LMFDB - Embedded newform 273.2.bd.a.127.2

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} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
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			127.2
Root			$1.77930i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54092 + 0.889651i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.582956 - 1.00971i) q^{4} +0.681820i q^{5} +(1.54092 + 0.889651i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.48409i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.54092 + 0.889651i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.582956 - 1.00971i) q^{4} +0.681820i q^{5} +(1.54092 + 0.889651i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.48409i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.606581 - 1.05063i) q^{10} +(-0.511171 + 0.295125i) q^{11} -1.16591 q^{12} +(3.45330 - 1.03669i) q^{13} -1.77930 q^{14} +(0.590473 - 0.340910i) q^{15} +(2.48624 + 4.30629i) q^{16} +(-3.14516 + 5.44757i) q^{17} -1.77930i q^{18} +(3.10599 + 1.79325i) q^{19} +(0.688440 + 0.397471i) q^{20} -1.00000i q^{21} +(0.525115 - 0.909527i) q^{22} +(1.84280 + 3.19182i) q^{23} +(-1.28526 + 0.742046i) q^{24} +4.53512 q^{25} +(-4.39897 + 4.66968i) q^{26} +1.00000 q^{27} +(1.00971 - 0.582956i) q^{28} +(3.22609 + 5.58775i) q^{29} +(-0.606581 + 1.05063i) q^{30} +4.30692i q^{31} +(-5.09166 - 2.93967i) q^{32} +(0.511171 + 0.295125i) q^{33} -11.1924i q^{34} +(-0.340910 + 0.590473i) q^{35} +(0.582956 + 1.00971i) q^{36} +(-9.12296 + 5.26714i) q^{37} -6.38145 q^{38} +(-2.62445 - 2.47230i) q^{39} +1.01188 q^{40} +(0.136350 - 0.0787215i) q^{41} +(0.889651 + 1.54092i) q^{42} +(2.36138 - 4.09004i) q^{43} +0.688179i q^{44} +(-0.590473 - 0.340910i) q^{45} +(-5.67921 - 3.27889i) q^{46} -11.2638i q^{47} +(2.48624 - 4.30629i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.98826 + 4.03467i) q^{50} +6.29031 q^{51} +(0.966372 - 4.09117i) q^{52} +12.2243 q^{53} +(-1.54092 + 0.889651i) q^{54} +(-0.201222 - 0.348526i) q^{55} +(0.742046 - 1.28526i) q^{56} -3.58649i q^{57} +(-9.94229 - 5.74019i) q^{58} +(-2.44791 - 1.41330i) q^{59} -0.794942i q^{60} +(-1.45571 + 2.52137i) q^{61} +(-3.83166 - 6.63663i) q^{62} +(-0.866025 + 0.500000i) q^{63} +0.516173 q^{64} +(0.706833 + 2.35453i) q^{65} -1.05023 q^{66} +(6.48168 - 3.74220i) q^{67} +(3.66698 + 6.35139i) q^{68} +(1.84280 - 3.19182i) q^{69} -1.21316i q^{70} +(6.05457 + 3.49561i) q^{71} +(1.28526 + 0.742046i) q^{72} -7.30193i q^{73} +(9.37183 - 16.2325i) q^{74} +(-2.26756 - 3.92753i) q^{75} +(3.62132 - 2.09077i) q^{76} -0.590249 q^{77} +(6.24355 + 1.47478i) q^{78} -3.33737 q^{79} +(-2.93611 + 1.69517i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.140069 + 0.242607i) q^{82} -13.6469i q^{83} +(-1.00971 - 0.582956i) q^{84} +(-3.71426 - 2.14443i) q^{85} +8.40323i q^{86} +(3.22609 - 5.58775i) q^{87} +(0.437992 + 0.758625i) q^{88} +(-10.6072 + 6.12405i) q^{89} +1.21316 q^{90} +(3.50899 + 0.828855i) q^{91} +4.29709 q^{92} +(3.72991 - 2.15346i) q^{93} +(10.0208 + 17.3565i) q^{94} +(-1.22267 + 2.11773i) q^{95} +5.87934i q^{96} +(-9.18669 - 5.30394i) q^{97} +(-1.54092 - 0.889651i) q^{98} -0.590249i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * 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 $

$2$	−1.54092	+	0.889651i	−1.08959	+	0.629078i	−0.933469	−	0.358659i	$-0.883234\pi$
$2$	−1.54092	+	0.889651i	−1.08959	+	0.629078i	−0.156126	+	0.987737i	$0.549901\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.582956	−	1.00971i	0.291478	−	0.504855i
$5$			0.681820i			0.304919i	0.988310	+	0.152460i	$0.0487194\pi$
$5$			0.681820i			0.304919i	−0.988310	+	0.152460i	$0.951281\pi$
$6$	1.54092	+	0.889651i	0.629078	+	0.363198i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	1.48409i		−	0.524706i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.606581	−	1.05063i	−0.191818	−	0.332238i
$11$	−0.511171	+	0.295125i	−0.154124	+	0.0889834i	−0.575078	−	0.818098i	$-0.695028\pi$
$11$	−0.511171	+	0.295125i	−0.154124	+	0.0889834i	0.420955	+	0.907082i	$0.361695\pi$
$12$	−1.16591			−0.336570
$13$	3.45330	−	1.03669i	0.957773	−	0.287525i
$13$	3.45330	−	1.03669i	0.957773	−	0.287525i
$14$	−1.77930			−0.475538
$15$	0.590473	−	0.340910i	0.152460	−	0.0880226i
$16$	2.48624	+	4.30629i	0.621559	+	1.07657i
$17$	−3.14516	+	5.44757i	−0.762812	+	1.32123i	0.178583	+	0.983925i	$0.442849\pi$
$17$	−3.14516	+	5.44757i	−0.762812	+	1.32123i	−0.941395	+	0.337305i	$0.890485\pi$
$18$		−	1.77930i		−	0.419385i
$19$	3.10599	+	1.79325i	0.712564	+	0.411399i	0.812010	−	0.583644i	$-0.198374\pi$
$19$	3.10599	+	1.79325i	0.712564	+	0.411399i	−0.0994459	+	0.995043i	$0.531707\pi$
$20$	0.688440	+	0.397471i	0.153940	+	0.0888773i
$21$		−	1.00000i		−	0.218218i
$22$	0.525115	−	0.909527i	0.111955	−	0.193912i
$23$	1.84280	+	3.19182i	0.384250	+	0.665541i	0.991665	−	0.128844i	$-0.0411267\pi$
$23$	1.84280	+	3.19182i	0.384250	+	0.665541i	−0.607415	+	0.794385i	$0.707793\pi$
$24$	−1.28526	+	0.742046i	−0.262353	+	0.151470i
$25$	4.53512			0.907024
$26$	−4.39897	+	4.66968i	−0.862709	+	0.915800i
$27$	1.00000			0.192450
$28$	1.00971	−	0.582956i	0.190817	−	0.110168i
$29$	3.22609	+	5.58775i	0.599070	+	1.03762i	0.992959	+	0.118461i	$0.0377962\pi$
$29$	3.22609	+	5.58775i	0.599070	+	1.03762i	−0.393889	+	0.919158i	$0.628870\pi$
$30$	−0.606581	+	1.05063i	−0.110746	+	0.191818i
$31$			4.30692i			0.773546i	0.922175	+	0.386773i	$0.126410\pi$
$31$			4.30692i			0.773546i	−0.922175	+	0.386773i	$0.873590\pi$
$32$	−5.09166	−	2.93967i	−0.900087	−	0.519665i
$33$	0.511171	+	0.295125i	0.0889834	+	0.0513746i
$34$		−	11.1924i		−	1.91947i
$35$	−0.340910	+	0.590473i	−0.0576243	+	0.0998082i
$36$	0.582956	+	1.00971i	0.0971594	+	0.168285i
$37$	−9.12296	+	5.26714i	−1.49981	+	0.865913i	−1.00000		0.000224832i	$-0.999928\pi$
$37$	−9.12296	+	5.26714i	−1.49981	+	0.865913i	−0.499805	+	0.866138i	$0.666595\pi$
$38$	−6.38145			−1.03521
$39$	−2.62445	−	2.47230i	−0.420248	−	0.395885i
$40$	1.01188			0.159993
$41$	0.136350	−	0.0787215i	0.0212942	−	0.0122942i	−0.489315	−	0.872107i	$-0.662753\pi$
$41$	0.136350	−	0.0787215i	0.0212942	−	0.0122942i	0.510609	+	0.859813i	$0.329420\pi$
$42$	0.889651	+	1.54092i	0.137276	+	0.237769i
$43$	2.36138	−	4.09004i	0.360108	−	0.623725i	−0.627871	−	0.778318i	$-0.716073\pi$
$43$	2.36138	−	4.09004i	0.360108	−	0.623725i	0.987978	+	0.154593i	$0.0494066\pi$
$44$			0.688179i			0.103747i
$45$	−0.590473	−	0.340910i	−0.0880226	−	0.0508199i
$46$	−5.67921	−	3.27889i	−0.837354	−	0.483447i
$47$		−	11.2638i		−	1.64299i	−0.570217	−	0.821494i	$-0.693141\pi$
$47$		−	11.2638i		−	1.64299i	0.570217	−	0.821494i	$-0.306859\pi$
$48$	2.48624	−	4.30629i	0.358857	−	0.621559i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−6.98826	+	4.03467i	−0.988289	+	0.570589i
