.0100106	+	0.0191710i
$859$	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
$861$	11.8222	−	11.4380i	0.402899	−	0.389807i
$862$	17.3412			0.590644
$863$	−29.0704	−	16.7838i	−0.989568	−	0.571327i	−0.0844227	−	0.996430i	$-0.526905\pi$
$863$	−29.0704	−	16.7838i	−0.989568	−	0.571327i	−0.905145	+	0.425103i	$0.860238\pi$
$864$	−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	−0.396398	−	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
$879$	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	−0.996778	−	0.0802098i	$-0.974441\pi$
$887$	−12.7745	+	22.1261i	−0.428925	+	0.742920i	0.567853	+	0.823130i	$0.307774\pi$
$888$	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	0.883318	−	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	$0.192780\pi$
$911$			34.3652i			1.13857i	−0.822140	+	0.569286i	$0.807220\pi$
$912$	−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	−0.00779650	+	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
$921$	−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	−0.482032	−	0.876154i	$-0.660101\pi$
$929$	15.7809	−	27.3334i	0.517756	−	0.896779i	0.999787	−	0.0206252i	$-0.00656569\pi$
$930$	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	$0.171920\pi$
$937$			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	0.652512	−	0.757778i	$-0.273715\pi$
$941$	−10.1230	−	17.5335i	−0.329999	−	0.571575i	−0.982511	+	0.186203i	$0.940382\pi$
$942$	−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	0.311586	−	0.950218i	$-0.399140\pi$
$947$	−10.9410	−	6.31679i	−0.355535	−	0.205268i	−0.667120	+	0.744950i	$0.732473\pi$
$948$	−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	$0.0158610\pi$
$953$			3.07523i			0.0996166i	−0.998759	+	0.0498083i	$0.984139\pi$
$954$	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	0.395979	+	0.918259i	$0.370405\pi$
$971$	−18.6107	+	32.2347i	−0.597246	+	1.03446i	−0.993226	+	0.116202i	$0.962928\pi$
$972$	−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	−0.831345	−	0.555757i	$-0.812428\pi$
$977$	−23.9340	+	13.8183i	−0.765717	+	0.442087i	0.0656276	+	0.997844i	$0.479095\pi$
$978$	−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	0.878727	−	0.477324i	$-0.158393\pi$
$983$	0.814813	+	1.41130i	0.0259885	+	0.0450134i	−0.852739	+	0.522338i	$0.825060\pi$
$984$	−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	0.988561	−	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
$996$	−0.559389	−	13.1946i	−0.0177249	−	0.418087i
$997$	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
$999$	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.89.10	yes	20
3.2	odd	2	inner	462.2.k.g.89.4	✓	20
7.3	odd	6	inner	462.2.k.g.353.4	yes	20
21.17	even	6	inner	462.2.k.g.353.10	yes	20

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.53534 + 0.801712i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.79481 + 3.10870i) q^{5} +(0.928784 + 1.46197i) q^{6} +(0.833981 - 2.51087i) q^{7} +1.00000i q^{8} +(1.71451 + 2.46180i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 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

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