LMFDB - Embedded newform 273.2.bd.b.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.3
Root			$1.33452 + 1.10411i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44724 + 0.835563i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.396329 - 0.686463i) q^{4} -2.68351i q^{5} +(-1.44724 - 0.835563i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.01762i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.44724 + 0.835563i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.396329 - 0.686463i) q^{4} -2.68351i q^{5} +(-1.44724 - 0.835563i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.01762i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.24224 + 3.88368i) q^{10} +(5.01670 - 2.89639i) q^{11} +0.792659 q^{12} +(-2.37557 - 2.71232i) q^{13} -1.67113 q^{14} +(2.32399 - 1.34176i) q^{15} +(2.47850 + 4.29290i) q^{16} +(0.868612 - 1.50448i) q^{17} -1.67113i q^{18} +(1.43393 + 0.827883i) q^{19} +(-1.84213 - 1.06356i) q^{20} +1.00000i q^{21} +(-4.84024 + 8.38353i) q^{22} +(1.17174 + 2.02951i) q^{23} +(1.74731 - 1.00881i) q^{24} -2.20124 q^{25} +(5.70432 + 1.94043i) q^{26} -1.00000 q^{27} +(0.686463 - 0.396329i) q^{28} +(-0.860801 - 1.49095i) q^{29} +(-2.24224 + 3.88368i) q^{30} +9.12637i q^{31} +(-3.67935 - 2.12427i) q^{32} +(5.01670 + 2.89639i) q^{33} +2.90312i q^{34} +(1.34176 - 2.32399i) q^{35} +(0.396329 + 0.686463i) q^{36} +(7.42886 - 4.28906i) q^{37} -2.76699 q^{38} +(1.16115 - 3.41346i) q^{39} -5.41430 q^{40} +(0.382603 - 0.220896i) q^{41} +(-0.835563 - 1.44724i) q^{42} +(5.56088 - 9.63172i) q^{43} -4.59170i q^{44} +(2.32399 + 1.34176i) q^{45} +(-3.39157 - 1.95812i) q^{46} +3.16304i q^{47} +(-2.47850 + 4.29290i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.18572 - 1.83928i) q^{50} +1.73722 q^{51} +(-2.80341 + 0.555770i) q^{52} -12.8205 q^{53} +(1.44724 - 0.835563i) q^{54} +(-7.77251 - 13.4624i) q^{55} +(1.00881 - 1.74731i) q^{56} +1.65577i q^{57} +(2.49157 + 1.43851i) q^{58} +(-4.85874 - 2.80519i) q^{59} -2.12711i q^{60} +(-3.22508 + 5.58600i) q^{61} +(-7.62565 - 13.2080i) q^{62} +(-0.866025 + 0.500000i) q^{63} -2.81417 q^{64} +(-7.27854 + 6.37488i) q^{65} -9.68047 q^{66} +(4.58974 - 2.64989i) q^{67} +(-0.688513 - 1.19254i) q^{68} +(-1.17174 + 2.02951i) q^{69} +4.48449i q^{70} +(-5.89229 - 3.40191i) q^{71} +(1.74731 + 1.00881i) q^{72} +0.600675i q^{73} +(-7.16755 + 12.4146i) q^{74} +(-1.10062 - 1.90633i) q^{75} +(1.13662 - 0.656229i) q^{76} +5.79279 q^{77} +(1.17170 + 5.91030i) q^{78} +6.10718 q^{79} +(11.5200 - 6.65110i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.369145 + 0.639378i) q^{82} -11.8380i q^{83} +(0.686463 + 0.396329i) q^{84} +(-4.03729 - 2.33093i) q^{85} +18.5858i q^{86} +(0.860801 - 1.49095i) q^{87} +(-5.84381 - 10.1218i) q^{88} +(-1.70843 + 0.986363i) q^{89} -4.48449 q^{90} +(-0.701147 - 3.53672i) q^{91} +1.85758 q^{92} +(-7.90367 + 4.56319i) q^{93} +(-2.64292 - 4.57767i) q^{94} +(2.22163 - 3.84798i) q^{95} -4.24855i q^{96} +(-2.32541 - 1.34257i) q^{97} +(-1.44724 - 0.835563i) q^{98} +5.79279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.44724	+	0.835563i	−1.02335	+	0.590832i	−0.915073	−	0.403289i	$-0.867867\pi$
$2$	−1.44724	+	0.835563i	−1.02335	+	0.590832i	−0.108278	+	0.994121i	$0.534534\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.396329	−	0.686463i	0.198165	−	0.343231i
$5$		−	2.68351i		−	1.20010i	−0.799961	−	0.600052i	$-0.795147\pi$
$5$		−	2.68351i		−	1.20010i	0.799961	−	0.600052i	$-0.204853\pi$
$6$	−1.44724	−	0.835563i	−0.590832	−	0.341117i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	2.01762i		−	0.713336i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.24224	+	3.88368i	0.709060	+	1.22813i
$11$	5.01670	−	2.89639i	1.51259	−	0.873295i	0.512700	−	0.858568i	$-0.328645\pi$
$11$	5.01670	−	2.89639i	1.51259	−	0.873295i	0.999892	−	0.0147278i	$-0.00468818\pi$
$12$	0.792659			0.228821
$13$	−2.37557	−	2.71232i	−0.658865	−	0.752261i
$13$	−2.37557	−	2.71232i	−0.658865	−	0.752261i
$14$	−1.67113			−0.446627
$15$	2.32399	−	1.34176i	0.600052	−	0.346440i
$16$	2.47850	+	4.29290i	0.619626	+	1.07322i
$17$	0.868612	−	1.50448i	0.210669	−	0.364890i	−0.741255	−	0.671224i	$-0.765769\pi$
$17$	0.868612	−	1.50448i	0.210669	−	0.364890i	0.951924	+	0.306334i	$0.0991023\pi$
$18$		−	1.67113i		−	0.393888i
$19$	1.43393	+	0.827883i	0.328967	+	0.189929i	0.655382	−	0.755297i	$-0.272507\pi$
$19$	1.43393	+	0.827883i	0.328967	+	0.189929i	−0.326415	+	0.945226i	$0.605841\pi$
$20$	−1.84213	−	1.06356i	−0.411913	−	0.237818i
$21$			1.00000i			0.218218i
$22$	−4.84024	+	8.38353i	−1.03194	+	1.78738i
$23$	1.17174	+	2.02951i	0.244325	+	0.423183i	0.961942	−	0.273255i	$-0.0881004\pi$
$23$	1.17174	+	2.02951i	0.244325	+	0.423183i	−0.717617	+	0.696438i	$0.754767\pi$
$24$	1.74731	−	1.00881i	0.356668	−	0.205922i
$25$	−2.20124			−0.440249
$26$	5.70432	+	1.94043i	1.11871	+	0.380549i
$27$	−1.00000			−0.192450
$28$	0.686463	−	0.396329i	0.129729	−	0.0748992i
$29$	−0.860801	−	1.49095i	−0.159847	−	0.276863i	0.774966	−	0.632002i	$-0.217767\pi$
$29$	−0.860801	−	1.49095i	−0.159847	−	0.276863i	−0.934813	+	0.355140i	$0.884433\pi$
$30$	−2.24224	+	3.88368i	−0.409376	+	0.709060i
$31$			9.12637i			1.63914i	0.572976	+	0.819572i	$0.305789\pi$
$31$			9.12637i			1.63914i	−0.572976	+	0.819572i	$0.694211\pi$
$32$	−3.67935	−	2.12427i	−0.650423	−	0.375522i
$33$	5.01670	+	2.89639i	0.873295	+	0.504197i
$34$			2.90312i			0.497881i
$35$	1.34176	−	2.32399i	0.226798	−	0.392826i
$36$	0.396329	+	0.686463i	0.0660549	+	0.114410i
$37$	7.42886	−	4.28906i	1.22130	−	0.705117i	0.256103	−	0.966649i	$-0.417561\pi$
$37$	7.42886	−	4.28906i	1.22130	−	0.705117i	0.965195	+	0.261533i	$0.0842280\pi$
$38$	−2.76699			−0.448865
$39$	1.16115	−	3.41346i	0.185933	−	0.546592i
$40$	−5.41430			−0.856077
$41$	0.382603	−	0.220896i	0.0597526	−	0.0344982i	−0.469826	−	0.882759i	$-0.655683\pi$
$41$	0.382603	−	0.220896i	0.0597526	−	0.0344982i	0.529579	+	0.848261i	$0.322350\pi$
$42$	−0.835563	−	1.44724i	−0.128930	−	0.223313i
$43$	5.56088	−	9.63172i	0.848026	−	1.46882i	−0.0349412	−	0.999389i	$-0.511124\pi$
$43$	5.56088	−	9.63172i	0.848026	−	1.46882i	0.882967	−	0.469435i	$-0.155542\pi$
$44$		−	4.59170i		−	0.692225i
$45$	2.32399	+	1.34176i	0.346440	+	0.200017i
$46$	−3.39157	−	1.95812i	−0.500060	−	0.288710i
$47$			3.16304i			0.461377i	0.973028	+	0.230688i	$0.0740978\pi$
$47$			3.16304i			0.461377i	−0.973028	+	0.230688i	$0.925902\pi$
$48$	−2.47850	+	4.29290i	−0.357741	+	0.619626i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.18572	−	1.83928i	0.450529	−	0.260113i
$51$	1.73722			0.243260
$52$	−2.80341	+	0.555770i	−0.388763	+	0.0770715i
$53$	−12.8205			−1.76103			−0.880514	−	0.474020i	$-0.842802\pi$