$51$	6.29031			0.880820
$52$	0.966372	−	4.09117i	0.134012	−	0.567344i
$53$	12.2243			1.67914			0.839571	−	0.543249i	$-0.182806\pi$
$53$	12.2243			1.67914			0.839571	+	0.543249i	$0.182806\pi$
$54$	−1.54092	+	0.889651i	−0.209693	+	0.121066i
$55$	−0.201222	−	0.348526i	−0.0271327	−	0.0469953i
$56$	0.742046	−	1.28526i	0.0991601	−	0.171750i
$57$		−	3.58649i		−	0.475042i
$58$	−9.94229	−	5.74019i	−1.30549	−	0.753723i
$59$	−2.44791	−	1.41330i	−0.318691	−	0.183996i	0.332118	−	0.943238i	$-0.392237\pi$
$59$	−2.44791	−	1.41330i	−0.318691	−	0.183996i	−0.650809	+	0.759242i	$0.725570\pi$
$60$		−	0.794942i		−	0.102627i
$61$	−1.45571	+	2.52137i	−0.186385	+	0.322828i	−0.944042	−	0.329825i	$-0.893010\pi$
$61$	−1.45571	+	2.52137i	−0.186385	+	0.322828i	0.757658	+	0.652652i	$0.226344\pi$
$62$	−3.83166	−	6.63663i	−0.486621	−	0.842852i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	0.516173			0.0645217
$65$	0.706833	+	2.35453i	0.0876718	+	0.292043i
$66$	−1.05023			−0.129274
$67$	6.48168	−	3.74220i	0.791863	−	0.457182i	−0.0487551	−	0.998811i	$-0.515525\pi$
$67$	6.48168	−	3.74220i	0.791863	−	0.457182i	0.840618	+	0.541629i	$0.182192\pi$
$68$	3.66698	+	6.35139i	0.444686	+	0.770219i
$69$	1.84280	−	3.19182i	0.221847	−	0.384250i
$70$		−	1.21316i		−	0.145001i
$71$	6.05457	+	3.49561i	0.718545	+	0.414852i	0.814217	−	0.580561i	$-0.197167\pi$
$71$	6.05457	+	3.49561i	0.718545	+	0.414852i	−0.0956717	+	0.995413i	$0.530500\pi$
$72$	1.28526	+	0.742046i	0.151470	+	0.0874510i
$73$		−	7.30193i		−	0.854626i	−0.904104	−	0.427313i	$-0.859460\pi$
$73$		−	7.30193i		−	0.854626i	0.904104	−	0.427313i	$-0.140540\pi$
$74$	9.37183	−	16.2325i	1.08945	−	1.88699i
$75$	−2.26756	−	3.92753i	−0.261835	−	0.453512i
$76$	3.62132	−	2.09077i	0.415393	−	0.239828i
$77$	−0.590249			−0.0672651
$78$	6.24355	+	1.47478i	0.706943	+	0.166986i
$79$	−3.33737			−0.375484			−0.187742	−	0.982218i	$-0.560117\pi$
$79$	−3.33737			−0.375484			−0.187742	+	0.982218i	$0.560117\pi$
$80$	−2.93611	+	1.69517i	−0.328267	+	0.189525i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.140069	+	0.242607i	−0.0154681	+	0.0267915i
$83$		−	13.6469i		−	1.49794i	−0.662605	−	0.748969i	$-0.730549\pi$
$83$		−	13.6469i		−	1.49794i	0.662605	−	0.748969i	$-0.269451\pi$
$84$	−1.00971	−	0.582956i	−0.110168	−	0.0636057i
$85$	−3.71426	−	2.14443i	−0.402868	−	0.232596i
$86$			8.40323i			0.906143i
$87$	3.22609	−	5.58775i	0.345873	−	0.599070i
$88$	0.437992	+	0.758625i	0.0466901	+	0.0808697i
$89$	−10.6072	+	6.12405i	−1.12436	+	0.649148i	−0.942510	−	0.334178i	$-0.891541\pi$
$89$	−10.6072	+	6.12405i	−1.12436	+	0.649148i	−0.181848	+	0.983327i	$0.558208\pi$
$90$	1.21316			0.127879
$91$	3.50899	+	0.828855i	0.367842	+	0.0868876i
$92$	4.29709			0.448002
$93$	3.72991	−	2.15346i	0.386773	−	0.223304i
$94$	10.0208	+	17.3565i	1.03357	+	1.79019i
$95$	−1.22267	+	2.11773i	−0.125443	+	0.217274i
$96$			5.87934i			0.600058i
$97$	−9.18669	−	5.30394i	−0.932767	−	0.538533i	−0.0450816	−	0.998983i	$-0.514355\pi$
$97$	−9.18669	−	5.30394i	−0.932767	−	0.538533i	−0.887686	+	0.460450i	$0.847688\pi$
$98$	−1.54092	−	0.889651i	−0.155656	−	0.0898683i
$99$		−	0.590249i		−	0.0593223i
$100$	2.64378	−	4.57916i	0.264378	−	0.457916i
$101$	−2.13453	−	3.69711i	−0.212393	−	0.367876i	0.740070	−	0.672530i	$-0.234792\pi$
$101$	−2.13453	−	3.69711i	−0.212393	−	0.367876i	−0.952463	+	0.304654i	$0.901459\pi$
$102$	−9.69287	+	5.59618i	−0.959737	+	0.554104i
$103$	−6.67783			−0.657987			−0.328993	−	0.944332i	$-0.606709\pi$
$103$	−6.67783			−0.657987			−0.328993	+	0.944332i	$0.606709\pi$
$104$	−1.53854	−	5.12502i	−0.150866	−	0.502549i
$105$	0.681820			0.0665388
$106$	−18.8367	+	10.8754i	−1.82959	+	1.05631i
$107$	2.51180	+	4.35056i	0.242824	+	0.420584i	0.961518	−	0.274743i	$-0.0885928\pi$
$107$	2.51180	+	4.35056i	0.242824	+	0.420584i	−0.718693	+	0.695327i	$0.755259\pi$
$108$	0.582956	−	1.00971i	0.0560950	−	0.0971594i
$109$			15.0818i			1.44458i	0.691591	+	0.722289i	$0.256910\pi$
$109$			15.0818i			1.44458i	−0.691591	+	0.722289i	$0.743090\pi$
$110$	0.620133	+	0.358034i	0.0591274	+	0.0341372i
$111$	9.12296	+	5.26714i	0.865913	+	0.499935i
$112$			4.97247i			0.469855i
$113$	1.17116	−	2.02851i	0.110174	−	0.190827i	−0.805666	−	0.592369i	$-0.798193\pi$
$113$	1.17116	−	2.02851i	0.110174	−	0.190827i	0.915840	+	0.401543i	$0.131526\pi$
$114$	3.19072	+	5.52650i	0.298839	+	0.517604i
$115$	−2.17625	+	1.25646i	−0.202936	+	0.117165i
$116$	7.52268			0.698463
$117$	−0.828855	+	3.50899i	−0.0766276	+	0.324406i
$118$	5.02938			0.462992
$119$	−5.44757	+	3.14516i	−0.499378	+	0.288316i
$120$	−0.505942	−	0.876317i	−0.0461860	−	0.0799964i
$121$	−5.32580	+	9.22456i	−0.484164	+	0.838596i
$122$		−	5.18030i		−	0.469002i
$123$	−0.136350	−	0.0787215i	−0.0122942	−	0.00709808i
$124$	4.34874	+	2.51075i	0.390529	+	0.225472i
$125$			6.50124i			0.581488i
$126$	0.889651	−	1.54092i	0.0792564	−	0.137276i
$127$	−1.16803	−	2.02309i	−0.103646	−	0.179520i	0.809538	−	0.587067i	$-0.199718\pi$
$127$	−1.16803	−	2.02309i	−0.103646	−	0.179520i	−0.913184	+	0.407547i	$0.866384\pi$
$128$	9.38794	−	5.42013i	0.829784	−	0.479076i
$129$	−4.72277			−0.415817
$130$	−3.18388	−	2.99931i	−0.279245	−	0.263057i
$131$	7.64336			0.667803			0.333902	−	0.942608i	$-0.391635\pi$
$131$	7.64336			0.667803			0.333902	+	0.942608i	$0.391635\pi$
$132$	0.595980	−	0.344089i	0.0518734	−	0.0299491i
$133$	1.79325	+	3.10599i	0.155494	+	0.269324i
$134$	−6.65850	+	11.5329i	−0.575207	+	0.996287i
$135$			0.681820i			0.0586817i
$136$	8.08470	+	4.66770i	0.693257	+	0.400252i
$137$	6.42558	+	3.70981i	0.548974	+	0.316951i	0.748708	−	0.662900i	$-0.230674\pi$
$137$	6.42558	+	3.70981i	0.548974	+	0.316951i	−0.199734	+	0.979850i	$0.564008\pi$
$138$			6.55779i			0.558236i
$139$	−1.81306	+	3.14032i	−0.153782	+	0.266358i	−0.932615	−	0.360873i	$-0.882479\pi$
$139$	−1.81306	+	3.14032i	−0.153782	+	0.266358i	0.778833	+	0.627232i	$0.215812\pi$
$140$	0.397471	+	0.688440i	0.0335924	+	0.0581838i
$141$	−9.75470	+	5.63188i	−0.821494	+	0.474290i
$142$	−12.4395			−1.04390
$143$	−1.45927	+	1.54908i	−0.122031	+	0.129540i
$144$	−4.97247			−0.414373
$145$	−3.80984	+	2.19961i	−0.316390	+	0.182668i
$146$	6.49617	+	11.2517i	0.537627	+	0.931197i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$			12.2821i			1.00958i
$149$	−3.12701	−	1.80538i	−0.256174	−	0.147902i	0.366414	−	0.930452i	$-0.380585\pi$
$149$	−3.12701	−	1.80538i	−0.256174	−	0.147902i	−0.622588	+	0.782550i	$0.713919\pi$
$150$	6.98826	+	4.03467i	0.570589	+	0.329430i
$151$		−	9.51624i		−	0.774421i	−0.921991	−	0.387210i	$-0.873439\pi$
$151$		−	9.51624i		−	0.774421i	0.921991	−	0.387210i	$-0.126561\pi$
$152$	2.66134	−	4.60958i	0.215863	−	0.373886i
$153$	−3.14516	−	5.44757i	−0.254271	−	0.440410i
$154$	0.909527	−	0.525115i	0.0732917	−	0.0423150i
