LMFDB - Embedded newform 273.2.bj.c.142.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (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} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 $ x^16 - 11x^14 + 88x^12 - 303x^10 + 758x^8 - 968x^6 + 867x^4 - 30*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.1
Root			$-2.25575 + 1.30236i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25575 - 1.30236i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.39228 + 4.14355i) q^{4} +(0.401974 + 0.232080i) q^{5} +2.60472i q^{6} +(-2.25575 + 1.38260i) q^{7} -7.25298i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.25575 - 1.30236i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.39228 + 4.14355i) q^{4} +(0.401974 + 0.232080i) q^{5} +2.60472i q^{6} +(-2.25575 + 1.38260i) q^{7} -7.25298i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.604503 - 1.04703i) q^{10} +(3.95602 - 2.28401i) q^{11} +(2.39228 - 4.14355i) q^{12} +(3.57555 - 0.464160i) q^{13} +(6.88906 - 0.181004i) q^{14} -0.464160i q^{15} +(-4.66143 + 8.07383i) q^{16} +(-2.16465 - 3.74928i) q^{17} +(2.25575 - 1.30236i) q^{18} +(2.65773 + 1.53444i) q^{19} +2.22080i q^{20} +(2.32524 + 1.26224i) q^{21} -11.8984 q^{22} +(1.87366 - 3.24527i) q^{23} +(-6.28127 + 3.62649i) q^{24} +(-2.39228 - 4.14355i) q^{25} +(-8.67006 - 3.60962i) q^{26} +1.00000 q^{27} +(-11.1253 - 6.03925i) q^{28} -5.57555 q^{29} +(-0.604503 + 1.04703i) q^{30} +(8.13504 - 4.69677i) q^{31} +(8.46753 - 4.88873i) q^{32} +(-3.95602 - 2.28401i) q^{33} +11.2766i q^{34} +(-1.22763 + 0.0322549i) q^{35} -4.78456 q^{36} +(-6.35076 - 3.66661i) q^{37} +(-3.99678 - 6.92263i) q^{38} +(-2.18975 - 2.86444i) q^{39} +(1.68327 - 2.91551i) q^{40} +4.95194i q^{41} +(-3.60128 - 5.87560i) q^{42} +8.16532 q^{43} +(18.9278 + 10.9280i) q^{44} +(-0.401974 + 0.232080i) q^{45} +(-8.45300 + 4.88034i) q^{46} +(-1.67480 - 0.966946i) q^{47} +9.32286 q^{48} +(3.17683 - 6.23761i) q^{49} +12.4624i q^{50} +(-2.16465 + 3.74928i) q^{51} +(10.4770 + 13.7051i) q^{52} +(3.31351 + 5.73917i) q^{53} +(-2.25575 - 1.30236i) q^{54} +2.12029 q^{55} +(10.0280 + 16.3609i) q^{56} -3.06888i q^{57} +(12.5771 + 7.26137i) q^{58} +(6.00330 - 3.46601i) q^{59} +(1.92327 - 1.11040i) q^{60} +(2.41090 - 4.17580i) q^{61} -24.4675 q^{62} +(-0.0694910 - 2.64484i) q^{63} -6.82180 q^{64} +(1.54500 + 0.643233i) q^{65} +(5.94921 + 10.3043i) q^{66} +(4.89895 - 2.82841i) q^{67} +(10.3569 - 17.9387i) q^{68} -3.74731 q^{69} +(2.81123 + 1.52605i) q^{70} -8.37533i q^{71} +(6.28127 + 3.62649i) q^{72} +(2.95857 - 1.70813i) q^{73} +(9.55049 + 16.5419i) q^{74} +(-2.39228 + 4.14355i) q^{75} +14.6832i q^{76} +(-5.76593 + 10.6218i) q^{77} +(1.20901 + 9.31330i) q^{78} +(-2.93341 + 5.08082i) q^{79} +(-3.74755 + 2.16365i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.44921 - 