$53$	−12.8205			−1.76103			−0.880514	+	0.474020i	$0.842802\pi$
$54$	1.44724	−	0.835563i	0.196944	−	0.113706i
$55$	−7.77251	−	13.4624i	−1.04804	−	1.81527i
$56$	1.00881	−	1.74731i	0.134808	−	0.233494i
$57$			1.65577i			0.219311i
$58$	2.49157	+	1.43851i	0.327159	+	0.188885i
$59$	−4.85874	−	2.80519i	−0.632554	−	0.365205i	0.149186	−	0.988809i	$-0.452335\pi$
$59$	−4.85874	−	2.80519i	−0.632554	−	0.365205i	−0.781741	+	0.623604i	$0.785668\pi$
$60$		−	2.12711i		−	0.274609i
$61$	−3.22508	+	5.58600i	−0.412929	+	0.715215i	−0.995209	−	0.0977743i	$-0.968828\pi$
$61$	−3.22508	+	5.58600i	−0.412929	+	0.715215i	0.582279	+	0.812989i	$0.302161\pi$
$62$	−7.62565	−	13.2080i	−0.968459	−	1.67742i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−2.81417			−0.351771
$65$	−7.27854	+	6.37488i	−0.902791	+	0.790706i
$66$	−9.68047			−1.19158
$67$	4.58974	−	2.64989i	0.560726	−	0.323736i	−0.192711	−	0.981256i	$-0.561728\pi$
$67$	4.58974	−	2.64989i	0.560726	−	0.323736i	0.753437	+	0.657520i	$0.228395\pi$
$68$	−0.688513	−	1.19254i	−0.0834945	−	0.144617i
$69$	−1.17174	+	2.02951i	−0.141061	+	0.244325i
$70$			4.48449i			0.535999i
$71$	−5.89229	−	3.40191i	−0.699286	−	0.403733i	0.107796	−	0.994173i	$-0.465621\pi$
$71$	−5.89229	−	3.40191i	−0.699286	−	0.403733i	−0.807081	+	0.590440i	$0.798954\pi$
$72$	1.74731	+	1.00881i	0.205922	+	0.118889i
$73$			0.600675i			0.0703037i	0.999382	+	0.0351518i	$0.0111915\pi$
$73$			0.600675i			0.0703037i	−0.999382	+	0.0351518i	$0.988809\pi$
$74$	−7.16755	+	12.4146i	−0.833211	+	1.44316i
$75$	−1.10062	−	1.90633i	−0.127089	−	0.220124i
$76$	1.13662	−	0.656229i	0.130379	−	0.0752746i
$77$	5.79279			0.660149
$78$	1.17170	+	5.91030i	0.132669	+	0.669210i
$79$	6.10718			0.687112			0.343556	−	0.939132i	$-0.388369\pi$
$79$	6.10718			0.687112			0.343556	+	0.939132i	$0.388369\pi$
$80$	11.5200	−	6.65110i	1.28798	−	0.743616i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.369145	+	0.639378i	−0.0407653	+	0.0706075i
$83$		−	11.8380i		−	1.29939i	−0.760194	−	0.649696i	$-0.774896\pi$
$83$		−	11.8380i		−	1.29939i	0.760194	−	0.649696i	$-0.225104\pi$
$84$	0.686463	+	0.396329i	0.0748992	+	0.0432431i
$85$	−4.03729	−	2.33093i	−0.437906	−	0.252825i
$86$			18.5858i			2.00416i
$87$	0.860801	−	1.49095i	0.0922876	−	0.159847i
$88$	−5.84381	−	10.1218i	−0.622953	−	1.07899i
$89$	−1.70843	+	0.986363i	−0.181093	+	0.104554i	−0.587806	−	0.809002i	$-0.700008\pi$
$89$	−1.70843	+	0.986363i	−0.181093	+	0.104554i	0.406713	+	0.913556i	$0.366675\pi$
$90$	−4.48449			−0.472706
$91$	−0.701147	−	3.53672i	−0.0735002	−	0.370749i
$92$	1.85758			0.193666
$93$	−7.90367	+	4.56319i	−0.819572	+	0.473180i
$94$	−2.64292	−	4.57767i	−0.272596	−	0.472150i
$95$	2.22163	−	3.84798i	0.227935	−	0.394795i
$96$		−	4.24855i		−	0.433616i
$97$	−2.32541	−	1.34257i	−0.236109	−	0.136318i	0.377278	−	0.926100i	$-0.376860\pi$
$97$	−2.32541	−	1.34257i	−0.236109	−	0.136318i	−0.613387	+	0.789782i	$0.710193\pi$
$98$	−1.44724	−	0.835563i	−0.146193	−	0.0844046i
$99$			5.79279i			0.582197i
$100$	−0.872418	+	1.51107i	−0.0872418	+	0.151107i
$101$	8.73866	+	15.1358i	0.869530	+	1.50607i	0.862478	+	0.506094i	$0.168911\pi$
$101$	8.73866	+	15.1358i	0.869530	+	1.50607i	0.00705156	+	0.999975i	$0.497755\pi$
$102$	−2.51418	+	1.45156i	−0.248940	+	0.143726i
$103$	−14.0766			−1.38701			−0.693503	−	0.720453i	$-0.743934\pi$
$103$	−14.0766			−1.38701			−0.693503	+	0.720453i	$0.743934\pi$
$104$	−5.47242	+	4.79300i	−0.536615	+	0.469992i
$105$	2.68351			0.261884
$106$	18.5543	−	10.7123i	1.80215	−	1.04047i
$107$	1.66741	+	2.88804i	0.161195	+	0.279198i	0.935297	−	0.353863i	$-0.115132\pi$
$107$	1.66741	+	2.88804i	0.161195	+	0.279198i	−0.774103	+	0.633060i	$0.781799\pi$
$108$	−0.396329	+	0.686463i	−0.0381368	+	0.0660549i
$109$			10.6928i			1.02418i	0.858931	+	0.512092i	$0.171129\pi$
$109$			10.6928i			1.02418i	−0.858931	+	0.512092i	$0.828871\pi$
$110$	22.4973	+	12.9888i	2.14504	+	1.23844i
$111$	7.42886	+	4.28906i	0.705117	+	0.407099i
$112$			4.95701i			0.468393i
$113$	−5.71922	+	9.90598i	−0.538019	+	0.931876i	0.460992	+	0.887405i	$0.347494\pi$
$113$	−5.71922	+	9.90598i	−0.538019	+	0.931876i	−0.999011	+	0.0444719i	$0.985839\pi$
$114$	−1.38350	−	2.39628i	−0.129576	−	0.224433i
$115$	5.44623	−	3.14438i	0.507863	−	0.293215i
$116$	−1.36464			−0.126704
$117$	3.53672	−	0.701147i	0.326970	−	0.0648211i
$118$	9.37566			0.863100
$119$	1.50448	−	0.868612i	0.137916	−	0.0796256i
$120$	−2.70715	−	4.68893i	−0.247128	−	0.428038i
$121$	11.2782	−	19.5344i	1.02529	−	1.77585i
$122$		−	10.7790i		−	0.975887i
$123$	0.382603	+	0.220896i	0.0344982	+	0.0199175i
$124$	6.26491	+	3.61705i	0.562606	+	0.324821i
$125$		−	7.51050i		−	0.671760i
$126$	0.835563	−	1.44724i	0.0744378	−	0.128930i
$127$	7.20442	+	12.4784i	0.639289	+	1.10728i	0.985589	+	0.169157i	$0.0541045\pi$
$127$	7.20442	+	12.4784i	0.639289	+	1.10728i	−0.346300	+	0.938124i	$0.612562\pi$
$128$	11.4315	−	6.59996i	1.01041	−	0.583359i
$129$	11.1218			0.979216
$130$	5.20716	−	15.3076i	0.456698	−	1.34257i
$131$	−3.76222			−0.328707			−0.164353	−	0.986402i	$-0.552554\pi$
$131$	−3.76222			−0.328707			−0.164353	+	0.986402i	$0.552554\pi$
$132$	3.97653	−	2.29585i	0.346113	−	0.199828i
$133$	0.827883	+	1.43393i	0.0717865	+	0.124338i
$134$	−4.42830	+	7.67004i	−0.382547	+	0.662590i
$135$			2.68351i			0.230960i
$136$	−3.03547	−	1.75253i	−0.260289	−	0.150278i
$137$	18.6282	+	10.7550i	1.59152	+	0.918863i	0.993047	+	0.117719i	$0.0375582\pi$
$137$	18.6282	+	10.7550i	1.59152	+	0.918863i	0.598471	+	0.801144i	$0.295775\pi$
$138$		−	3.91625i		−	0.333373i
$139$	−1.99589	+	3.45699i	−0.169289	+	0.293218i	−0.938170	−	0.346174i	$-0.887481\pi$
$139$	−1.99589	+	3.45699i	−0.169289	+	0.293218i	0.768881	+	0.639392i	$0.220814\pi$
$140$	−1.06356	−	1.84213i	−0.0898868	−	0.155689i
$141$	−2.73927	+	1.58152i	−0.230688	+	0.133188i
$142$	11.3700			0.954153
$143$	−19.7735	−	6.72629i	−1.65354	−	0.562481i
$144$	−4.95701			−0.413084
$145$	−4.00099	+	2.30997i	−0.332264	+	0.191833i
$146$	−0.501902	−	0.869319i	−0.0415377	−	0.0719454i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$		−	6.79952i		−	0.558917i
$149$	9.07552	+	5.23976i	0.743496	+	0.429258i	0.823339	−	0.567550i	$-0.192109\pi$
$149$	9.07552	+	5.23976i	0.743496	+	0.429258i	−0.0798431	+	0.996807i	$0.525442\pi$
$150$	3.18572	+	1.83928i	0.260113	+	0.150176i
$151$			17.5261i			1.42625i	0.701035	+	0.713126i	$0.252721\pi$
$151$			17.5261i			1.42625i	−0.701035	+	0.713126i	$0.747279\pi$
$152$	1.67035	−	2.89313i	0.135483	−	0.234664i
$153$	0.868612	+	1.50448i	0.0702232	+	0.121630i
$154$	−8.38353	+	4.84024i	−0.675564	+	0.390037i
$155$	24.4907			1.96714
$156$	−1.88302	−	2.14994i	−0.150762	−	0.172133i
$157$	−18.5395			−1.47961			−0.739805	−	0.672822i	$-0.765082\pi$