$155$	−2.93655			−0.235869
$156$	−4.02625	+	1.20868i	−0.322358	+	0.0967722i
$157$	16.0302			1.27935			0.639675	−	0.768645i	$-0.279069\pi$
$157$	16.0302			1.27935			0.639675	+	0.768645i	$0.279069\pi$
$158$	5.14263	−	2.96910i	0.409125	−	0.236209i
$159$	−6.11217	−	10.5866i	−0.484727	−	0.839571i
$160$	2.00433	−	3.47159i	0.158456	−	0.274454i
$161$			3.68560i			0.290466i
$162$	1.54092	+	0.889651i	0.121066	+	0.0698976i
$163$	−14.7998	−	8.54465i	−1.15921	−	0.669268i	−0.208093	−	0.978109i	$-0.566726\pi$
$163$	−14.7998	−	8.54465i	−1.15921	−	0.669268i	−0.951114	+	0.308841i	$0.900059\pi$
$164$		−	0.183565i		−	0.0143340i
$165$	−0.201222	+	0.348526i	−0.0156651	+	0.0271327i
$166$	12.1409	+	21.0287i	0.942319	+	1.63215i
$167$	3.12443	−	1.80389i	0.241776	−	0.139589i	−0.374217	−	0.927341i	$-0.622088\pi$
$167$	3.12443	−	1.80389i	0.241776	−	0.139589i	0.615993	+	0.787752i	$0.288755\pi$
$168$	−1.48409			−0.114500
$169$	10.8506	−	7.15997i	0.834659	−	0.550767i
$170$	7.63117			0.585284
$171$	−3.10599	+	1.79325i	−0.237521	+	0.137133i
$172$	−2.75317	−	4.76863i	−0.209927	−	0.363604i
$173$	4.92745	−	8.53459i	0.374627	−	0.648873i	−0.615644	−	0.788024i	$-0.711104\pi$
$173$	4.92745	−	8.53459i	0.374627	−	0.648873i	0.990271	+	0.139151i	$0.0444375\pi$
$174$			11.4804i			0.870325i
$175$	3.92753	+	2.26756i	0.296893	+	0.171411i
$176$	−2.54178	−	1.46750i	−0.191594	−	0.110617i
$177$			2.82660i			0.212460i
$178$	10.8965	−	18.8734i	0.816730	−	1.41462i
$179$	5.33000	+	9.23184i	0.398383	+	0.690020i	0.993527	−	0.113600i	$-0.0362381\pi$
$179$	5.33000	+	9.23184i	0.398383	+	0.690020i	−0.595143	+	0.803619i	$0.702905\pi$
$180$	−0.688440	+	0.397471i	−0.0513133	+	0.0296258i
$181$	−24.9606			−1.85530			−0.927652	−	0.373447i	$-0.878176\pi$
$181$	−24.9606			−1.85530			−0.927652	+	0.373447i	$0.878176\pi$
$182$	−6.14446	+	1.84458i	−0.455458	+	0.136729i
$183$	2.91142			0.215219
$184$	4.73696	−	2.73488i	0.349213	−	0.201618i
$185$	−3.59124	−	6.22022i	−0.264033	−	0.457319i
$186$	−3.83166	+	6.63663i	−0.280951	+	0.486621i
$187$		−	3.71285i		−	0.271511i
$188$	−11.3731	−	6.56628i	−0.829471	−	0.478895i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	4.35100i		−	0.315655i
$191$	7.91417	−	13.7078i	0.572649	−	0.991858i	−0.423643	−	0.905829i	$-0.639249\pi$
$191$	7.91417	−	13.7078i	0.572649	−	0.991858i	0.996293	−	0.0860288i	$-0.0274177\pi$
$192$	−0.258087	−	0.447019i	−0.0186258	−	0.0322608i
$193$	−16.3218	+	9.42342i	−1.17487	+	0.678312i	−0.954823	−	0.297176i	$-0.903955\pi$
$193$	−16.3218	+	9.42342i	−1.17487	+	0.678312i	−0.220049	+	0.975489i	$0.570622\pi$
$194$	18.8746			1.35512
$195$	1.68567	−	1.78940i	0.120713	−	0.128142i
$196$	1.16591			0.0832795
$197$	−11.5299	+	6.65681i	−0.821474	+	0.474278i	−0.850924	−	0.525288i	$-0.823957\pi$
$197$	−11.5299	+	6.65681i	−0.821474	+	0.474278i	0.0294508	+	0.999566i	$0.490624\pi$
$198$	0.525115	+	0.909527i	0.0373183	+	0.0646372i
$199$	10.3046	−	17.8482i	0.730476	−	1.26522i	−0.226204	−	0.974080i	$-0.572632\pi$
$199$	10.3046	−	17.8482i	0.730476	−	1.26522i	0.956680	−	0.291142i	$-0.0940352\pi$
$200$		−	6.73054i		−	0.475921i
$201$	−6.48168	−	3.74220i	−0.457182	−	0.263954i
$202$	6.57827	+	3.79797i	0.462846	+	0.267224i
$203$			6.45218i			0.452854i
$204$	3.66698	−	6.35139i	0.256740	−	0.444686i
$205$	0.0536739	+	0.0929659i	0.00374875	+	0.00649302i
$206$	10.2900	−	5.94094i	0.716939	−	0.413925i
$207$	−3.68560			−0.256167
$208$	13.0500	+	12.2935i	0.904854	+	0.852398i
$209$	−2.11692			−0.146431
$210$	−1.05063	+	0.606581i	−0.0725004	+	0.0418581i
$211$	9.25869	+	16.0365i	0.637394	+	1.10400i	0.986002	+	0.166731i	$0.0533211\pi$
$211$	9.25869	+	16.0365i	0.637394	+	1.10400i	−0.348608	+	0.937269i	$0.613346\pi$
$212$	7.12626	−	12.3430i	0.489433	−	0.847724i
$213$		−	6.99122i		−	0.479030i
$214$	−7.74095	−	4.46924i	−0.529161	−	0.305511i
$215$	2.78867	+	1.61004i	0.190186	+	0.109804i
$216$		−	1.48409i		−	0.100980i
$217$	−2.15346	+	3.72991i	−0.146187	+	0.253203i
$218$	−13.4176	−	23.2399i	−0.908752	−	1.57401i
$219$	−6.32366	+	3.65097i	−0.427313	+	0.246709i
$220$	−0.469214			−0.0316344
$221$	−5.21375	+	22.0726i	−0.350715	+	1.48477i
$222$	−18.7437			−1.25799
$223$	12.8214	−	7.40244i	0.858585	−	0.495704i	−0.00495319	−	0.999988i	$-0.501577\pi$
$223$	12.8214	−	7.40244i	0.858585	−	0.495704i	0.863538	+	0.504283i	$0.168243\pi$
$224$	−2.93967	−	5.09166i	−0.196415	−	0.340201i
$225$	−2.26756	+	3.92753i	−0.151171	+	0.261835i
$226$			4.16770i			0.277232i
$227$	0.134514	+	0.0776616i	0.00892800	+	0.00515458i	0.504457	−	0.863437i	$-0.331693\pi$
$227$	0.134514	+	0.0776616i	0.00892800	+	0.00515458i	−0.495529	+	0.868591i	$0.665026\pi$
$228$	−3.62132	−	2.09077i	−0.239828	−	0.138464i
$229$		−	24.8216i		−	1.64026i	−0.572179	−	0.820129i	$-0.693902\pi$
$229$		−	24.8216i		−	1.64026i	0.572179	−	0.820129i	$-0.306098\pi$
$230$	2.23562	−	3.87220i	0.147412	−	0.255325i
$231$	0.295125	+	0.511171i	0.0194178	+	0.0336326i
$232$	8.29274	−	4.78782i	0.544445	−	0.314336i
$233$	9.79706			0.641826			0.320913	−	0.947109i	$-0.396010\pi$
$233$	9.79706			0.641826			0.320913	+	0.947109i	$0.396010\pi$
$234$	−1.84458	−	6.14446i	−0.120584	−	0.401676i
$235$	7.67985			0.500978
$236$	−2.85405	+	1.64779i	−0.185783	+	0.107262i
$237$	1.66869	+	2.89025i	0.108393	+	0.187742i
$238$	5.59618	−	9.69287i	0.362746	−	0.628295i
$239$		−	17.2503i		−	1.11583i	−0.829899	−	0.557914i	$-0.811602\pi$
$239$		−	17.2503i		−	1.11583i	0.829899	−	0.557914i	$-0.188398\pi$
$240$	2.93611	+	1.69517i	0.189525	+	0.109422i
$241$	−0.724610	−	0.418354i	−0.0466762	−	0.0269485i	0.476480	−	0.879185i	$-0.341912\pi$
$241$	−0.724610	−	0.418354i	−0.0466762	−	0.0269485i	−0.523157	+	0.852237i	$0.675246\pi$
$242$		−	18.9524i		−	1.21831i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.69723	+	2.93969i	0.108654	+	0.188194i
$245$	−0.590473	+	0.340910i	−0.0377240	+	0.0217799i
$246$	0.280138			0.0178610
$247$	12.5850	+	2.97268i	0.800762	+	0.189147i
$248$	6.39188			0.405884
$249$	−11.8185	+	6.82343i	−0.748969	+	0.432417i
$250$	−5.78383	−	10.0179i	−0.365801	−	0.633587i
$251$	−7.30458	+	12.6519i	−0.461061	+	0.798581i	−0.999014	−	0.0443934i	$-0.985864\pi$
$251$	−7.30458	+	12.6519i	−0.461061	+	0.798581i	0.537953	+	0.842975i	$0.319198\pi$
$252$			1.16591i			0.0734456i
$253$	−1.88397	−	1.08771i	−0.118444	−	0.0683838i
$254$	3.59968	+	2.07828i	0.225864	+	0.130403i
$255$			4.28886i			0.268579i
$256$	−10.1602	+	17.5980i	−0.635013	+	1.09988i
$257$	−6.26506	−	10.8514i	−0.390804	−	0.676892i	0.601752	−	0.798683i	$-0.294470\pi$
$257$	−6.26506	−	10.8514i	−0.390804	−	0.676892i	−0.992556	+	0.121791i	$0.961136\pi$
$258$	7.27741	−	4.20161i	0.453072	−	0.261581i
$259$	−10.5343			−0.654569
$260$	2.78944	+	0.658892i	0.172994	+	0.0408627i
$261$	−6.45218			−0.399380
$262$	−11.7778	+	6.79992i	−0.727635	+	0.420100i