11.1704i) q^{82} -0.731307i q^{83} +(0.332483 + 12.6544i) q^{84} -2.00949i q^{85} +(-18.4189 - 10.6342i) q^{86} +(2.78777 + 4.82857i) q^{87} +(-16.5659 - 28.6930i) q^{88} +(2.72722 + 1.57456i) q^{89} +1.20901 q^{90} +(-7.42381 + 5.99059i) q^{91} +17.9292 q^{92} +(-8.13504 - 4.69677i) q^{93} +(2.51862 + 4.36238i) q^{94} +(0.712225 + 1.23361i) q^{95} +(-8.46753 - 4.88873i) q^{96} -1.96330i q^{97} +(-15.2897 + 9.93311i) q^{98} +4.56802i 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} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.25575	−	1.30236i	−1.59506	−	0.920907i	−0.992420	−	0.122892i	$-0.960783\pi$
$2$	−2.25575	−	1.30236i	−1.59506	−	0.920907i	−0.602637	−	0.798015i	$-0.705883\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	2.39228	+	4.14355i	1.19614	+	2.07177i
$5$	0.401974	+	0.232080i	0.179768	+	0.103789i	0.587184	−	0.809454i	$-0.300237\pi$
$5$	0.401974	+	0.232080i	0.179768	+	0.103789i	−0.407415	+	0.913243i	$0.633570\pi$
$6$			2.60472i			1.06337i
$7$	−2.25575	+	1.38260i	−0.852594	+	0.522574i
$7$	−2.25575	+	1.38260i	−0.852594	+	0.522574i
$8$		−	7.25298i		−	2.56432i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.604503	−	1.04703i	−0.191161	−	0.331100i
$11$	3.95602	−	2.28401i	1.19279	−	0.688655i	0.233849	−	0.972273i	$-0.424868\pi$
$11$	3.95602	−	2.28401i	1.19279	−	0.688655i	0.958937	+	0.283618i	$0.0915347\pi$
$12$	2.39228	−	4.14355i	0.690591	−	1.19614i
$13$	3.57555	−	0.464160i	0.991679	−	0.128735i
$13$	3.57555	−	0.464160i	0.991679	−	0.128735i
$14$	6.88906	−	0.181004i	1.84118	−	0.0483754i
$15$		−	0.464160i		−	0.119846i
$16$	−4.66143	+	8.07383i	−1.16536	+	2.01846i
$17$	−2.16465	−	3.74928i	−0.525005	−	0.909335i	−0.999576	−	0.0291177i	$-0.990730\pi$
$17$	−2.16465	−	3.74928i	−0.525005	−	0.909335i	0.474571	−	0.880217i	$-0.342603\pi$
$18$	2.25575	−	1.30236i	0.531686	−	0.306969i
$19$	2.65773	+	1.53444i	0.609724	+	0.352024i	0.772858	−	0.634580i	$-0.218827\pi$
$19$	2.65773	+	1.53444i	0.609724	+	0.352024i	−0.163133	+	0.986604i	$0.552160\pi$
$20$			2.22080i			0.496586i
$21$	2.32524	+	1.26224i	0.507410	+	0.275443i
$22$	−11.8984			−2.53675
$23$	1.87366	−	3.24527i	0.390684	−	0.676685i	−0.601856	−	0.798605i	$-0.705572\pi$
$23$	1.87366	−	3.24527i	0.390684	−	0.676685i	0.992540	+	0.121920i	$0.0389051\pi$
$24$	−6.28127	+	3.62649i	−1.28216	+	0.740254i
$25$	−2.39228	−	4.14355i	−0.478456	−	0.828709i
$26$	−8.67006	−	3.60962i	−1.70034	−	0.707905i
$27$	1.00000			0.192450
$28$	−11.1253	−	6.03925i	−2.10248	−	1.14131i
$29$	−5.57555			−1.03535			−0.517677	−	0.855576i	$-0.673203\pi$
$29$	−5.57555			−1.03535			−0.517677	+	0.855576i	$0.673203\pi$
$30$	−0.604503	+	1.04703i	−0.110367	+	0.191161i
$31$	8.13504	−	4.69677i	1.46110	−	0.843565i	0.462035	−	0.886862i	$-0.347120\pi$
$31$	8.13504	−	4.69677i	1.46110	−	0.843565i	0.999062	+	0.0432970i	$0.0137862\pi$