$157$	−18.5395			−1.47961			−0.739805	+	0.672822i	$0.765082\pi$
$158$	−8.83854	+	5.10293i	−0.703156	+	0.405967i
$159$	−6.41024	−	11.1029i	−0.508365	−	0.880514i
$160$	−5.70052	+	9.87358i	−0.450665	+	0.780575i
$161$			2.34348i			0.184692i
$162$	1.44724	+	0.835563i	0.113706	+	0.0656480i
$163$	−15.4776	−	8.93600i	−1.21230	−	0.699921i	−0.249040	−	0.968493i	$-0.580115\pi$
$163$	−15.4776	−	8.93600i	−1.21230	−	0.699921i	−0.963260	+	0.268572i	$0.913448\pi$
$164$		−	0.350191i		−	0.0273453i
$165$	7.77251	−	13.4624i	0.605089	−	1.04804i
$166$	9.89141	+	17.1324i	0.767722	+	1.32973i
$167$	−0.859414	+	0.496183i	−0.0665034	+	0.0383958i	−0.532883	−	0.846189i	$-0.678891\pi$
$167$	−0.859414	+	0.496183i	−0.0665034	+	0.0383958i	0.466380	+	0.884585i	$0.345558\pi$
$168$	2.01762			0.155663
$169$	−1.71332	+	12.8866i	−0.131794	+	0.991277i
$170$	7.79056			0.597509
$171$	−1.43393	+	0.827883i	−0.109656	+	0.0633098i
$172$	−4.40788	−	7.63467i	−0.336098	−	0.582138i
$173$	−10.3417	+	17.9123i	−0.786265	+	1.36185i	0.141976	+	0.989870i	$0.454654\pi$
$173$	−10.3417	+	17.9123i	−0.786265	+	1.36185i	−0.928241	+	0.371980i	$0.878679\pi$
$174$			2.87701i			0.218106i
$175$	−1.90633	−	1.10062i	−0.144105	−	0.0831992i
$176$	24.8678	+	14.3574i	1.87448	+	1.08223i
$177$		−	5.61039i		−	0.421703i
$178$	1.64834	−	2.85500i	0.123548	−	0.213991i
$179$	−1.55711	−	2.69700i	−0.116384	−	0.201583i	0.801948	−	0.597394i	$-0.203797\pi$
$179$	−1.55711	−	2.69700i	−0.116384	−	0.201583i	−0.918332	+	0.395811i	$0.870464\pi$
$180$	1.84213	−	1.06356i	0.137304	−	0.0792727i
$181$	18.3738			1.36572			0.682858	−	0.730551i	$-0.260737\pi$
$181$	18.3738			1.36572			0.682858	+	0.730551i	$0.260737\pi$
$182$	3.96988	+	4.53262i	0.294267	+	0.335980i
$183$	−6.45016			−0.476810
$184$	4.09478	−	2.36412i	0.301871	−	0.174286i
$185$	−11.5097	−	19.9355i	−0.846213	−	1.46568i
$186$	7.62565	−	13.2080i	0.559140	−	0.968459i
$187$		−	10.0634i		−	0.735907i
$188$	2.17131	+	1.25361i	0.158359	+	0.0914286i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$			7.42526i			0.538685i
$191$	−2.00723	+	3.47662i	−0.145238	+	0.251559i	−0.929462	−	0.368919i	$-0.879728\pi$
$191$	−2.00723	+	3.47662i	−0.145238	+	0.251559i	0.784224	+	0.620478i	$0.213061\pi$
$192$	−1.40708	−	2.43714i	−0.101547	−	0.175885i
$193$	4.85461	−	2.80281i	0.349442	−	0.201751i	−0.314997	−	0.949093i	$-0.602004\pi$
$193$	4.85461	−	2.80281i	0.349442	−	0.201751i	0.664440	+	0.747342i	$0.268670\pi$
$194$	4.48722			0.322163
$195$	−9.16007	−	3.11596i	−0.655967	−	0.223139i
$196$	0.792659			0.0566185
$197$	−14.9461	+	8.62914i	−1.06487	+	0.614801i	−0.926774	−	0.375618i	$-0.877430\pi$
$197$	−14.9461	+	8.62914i	−1.06487	+	0.614801i	−0.138092	+	0.990419i	$0.544097\pi$
$198$	−4.84024	−	8.38353i	−0.343981	−	0.595792i
$199$	−12.5894	+	21.8055i	−0.892439	+	1.54575i	−0.0554975	+	0.998459i	$0.517674\pi$
$199$	−12.5894	+	21.8055i	−0.892439	+	1.54575i	−0.836942	+	0.547292i	$0.815659\pi$
$200$			4.44127i			0.314045i
$201$	4.58974	+	2.64989i	0.323736	+	0.186909i
$202$	−25.2938	−	14.6034i	−1.77967	−	1.02749i
$203$		−	1.72160i		−	0.120833i
$204$	0.688513	−	1.19254i	0.0482056	−	0.0834945i
$205$	−0.592778	−	1.02672i	−0.0414014	−	0.0717093i
$206$	20.3721	−	11.7619i	1.41939	−	0.819488i
$207$	−2.34348			−0.162883
$208$	5.75583	−	16.9206i	0.399095	−	1.17323i
$209$	9.59149			0.663458
$210$	−3.88368	+	2.24224i	−0.267999	+	0.154729i
$211$	−0.846689	−	1.46651i	−0.0582885	−	0.100959i	0.835409	−	0.549629i	$-0.185231\pi$
$211$	−0.846689	−	1.46651i	−0.0582885	−	0.100959i	−0.893697	+	0.448671i	$0.851898\pi$
$212$	−5.08113	+	8.80078i	−0.348974	+	0.604440i
$213$		−	6.80383i		−	0.466191i
$214$	−4.82628	−	2.78645i	−0.329918	−	0.190478i
$215$	−25.8469	−	14.9227i	−1.76274	−	1.01772i
$216$			2.01762i			0.137282i
$217$	−4.56319	+	7.90367i	−0.309769	+	0.536536i
$218$	−8.93450	−	15.4750i	−0.605121	−	1.04810i
$219$	−0.520200	+	0.300338i	−0.0351518	+	0.0202949i
$220$	−12.3219			−0.830742
$221$	−6.14408	+	1.21805i	−0.413295	+	0.0819349i
$222$	−14.3351			−0.962109
$223$	−5.34489	+	3.08587i	−0.357920	+	0.206645i	−0.668168	−	0.744010i	$-0.732921\pi$
$223$	−5.34489	+	3.08587i	−0.357920	+	0.206645i	0.310248	+	0.950656i	$0.399588\pi$
$224$	−2.12427	−	3.67935i	−0.141934	−	0.245837i
$225$	1.10062	−	1.90633i	0.0733748	−	0.127089i
$226$		−	19.1151i		−	1.27152i
$227$	−11.2554	−	6.49833i	−0.747050	−	0.431309i	0.0775773	−	0.996986i	$-0.475282\pi$
$227$	−11.2554	−	6.49833i	−0.747050	−	0.431309i	−0.824627	+	0.565677i	$0.808615\pi$
$228$	1.13662	+	0.656229i	0.0752746	+	0.0434598i
$229$		−	16.0448i		−	1.06027i	−0.847913	−	0.530136i	$-0.822141\pi$
$229$		−	16.0448i		−	1.06027i	0.847913	−	0.530136i	$-0.177859\pi$
$230$	−5.25465	+	9.10132i	−0.346482	+	0.600124i
$231$	2.89639	+	5.01670i	0.190569	+	0.330075i
$232$	−3.00817	+	1.73677i	−0.197496	+	0.114024i
$233$	−9.11345			−0.597042			−0.298521	−	0.954403i	$-0.596493\pi$
$233$	−9.11345			−0.597042			−0.298521	+	0.954403i	$0.596493\pi$
$234$	−4.53262	+	3.96988i	−0.296307	+	0.259519i
$235$	8.48806			0.553700
$236$	−3.85132	+	2.22356i	−0.250700	+	0.144742i
$237$	3.05359	+	5.28897i	0.198352	+	0.343556i
$238$	−1.45156	+	2.51418i	−0.0940907	+	0.162970i
$239$		−	20.9648i		−	1.35610i	−0.735016	−	0.678050i	$-0.762825\pi$
$239$		−	20.9648i		−	1.35610i	0.735016	−	0.678050i	$-0.237175\pi$
$240$	11.5200	+	6.65110i	0.743616	+	0.429327i
$241$	−4.09183	−	2.36242i	−0.263578	−	0.152177i	0.362388	−	0.932027i	$-0.381962\pi$
$241$	−4.09183	−	2.36242i	−0.263578	−	0.152177i	−0.625966	+	0.779851i	$0.715295\pi$
$242$			37.6945i			2.42310i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.55639	+	4.42780i	0.163656	+	0.283461i
$245$	2.32399	−	1.34176i	0.148474	−	0.0857217i
$246$	−0.738290			−0.0470717
$247$	−1.16093	−	5.85598i	−0.0738685	−	0.372607i
$248$	18.4135			1.16926
$249$	10.2520	−	5.91901i	0.649696	−	0.375102i
$250$	6.27549	+	10.8695i	0.396897	+	0.687446i
$251$	−9.86689	+	17.0900i	−0.622793	+	1.07871i	0.366171	+	0.930548i	$0.380669\pi$
$251$	−9.86689	+	17.0900i	−0.622793	+	1.07871i	−0.988963	+	0.148161i	$0.952665\pi$
$252$			0.792659i			0.0499328i
$253$	11.7565	+	6.78764i	0.739127	+	0.426735i
$254$	−20.8530	−	12.0395i	−1.30843	−	0.755425i
$255$		−	4.66187i		−	0.291937i
$256$	−8.21519	+	14.2291i	−0.513449	+	0.889320i
$257$	−10.3602	−	17.9444i	−0.646253	−	1.11934i	−0.984011	−	0.178109i	$-0.943002\pi$
$257$	−10.3602	−	17.9444i	−0.646253	−	1.11934i	0.337758	−	0.941233i	$-0.390331\pi$
$258$	−16.0958	+	9.29292i	−1.00208	+	0.578552i
$259$	8.57811			0.533018
$260$	1.49142	+	7.52300i	0.0924938	+	0.466556i
$261$	1.72160			0.106565
$262$	5.44482	−	3.14357i	0.336382	−	0.194210i
$263$	11.5927	+	20.0792i	0.714839	+	1.23814i	0.963022	+	0.269424i	$0.0868331\pi$
$263$	11.5927	+	20.0792i	0.714839	+	1.23814i	−0.248183	+	0.968713i	$0.579834\pi$