$263$	−9.62427	−	16.6697i	−0.593458	−	1.02790i	−0.993762	−	0.111517i	$-0.964429\pi$
$263$	−9.62427	−	16.6697i	−0.593458	−	1.02790i	0.400304	−	0.916382i	$-0.368904\pi$
$264$	0.437992	−	0.758625i	0.0269566	−	0.0466901i
$265$			8.33480i			0.512003i
$266$	−5.52650	−	3.19072i	−0.338851	−	0.195636i
$267$	10.6072	+	6.12405i	0.649148	+	0.374786i
$268$		−	8.72615i		−	0.533035i
$269$	−3.36396	+	5.82655i	−0.205104	+	0.355251i	−0.950166	−	0.311744i	$-0.899087\pi$
$269$	−3.36396	+	5.82655i	−0.205104	+	0.355251i	0.745062	+	0.666996i	$0.232420\pi$
$270$	−0.606581	−	1.05063i	−0.0369154	−	0.0639393i
$271$	13.8793	−	8.01324i	0.843109	−	0.486769i	−0.0152106	−	0.999884i	$-0.504842\pi$
$271$	13.8793	−	8.01324i	0.843109	−	0.486769i	0.858320	+	0.513115i	$0.171509\pi$
$272$	−31.2784			−1.89653
$273$	−1.03669	−	3.45330i	−0.0627430	−	0.209003i
$274$	−13.2017			−0.797546
$275$	−2.31822	+	1.33843i	−0.139794	+	0.0807101i
$276$	−2.14854	−	3.72139i	−0.129327	−	0.224001i
$277$	−2.01427	+	3.48882i	−0.121026	+	0.209623i	−0.920172	−	0.391513i	$-0.871952\pi$
$277$	−2.01427	+	3.48882i	−0.121026	+	0.209623i	0.799147	+	0.601136i	$0.205285\pi$
$278$		−	6.45198i		−	0.386964i
$279$	−3.72991	−	2.15346i	−0.223304	−	0.128924i
$280$	0.876317	+	0.505942i	0.0523700	+	0.0302358i
$281$			13.1699i			0.785649i	0.919614	+	0.392824i	$0.128502\pi$
$281$			13.1699i			0.785649i	−0.919614	+	0.392824i	$0.871498\pi$
$282$	10.0208	−	17.3565i	0.596730	−	1.03357i
$283$	−3.16041	−	5.47399i	−0.187867	−	0.325395i	0.756672	−	0.653795i	$-0.226824\pi$
$283$	−3.16041	−	5.47399i	−0.187867	−	0.325395i	−0.944539	+	0.328400i	$0.893491\pi$
$284$	7.05910	−	4.07557i	0.418881	−	0.241841i
$285$	2.44534			0.144850
$286$	0.870489	−	3.68525i	0.0514731	−	0.217913i
$287$	0.157443			0.00929356
$288$	5.09166	−	2.93967i	0.300029	−	0.173222i
$289$	−11.2840	−	19.5445i	−0.663765	−	1.14968i
$290$	3.91377	−	6.77885i	0.229825	−	0.398068i
$291$			10.6079i			0.621845i
$292$	−7.37283	−	4.25671i	−0.431462	−	0.249105i
$293$	18.2143	+	10.5160i	1.06409	+	0.614354i	0.926561	−	0.376144i	$-0.122750\pi$
$293$	18.2143	+	10.5160i	1.06409	+	0.614354i	0.137530	+	0.990498i	$0.456084\pi$
$294$			1.77930i			0.103771i
$295$	0.963617	−	1.66903i	0.0561039	−	0.0971749i
$296$	7.81693	+	13.5393i	0.454350	+	0.786957i
$297$	−0.511171	+	0.295125i	−0.0296611	+	0.0171249i
$298$	6.42462			0.372168
$299$	9.67265	+	9.11192i	0.559384	+	0.526956i
$300$	−5.28756			−0.305277
$301$	4.09004	−	2.36138i	0.235746	−	0.136108i
$302$	8.46613	+	14.6638i	0.487171	+	0.843805i
$303$	−2.13453	+	3.69711i	−0.122625	+	0.212393i
$304$			17.8337i			1.02283i
$305$	−1.71912	−	0.992533i	−0.0984364	−	0.0568323i
$306$	9.69287	+	5.59618i	0.554104	+	0.319912i
$307$			28.5122i			1.62728i	0.581372	+	0.813638i	$0.302516\pi$
$307$			28.5122i			1.62728i	−0.581372	+	0.813638i	$0.697484\pi$
$308$	−0.344089	+	0.595980i	−0.0196063	+	0.0339591i
$309$	3.33892	+	5.78317i	0.189944	+	0.328993i
$310$	4.52498	−	2.61250i	0.257002	−	0.148380i
$311$	−23.5329			−1.33443			−0.667213	−	0.744867i	$-0.732513\pi$
$311$	−23.5329			−1.33443			−0.667213	+	0.744867i	$0.732513\pi$
$312$	−3.66913	+	3.89492i	−0.207723	+	0.220506i
$313$	−16.4524			−0.929942			−0.464971	−	0.885326i	$-0.653935\pi$
$313$	−16.4524			−0.929942			−0.464971	+	0.885326i	$0.653935\pi$
$314$	−24.7013	+	14.2613i	−1.39397	+	0.804811i
$315$	−0.340910	−	0.590473i	−0.0192081	−	0.0332694i
$316$	−1.94554	+	3.36978i	−0.109445	+	0.189565i
$317$		−	15.7235i		−	0.883119i	−0.897232	−	0.441560i	$-0.854425\pi$
$317$		−	15.7235i		−	0.883119i	0.897232	−	0.441560i	$-0.145575\pi$
$318$	18.8367	+	10.8754i	1.05631	+	0.609862i
$319$	−3.29817	−	1.90420i	−0.184662	−	0.106615i
$320$			0.351937i			0.0196739i
$321$	2.51180	−	4.35056i	0.140195	−	0.242824i
$322$	−3.27889	−	5.67921i	−0.182726	−	0.316490i
$323$	−19.5377	+	11.2801i	−1.08710	+	0.627640i
$324$	−1.16591			−0.0647729
$325$	15.6611	−	4.70149i	0.868724	−	0.260792i
$326$	30.4070			1.68409
$327$	13.0613	−	7.54092i	0.722289	−	0.417014i
$328$	−0.116830	−	0.202355i	−0.00645086	−	0.0111732i
$329$	5.63188	−	9.75470i	0.310495	−	0.537794i
$330$		−	0.716068i		−	0.0394183i
$331$	−3.83980	−	2.21691i	−0.211055	−	0.121852i	0.390747	−	0.920498i	$-0.372217\pi$
$331$	−3.83980	−	2.21691i	−0.211055	−	0.121852i	−0.601801	+	0.798646i	$0.705550\pi$
$332$	−13.7794	−	7.95552i	−0.756241	−	0.436616i
$333$		−	10.5343i		−	0.577275i
$334$	−3.20967	+	5.55931i	−0.175625	+	0.304192i
$335$	2.55151	+	4.41934i	0.139404	+	0.241454i
$336$	4.30629	−	2.48624i	0.234927	−	0.135635i
$337$	4.04766			0.220490			0.110245	−	0.993904i	$-0.464836\pi$
$337$	4.04766			0.220490			0.110245	+	0.993904i	$0.464836\pi$
$338$	−10.3500	+	20.6862i	−0.562965	+	1.12518i
$339$	−2.34233			−0.127218
$340$	−4.33050	+	2.50022i	−0.234855	+	0.135593i
$341$	−1.27108	−	2.20157i	−0.0688328	−	0.119222i
$342$	3.19072	−	5.52650i	0.172535	−	0.298839i
$343$			1.00000i			0.0539949i
$344$	−6.06999	−	3.50451i	−0.327272	−	0.188951i
$345$	2.17625	+	1.25646i	0.117165	+	0.0676454i
$346$			17.5348i			0.942678i
$347$	−12.4759	+	21.6090i	−0.669743	+	1.16003i	0.308232	+	0.951311i	$0.400263\pi$
$347$	−12.4759	+	21.6090i	−0.669743	+	1.16003i	−0.977976	+	0.208719i	$0.933071\pi$
$348$	−3.76134	−	6.51483i	−0.201629	−	0.349232i
$349$	21.8911	−	12.6388i	1.17180	−	0.676541i	0.217700	−	0.976016i	$-0.430145\pi$
$349$	21.8911	−	12.6388i	1.17180	−	0.676541i	0.954104	+	0.299474i	$0.0968113\pi$
$350$	−8.06935			−0.431325
$351$	3.45330	−	1.03669i	0.184324	−	0.0553342i
$352$	3.47028			0.184966
$353$	−18.2241	+	10.5217i	−0.969973	+	0.560014i	−0.899228	−	0.437480i	$-0.855871\pi$
$353$	−18.2241	+	10.5217i	−0.969973	+	0.560014i	−0.0707453	+	0.997494i	$0.522538\pi$
$354$	−2.51469	−	4.35557i	−0.133654	−	0.231496i
$355$	−2.38338	+	4.12813i	−0.126496	+	0.219098i
$356$			14.2802i			0.756850i
$357$	5.44757	+	3.14516i	0.288316	+	0.166459i
$358$	−16.4262	−	9.48368i	−0.868153	−	0.501228i
$359$			4.11834i			0.217358i	0.994077	+	0.108679i	$0.0346620\pi$
$359$			4.11834i			0.217358i	−0.994077	+	0.108679i	$0.965338\pi$
$360$	−0.505942	+	0.876317i	−0.0266655	+	0.0461860i
$361$	−3.06854	−	5.31486i	−0.161502	−	0.279730i
$362$	38.4622	−	22.2062i	2.02153	−	1.16713i
$363$	10.6516			0.559064
$364$	2.88249	−	3.05987i	0.151084	−	0.160381i
$365$	4.97860			0.260592
$366$	−4.48627	+	2.59015i	−0.234501	+	0.135389i
$367$	−6.75164	−	11.6942i	−0.352433	−	0.610431i	0.634242	−	0.773134i	$-0.281312\pi$
$367$	−6.75164	−	11.6942i	−0.352433	−	0.610431i	−0.986675	+	0.162703i	$0.947979\pi$
$368$	−9.16327	+	15.8712i	−0.477668	+	0.827346i
$369$			0.157443i			0.00819615i
$370$	11.0676	+	6.38990i	0.575379	+	0.332195i
$371$	10.5866	+	6.11217i	0.549629	+	0.317328i
$372$		−	5.02150i		−	0.260353i
$373$	−12.4091	+	21.4931i	−0.642517	+	1.11287i	0.342352	+	0.939572i	$0.388777\pi$