$32$	8.46753	−	4.88873i	1.49686	−	0.864213i
$33$	−3.95602	−	2.28401i	−0.688655	−	0.397595i
$34$			11.2766i			1.93392i
$35$	−1.22763	+	0.0322549i	−0.207507	+	0.00545208i
$36$	−4.78456			−0.797426
$37$	−6.35076	−	3.66661i	−1.04406	−	0.602787i	−0.123078	−	0.992397i	$-0.539277\pi$
$37$	−6.35076	−	3.66661i	−1.04406	−	0.602787i	−0.920980	+	0.389610i	$0.872610\pi$
$38$	−3.99678	−	6.92263i	−0.648363	−	1.12300i
$39$	−2.18975	−	2.86444i	−0.350640	−	0.458677i
$40$	1.68327	−	2.91551i	0.266149	−	0.460983i
$41$			4.95194i			0.773363i	0.922213	+	0.386682i	$0.126379\pi$
$41$			4.95194i			0.773363i	−0.922213	+	0.386682i	$0.873621\pi$
$42$	−3.60128	−	5.87560i	−0.555690	−	0.906624i
$43$	8.16532			1.24520			0.622600	−	0.782540i	$-0.286076\pi$
$43$	8.16532			1.24520			0.622600	+	0.782540i	$0.286076\pi$
$44$	18.9278	+	10.9280i	2.85348	+	1.64745i
$45$	−0.401974	+	0.232080i	−0.0599228	+	0.0345964i
$46$	−8.45300	+	4.88034i	−1.24633	+	0.719567i
$47$	−1.67480	−	0.966946i	−0.244295	−	0.141044i	0.372854	−	0.927890i	$-0.378379\pi$
$47$	−1.67480	−	0.966946i	−0.244295	−	0.141044i	−0.617149	+	0.786846i	$0.711712\pi$
$48$	9.32286			1.34564
$49$	3.17683	−	6.23761i	0.453833	−	0.891087i
$50$			12.4624i			1.76245i
$51$	−2.16465	+	3.74928i	−0.303112	+	0.525005i
$52$	10.4770	+	13.7051i	1.45290	+	1.90055i
$53$	3.31351	+	5.73917i	0.455145	+	0.788335i	0.998697	−	0.0510411i	$-0.0162539\pi$
$53$	3.31351	+	5.73917i	0.455145	+	0.788335i	−0.543551	+	0.839376i	$0.682921\pi$
$54$	−2.25575	−	1.30236i	−0.306969	−	0.177229i
$55$	2.12029			0.285900
$56$	10.0280	+	16.3609i	1.34004	+	2.18632i
$57$		−	3.06888i		−	0.406483i
$58$	12.5771	+	7.26137i	1.65145	+	0.953464i
$59$	6.00330	−	3.46601i	0.781563	−	0.451236i	−0.0554207	−	0.998463i	$-0.517650\pi$
$59$	6.00330	−	3.46601i	0.781563	−	0.451236i	0.836984	+	0.547227i	$0.184317\pi$
$60$	1.92327	−	1.11040i	0.248293	−	0.143352i
$61$	2.41090	−	4.17580i	0.308684	−	0.534657i	−0.669391	−	0.742911i	$-0.733445\pi$
$61$	2.41090	−	4.17580i	0.308684	−	0.534657i	0.978075	+	0.208254i	$0.0667781\pi$
$62$	−24.4675			−3.10738
$63$	−0.0694910	−	2.64484i	−0.00875504	−	0.333218i
$64$	−6.82180			−0.852725
$65$	1.54500	+	0.643233i	0.191634	+	0.0797833i
$66$	5.94921	+	10.3043i	0.732297	+	1.26837i
$67$	4.89895	−	2.82841i	0.598503	−	0.345546i	−0.169950	−	0.985453i	$-0.554361\pi$
$67$	4.89895	−	2.82841i	0.598503	−	0.345546i	0.768452	+	0.639907i	$0.221027\pi$
$68$	10.3569	−	17.9387i	1.25596	−	2.17538i
$69$	−3.74731			−0.451123
$70$	2.81123	+	1.52605i	0.336007	+	0.182398i
$71$		−	8.37533i		−	0.993968i	−0.867760	−	0.496984i	$-0.834441\pi$
$71$		−	8.37533i		−	0.993968i	0.867760	−	0.496984i	$-0.165559\pi$
$72$	6.28127	+	3.62649i	0.740254	+	0.427386i
$73$	2.95857	−	1.70813i	0.346275	−	0.199922i	−0.316769	−	0.948503i	$-0.602598\pi$
$73$	2.95857	−	1.70813i	0.346275	−	0.199922i	0.663043	+	0.748581i	$0.269265\pi$