$264$	5.84381	−	10.1218i	0.359662	−	0.622953i
$265$			34.4039i			2.11342i
$266$	−2.39628	−	1.38350i	−0.146926	−	0.0848275i
$267$	−1.70843	−	0.986363i	−0.104554	−	0.0603645i
$268$		−	4.20092i		−	0.256612i
$269$	2.64703	−	4.58480i	0.161393	−	0.279540i	−0.773976	−	0.633215i	$-0.781735\pi$
$269$	2.64703	−	4.58480i	0.161393	−	0.279540i	0.935368	+	0.353675i	$0.115068\pi$
$270$	−2.24224	−	3.88368i	−0.136459	−	0.236353i
$271$	24.8116	−	14.3250i	1.50720	−	0.870182i	0.507234	−	0.861808i	$-0.330668\pi$
$271$	24.8116	−	14.3250i	1.50720	−	0.870182i	0.999965	−	0.00837368i	$-0.00266546\pi$
$272$	8.61144			0.522145
$273$	2.71232	−	2.37557i	0.164157	−	0.143776i
$274$	−35.9460			−2.17158
$275$	−11.0430	+	6.37567i	−0.665917	+	0.384467i
$276$	0.928790	+	1.60871i	0.0559066	+	0.0968331i
$277$	5.78609	−	10.0218i	0.347652	−	0.602151i	−0.638180	−	0.769887i	$-0.720312\pi$
$277$	5.78609	−	10.0218i	0.347652	−	0.602151i	0.985832	+	0.167736i	$0.0536457\pi$
$278$		−	6.67077i		−	0.400086i
$279$	−7.90367	−	4.56319i	−0.473180	−	0.273191i
$280$	−4.68893	−	2.70715i	−0.280217	−	0.161783i
$281$		−	2.83330i		−	0.169021i	−0.996423	−	0.0845103i	$-0.973067\pi$
$281$		−	2.83330i		−	0.169021i	0.996423	−	0.0845103i	$-0.0269326\pi$
$282$	2.64292	−	4.57767i	0.157383	−	0.272596i
$283$	4.37671	+	7.58068i	0.260168	+	0.450625i	0.966286	−	0.257469i	$-0.0828886\pi$
$283$	4.37671	+	7.58068i	0.260168	+	0.450625i	−0.706118	+	0.708094i	$0.749555\pi$
$284$	−4.67057	+	2.69656i	−0.277148	+	0.160011i
$285$	4.44327			0.263196
$286$	34.2371	−	6.78743i	2.02448	−	0.401349i
$287$	0.441792			0.0260782
$288$	3.67935	−	2.12427i	0.216808	−	0.125174i
$289$	6.99102	+	12.1088i	0.411237	+	0.712283i
$290$	3.86025	−	6.68615i	0.226682	−	0.392624i
$291$		−	2.68515i		−	0.157406i
$292$	0.412341	+	0.238065i	0.0241304	+	0.0139317i
$293$	13.0177	+	7.51578i	0.760503	+	0.439077i	0.829476	−	0.558542i	$-0.188639\pi$
$293$	13.0177	+	7.51578i	0.760503	+	0.439077i	−0.0689732	+	0.997619i	$0.521972\pi$
$294$		−	1.67113i		−	0.0974620i
$295$	−7.52778	+	13.0385i	−0.438284	+	0.759130i
$296$	−8.65368	−	14.9886i	−0.502985	−	0.871195i
$297$	−5.01670	+	2.89639i	−0.291098	+	0.168066i
$298$	−17.5126			−1.01448
$299$	2.72113	−	7.99938i	0.157367	−	0.462616i
$300$	−1.74484			−0.100738
$301$	9.63172	−	5.56088i	0.555163	−	0.320524i
$302$	−14.6441	−	25.3644i	−0.842676	−	1.45956i
$303$	−8.73866	+	15.1358i	−0.502023	+	0.869530i
$304$			8.20764i			0.470741i
$305$	14.9901	+	8.65455i	0.858332	+	0.495558i
$306$	−2.51418	−	1.45156i	−0.143726	−	0.0829802i
$307$		−	19.6735i		−	1.12282i	−0.827536	−	0.561412i	$-0.810258\pi$
$307$		−	19.6735i		−	1.12282i	0.827536	−	0.561412i	$-0.189742\pi$
$308$	2.29585	−	3.97653i	0.130818	−	0.226584i
$309$	−7.03829	−	12.1907i	−0.400394	−	0.693503i
$310$	−35.4439	+	20.4635i	−2.01308	+	1.16225i
$311$	21.4272			1.21503			0.607513	−	0.794310i	$-0.292167\pi$
$311$	21.4272			1.21503			0.607513	+	0.794310i	$0.292167\pi$
$312$	−6.88706	−	2.34276i	−0.389903	−	0.132632i
$313$	3.09742			0.175077			0.0875384	−	0.996161i	$-0.472100\pi$
$313$	3.09742			0.175077			0.0875384	+	0.996161i	$0.472100\pi$
$314$	26.8310	−	15.4909i	1.51416	−	0.874201i
$315$	1.34176	+	2.32399i	0.0755994	+	0.130942i
$316$	2.42046	−	4.19235i	0.136161	−	0.235838i
$317$			24.9862i			1.40337i	0.712489	+	0.701684i	$0.247568\pi$
$317$			24.9862i			1.40337i	−0.712489	+	0.701684i	$0.752432\pi$
$318$	18.5543	+	10.7123i	1.04047	+	0.600717i
$319$	−8.63677	−	4.98644i	−0.483566	−	0.279187i
$320$			7.55185i			0.422161i
$321$	−1.66741	+	2.88804i	−0.0930659	+	0.161195i
$322$	−1.95812	−	3.39157i	−0.109122	−	0.189005i
$323$	2.49107	−	1.43822i	0.138607	−	0.0800246i
$324$	−0.792659			−0.0440366
$325$	5.22921	+	5.97047i	0.290064	+	0.331182i
$326$	29.8663			1.65414
$327$	−9.26023	+	5.34640i	−0.512092	+	0.295656i
$328$	−0.445684	−	0.771947i	−0.0246088	−	0.0426237i
$329$	−1.58152	+	2.73927i	−0.0871920	+	0.151021i
$330$			25.9777i			1.43002i
$331$	10.7566	+	6.21030i	0.591234	+	0.341349i	0.765585	−	0.643334i	$-0.222449\pi$
$331$	10.7566	+	6.21030i	0.591234	+	0.341349i	−0.174351	+	0.984684i	$0.555783\pi$
$332$	−8.12636	−	4.69176i	−0.445992	−	0.257494i
$333$			8.57811i			0.470078i
$334$	0.829183	−	1.43619i	0.0453709	−	0.0785847i
$335$	−7.11102	−	12.3166i	−0.388516	−	0.672930i
$336$	−4.29290	+	2.47850i	−0.234197	+	0.135214i
$337$	1.91449			0.104289			0.0521444	−	0.998640i	$-0.483394\pi$
$337$	1.91449			0.104289			0.0521444	+	0.998640i	$0.483394\pi$
$338$	−8.28798	−	20.0816i	−0.450807	−	1.09229i
$339$	−11.4384			−0.621251
$340$	−3.20020	+	1.84763i	−0.173555	+	0.100202i
$341$	26.4336	+	45.7843i	1.43146	+	2.47936i
$342$	1.38350	−	2.39628i	0.0748109	−	0.129576i
$343$			1.00000i			0.0539949i
$344$	−19.4331	−	11.2197i	−1.04776	−	0.604927i
$345$	5.44623	+	3.14438i	0.293215	+	0.169288i
$346$		−	34.5645i		−	1.85820i
$347$	5.40203	−	9.35659i	0.289996	−	0.502288i	−0.683812	−	0.729658i	$-0.739679\pi$
$347$	5.40203	−	9.35659i	0.289996	−	0.502288i	0.973808	+	0.227370i	$0.0730126\pi$
$348$	−0.682322	−	1.18182i	−0.0365763	−	0.0633520i
$349$	2.17430	−	1.25533i	0.116387	−	0.0671963i	−0.440676	−	0.897666i	$-0.645261\pi$
$349$	2.17430	−	1.25533i	0.116387	−	0.0671963i	0.557064	+	0.830470i	$0.311928\pi$
$350$	3.67855			0.196627
$351$	2.37557	+	2.71232i	0.126799	+	0.144773i
$352$	−24.6109			−1.31177
$353$	−15.3551	+	8.86526i	−0.817269	+	0.471850i	−0.849474	−	0.527631i	$-0.823080\pi$
$353$	−15.3551	+	8.86526i	−0.817269	+	0.471850i	0.0322050	+	0.999481i	$0.489747\pi$
$354$	4.68783	+	8.11956i	0.249155	+	0.431550i
$355$	−9.12908	+	15.8120i	−0.484521	+	0.839216i
$356$			1.56370i			0.0828759i
$357$	1.50448	+	0.868612i	0.0796256	+	0.0459718i
$358$	4.50702	+	2.60213i	0.238204	+	0.137527i
$359$		−	8.10815i		−	0.427932i	−0.976841	−	0.213966i	$-0.931362\pi$
$359$		−	8.10815i		−	0.427932i	0.976841	−	0.213966i	$-0.0686381\pi$
$360$	2.70715	−	4.68893i	0.142679	−	0.247128i
$361$	−8.12922	−	14.0802i	−0.427854	−	0.741064i
$362$	−26.5913	+	15.3525i	−1.39761	+	0.806909i
$363$	22.5564			1.18390
$364$	−2.70571	−	0.920395i	−0.141818	−	0.0482418i
$365$	1.61192			0.0843717
$366$	9.33491	−	5.38951i	0.487944	−	0.281714i
$367$	3.73248	+	6.46484i	0.194834	+	0.337462i	0.946846	−	0.321687i	$-0.104250\pi$
$367$	3.73248	+	6.46484i	0.194834	+	0.337462i	−0.752012	+	0.659149i	$0.770917\pi$
$368$	−5.80833	+	10.0603i	−0.302780	+	0.524430i
$369$			0.441792i			0.0229988i
$370$	33.3146	+	19.2342i	1.73195	+	0.999939i
$371$	−11.1029	−	6.41024i	−0.576432	−	0.332803i
$372$			7.23410i			0.375071i
$373$	4.99008	−	8.64307i	0.258376	−	0.447521i	−0.707431	−	0.706783i	$-0.750146\pi$
$373$	4.99008	−	8.64307i	0.258376	−	0.447521i	0.965807	+	0.259262i	$0.0834792\pi$