$373$	−12.4091	+	21.4931i	−0.642517	+	1.11287i	−0.984869	+	0.173301i	$0.944557\pi$
$374$	3.30314	+	5.72121i	0.170801	+	0.295837i
$375$	5.63024	−	3.25062i	0.290744	−	0.167861i
$376$	−16.7165			−0.862086
$377$	16.9334	+	15.9517i	0.872114	+	0.821557i
$378$	−1.77930			−0.0915174
$379$	31.2311	−	18.0313i	1.60423	−	0.926205i	0.613606	−	0.789612i	$-0.289718\pi$
$379$	31.2311	−	18.0313i	1.60423	−	0.926205i	0.990627	−	0.136593i	$-0.0436151\pi$
$380$	1.42553	+	2.46909i	0.0731280	+	0.126661i
$381$	−1.16803	+	2.02309i	−0.0598400	+	0.103646i
$382$			28.1634i			1.44096i
$383$	−21.2355	−	12.2603i	−1.08509	−	0.626474i	−0.152821	−	0.988254i	$-0.548836\pi$
$383$	−21.2355	−	12.2603i	−1.08509	−	0.626474i	−0.932264	+	0.361780i	$0.882169\pi$
$384$	−9.38794	−	5.42013i	−0.479076	−	0.276595i
$385$		−	0.402444i		−	0.0205104i
$386$	16.7671	−	29.0415i	0.853423	−	1.47817i
$387$	2.36138	+	4.09004i	0.120036	+	0.207908i
$388$	−10.7109	+	6.18393i	−0.543763	+	0.313941i
$389$	38.3037			1.94208			0.971038	−	0.238925i	$-0.0767950\pi$
$389$	38.3037			1.94208			0.971038	+	0.238925i	$0.0767950\pi$
$390$	−1.00554	+	4.25697i	−0.0509173	+	0.215560i
$391$	−23.1836			−1.17244
$392$	1.28526	−	0.742046i	0.0649155	−	0.0374790i
$393$	−3.82168	−	6.61934i	−0.192778	−	0.333902i
$394$	11.8445	−	20.5152i	0.596716	−	1.03354i
$395$		−	2.27549i		−	0.114492i
$396$	−0.595980	−	0.344089i	−0.0299491	−	0.0172911i
$397$	−13.5534	−	7.82508i	−0.680227	−	0.392729i	0.119713	−	0.992808i	$-0.461802\pi$
$397$	−13.5534	−	7.82508i	−0.680227	−	0.392729i	−0.799941	+	0.600079i	$0.795136\pi$
$398$			36.6701i			1.83811i
$399$	1.79325	−	3.10599i	0.0897746	−	0.155494i
$400$	11.2754	+	19.5295i	0.563769	+	0.976477i
$401$	26.4453	−	15.2682i	1.32062	−	0.762458i	0.336789	−	0.941580i	$-0.390659\pi$
$401$	26.4453	−	15.2682i	1.32062	−	0.762458i	0.983827	+	0.179122i	$0.0573257\pi$
$402$	13.3170			0.664191
$403$	4.46492	+	14.8731i	0.222414	+	0.740882i
$404$	−4.97734			−0.247632
$405$	0.590473	−	0.340910i	0.0293409	−	0.0169400i
$406$	−5.74019	−	9.94229i	−0.284881	−	0.493428i
$407$	3.10893	−	5.38482i	0.154104	−	0.266916i
$408$		−	9.33541i		−	0.462171i
$409$	−7.93833	−	4.58320i	−0.392525	−	0.226625i	0.290729	−	0.956806i	$-0.406102\pi$
$409$	−7.93833	−	4.58320i	−0.392525	−	0.226625i	−0.683254	+	0.730181i	$0.739436\pi$
$410$	−0.165414	−	0.0955020i	−0.00816923	−	0.00471651i
$411$		−	7.41962i		−	0.365983i
$412$	−3.89289	+	6.74268i	−0.191789	+	0.332188i
$413$	−1.41330	−	2.44791i	−0.0695440	−	0.120454i
$414$	5.67921	−	3.27889i	0.279118	−	0.161149i
$415$	9.30470			0.456750
$416$	−20.6305	−	4.87312i	−1.01150	−	0.238924i
$417$	3.62613			0.177572
$418$	3.26201	−	1.88332i	0.159550	−	0.0921163i
$419$	−13.1190	−	22.7227i	−0.640904	−	1.11008i	−0.985231	−	0.171229i	$-0.945226\pi$
$419$	−13.1190	−	22.7227i	−0.640904	−	1.11008i	0.344327	−	0.938850i	$-0.388107\pi$
$420$	0.397471	−	0.688440i	0.0193946	−	0.0335924i
$421$		−	8.78689i		−	0.428247i	−0.976807	−	0.214123i	$-0.931311\pi$
$421$		−	8.78689i		−	0.428247i	0.976807	−	0.214123i	$-0.0686894\pi$
$422$	−28.5338	−	16.4740i	−1.38900	−	0.801942i
$423$	9.75470	+	5.63188i	0.474290	+	0.273831i
$424$		−	18.1421i		−	0.881056i
$425$	−14.2637	+	24.7054i	−0.691889	+	1.19839i
$426$	6.21974	+	10.7729i	0.301347	+	0.521949i
$427$	−2.52137	+	1.45571i	−0.122017	+	0.0704468i
$428$	5.85707			0.283112
$429$	2.07118	+	0.489231i	0.0999974	+	0.0236203i
$430$	−5.72949			−0.276300
$431$	32.9199	−	19.0063i	1.58570	−	0.915502i	0.591692	−	0.806164i	$-0.298460\pi$
$431$	32.9199	−	19.0063i	1.58570	−	0.915502i	0.994005	−	0.109338i	$-0.0348731\pi$
$432$	2.48624	+	4.30629i	0.119619	+	0.207186i
$433$	−1.06416	+	1.84318i	−0.0511403	+	0.0885776i	−0.890462	−	0.455057i	$-0.849619\pi$
$433$	−1.06416	+	1.84318i	−0.0511403	+	0.0885776i	0.839322	+	0.543635i	$0.182952\pi$
$434$		−	7.66332i		−	0.367851i
$435$	3.80984	+	2.19961i	0.182668	+	0.105463i
$436$	15.2283	+	8.79205i	0.729302	+	0.421063i
$437$			13.2184i			0.632320i
$438$	6.49617	−	11.2517i	0.310399	−	0.537627i
$439$	10.3194	+	17.8737i	0.492518	+	0.853066i	0.999963	−	0.00861803i	$-0.00274324\pi$
$439$	10.3194	+	17.8737i	0.492518	+	0.853066i	−0.507445	+	0.861684i	$0.669410\pi$
$440$	−0.517245	+	0.298632i	−0.0246587	+	0.0142367i
$441$	−1.00000			−0.0476190
$442$	−11.6030	−	38.6506i	−0.551896	−	1.83842i
$443$	−14.0681			−0.668395			−0.334197	−	0.942503i	$-0.608465\pi$
$443$	−14.0681			−0.668395			−0.334197	+	0.942503i	$0.608465\pi$
$444$	10.6366	−	6.14103i	0.504789	−	0.291440i
$445$	−4.17550	−	7.23218i	−0.197938	−	0.342838i
$446$	−13.1712	+	22.8131i	−0.623673	+	1.08023i
$447$			3.61075i			0.170783i
$448$	0.447019	+	0.258087i	0.0211197	+	0.0121934i
$449$	−5.41489	−	3.12629i	−0.255545	−	0.147539i	0.366756	−	0.930317i	$-0.380468\pi$
$449$	−5.41489	−	3.12629i	−0.255545	−	0.147539i	−0.622300	+	0.782778i	$0.713802\pi$
$450$		−	8.06935i		−	0.380393i
$451$	−0.0464653	+	0.0804802i	−0.00218796	+	0.00378967i
$452$	−1.36547	−	2.36507i	−0.0642265	−	0.111244i
$453$	−8.24131	+	4.75812i	−0.387210	+	0.223556i
$454$	−0.276367			−0.0129705
$455$	−0.565129	+	2.39250i	−0.0264937	+	0.112162i
$456$	−5.32269			−0.249258
$457$	29.4370	−	16.9955i	1.37700	−	0.795014i	0.385206	−	0.922830i	$-0.374130\pi$
$457$	29.4370	−	16.9955i	1.37700	−	0.795014i	0.991798	+	0.127817i	$0.0407970\pi$
$458$	22.0826	+	38.2481i	1.03185	+	1.78722i
$459$	−3.14516	+	5.44757i	−0.146803	+	0.254271i
$460$			2.92984i			0.136604i
$461$	−10.2996	−	5.94647i	−0.479700	−	0.276955i	0.240592	−	0.970626i	$-0.422659\pi$
$461$	−10.2996	−	5.94647i	−0.479700	−	0.276955i	−0.720291	+	0.693672i	$0.755992\pi$
$462$	−0.909527	−	0.525115i	−0.0423150	−	0.0244306i
$463$		−	13.4263i		−	0.623972i	−0.950087	−	0.311986i	$-0.899006\pi$
$463$		−	13.4263i		−	0.623972i	0.950087	−	0.311986i	$-0.100994\pi$
$464$	−16.0416	+	27.7849i	−0.744715	+	1.28988i
$465$	1.46827	+	2.54312i	0.0680896	+	0.117935i
$466$	−15.0965	+	8.71596i	−0.699331	+	0.403759i
$467$	39.4492			1.82549			0.912745	−	0.408530i	$-0.133958\pi$
$467$	39.4492			1.82549			0.912745	+	0.408530i	$0.133958\pi$
$468$	3.05987	+	2.88249i	0.141443	+	0.133243i
$469$	7.48440			0.345597
$470$	−11.8340	+	6.83239i	−0.545864	+	0.315154i
$471$	−8.01511	−	13.8826i	−0.369317	−	0.639675i
$472$	−2.09747	+	3.63292i	−0.0965439	+	0.167219i
$473$			2.78761i			0.128174i
$474$	−5.14263	−	2.96910i	−0.236209	−	0.136375i
$475$	14.0861	+	8.13259i	0.646313	+	0.373149i
$476$			7.33395i			0.336151i
$477$	−6.11217	+	10.5866i	−0.279857	+	0.484727i
$478$	15.3467	+	26.5813i	0.701943	+	1.21580i
$479$	−29.1368	+	16.8221i	−1.33130	+	0.768624i	−0.985498	−	0.169686i	$-0.945725\pi$
$479$	−29.1368	+	16.8221i	−1.33130	+	0.768624i	−0.345797	+	0.938309i	$0.612391\pi$
$480$	−4.00865			−0.182969
$481$	−26.0439	+	27.6467i	−1.18750	+	1.26058i