$74$	9.55049	+	16.5419i	1.11022	+	1.92296i
$75$	−2.39228	+	4.14355i	−0.276236	+	0.478456i
$76$			14.6832i			1.68428i
$77$	−5.76593	+	10.6218i	−0.657089	+	1.21046i
$78$	1.20901	+	9.31330i	0.136893	+	1.05452i
$79$	−2.93341	+	5.08082i	−0.330035	+	0.571637i	−0.982518	−	0.186166i	$-0.940394\pi$
$79$	−2.93341	+	5.08082i	−0.330035	+	0.571637i	0.652483	+	0.757803i	$0.273727\pi$
$80$	−3.74755	+	2.16365i	−0.418989	+	0.241903i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.44921	−	11.1704i	0.712196	−	1.23356i
$83$		−	0.731307i		−	0.0802714i	−0.999194	−	0.0401357i	$-0.987221\pi$
$83$		−	0.731307i		−	0.0802714i	0.999194	−	0.0401357i	$-0.0127790\pi$
$84$	0.332483	+	12.6544i	0.0362769	+	1.38071i
$85$		−	2.00949i		−	0.217960i
$86$	−18.4189	−	10.6342i	−1.98617	−	1.14671i
$87$	2.78777	+	4.82857i	0.298881	+	0.517677i
$88$	−16.5659	−	28.6930i	−1.76593	−	3.05868i
$89$	2.72722	+	1.57456i	0.289084	+	0.166903i	0.637529	−	0.770426i	$-0.279957\pi$
$89$	2.72722	+	1.57456i	0.289084	+	0.166903i	−0.348444	+	0.937329i	$0.613290\pi$
$90$	1.20901			0.127440
$91$	−7.42381	+	5.99059i	−0.778226	+	0.627984i
$92$	17.9292			1.86925
$93$	−8.13504	−	4.69677i	−0.843565	−	0.487032i
$94$	2.51862	+	4.36238i	0.259776	+	0.449945i
$95$	0.712225	+	1.23361i	0.0730728	+	0.126566i
$96$	−8.46753	−	4.88873i	−0.864213	−	0.498954i
$97$		−	1.96330i		−	0.199343i	−0.995020	−	0.0996717i	$-0.968221\pi$
$97$		−	1.96330i		−	0.199343i	0.995020	−	0.0996717i	$-0.0317793\pi$
$98$	−15.2897	+	9.93311i	−1.54450	+	1.00340i
$99$			4.56802i			0.459104i
$100$	11.4460	−	19.8250i	1.14460	−	1.98250i
$101$	7.82608	+	13.5552i	0.778724	+	1.34879i	0.932677	+	0.360711i	$0.117466\pi$
$101$	7.82608	+	13.5552i	0.778724	+	1.34879i	−0.153953	+	0.988078i	$0.549201\pi$
$102$	9.76582	−	5.63830i	0.966961	−	0.558275i
$103$	−2.22763	+	3.85837i	−0.219495	+	0.380176i	−0.954654	−	0.297719i	$-0.903774\pi$
$103$	−2.22763	+	3.85837i	−0.219495	+	0.380176i	0.735159	+	0.677895i	$0.237108\pi$
$104$	−3.36654	−	25.9334i	−0.330117	−	2.54298i
$105$	0.641748	+	1.04703i	0.0626282	+	0.102180i
$106$		−	17.2615i		−	1.67659i
$107$	5.29167	−	9.16544i	0.511565	−	0.886056i	−0.488345	−	0.872650i	$-0.662399\pi$
$107$	5.29167	−	9.16544i	0.511565	−	0.886056i	0.999910	−	0.0134057i	$-0.00426730\pi$
$108$	2.39228	+	4.14355i	0.230197	+	0.398713i
$109$	−17.2504	+	9.95954i	−1.65229	+	0.953951i	−0.676164	+	0.736751i	$0.736359\pi$
$109$	−17.2504	+	9.95954i	−1.65229	+	0.953951i	−0.976127	+	0.217199i	$0.930308\pi$
$110$	−4.78286	−	2.76138i	−0.456027	−	0.263288i
$111$			7.33322i			0.696039i
$112$	−0.647855	−	24.6575i	−0.0612165	−	2.32991i
$113$	−5.20257			−0.489416			−0.244708	−	0.969597i	$-0.578692\pi$
$113$	−5.20257			−0.489416			−0.244708	+	0.969597i	$0.578692\pi$
$114$	−3.99678	+	6.92263i	−0.374333	+	0.648363i
$115$	1.50632	−	0.869676i	0.140465	−	0.0810977i