$374$	8.40858	+	14.5641i	0.434797	+	0.753091i
$375$	6.50428	−	3.75525i	0.335880	−	0.193920i
$376$	6.38180			0.329116
$377$	−1.99904	+	5.87663i	−0.102956	+	0.302662i
$378$	1.67113			0.0859534
$379$	11.4092	−	6.58710i	0.586051	−	0.338356i	−0.177484	−	0.984124i	$-0.556796\pi$
$379$	11.4092	−	6.58710i	0.586051	−	0.338356i	0.763534	+	0.645767i	$0.223462\pi$
$380$	−1.76100	−	3.05014i	−0.0903373	−	0.156469i
$381$	−7.20442	+	12.4784i	−0.369094	+	0.639289i
$382$		−	6.70866i		−	0.343245i
$383$	−20.7301	−	11.9685i	−1.05926	−	0.611563i	−0.134032	−	0.990977i	$-0.542792\pi$
$383$	−20.7301	−	11.9685i	−1.05926	−	0.611563i	−0.925227	+	0.379414i	$0.876126\pi$
$384$	11.4315	+	6.59996i	0.583359	+	0.336803i
$385$		−	15.5450i		−	0.792248i
$386$	−4.68384	+	8.11265i	−0.238401	+	0.412923i
$387$	5.56088	+	9.63172i	0.282675	+	0.489608i
$388$	−1.84325	+	1.06420i	−0.0935770	+	0.0540267i
$389$	−31.9544			−1.62015			−0.810076	−	0.586325i	$-0.800574\pi$
$389$	−31.9544			−1.62015			−0.810076	+	0.586325i	$0.800574\pi$
$390$	15.8604	−	3.14428i	0.803121	−	0.159217i
$391$	4.07115			0.205887
$392$	1.74731	−	1.00881i	0.0882524	−	0.0509525i
$393$	−1.88111	−	3.25818i	−0.0948894	−	0.164353i
$394$	14.4204	−	24.9768i	0.726488	−	1.25831i
$395$		−	16.3887i		−	0.824605i
$396$	3.97653	+	2.29585i	0.199828	+	0.115371i
$397$	−7.29481	−	4.21166i	−0.366116	−	0.211377i	0.305644	−	0.952146i	$-0.401128\pi$
$397$	−7.29481	−	4.21166i	−0.366116	−	0.211377i	−0.671760	+	0.740769i	$0.734462\pi$
$398$		−	42.0769i		−	2.10913i
$399$	−0.827883	+	1.43393i	−0.0414460	+	0.0717865i
$400$	−5.45579	−	9.44971i	−0.272790	−	0.472486i
$401$	5.55732	−	3.20852i	0.277520	−	0.160226i	−0.354780	−	0.934950i	$-0.615444\pi$
$401$	5.55732	−	3.20852i	0.277520	−	0.160226i	0.632300	+	0.774724i	$0.282111\pi$
$402$	−8.85660			−0.441727
$403$	24.7536	−	21.6803i	1.23306	−	1.07997i
$404$	13.8536			0.689240
$405$	−2.32399	+	1.34176i	−0.115480	+	0.0666724i
$406$	1.43851	+	2.49157i	0.0713919	+	0.123654i
$407$	24.8456	−	43.0338i	1.23155	−	2.13311i
$408$		−	3.50506i		−	0.173526i
$409$	4.66205	+	2.69164i	0.230524	+	0.133093i	0.610814	−	0.791774i	$-0.290842\pi$
$409$	4.66205	+	2.69164i	0.230524	+	0.133093i	−0.380290	+	0.924867i	$0.624176\pi$
$410$	1.71578	+	0.990606i	0.0847363	+	0.0489225i
$411$			21.5100i			1.06101i
$412$	−5.57896	+	9.66305i	−0.274856	+	0.476064i
$413$	−2.80519	−	4.85874i	−0.138035	−	0.239083i
$414$	3.39157	−	1.95812i	0.166687	−	0.0962365i
$415$	−31.7675			−1.55940
$416$	2.97886	+	15.0259i	0.146050	+	0.736707i
$417$	−3.99178			−0.195478
$418$	−13.8812	+	8.01429i	−0.678950	+	0.391992i
$419$	7.10815	+	12.3117i	0.347256	+	0.601465i	0.985761	−	0.168153i	$-0.0537801\pi$
$419$	7.10815	+	12.3117i	0.347256	+	0.601465i	−0.638505	+	0.769618i	$0.720447\pi$
$420$	1.06356	−	1.84213i	0.0518962	−	0.0898868i
$421$			26.7633i			1.30436i	0.758063	+	0.652182i	$0.226146\pi$
$421$			26.7633i			1.30436i	−0.758063	+	0.652182i	$0.773854\pi$
$422$	2.45072	+	1.41492i	0.119299	+	0.0688774i
$423$	−2.73927	−	1.58152i	−0.133188	−	0.0768961i
$424$			25.8668i			1.25620i
$425$	−1.91203	+	3.31173i	−0.0927470	+	0.160642i
$426$	5.68502	+	9.84675i	0.275440	+	0.477077i
$427$	−5.58600	+	3.22508i	−0.270326	+	0.156073i
$428$	2.64338			0.127772
$429$	−4.06159	−	20.4875i	−0.196096	−	0.989144i
$430$	49.8754			2.40520
$431$	−11.2378	+	6.48816i	−0.541307	+	0.312524i	−0.745608	−	0.666384i	$-0.767841\pi$
$431$	−11.2378	+	6.48816i	−0.541307	+	0.312524i	0.204301	+	0.978908i	$0.434508\pi$
$432$	−2.47850	−	4.29290i	−0.119247	−	0.206542i
$433$	−6.21120	+	10.7581i	−0.298491	+	0.517002i	−0.975791	−	0.218705i	$-0.929817\pi$
$433$	−6.21120	+	10.7581i	−0.298491	+	0.517002i	0.677300	+	0.735707i	$0.263150\pi$
$434$		−	15.2513i		−	0.732086i
$435$	−4.00099	−	2.30997i	−0.191833	−	0.110755i
$436$	7.34021	+	4.23787i	0.351532	+	0.202957i
$437$			3.88025i			0.185618i
$438$	0.501902	−	0.869319i	0.0239818	−	0.0415377i
$439$	−10.2785	−	17.8029i	−0.490567	−	0.849688i	0.509374	−	0.860545i	$-0.329877\pi$
$439$	−10.2785	−	17.8029i	−0.490567	−	0.849688i	−0.999941	+	0.0108579i	$0.996544\pi$
$440$	−27.1619	+	15.6820i	−1.29489	+	0.747608i
$441$	−1.00000			−0.0476190
$442$	7.87418	−	6.89657i	0.374537	−	0.328036i
$443$	24.1703			1.14836			0.574182	−	0.818728i	$-0.305320\pi$
$443$	24.1703			1.14836			0.574182	+	0.818728i	$0.305320\pi$
$444$	5.88856	−	3.39976i	0.279459	−	0.161345i
$445$	2.64692	+	4.58460i	0.125476	+	0.217331i
$446$	5.15688	−	8.93198i	0.244185	−	0.422941i
$447$			10.4795i			0.495664i
$448$	−2.43714	−	1.40708i	−0.115144	−	0.0664784i
$449$	−19.1099	−	11.0331i	−0.901854	−	0.520685i	−0.0240525	−	0.999711i	$-0.507657\pi$
$449$	−19.1099	−	11.0331i	−0.901854	−	0.520685i	−0.877801	+	0.479025i	$0.840990\pi$
$450$			3.67855i			0.173409i
$451$	1.27960	−	2.21634i	0.0602542	−	0.104363i
$452$	4.53339	+	7.85207i	0.213233	+	0.369330i
$453$	−15.1780	+	8.76304i	−0.713126	+	0.411724i
$454$	21.7190			1.01933
$455$	−9.49084	+	1.88154i	−0.444937	+	0.0882078i
$456$	3.34070			0.156443
$457$	−11.2149	+	6.47492i	−0.524611	+	0.302884i	−0.738819	−	0.673904i	$-0.764616\pi$
$457$	−11.2149	+	6.47492i	−0.524611	+	0.302884i	0.214208	+	0.976788i	$0.431283\pi$
$458$	13.4064	+	23.2206i	0.626442	+	1.08503i
$459$	−0.868612	+	1.50448i	−0.0405434	+	0.0702232i
$460$		−	4.98484i		−	0.232419i
$461$	−0.621751	−	0.358968i	−0.0289578	−	0.0167188i	0.485451	−	0.874264i	$-0.338655\pi$
$461$	−0.621751	−	0.358968i	−0.0289578	−	0.0167188i	−0.514409	+	0.857545i	$0.671989\pi$
$462$	−8.38353	−	4.84024i	−0.390037	−	0.225188i
$463$		−	30.2503i		−	1.40585i	−0.711263	−	0.702926i	$-0.751876\pi$
$463$		−	30.2503i		−	1.40585i	0.711263	−	0.702926i	$-0.248124\pi$
$464$	4.26700	−	7.39066i	0.198091	−	0.343103i
$465$	12.2454	+	21.2096i	0.567865	+	0.983572i
$466$	13.1893	−	7.61486i	0.610983	−	0.352751i
$467$	21.6830			1.00337			0.501684	−	0.865051i	$-0.332714\pi$
$467$	21.6830			1.00337			0.501684	+	0.865051i	$0.332714\pi$
$468$	0.920395	−	2.70571i	0.0425453	−	0.125072i
$469$	5.29978			0.244721
$470$	−12.2842	+	7.09230i	−0.566629	+	0.327143i
$471$	−9.26973	−	16.0556i	−0.427126	−	0.739805i
$472$	−5.65981	+	9.80308i	−0.260514	+	0.451223i
$473$		−	64.4260i		−	2.96231i
$474$	−8.83854	−	5.10293i	−0.405967	−	0.234385i
$475$	−3.15644	−	1.82237i	−0.144827	−	0.0836161i
$476$		−	1.37703i		−	0.0631159i
$477$	6.41024	−	11.1029i	0.293505	−	0.508365i
$478$	17.5174	+	30.3410i	0.801227	+	1.38777i
$479$	16.6961	−	9.63951i	0.762866	−	0.440441i	−0.0674581	−	0.997722i	$-0.521489\pi$
$479$	16.6961	−	9.63951i	0.762866	−	0.440441i	0.830324	+	0.557281i	$0.188156\pi$
$480$	−11.4010			−0.520384
$481$	−29.2811	−	9.96047i	−1.33510	−	0.454158i
$482$	7.89580			0.359644
$483$	−2.02951	+	1.17174i	−0.0923460	+	0.0533160i
$484$	−8.93976	−	15.4841i	−0.406353	−	0.703823i