$482$	1.48875			0.0678109
$483$	3.19182	−	1.84280i	0.145233	−	0.0838503i
$484$	6.20942	+	10.7550i	0.282246	+	0.488865i
$485$	3.61633	−	6.26367i	0.164209	−	0.284419i
$486$		−	1.77930i		−	0.0807107i
$487$	−16.0598	−	9.27213i	−0.727739	−	0.420161i	0.0898552	−	0.995955i	$-0.471360\pi$
$487$	−16.0598	−	9.27213i	−0.727739	−	0.420161i	−0.817595	+	0.575794i	$0.804693\pi$
$488$	3.74194	+	2.16041i	0.169390	+	0.0977972i
$489$			17.0893i			0.772805i
$490$	0.606581	−	1.05063i	0.0274026	−	0.0474626i
$491$	−14.0907	−	24.4059i	−0.635906	−	1.10142i	−0.986322	−	0.164827i	$-0.947293\pi$
$491$	−14.0907	−	24.4059i	−0.635906	−	1.10142i	0.350417	−	0.936594i	$-0.386040\pi$
$492$	−0.158972	+	0.0917824i	−0.00716700	+	0.00413787i
$493$	−40.5862			−1.82791
$494$	−22.0371	+	6.61555i	−0.991494	+	0.297648i
$495$	0.402444			0.0180885
$496$	−18.5469	+	10.7080i	−0.832778	+	0.480805i
$497$	3.49561	+	6.05457i	0.156799	+	0.271585i
$498$	12.1409	−	21.0287i	0.544048	−	0.942319i
$499$			14.1038i			0.631373i	0.948864	+	0.315686i	$0.102235\pi$
$499$			14.1038i			0.631373i	−0.948864	+	0.315686i	$0.897765\pi$
$500$	6.56436	+	3.78994i	0.293567	+	0.169491i
$501$	−3.12443	−	1.80389i	−0.139589	−	0.0805920i
$502$		−	25.9941i		−	1.16017i
$503$	−11.1354	+	19.2870i	−0.496502	+	0.859967i	−0.999992	−	0.00403432i	$-0.998716\pi$
$503$	−11.1354	+	19.2870i	−0.496502	+	0.859967i	0.503490	+	0.864001i	$0.332049\pi$
$504$	0.742046	+	1.28526i	0.0330534	+	0.0572501i
$505$	2.52076	−	1.45536i	0.112172	−	0.0647628i
$506$	3.87073			0.172075
$507$	−11.6260	−	5.81688i	−0.516329	−	0.258337i
$508$	−2.72364			−0.120842
$509$	−6.00319	+	3.46595i	−0.266087	+	0.153625i	−0.627108	−	0.778932i	$-0.715762\pi$
$509$	−6.00319	+	3.46595i	−0.266087	+	0.153625i	0.361021	+	0.932558i	$0.382428\pi$
$510$	−3.81559	−	6.60879i	−0.168957	−	0.292642i
$511$	3.65097	−	6.32366i	0.161509	−	0.279742i
$512$		−	14.4756i		−	0.639739i
$513$	3.10599	+	1.79325i	0.137133	+	0.0791737i
$514$	19.3079	+	11.1474i	0.851636	+	0.491692i
$515$		−	4.55308i		−	0.200633i
$516$	−2.75317	+	4.76863i	−0.121201	+	0.209927i
$517$	3.32421	+	5.75770i	0.146199	+	0.253223i
$518$	16.2325	−	9.37183i	0.713215	−	0.411775i
$519$	−9.85489			−0.432582
$520$	3.49434	−	1.04901i	0.153237	−	0.0460019i
$521$	18.8949			0.827801			0.413900	−	0.910322i	$-0.364166\pi$
$521$	18.8949			0.827801			0.413900	+	0.910322i	$0.364166\pi$
$522$	9.94229	−	5.74019i	0.435162	−	0.251241i
$523$	−6.27981	−	10.8770i	−0.274597	−	0.475616i	0.695436	−	0.718588i	$-0.255211\pi$
$523$	−6.27981	−	10.8770i	−0.274597	−	0.475616i	−0.970033	+	0.242972i	$0.921878\pi$
$524$	4.45574	−	7.71757i	0.194650	−	0.337144i
$525$		−	4.53512i		−	0.197929i
$526$	29.6605	+	17.1245i	1.29326	+	0.746663i
$527$	−23.4623	−	13.5459i	−1.02203	−	0.590071i
$528$			2.93500i			0.127729i
$529$	4.70818	−	8.15481i	0.204704	−	0.354557i
$530$	−7.41506	−	12.8433i	−0.322090	−	0.557876i
$531$	2.44791	−	1.41330i	0.106230	−	0.0613320i
$532$	4.18154			0.181293
$533$	0.389247	−	0.413201i	0.0168601	−	0.0178977i
$534$	−21.7931			−0.943079
$535$	−2.96630	+	1.71259i	−0.128244	+	0.0740418i
$536$	−5.55377	−	9.61941i	−0.239886	−	0.415495i
$537$	5.33000	−	9.23184i	0.230007	−	0.398383i
$538$		−	11.9710i		−	0.516106i
$539$	−0.511171	−	0.295125i	−0.0220177	−	0.0127119i
$540$	0.688440	+	0.397471i	0.0296258	+	0.0171044i
$541$			19.5342i			0.839840i	0.907561	+	0.419920i	$0.137942\pi$
$541$			19.5342i			0.839840i	−0.907561	+	0.419920i	$0.862058\pi$
$542$	−14.2580	+	24.6955i	−0.612432	+	1.06076i
$543$	12.4803	+	21.6165i	0.535580	+	0.927652i
$544$	32.0281	−	18.4914i	1.37319	−	0.792814i
$545$	−10.2831			−0.440479
$546$	4.66968	+	4.39897i	0.199844	+	0.188259i
$547$	23.0987			0.987630			0.493815	−	0.869567i	$-0.335602\pi$
$547$	23.0987			0.987630			0.493815	+	0.869567i	$0.335602\pi$
$548$	7.49167	−	4.32532i	0.320028	−	0.184768i
$549$	−1.45571	−	2.52137i	−0.0621282	−	0.107609i
$550$	2.38146	−	4.12481i	0.101546	−	0.175883i
$551$			23.1407i			0.985827i
$552$	−4.73696	−	2.73488i	−0.201618	−	0.116404i
$553$	−2.89025	−	1.66869i	−0.122906	−	0.0709598i
$554$		−	7.16799i		−	0.304539i
$555$	−3.59124	+	6.22022i	−0.152440	+	0.264033i
$556$	2.11387	+	3.66134i	0.0896483	+	0.155275i
$557$	−11.6909	+	6.74976i	−0.495361	+	0.285997i	−0.726796	−	0.686854i	$-0.758991\pi$
$557$	−11.6909	+	6.74976i	−0.495361	+	0.285997i	0.231435	+	0.972850i	$0.425658\pi$
$558$	7.66332			0.324414
$559$	3.91449	−	16.5721i	0.165565	−	0.700927i
$560$	−3.39033			−0.143268
$561$	−3.21542	+	1.85643i	−0.135755	+	0.0783783i
$562$	−11.7166	−	20.2937i	−0.494234	−	0.856039i
$563$	−0.0675210	+	0.116950i	−0.00284567	+	0.00492885i	−0.867445	−	0.497534i	$-0.834239\pi$
$563$	−0.0675210	+	0.116950i	−0.00284567	+	0.00492885i	0.864599	+	0.502462i	$0.167572\pi$
$564$			13.1326i			0.552980i
$565$	1.38308	+	0.798523i	0.0581867	+	0.0335941i
$566$	9.73988	+	5.62332i	0.409398	+	0.236366i
$567$		−	1.00000i		−	0.0419961i
$568$	5.18781	−	8.98554i	0.217676	−	0.377025i
$569$	−5.23472	−	9.06680i	−0.219451	−	0.380100i	0.735189	−	0.677862i	$-0.237093\pi$
$569$	−5.23472	−	9.06680i	−0.219451	−	0.380100i	−0.954640	+	0.297762i	$0.903760\pi$
$570$	−3.76808	+	2.17550i	−0.157827	+	0.0911216i
$571$	38.7700			1.62247			0.811237	−	0.584718i	$-0.198795\pi$
$571$	38.7700			1.62247			0.811237	+	0.584718i	$0.198795\pi$
$572$	0.713425	+	2.37649i	0.0298298	+	0.0993660i
$573$	−15.8283			−0.661239
$574$	−0.242607	+	0.140069i	−0.0101262	+	0.00584638i
$575$	8.35732	+	14.4753i	0.348524	+	0.603662i
$576$	−0.258087	+	0.447019i	−0.0107536	+	0.0186258i
$577$		−	25.0470i		−	1.04272i	−0.853337	−	0.521359i	$-0.825425\pi$
$577$		−	25.0470i		−	1.04272i	0.853337	−	0.521359i	$-0.174575\pi$
$578$	34.7755	+	20.0777i	1.44647	+	0.835120i
$579$	16.3218	+	9.42342i	0.678312	+	0.391624i
$580$			5.12911i			0.212975i
$581$	6.82343	−	11.8185i	0.283084	−	0.490315i
$582$	−9.43731	−	16.3459i	−0.391189	−	0.677559i
$583$	−6.24873	+	3.60770i	−0.258796	+	0.149416i
$584$	−10.8367			−0.448428
$585$	−2.39250	−	0.565129i	−0.0989176	−	0.0233652i
$586$	−37.4224			−1.54591
$587$	11.4731	−	6.62398i	0.473544	−	0.273401i	−0.244178	−	0.969730i	$-0.578518\pi$
$587$	11.4731	−	6.62398i	0.473544	−	0.273401i	0.717722	+	0.696330i	$0.245185\pi$
$588$	−0.582956	−	1.00971i	−0.0240407	−	0.0416397i
$589$	−7.72337	+	13.3773i	−0.318236	+	0.551201i
$590$			3.42913i			0.141175i
$591$	11.5299	+	6.65681i	0.474278	+	0.273825i
$592$	−45.3637	−	26.1907i	−1.86444	−	1.07643i
$593$			12.0199i			0.493597i	0.969067	+	0.246798i	$0.0793786\pi$
$593$			12.0199i			0.493597i	−0.969067	+	0.246798i	$0.920621\pi$
$594$	0.525115	−	0.909527i	0.0215457	−	0.0373183i
$595$	−2.14443	−	3.71426i	−0.0879131	−	0.152270i
$596$	−3.64581	+	2.10491i	−0.149338	+	0.0862206i
$597$	−20.6093			−0.843481
$598$	−23.0112	−	5.43545i	−0.940998	−	0.222272i