$116$	−13.3383	−	23.1026i	−1.23843	−	2.14502i
$117$	−1.38580	+	3.32860i	−0.128117	+	0.307729i
$118$	−18.0559			−1.66218
$119$	10.0667	+	5.46461i	0.922810	+	0.500940i
$120$	−3.36654			−0.307322
$121$	4.93341	−	8.54492i	0.448492	−	0.776811i
$122$	−10.8768	+	6.27971i	−0.984738	+	0.568539i
$123$	4.28851	−	2.47597i	0.386682	−	0.223251i
$124$	38.9226	+	22.4720i	3.49535	+	2.01804i
$125$		−	4.54160i		−	0.406213i
$126$	−3.28777	+	6.05660i	−0.292898	+	0.539565i
$127$	−3.48684			−0.309407			−0.154703	−	0.987961i	$-0.549442\pi$
$127$	−3.48684			−0.309407			−0.154703	+	0.987961i	$0.549442\pi$
$128$	−1.54677	−	0.893026i	−0.136716	−	0.0789331i
$129$	−4.08266	−	7.07138i	−0.359458	−	0.622600i
$130$	−2.64742	−	3.46312i	−0.232194	−	0.303736i
$131$	−9.88584	+	17.1228i	−0.863730	+	1.49602i	0.00457315	+	0.999990i	$0.498544\pi$
$131$	−9.88584	+	17.1228i	−0.863730	+	1.49602i	−0.868303	+	0.496034i	$0.834789\pi$
$132$		−	21.8560i		−	1.90232i
$133$	−8.11669	+	0.213259i	−0.703806	+	0.0184919i
$134$	−14.7344			−1.27286
$135$	0.401974	+	0.232080i	0.0345964	+	0.0199743i
$136$	−27.1935	+	15.7002i	−2.33182	+	1.34628i
$137$	2.71225	−	1.56592i	0.231723	−	0.133785i	−0.379644	−	0.925133i	$-0.623953\pi$
$137$	2.71225	−	1.56592i	0.231723	−	0.133785i	0.611367	+	0.791348i	$0.290620\pi$
$138$	8.45300	+	4.88034i	0.719567	+	0.415442i
$139$	10.5999			0.899073			0.449537	−	0.893262i	$-0.351589\pi$
$139$	10.5999			0.899073			0.449537	+	0.893262i	$0.351589\pi$
$140$	−3.07048	−	5.00957i	−0.259503	−	0.423386i
$141$			1.93389i			0.162863i
$142$	−10.9077	+	18.8927i	−0.915352	+	1.58544i
$143$	13.0848	−	10.0028i	1.09421	−	0.836478i
$144$	−4.66143	−	8.07383i	−0.388453	−	0.672819i
$145$	−2.24123	−	1.29397i	−0.186124	−	0.107459i
$146$	−8.89841			−0.736438
$147$	−6.99034	+	0.367585i	−0.576554	+	0.0303179i
$148$		−	35.0862i		−	2.88407i
$149$	−13.0885	−	7.55666i	−1.07225	−	0.619066i	−0.143457	−	0.989657i	$-0.545822\pi$
$149$	−13.0885	−	7.55666i	−1.07225	−	0.619066i	−0.928796	+	0.370591i	$0.879155\pi$
$150$	10.7928	−	6.23121i	0.881226	−	0.508776i
$151$	2.89569	−	1.67183i	0.235648	−	0.136052i	−0.377527	−	0.925999i	$-0.623225\pi$
$151$	2.89569	−	1.67183i	0.235648	−	0.136052i	0.613175	+	0.789947i	$0.289892\pi$
$152$	11.1293	−	19.2764i	0.902702	−	1.56353i
$153$	4.32930			0.350003
$154$	26.8399	−	16.4507i	2.16282	−	1.32564i
$155$	4.36011			0.350212
$156$	6.63044	−	15.9259i	0.530860	−	1.27509i
$157$	10.3755	+	17.9709i	0.828056	+	1.43423i	0.899561	+	0.436794i	$0.143886\pi$
$157$	10.3755	+	17.9709i	0.828056	+	1.43423i	−0.0715057	+	0.997440i	$0.522780\pi$
$158$	13.2341	−	7.64072i	1.05285	−	0.607863i
$159$	3.31351	−	5.73917i	0.262778	−	0.455145i
$160$	4.53830			0.358785
$161$	0.260404	+	9.91103i	0.0205227	+	0.781099i
$162$			2.60472i			0.204646i
$163$	7.08522	+	4.09065i	0.554957	+	0.320405i	0.751119	−	0.660167i	$-0.229515\pi$