$485$	−3.60281	+	6.24026i	−0.163595	+	0.283356i
$486$			1.67113i			0.0758038i
$487$	20.3590	+	11.7543i	0.922555	+	0.532637i	0.884449	−	0.466636i	$-0.154534\pi$
$487$	20.3590	+	11.7543i	0.922555	+	0.532637i	0.0381057	+	0.999274i	$0.487868\pi$
$488$	11.2704	+	6.50698i	0.510188	+	0.294557i
$489$		−	17.8720i		−	0.808200i
$490$	−2.24224	+	3.88368i	−0.101294	+	0.175447i
$491$	13.1685	+	22.8085i	0.594285	+	1.02933i	0.993647	+	0.112539i	$0.0358984\pi$
$491$	13.1685	+	22.8085i	0.594285	+	1.02933i	−0.399362	+	0.916793i	$0.630768\pi$
$492$	0.303274	−	0.175095i	0.0136726	−	0.00789391i
$493$	−2.99081			−0.134699
$494$	6.57318	+	7.50495i	0.295742	+	0.337664i
$495$	15.5450			0.698697
$496$	−39.1786	+	22.6198i	−1.75917	+	1.01566i
$497$	−3.40191	−	5.89229i	−0.152597	−	0.264305i
$498$	−9.89141	+	17.1324i	−0.443245	+	0.767722i
$499$			12.8363i			0.574634i	0.957836	+	0.287317i	$0.0927633\pi$
$499$			12.8363i			0.574634i	−0.957836	+	0.287317i	$0.907237\pi$
$500$	−5.15568	−	2.97663i	−0.230569	−	0.133119i
$501$	−0.859414	−	0.496183i	−0.0383958	−	0.0221678i
$502$		−	32.9776i		−	1.47186i
$503$	10.1563	−	17.5913i	0.452849	−	0.784357i	−0.545713	−	0.837972i	$-0.683741\pi$
$503$	10.1563	−	17.5913i	0.452849	−	0.784357i	0.998562	+	0.0536153i	$0.0170745\pi$
$504$	1.00881	+	1.74731i	0.0449359	+	0.0778313i
$505$	40.6172	−	23.4503i	1.80744	−	1.04353i
$506$	−22.6860			−1.00852
$507$	−12.0168	+	4.95952i	−0.533684	+	0.220260i
$508$	11.4213			0.506738
$509$	−16.7221	+	9.65451i	−0.741194	+	0.427929i	−0.822503	−	0.568760i	$-0.807423\pi$
$509$	−16.7221	+	9.65451i	−0.741194	+	0.427929i	0.0813091	+	0.996689i	$0.474090\pi$
$510$	3.89528	+	6.74682i	0.172486	+	0.298754i
$511$	−0.300338	+	0.520200i	−0.0132861	+	0.0230123i
$512$		−	1.05739i		−	0.0467304i
$513$	−1.43393	−	0.827883i	−0.0633098	−	0.0365519i
$514$	29.9874	+	17.3132i	1.32269	+	0.763653i
$515$			37.7747i			1.66455i
$516$	4.40788	−	7.63467i	0.194046	−	0.336098i
$517$	9.16140	+	15.8680i	0.402918	+	0.697874i
$518$	−12.4146	+	7.16755i	−0.545465	+	0.314924i
$519$	−20.6834			−0.907900
$520$	12.8621	+	14.6853i	0.564039	+	0.643993i
$521$	−12.5091			−0.548034			−0.274017	−	0.961725i	$-0.588353\pi$
$521$	−12.5091			−0.548034			−0.274017	+	0.961725i	$0.588353\pi$
$522$	−2.49157	+	1.43851i	−0.109053	+	0.0629617i
$523$	17.1504	+	29.7053i	0.749933	+	1.29892i	0.947854	+	0.318704i	$0.103248\pi$
$523$	17.1504	+	29.7053i	0.749933	+	1.29892i	−0.197921	+	0.980218i	$0.563419\pi$
$524$	−1.49108	+	2.58262i	−0.0651380	+	0.112822i
$525$		−	2.20124i		−	0.0960702i
$526$	−33.5549	−	19.3729i	−1.46306	−	0.844699i
$527$	13.7304	+	7.92728i	0.598108	+	0.345318i
$528$			28.7149i			1.24966i
$529$	8.75405	−	15.1625i	0.380611	−	0.659237i
$530$	−28.7466	−	49.7906i	−1.24867	−	2.16277i
$531$	4.85874	−	2.80519i	0.210851	−	0.121735i
$532$	1.31246			0.0569022
$533$	−1.50804	−	0.512987i	−0.0653205	−	0.0222199i
$534$	3.29667			0.142661
$535$	7.75010	−	4.47452i	0.335066	−	0.193450i
$536$	−5.34647	−	9.26035i	−0.230932	−	0.399986i
$537$	1.55711	−	2.69700i	0.0671944	−	0.116384i
$538$			8.84705i			0.381423i
$539$	5.01670	+	2.89639i	0.216085	+	0.124756i
$540$	1.84213	+	1.06356i	0.0792727	+	0.0457681i
$541$		−	25.1013i		−	1.07919i	−0.841924	−	0.539596i	$-0.818577\pi$
$541$		−	25.1013i		−	1.07919i	0.841924	−	0.539596i	$-0.181423\pi$
$542$	−23.9389	+	41.4633i	−1.02826	+	1.78100i
$543$	9.18691	+	15.9122i	0.394248	+	0.682858i
$544$	−6.39186	+	3.69034i	−0.274049	+	0.158222i
$545$	28.6943			1.22913
$546$	−1.94043	+	5.70432i	−0.0830426	+	0.244123i
$547$	−15.0430			−0.643192			−0.321596	−	0.946877i	$-0.604219\pi$
$547$	−15.0430			−0.643192			−0.321596	+	0.946877i	$0.604219\pi$
$548$	14.7658	−	8.52506i	0.630766	−	0.364173i
$549$	−3.22508	−	5.58600i	−0.137643	−	0.238405i
$550$	10.6545	−	18.4542i	0.454311	−	0.786890i
$551$		−	2.85057i		−	0.121438i
$552$	4.09478	+	2.36412i	0.174286	+	0.100624i
$553$	5.28897	+	3.05359i	0.224910	+	0.129852i
$554$			19.3385i			0.821616i
$555$	11.5097	−	19.9355i	0.488561	−	0.846213i
$556$	1.58206	+	2.74021i	0.0670943	+	0.116211i
$557$	−18.5048	+	10.6837i	−0.784072	+	0.452684i	−0.837871	−	0.545868i	$-0.816200\pi$
$557$	−18.5048	+	10.6837i	−0.784072	+	0.452684i	0.0537997	+	0.998552i	$0.482867\pi$
$558$	15.2513			0.645639
$559$	−39.3345	+	7.79799i	−1.66367	+	0.329820i
$560$	13.3022			0.562121
$561$	8.71514	−	5.03169i	0.367953	−	0.212438i
$562$	2.36740	+	4.10046i	0.0998628	+	0.172967i
$563$	1.17404	−	2.03350i	0.0494799	−	0.0857016i	−0.840225	−	0.542238i	$-0.817577\pi$
$563$	1.17404	−	2.03350i	0.0494799	−	0.0857016i	0.889705	+	0.456537i	$0.150910\pi$
$564$			2.50721i			0.105573i
$565$	26.5828	+	15.3476i	1.11835	+	0.645679i
$566$	−12.6683	−	7.31403i	−0.532487	−	0.307432i
$567$		−	1.00000i		−	0.0419961i
$568$	−6.86376	+	11.8884i	−0.287997	+	0.498826i
$569$	5.05756	+	8.75995i	0.212024	+	0.367236i	0.952348	−	0.305014i	$-0.0986612\pi$
$569$	5.05756	+	8.75995i	0.212024	+	0.367236i	−0.740324	+	0.672250i	$0.765328\pi$
$570$	−6.43046	+	3.71263i	−0.269342	+	0.155505i
$571$	−28.1994			−1.18011			−0.590053	−	0.807364i	$-0.700893\pi$
$571$	−28.1994			−1.18011			−0.590053	+	0.807364i	$0.700893\pi$
$572$	−12.4542	+	10.9079i	−0.520734	+	0.456083i
$573$	−4.01446			−0.167706
$574$	−0.639378	+	0.369145i	−0.0266871	+	0.0154078i
$575$	−2.57929	−	4.46745i	−0.107564	−	0.186306i
$576$	1.40708	−	2.43714i	0.0586284	−	0.101547i
$577$			22.7245i			0.946034i	0.881053	+	0.473017i	$0.156835\pi$
$577$			22.7245i			0.946034i	−0.881053	+	0.473017i	$0.843165\pi$
$578$	−20.2353	−	11.6829i	−0.841679	−	0.485944i
$579$	4.85461	+	2.80281i	0.201751	+	0.116481i
$580$			3.66204i			0.152058i
$581$	5.91901	−	10.2520i	0.245562	−	0.425326i
$582$	2.24361	+	3.88604i	0.0930006	+	0.161082i
$583$	−64.3165	+	37.1331i	−2.66372	+	1.53790i
$584$	1.21193			0.0501501
$585$	−1.88154	−	9.49084i	−0.0777920	−	0.392398i
$586$	−25.1196			−1.03768
$587$	30.2201	−	17.4476i	1.24732	−	0.720138i	0.276742	−	0.960944i	$-0.410745\pi$
$587$	30.2201	−	17.4476i	1.24732	−	0.720138i	0.970573	+	0.240806i	$0.0774119\pi$
$588$	0.396329	+	0.686463i	0.0163444	+	0.0283092i
$589$	−7.55556	+	13.0866i	−0.311322	+	0.539225i
$590$		−	25.1597i		−	1.03581i
$591$	−14.9461	−	8.62914i	−0.614801	−	0.354956i
$592$	36.8250	+	21.2609i	1.51350	+	0.873818i
$593$			17.0082i			0.698443i	0.937040	+	0.349222i	$0.113554\pi$
$593$			17.0082i			0.698443i	−0.937040	+	0.349222i	$0.886446\pi$
$594$	4.84024	−	8.38353i	0.198597	−	0.343981i
$595$	−2.33093	−	4.03729i	−0.0955589	−	0.165513i
$596$	7.19380	−	4.15334i	0.294669	−	0.170127i
$597$	−25.1788			−1.03050
$598$	2.74587	+	13.8507i	0.112287	+	0.566396i
$599$	−15.0841			−0.616318			−0.308159	−	0.951335i	$-0.599713\pi$
$599$	−15.0841			−0.616318			−0.308159	+	0.951335i	$0.599713\pi$