$599$	−20.5324			−0.838931			−0.419465	−	0.907771i	$-0.637782\pi$
$599$	−20.5324			−0.838931			−0.419465	+	0.907771i	$0.637782\pi$
$600$	−5.82882	+	3.36527i	−0.237961	+	0.137387i
$601$	17.5897	+	30.4663i	0.717500	+	1.24275i	0.961987	+	0.273094i	$0.0880471\pi$
$601$	17.5897	+	30.4663i	0.717500	+	1.24275i	−0.244487	+	0.969653i	$0.578620\pi$
$602$	−4.20161	+	7.27741i	−0.171245	+	0.296605i
$603$			7.48440i			0.304788i
$604$	−9.60864	−	5.54755i	−0.390970	−	0.225727i
$605$	−6.28949	−	3.63124i	−0.255704	−	0.147631i
$606$		−	7.59593i		−	0.308564i
$607$	14.7872	−	25.6122i	0.600194	−	1.03957i	−0.392598	−	0.919710i	$-0.628424\pi$
$607$	14.7872	−	25.6122i	0.600194	−	1.03957i	0.992791	−	0.119855i	$-0.0382431\pi$
$608$	−10.5431	−	18.2612i	−0.427579	−	0.740589i
$609$	5.58775	−	3.22609i	0.226427	−	0.130728i
$610$	3.53203			0.143008
$611$	−11.6770	−	38.8971i	−0.472400	−	1.57361i
$612$	−7.33395			−0.296458
$613$	30.6372	−	17.6884i	1.23743	−	0.714428i	0.268859	−	0.963180i	$-0.413354\pi$
$613$	30.6372	−	17.6884i	1.23743	−	0.714428i	0.968567	+	0.248751i	$0.0800202\pi$
$614$	−25.3659	−	43.9350i	−1.02368	−	1.77307i
$615$	0.0536739	−	0.0929659i	0.00216434	−	0.00374875i
$616$			0.875984i			0.0352944i
$617$	9.39554	+	5.42451i	0.378250	+	0.218383i	0.677057	−	0.735931i	$-0.263255\pi$
$617$	9.39554	+	5.42451i	0.378250	+	0.218383i	−0.298807	+	0.954314i	$0.596589\pi$
$618$	−10.2900	−	5.94094i	−0.413925	−	0.238980i
$619$			21.5126i			0.864665i	0.901714	+	0.432332i	$0.142309\pi$
$619$			21.5126i			0.864665i	−0.901714	+	0.432332i	$0.857691\pi$
$620$	−1.71188	+	2.96506i	−0.0687507	+	0.119080i
$621$	1.84280	+	3.19182i	0.0739490	+	0.128083i
$622$	36.2623	−	20.9360i	1.45398	−	0.839458i
$623$	−12.2481			−0.490710
$624$	4.12146	−	17.4484i	0.164990	−	0.698493i
$625$	18.2429			0.729717
$626$	25.3518	−	14.6368i	1.01326	−	0.585006i
$627$	1.05846	+	1.83331i	0.0422709	+	0.0732153i
$628$	9.34491	−	16.1859i	0.372903	−	0.645886i
$629$		−	66.2639i		−	2.64212i
$630$	1.05063	+	0.606581i	0.0418581	+	0.0241668i
$631$	0.427963	+	0.247084i	0.0170369	+	0.00983628i	0.508494	−	0.861065i	$-0.330202\pi$
$631$	0.427963	+	0.247084i	0.0170369	+	0.00983628i	−0.491457	+	0.870902i	$0.663536\pi$
$632$			4.95297i			0.197019i
$633$	9.25869	−	16.0365i	0.368000	−	0.637394i
$634$	13.9884	+	24.2286i	0.555551	+	0.962242i
$635$	1.37938	−	0.796386i	0.0547391	−	0.0316036i
$636$	−14.2525			−0.565149
$637$	2.62445	+	2.47230i	0.103984	+	0.0979562i
$638$	6.77628			0.268275
$639$	−6.05457	+	3.49561i	−0.239515	+	0.138284i
$640$	3.69555	+	6.40088i	0.146079	+	0.253017i
$641$	5.03165	−	8.71508i	0.198738	−	0.344225i	−0.749381	−	0.662139i	$-0.769649\pi$
$641$	5.03165	−	8.71508i	0.198738	−	0.344225i	0.948120	+	0.317914i	$0.102982\pi$
$642$			8.93848i			0.352774i
$643$	26.2798	+	15.1727i	1.03637	+	0.598351i	0.918804	−	0.394713i	$-0.129156\pi$
$643$	26.2798	+	15.1727i	1.03637	+	0.598351i	0.117570	+	0.993065i	$0.462489\pi$
$644$	3.72139	+	2.14854i	0.146643	+	0.0846644i
$645$		−	3.22008i		−	0.126790i
$646$	20.0707	−	34.7634i	0.789669	−	1.36775i
$647$	−16.2672	−	28.1757i	−0.639531	−	1.10770i	−0.985536	−	0.169467i	$-0.945795\pi$
$647$	−16.2672	−	28.1757i	−0.639531	−	1.10770i	0.346005	−	0.938233i	$-0.387538\pi$
$648$	−1.28526	+	0.742046i	−0.0504899	+	0.0291503i
$649$	1.66840			0.0654904
$650$	−19.9499	+	21.1776i	−0.782498	+	0.830652i
$651$	4.30692			0.168802
$652$	−17.2552	+	9.96231i	−0.675767	+	0.390154i
$653$	−12.5091	−	21.6665i	−0.489521	−	0.847875i	0.510407	−	0.859933i	$-0.329495\pi$
$653$	−12.5091	−	21.6665i	−0.489521	−	0.847875i	−0.999927	+	0.0120584i	$0.996162\pi$
$654$	−13.4176	+	23.2399i	−0.524668	+	0.908752i
$655$			5.21139i			0.203626i
$656$	0.677995	+	0.391440i	0.0264712	+	0.0152832i
$657$	6.32366	+	3.65097i	0.246709	+	0.142438i
$658$			20.0416i			0.781303i
$659$	−12.6608	+	21.9292i	−0.493195	+	0.854239i	−0.999969	−	0.00783961i	$-0.997505\pi$
$659$	−12.6608	+	21.9292i	−0.493195	+	0.854239i	0.506774	+	0.862079i	$0.330838\pi$
$660$	0.234607	+	0.406351i	0.00913207	+	0.0158172i
$661$	−6.39169	+	3.69024i	−0.248608	+	0.143534i	−0.619127	−	0.785291i	$-0.712513\pi$
$661$	−6.39169	+	3.69024i	−0.248608	+	0.143534i	0.370519	+	0.928825i	$0.379180\pi$
$662$	7.88910			0.306619
$663$	21.7223	−	6.52107i	0.843626	−	0.253257i
$664$	−20.2532			−0.785977
$665$	−2.11773	+	1.22267i	−0.0821220	+	0.0474131i
$666$	9.37183	+	16.2325i	0.363151	+	0.628996i
$667$	−11.8901	+	20.5942i	−0.460385	+	0.797411i
$668$		−	4.20636i		−	0.162749i
$669$	−12.8214	−	7.40244i	−0.495704	−	0.286195i
$670$	−7.86333	−	4.53990i	−0.303787	−	0.175391i
$671$		−	1.71846i		−	0.0663406i
$672$	−2.93967	+	5.09166i	−0.113400	+	0.196415i
$673$	−14.5366	−	25.1781i	−0.560344	−	0.970545i	−0.997466	−	0.0711425i	$-0.977335\pi$
$673$	−14.5366	−	25.1781i	−0.560344	−	0.970545i	0.437122	−	0.899402i	$-0.355998\pi$
$674$	−6.23712	+	3.60100i	−0.240245	+	0.138705i
$675$	4.53512			0.174557
$676$	−0.904087	−	15.1299i	−0.0347726	−	0.581918i
$677$	33.7362			1.29659			0.648293	−	0.761391i	$-0.275483\pi$
$677$	33.7362			1.29659			0.648293	+	0.761391i	$0.275483\pi$
$678$	3.60934	−	2.08385i	0.138616	−	0.0800299i
$679$	−5.30394	−	9.18669i	−0.203547	−	0.352553i
$680$	−3.18253	+	5.51231i	−0.122045	+	0.211387i
$681$		−	0.155323i		−	0.00595200i
$682$	3.91726	+	2.26163i	0.150000	+	0.0866024i
$683$	−26.9995	−	15.5882i	−1.03311	−	0.596465i	−0.115235	−	0.993338i	$-0.536762\pi$
$683$	−26.9995	−	15.5882i	−1.03311	−	0.596465i	−0.917874	+	0.396873i	$0.870095\pi$
$684$			4.18154i			0.159885i
$685$	−2.52942	+	4.38109i	−0.0966443	+	0.167393i
$686$	−0.889651	−	1.54092i	−0.0339670	−	0.0588326i
$687$	−21.4961	+	12.4108i	−0.820129	+	0.473502i
$688$	23.4838			0.895313
$689$	42.2143	−	12.6728i	1.60824	−	0.482795i
$690$	−4.47123			−0.170217
$691$	−10.7744	+	6.22058i	−0.409876	+	0.236642i	−0.690737	−	0.723107i	$-0.742714\pi$
$691$	−10.7744	+	6.22058i	−0.409876	+	0.236642i	0.280860	+	0.959749i	$0.409380\pi$
$692$	−5.74497	−	9.95058i	−0.218391	−	0.378264i
$693$	0.295125	−	0.511171i	0.0112109	−	0.0194178i
$694$		−	44.3969i		−	1.68528i
$695$	−2.14113	−	1.23618i	−0.0812178	−	0.0468911i
$696$	−8.29274	−	4.78782i	−0.314336	−	0.181482i
$697$			0.990365i			0.0375128i
$698$	−22.4883	+	38.9509i	−0.851195	+	1.47431i
$699$	−4.89853	−	8.48450i	−0.185279	−	0.320913i
$700$	4.57916	−	2.64378i	0.173076	−	0.0999254i
$701$	37.9806			1.43451			0.717253	−	0.696813i	$-0.245399\pi$
$701$	37.9806			1.43451			0.717253	+	0.696813i	$0.245399\pi$
$702$	−4.39897	+	4.66968i	−0.166029	+	0.176246i
$703$	−37.7811			−1.42494
$704$	−0.263853	+	0.152335i	−0.00994432	+	0.00574136i
$705$	−3.83993	−	6.65095i	−0.144620	−	0.250489i
$706$	18.7213	−	32.4262i	0.704585	−	1.22038i
$707$		−	4.26905i		−	0.160554i
$708$	2.85405	+	1.64779i	0.107262	+	0.0619276i