$600$	−3.84625	+	2.22063i	−0.157023	+	0.0906570i
$601$	7.11868	+	12.3299i	0.290377	+	0.502947i	0.973899	−	0.226982i	$-0.0728860\pi$
$601$	7.11868	+	12.3299i	0.290377	+	0.502947i	−0.683522	+	0.729930i	$0.739553\pi$
$602$	−9.29292	+	16.0958i	−0.378751	+	0.656016i
$603$			5.29978i			0.215824i
$604$	12.0310	+	6.94611i	0.489535	+	0.282633i
$605$	−52.4208	−	30.2652i	−2.13121	−	1.23045i
$606$		−	29.2068i		−	1.18645i
$607$	20.5084	−	35.5216i	0.832412	−	1.44178i	−0.0637090	−	0.997969i	$-0.520293\pi$
$607$	20.5084	−	35.5216i	0.832412	−	1.44178i	0.896121	−	0.443811i	$-0.146374\pi$
$608$	−3.51730	−	6.09214i	−0.142645	−	0.247069i
$609$	1.49095	−	0.860801i	0.0604164	−	0.0348814i
$610$	−28.9257			−1.17117
$611$	8.57916	−	7.51402i	0.347076	−	0.303985i
$612$	1.37703			0.0556630
$613$	21.1621	−	12.2179i	0.854729	−	0.493478i	−0.00751482	−	0.999972i	$-0.502392\pi$
$613$	21.1621	−	12.2179i	0.854729	−	0.493478i	0.862244	+	0.506494i	$0.169059\pi$
$614$	16.4384	+	28.4722i	0.663401	+	1.14904i
$615$	0.592778	−	1.02672i	0.0239031	−	0.0414014i
$616$		−	11.6876i		−	0.470908i
$617$	−30.8340	−	17.8020i	−1.24133	−	0.716681i	−0.271964	−	0.962308i	$-0.587673\pi$
$617$	−30.8340	−	17.8020i	−1.24133	−	0.716681i	−0.969365	+	0.245626i	$0.921006\pi$
$618$	20.3721	+	11.7619i	0.819488	+	0.473132i
$619$			38.0783i			1.53050i	0.643735	+	0.765249i	$0.277384\pi$
$619$			38.0783i			1.53050i	−0.643735	+	0.765249i	$0.722616\pi$
$620$	9.70640	−	16.8120i	0.389818	−	0.675185i
$621$	−1.17174	−	2.02951i	−0.0470203	−	0.0814416i
$622$	−31.0103	+	17.9038i	−1.24340	+	0.717876i
$623$	−1.97273			−0.0790356
$624$	17.5316	−	3.47559i	0.701824	−	0.139135i
$625$	−31.1607			−1.24643
$626$	−4.48271	+	2.58809i	−0.179165	+	0.103441i
$627$	4.79575	+	8.30648i	0.191524	+	0.331729i
$628$	−7.34773	+	12.7266i	−0.293206	+	0.507848i
$629$		−	14.9021i		−	0.594186i
$630$	−3.88368	−	2.24224i	−0.154729	−	0.0893331i
$631$	−22.9448	−	13.2472i	−0.913419	−	0.527362i	−0.0318891	−	0.999491i	$-0.510152\pi$
$631$	−22.9448	−	13.2472i	−0.913419	−	0.527362i	−0.881530	+	0.472129i	$0.843486\pi$
$632$		−	12.3220i		−	0.490141i
$633$	0.846689	−	1.46651i	0.0336529	−	0.0582885i
$634$	−20.8776	−	36.1610i	−0.829154	−	1.43614i
$635$	33.4860	−	19.3332i	1.32885	−	0.767213i
$636$	−10.1623			−0.402960
$637$	1.16115	−	3.41346i	0.0460064	−	0.135246i
$638$	16.6659			0.659810
$639$	5.89229	−	3.40191i	0.233095	−	0.134578i
$640$	−17.7111	−	30.6765i	−0.700092	−	1.21259i
$641$	13.5815	−	23.5238i	0.536436	−	0.929134i	−0.462657	−	0.886538i	$-0.653104\pi$
$641$	13.5815	−	23.5238i	0.536436	−	0.929134i	0.999092	−	0.0425965i	$-0.0135630\pi$
$642$		−	5.57291i		−	0.219945i
$643$	−6.34074	−	3.66083i	−0.250054	−	0.144369i	0.369735	−	0.929137i	$-0.379449\pi$
$643$	−6.34074	−	3.66083i	−0.250054	−	0.144369i	−0.619789	+	0.784768i	$0.712782\pi$
$644$	1.60871	+	0.928790i	0.0633921	+	0.0365995i
$645$		−	29.8454i		−	1.17516i
$646$	−2.40344	+	4.16288i	−0.0945622	+	0.163786i
$647$	5.16017	+	8.93768i	0.202867	+	0.351376i	0.949451	−	0.313915i	$-0.101641\pi$
$647$	5.16017	+	8.93768i	0.202867	+	0.351376i	−0.746584	+	0.665291i	$0.768307\pi$
$648$	−1.74731	+	1.00881i	−0.0686408	+	0.0396298i
$649$	−32.4998			−1.27573
$650$	−12.5566	−	4.27135i	−0.492511	−	0.167536i
$651$	−9.12637			−0.357691
$652$	−12.2685	+	7.08320i	−0.480470	+	0.277399i
$653$	6.43893	+	11.1525i	0.251975	+	0.436433i	0.964069	−	0.265650i	$-0.0855867\pi$
$653$	6.43893	+	11.1525i	0.251975	+	0.436433i	−0.712095	+	0.702083i	$0.752253\pi$
$654$	8.93450	−	15.4750i	0.349367	−	0.605121i
$655$			10.0960i			0.394482i
$656$	1.89657	+	1.09498i	0.0740486	+	0.0427520i
$657$	−0.520200	−	0.300338i	−0.0202949	−	0.0117173i
$658$		−	5.28583i		−	0.206063i
$659$	13.8947	−	24.0664i	0.541262	−	0.937494i	−0.457570	−	0.889174i	$-0.651280\pi$
$659$	13.8947	−	24.0664i	0.541262	−	0.937494i	0.998832	−	0.0483199i	$-0.0153867\pi$
$660$	−6.16095	−	10.6711i	−0.239815	−	0.415371i
$661$	6.29607	−	3.63504i	0.244889	−	0.141387i	−0.372533	−	0.928019i	$-0.621511\pi$
$661$	6.29607	−	3.63504i	0.244889	−	0.141387i	0.617422	+	0.786632i	$0.288177\pi$
$662$	−20.7564			−0.806720
$663$	−4.12690	−	4.71190i	−0.160276	−	0.182995i
$664$	−23.8846			−0.926902
$665$	3.84798	−	2.22163i	0.149218	−	0.0861513i
$666$	−7.16755	−	12.4146i	−0.277737	−	0.481055i
$667$	2.01727	−	3.49402i	0.0781090	−	0.135289i
$668$			0.786607i			0.0304347i
$669$	−5.34489	−	3.08587i	−0.206645	−	0.119307i
$670$	20.5826	+	11.8834i	0.795177	+	0.459096i
$671$			37.3644i			1.44244i
$672$	2.12427	−	3.67935i	0.0819456	−	0.141934i
$673$	13.4894	+	23.3644i	0.519979	+	0.900630i	0.999730	+	0.0232258i	$0.00739366\pi$
$673$	13.4894	+	23.3644i	0.519979	+	0.900630i	−0.479751	+	0.877405i	$0.659273\pi$
$674$	−2.77072	+	1.59967i	−0.106724	+	0.0616171i
$675$	2.20124			0.0847259
$676$	8.16713	+	6.28347i	0.314121	+	0.241672i
$677$	−11.5807			−0.445084			−0.222542	−	0.974923i	$-0.571435\pi$
$677$	−11.5807			−0.445084			−0.222542	+	0.974923i	$0.571435\pi$
$678$	16.5541	−	9.55753i	0.635758	−	0.367055i
$679$	−1.34257	−	2.32541i	−0.0515233	−	0.0892409i
$680$	−4.70293	+	8.14572i	−0.180349	+	0.312374i
$681$		−	12.9967i		−	0.498033i
$682$	−76.5112	−	44.1738i	−2.92977	−	1.69150i
$683$	13.8349	+	7.98756i	0.529376	+	0.305635i	0.740762	−	0.671767i	$-0.234464\pi$
$683$	13.8349	+	7.98756i	0.529376	+	0.305635i	−0.211386	+	0.977403i	$0.567798\pi$
$684$			1.31246i			0.0501831i
$685$	28.8612	−	49.9891i	1.10273	−	1.90999i
$686$	−0.835563	−	1.44724i	−0.0319019	−	0.0552558i
$687$	13.8952	−	8.02241i	0.530136	−	0.306074i
$688$	55.1307			2.10184
$689$	30.4560	+	34.7732i	1.16028	+	1.32475i
$690$	−10.5093			−0.400082
$691$	−12.1060	+	6.98938i	−0.460532	+	0.265888i	−0.712268	−	0.701908i	$-0.752332\pi$
$691$	−12.1060	+	6.98938i	−0.460532	+	0.265888i	0.251736	+	0.967796i	$0.418999\pi$
$692$	8.19744	+	14.1984i	0.311620	+	0.539741i
$693$	−2.89639	+	5.01670i	−0.110025	+	0.190569i
$694$			18.0549i			0.685356i
$695$	9.27687	+	5.35600i	0.351892	+	0.203165i
$696$	−3.00817	−	1.73677i	−0.114024	−	0.0658320i
$697$		−	0.767492i		−	0.0290709i
$698$	−2.09781	+	3.63352i	−0.0794035	+	0.137531i
$699$	−4.55672	−	7.89248i	−0.172351	−	0.298521i
$700$	−1.51107	+	0.872418i	−0.0571132	+	0.0329743i
$701$	17.3224			0.654259			0.327129	−	0.944980i	$-0.393919\pi$
$701$	17.3224			0.654259			0.327129	+	0.944980i	$0.393919\pi$
$702$	−5.70432	−	1.94043i	−0.215296	−	0.0732366i
$703$	14.2033			0.535689
$704$	−14.1178	+	8.15093i	−0.532085	+	0.307200i
$705$	4.24403	+	7.35087i	0.159839	+	0.276850i
$706$	14.8150	−	25.6603i	0.557568	−	0.965737i
$707$			17.4773i			0.657303i
$708$	−3.85132	−	2.22356i	−0.144742	−	0.0835666i
$709$	16.2808	+	9.39973i	0.611439	+	0.353014i	0.773528	−	0.633762i	$-0.218490\pi$
$709$	16.2808	+	9.39973i	0.611439	+	0.353014i	−0.162090	+	0.986776i	$0.551823\pi$
$710$		−	30.5117i		−	1.14508i
$711$	−3.05359	+	5.28897i	−0.114519	+	0.198352i
$712$	1.99010	+	3.44696i	0.0745823	+	0.129180i
$713$	−18.5221	+	10.6937i	−0.693658	+	0.400483i
$714$	−2.90312			−0.108647
$715$	−18.0501	+	53.0624i	−0.675035	+	1.98442i
$716$	−2.46852			−0.0922529
$717$	18.1560	−	10.4824i	0.678050	−	0.391472i
$718$	6.77486	+	11.7344i	0.252836	+	0.437924i
$719$	7.77534	−	13.4673i	0.289971	−	0.502245i	−0.683831	−	0.729640i	$-0.739688\pi$
$719$	7.77534	−	13.4673i	0.289971	−	0.502245i	0.973803	+	0.227395i	$0.0730209\pi$
$720$			13.3022i			0.495744i
$721$	−12.1907	−	7.03829i	−0.454005	−	0.262120i
$722$	23.5298	+	13.5849i	0.875689	+	0.505579i
$723$		−	4.72484i		−	0.175719i
$724$	7.28209	−	12.6129i	0.270637	−	0.468757i
$725$	1.89483	+	3.28195i	0.0703724	+	0.121889i
$726$	−32.6444	+	18.8473i	−1.21155	+	0.699487i
$727$	13.4907			0.500343			0.250171	−	0.968202i	$-0.419513\pi$
$727$	13.4907			0.500343			0.250171	+	0.968202i	$0.419513\pi$
$728$	−7.13575	+	1.41465i	−0.264469	+	0.0524303i
$729$	1.00000			0.0370370
$730$	−2.33283	+	1.34686i	−0.0863419	+	0.0498495i
$731$	−9.66050	−	16.7325i	−0.357306	−	0.618873i
$732$	−2.55639	+	4.42780i	−0.0944869	+	0.163656i
$733$		−	18.7477i		−	0.692463i	−0.938149	−	0.346231i	$-0.887461\pi$
$733$		−	18.7477i		−	0.692463i	0.938149	−	0.346231i	$-0.112539\pi$
$734$	−10.8036	−	6.23744i	−0.398767	−	0.230228i
$735$	2.32399	+	1.34176i	0.0857217	+	0.0494914i
$736$		−	9.95639i		−	0.366997i
$737$	15.3502	−	26.5874i	0.565434	−	0.979360i
$738$	−0.369145	−	0.639378i	−0.0135884	−	0.0235358i
$739$	−0.689920	+	0.398326i	−0.0253791	+	0.0146526i	−0.512636	−	0.858606i	$-0.671331\pi$
$739$	−0.689920	+	0.398326i	−0.0253791	+	0.0146526i	0.487257	+	0.873259i	$0.337998\pi$
$740$	−18.2466			−0.670758
$741$	4.49096	−	3.93339i	0.164980	−	0.144497i
$742$	21.4246			0.786523
$743$	5.11716	−	2.95439i	0.187730	−	0.108386i	−0.403189	−	0.915117i	$-0.632098\pi$
$743$	5.11716	−	2.95439i	0.187730	−	0.108386i	0.590920	+	0.806730i	$0.298765\pi$
$744$	9.20676	+	15.9466i	0.337536	+	0.584630i
$745$	14.0610	−	24.3543i	0.515154	−	0.892272i
$746$			16.6781i			0.610628i
$747$	10.2520	+	5.91901i	0.375102	+	0.216565i
$748$	−6.90813	−	3.98841i	−0.252586	−	0.145831i
$749$			3.33482i			0.121852i
$750$	−6.27549	+	10.8695i	−0.229149	+	0.396897i
$751$	−13.7632	−	23.8386i	−0.502227	−	0.869882i	−0.999997	−	0.00257299i	$-0.999181\pi$
$751$	−13.7632	−	23.8386i	−0.502227	−	0.869882i	0.497770	−	0.867309i	$-0.334152\pi$
$752$	−13.5786	+	7.83961i	−0.495160	+	0.285881i
$753$	−19.7338			−0.719139
$754$	−2.01721	−	10.1752i	−0.0734624	−	0.370559i
$755$	47.0315			1.71165
$756$	−0.686463	+	0.396329i	−0.0249664	+	0.0144144i
$757$	1.32346	+	2.29229i	0.0481018	+	0.0833148i	0.889074	−	0.457764i	$-0.151349\pi$
$757$	1.32346	+	2.29229i	0.0481018	+	0.0833148i	−0.840972	+	0.541079i	$0.818016\pi$
$758$	−11.0079	+	19.0662i	−0.399824	+	0.692515i
$759$			13.5753i			0.492751i
$760$	−7.76376	−	4.48241i	−0.281621	−	0.162594i
$761$	28.5769	+	16.4989i	1.03591	+	0.598083i	0.918672	−	0.395021i	$-0.129263\pi$
$761$	28.5769	+	16.4989i	1.03591	+	0.598083i	0.117238	+	0.993104i	$0.462596\pi$
$762$		−	24.0790i		−	0.872289i
$763$	−5.34640	+	9.26023i	−0.193553	+	0.335243i
$764$	1.59105	+	2.75577i	0.0575621	+	0.0997004i
$765$	4.03729	−	2.33093i	0.145969	−	0.0842751i
$766$	40.0018			1.44532
$767$	3.93371	+	19.8424i	0.142038	+	0.716467i
$768$	−16.4304			−0.592880
$769$	9.46444	−	5.46430i	0.341296	−	0.197048i	−0.319549	−	0.947570i	$-0.603531\pi$
$769$	9.46444	−	5.46430i	0.341296	−	0.197048i	0.660845	+	0.750522i	$0.270198\pi$

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44724 + 0.835563i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.396329 - 0.686463i) q^{4} -2.68351i q^{5} +(-1.44724 - 0.835563i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.01762i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.44724 + 0.835563i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.396329 - 0.686463i) q^{4} -2.68351i q^{5} +(-1.44724 - 0.835563i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.01762i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.24224 + 3.88368i) q^{10} +(5.01670 - 2.89639i) q^{11} +0.792659 q^{12} +(-2.37557 - 2.71232i) q^{13} -1.67113 q^{14} +(2.32399 - 1.34176i) q^{15} +(2.47850 + 4.29290i) q^{16} +(0.868612 - 1.50448i) q^{17} -1.67113i q^{18} +(1.43393 + 0.827883i) q^{19} +(-1.84213 - 1.06356i) q^{20} +1.00000i q^{21} +(-4.84024 + 8.38353i) q^{22} +(1.17174 + 2.02951i) q^{23} +(1.74731 - 1.00881i) q^{24} -2.20124 q^{25} +(5.70432 + 1.94043i) q^{26} -1.00000 q^{27} +(0.686463 - 0.396329i) q^{28} +(-0.860801 - 1.49095i) q^{29} +(-2.24224 + 3.88368i) q^{30} +9.12637i q^{31} +(-3.67935 - 2.12427i) q^{32} +(5.01670 + 2.89639i) q^{33} +2.90312i q^{34} +(1.34176 - 2.32399i) q^{35} +(0.396329 + 0.686463i) q^{36} +(7.42886 - 4.28906i) q^{37} -2.76699 q^{38} +(1.16115 - 3.41346i) q^{39} -5.41430 q^{40} +(0.382603 - 0.220896i) q^{41} +(-0.835563 - 1.44724i) q^{42} +(5.56088 - 9.63172i) q^{43} -4.59170i q^{44} +(2.32399 + 1.34176i) q^{45} +(-3.39157 - 1.95812i) q^{46} +3.16304i q^{47} +(-2.47850 + 4.29290i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.18572 - 1.83928i) q^{50} +1.73722 q^{51} +(-2.80341 + 0.555770i) q^{52} -12.8205 q^{53} +(1.44724 - 0.835563i) q^{54} +(-7.77251 - 13.4624i) q^{55} +(1.00881 - 1.74731i) q^{56} +1.65577i q^{57} +(2.49157 + 1.43851i) q^{58} +(-4.85874 - 2.80519i) q^{59} -2.12711i q^{60} +(-3.22508 + 5.58600i) q^{61} +(-7.62565 - 13.2080i) q^{62} +(-0.866025 + 0.500000i) q^{63} -2.81417 q^{64} +(-7.27854 + 6.37488i) q^{65} -9.68047 q^{66} +(4.58974 - 2.64989i) q^{67} +(-0.688513 - 1.19254i) q^{68} +(-1.17174 + 2.02951i) q^{69} +4.48449i q^{70} +(-5.89229 - 3.40191i) q^{71} +(1.74731 + 1.00881i) q^{72} +0.600675i q^{73} +(-7.16755 + 12.4146i) q^{74} +(-1.10062 - 1.90633i) q^{75} +(1.13662 - 0.656229i) q^{76} +5.79279 q^{77} +(1.17170 + 5.91030i) q^{78} +6.10718 q^{79} +(11.5200 - 6.65110i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.369145 + 0.639378i) q^{82} -11.8380i q^{83} +(0.686463 + 0.396329i) q^{84} +(-4.03729 - 2.33093i) q^{85} +18.5858i q^{86} +(0.860801 - 1.49095i) q^{87} +(-5.84381 - 10.1218i) q^{88} +(-1.70843 + 0.986363i) q^{89} -4.48449 q^{90} +(-0.701147 - 3.53672i) q^{91} +1.85758 q^{92} +(-7.90367 + 4.56319i) q^{93} +(-2.64292 - 4.57767i) q^{94} +(2.22163 - 3.84798i) q^{95} -4.24855i q^{96} +(-2.32541 - 1.34257i) q^{97} +(-1.44724 - 0.835563i) q^{98} +5.79279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Introduction

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