$709$	44.2642	+	25.5559i	1.66238	+	0.959774i	0.971576	+	0.236729i	$0.0760753\pi$
$709$	44.2642	+	25.5559i	1.66238	+	0.959774i	0.690801	+	0.723045i	$0.257258\pi$
$710$		−	8.48148i		−	0.318304i
$711$	1.66869	−	2.89025i	0.0625806	−	0.108393i
$712$	9.08866	+	15.7420i	0.340612	+	0.589957i
$713$	−13.7469	+	7.93680i	−0.514827	+	0.297235i
$714$	−11.1924			−0.418864
$715$	−1.05619	−	0.994963i	−0.0394993	−	0.0372095i
$716$	12.4286			0.464480
$717$	−14.9392	+	8.62514i	−0.557914	+	0.322112i
$718$	−3.66389	−	6.34604i	−0.136735	−	0.236832i
$719$	21.2494	−	36.8050i	0.792467	−	1.37259i	−0.131968	−	0.991254i	$-0.542130\pi$
$719$	21.2494	−	36.8050i	0.792467	−	1.37259i	0.924435	−	0.381339i	$-0.124537\pi$
$720$		−	3.39033i		−	0.126350i
$721$	−5.78317	−	3.33892i	−0.215377	−	0.124348i
$722$	9.45674	+	5.45985i	0.351944	+	0.203195i
$723$			0.836707i			0.0311175i
$724$	−14.5509	+	25.2029i	−0.540780	+	0.936659i
$725$	14.6307	+	25.3411i	0.543371	+	0.941146i
$726$	−16.4133	+	9.47621i	−0.609154	+	0.351695i
$727$	−10.7589			−0.399024			−0.199512	−	0.979895i	$-0.563936\pi$
$727$	−10.7589			−0.399024			−0.199512	+	0.979895i	$0.563936\pi$
$728$	1.23010	−	5.20766i	0.0455904	−	0.193009i
$729$	1.00000			0.0370370
$730$	−7.67163	+	4.42922i	−0.283940	+	0.163933i
$731$	14.8538	+	25.7276i	0.549389	+	0.951570i
$732$	1.69723	−	2.93969i	0.0627315	−	0.108654i
$733$			18.9597i			0.700291i	0.936695	+	0.350145i	$0.113868\pi$
$733$			18.9597i			0.700291i	−0.936695	+	0.350145i	$0.886132\pi$
$734$	20.8075	+	12.0132i	0.768018	+	0.443415i
$735$	0.590473	+	0.340910i	0.0217799	+	0.0125747i
$736$		−	21.6689i		−	0.798726i
$737$	−2.20883	+	3.82580i	−0.0813633	+	0.140925i
$738$	−0.140069	−	0.242607i	−0.00515602	−	0.00893049i
$739$	−35.4704	+	20.4789i	−1.30480	+	0.753327i	−0.981223	−	0.192875i	$-0.938219\pi$
$739$	−35.4704	+	20.4789i	−1.30480	+	0.753327i	−0.323577	+	0.946202i	$0.604886\pi$
$740$	−8.37415			−0.307840
$741$	−3.71806	−	12.3852i	−0.136586	−	0.454983i
$742$	−21.7508			−0.798497
$743$	1.44385	−	0.833608i	0.0529698	−	0.0305821i	−0.473281	−	0.880911i	$-0.656931\pi$
$743$	1.44385	−	0.833608i	0.0529698	−	0.0305821i	0.526251	+	0.850329i	$0.323597\pi$
$744$	−3.19594	−	5.53553i	−0.117169	−	0.202942i
$745$	1.23094	−	2.13205i	0.0450982	−	0.0781124i
$746$		−	44.1589i		−	1.61677i
$747$	11.8185	+	6.82343i	0.432417	+	0.249656i
$748$	−3.74890	−	2.16443i	−0.137073	−	0.0791394i
$749$			5.02359i			0.183558i
$750$	−5.78383	+	10.0179i	−0.211196	+	0.365801i
$751$	−22.6519	−	39.2342i	−0.826578	−	1.43167i	−0.900708	−	0.434426i	$-0.856951\pi$
$751$	−22.6519	−	39.2342i	−0.826578	−	1.43167i	0.0741298	−	0.997249i	$-0.476382\pi$
$752$	48.5050	−	28.0044i	1.76879	−	1.02121i
$753$	14.6092			0.532388
$754$	−40.2845	−	9.51556i	−1.46707	−	0.346536i
$755$	6.48836			0.236136
$756$	1.00971	−	0.582956i	0.0367228	−	0.0212019i
$757$	17.6624	+	30.5921i	0.641950	+	1.11189i	0.984997	+	0.172571i	$0.0552075\pi$
$757$	17.6624	+	30.5921i	0.641950	+	1.11189i	−0.343047	+	0.939318i	$0.611459\pi$
$758$	−32.0831	+	55.5695i	−1.16531	+	2.01838i
$759$			2.17542i			0.0789628i
$760$	3.14290	+	1.81456i	0.114005	+	0.0658209i
$761$	5.89485	+	3.40340i	0.213688	+	0.123373i	0.603024	−	0.797723i	$-0.293962\pi$
$761$	5.89485	+	3.40340i	0.213688	+	0.123373i	−0.389336	+	0.921096i	$0.627296\pi$
$762$		−	4.15655i		−	0.150576i
$763$	−7.54092	+	13.0613i	−0.273000	+	0.472849i
$764$	−9.22723	−	15.9820i	−0.333830	−	0.578210i
$765$	3.71426	−	2.14443i	0.134289	−	0.0775320i
$766$	43.6297			1.57640
$767$	−9.91851	−	2.34284i	−0.358137	−	0.0845951i
$768$	20.3204			0.733250
$769$	0.422326	−	0.243830i	0.0152295	−	0.00879273i	−0.492366	−	0.870388i	$-0.663868\pi$
$769$	0.422326	−	0.243830i	0.0152295	−	0.00879273i	0.507595	+	0.861596i	$0.330534\pi$
$770$	0.3580

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)

\(f(q)\)	\(=\)	\(q+(-1.54092 + 0.889651i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.582956 - 1.00971i) q^{4} +0.681820i q^{5} +(1.54092 + 0.889651i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.48409i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.54092 + 0.889651i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.582956 - 1.00971i) q^{4} +0.681820i q^{5} +(1.54092 + 0.889651i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.48409i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.606581 - 1.05063i) q^{10} +(-0.511171 + 0.295125i) q^{11} -1.16591 q^{12} +(3.45330 - 1.03669i) q^{13} -1.77930 q^{14} +(0.590473 - 0.340910i) q^{15} +(2.48624 + 4.30629i) q^{16} +(-3.14516 + 5.44757i) q^{17} -1.77930i q^{18} +(3.10599 + 1.79325i) q^{19} +(0.688440 + 0.397471i) q^{20} -1.00000i q^{21} +(0.525115 - 0.909527i) q^{22} +(1.84280 + 3.19182i) q^{23} +(-1.28526 + 0.742046i) q^{24} +4.53512 q^{25} +(-4.39897 + 4.66968i) q^{26} +1.00000 q^{27} +(1.00971 - 0.582956i) q^{28} +(3.22609 + 5.58775i) q^{29} +(-0.606581 + 1.05063i) q^{30} +4.30692i q^{31} +(-5.09166 - 2.93967i) q^{32} +(0.511171 + 0.295125i) q^{33} -11.1924i q^{34} +(-0.340910 + 0.590473i) q^{35} +(0.582956 + 1.00971i) q^{36} +(-9.12296 + 5.26714i) q^{37} -6.38145 q^{38} +(-2.62445 - 2.47230i) q^{39} +1.01188 q^{40} +(0.136350 - 0.0787215i) q^{41} +(0.889651 + 1.54092i) q^{42} +(2.36138 - 4.09004i) q^{43} +0.688179i q^{44} +(-0.590473 - 0.340910i) q^{45} +(-5.67921 - 3.27889i) q^{46} -11.2638i q^{47} +(2.48624 - 4.30629i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.98826 + 4.03467i) q^{50} +6.29031 q^{51} +(0.966372 - 4.09117i) q^{52} +12.2243 q^{53} +(-1.54092 + 0.889651i) q^{54} +(-0.201222 - 0.348526i) q^{55} +(0.742046 - 1.28526i) q^{56} -3.58649i q^{57} +(-9.94229 - 5.74019i) q^{58} +(-2.44791 - 1.41330i) q^{59} -0.794942i q^{60} +(-1.45571 + 2.52137i) q^{61} +(-3.83166 - 6.63663i) q^{62} +(-0.866025 + 0.500000i) q^{63} +0.516173 q^{64} +(0.706833 + 2.35453i) q^{65} -1.05023 q^{66} +(6.48168 - 3.74220i) q^{67} +(3.66698 + 6.35139i) q^{68} +(1.84280 - 3.19182i) q^{69} -1.21316i q^{70} +(6.05457 + 3.49561i) q^{71} +(1.28526 + 0.742046i) q^{72} -7.30193i q^{73} +(9.37183 - 16.2325i) q^{74} +(-2.26756 - 3.92753i) q^{75} +(3.62132 - 2.09077i) q^{76} -0.590249 q^{77} +(6.24355 + 1.47478i) q^{78} -3.33737 q^{79} +(-2.93611 + 1.69517i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.140069 + 0.242607i) q^{82} -13.6469i q^{83} +(-1.00971 - 0.582956i) q^{84} +(-3.71426 - 2.14443i) q^{85} +8.40323i q^{86} +(3.22609 - 5.58775i) q^{87} +(0.437992 + 0.758625i) q^{88} +(-10.6072 + 6.12405i) q^{89} +1.21316 q^{90} +(3.50899 + 0.828855i) q^{91} +4.29709 q^{92} +(3.72991 - 2.15346i) q^{93} +(10.0208 + 17.3565i) q^{94} +(-1.22267 + 2.11773i) q^{95} +5.87934i q^{96} +(-9.18669 - 5.30394i) q^{97} +(-1.54092 - 0.889651i) q^{98} -0.590249i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more