$163$	7.08522	+	4.09065i	0.554957	+	0.320405i	−0.196162	+	0.980572i	$0.562848\pi$
$164$	−20.5186	+	11.8464i	−1.60223	+	0.925050i
$165$	−1.06015	−	1.83623i	−0.0825323	−	0.142950i
$166$	−0.952424	+	1.64965i	−0.0739225	+	0.128037i
$167$			18.8241i			1.45665i	0.685229	+	0.728327i	$0.259702\pi$
$167$			18.8241i			1.45665i	−0.685229	+	0.728327i	$0.740298\pi$
$168$	9.15499	−	16.8649i	0.706323	−	1.30116i
$169$	12.5691	−	3.31925i	0.966855	−	0.255327i
$170$	−2.61707	+	4.53290i	−0.200720	+	0.347658i
$171$	−2.65773	+	1.53444i	−0.203241	+	0.117341i
$172$	19.5337	+	33.8334i	1.48943	+	2.57977i
$173$	4.32180	−	7.48558i	0.328580	−	0.569118i	−0.653650	−	0.756797i	$-0.726763\pi$
$173$	4.32180	−	7.48558i	0.328580	−	0.569118i	0.982230	+	0.187679i	$0.0600965\pi$
$174$		−	14.5227i		−	1.10097i
$175$	11.1253	+	6.03925i	0.840990	+	0.456524i
$176$			42.5870i			3.21012i
$177$	−6.00330	−	3.46601i	−0.451236	−	0.260521i
$178$	−4.10128	−	7.10363i	−0.307404	−	0.532440i
$179$	−9.96461	−	17.2592i	−0.744790	−	1.29001i	−0.950293	−	0.311357i	$-0.899216\pi$
$179$	−9.96461	−	17.2592i	−0.744790	−	1.29001i	0.205503	−	0.978656i	$-0.434117\pi$
$180$	−1.92327	−	1.11040i	−0.143352	−	0.0827643i
$181$	0.259128			0.0192608			0.00963041	−	0.999954i	$-0.496934\pi$
$181$	0.259128			0.0192608			0.00963041	+	0.999954i	$0.496934\pi$
$182$	24.5482	−	3.84482i	1.81963	−	0.284997i
$183$	−4.82180			−0.356438
$184$	−23.5379	−	13.5896i	−1.73523	−	1.00184i
$185$	−1.70189	−	2.94777i	−0.125126	−	0.216724i
$186$	12.2338	+	21.1895i	0.897023	+	1.55369i
$187$	−17.1268	−	9.88817i	−1.25244	−	0.723094i
$188$		−	9.25282i		−	0.674831i
$189$	−2.25575	+	1.38260i	−0.164082	+	0.100569i
$190$		−	3.71029i		−	0.269173i
$191$	−9.81964	+	17.0081i	−0.710524	+	1.23066i	0.254136	+	0.967168i	$0.418209\pi$
$191$	−9.81964	+	17.0081i	−0.710524	+	1.23066i	−0.964661	+	0.263496i	$0.915125\pi$
$192$	3.41090	+	5.90785i	0.246161	+	0.426363i
$193$	−21.2359	+	12.2606i	−1.52860	+	0.882536i	−0.529176	+	0.848512i	$0.677499\pi$
$193$	−21.2359	+	12.2606i	−1.52860	+	0.882536i	−0.999421	+	0.0340235i	$0.989168\pi$
$194$	−2.55693	+	4.42873i	−0.183577	+	0.317964i
$195$	−0.215444	−	1.65963i	−0.0154283	−	0.118848i
$196$	33.4457	−	1.75873i	2.38898	−	0.125624i
$197$			21.3481i			1.52099i	0.649345	+	0.760494i	$0.275043\pi$
$197$			21.3481i			1.52099i	−0.649345	+	0.760494i	$0.724957\pi$
$198$	5.94921	−	10.3043i	0.422792	−	0.732297i
$199$	−8.64175	−	14.9679i	−0.612597	−	1.06105i	−0.990801	−	0.135327i	$-0.956791\pi$
$199$	−8.64175	−	14.9679i	−0.612597	−	1.06105i	0.378204	−	0.925722i	$-0.376542\pi$
$200$	−30.0531	+	17.3511i	−2.12507	+	1.22691i
$201$	−4.89895	−	2.82841i	−0.345546	−	0.199501i
$202$		−	40.7695i		−	2.86853i
$203$	12.5771	−	7.70876i	0.882736	−	0.541049i
$204$	−20.7138			−1.45025
$205$	−1.14925	+	1.99055i	−0.0802669	+	0.139026i
$206$	10.0500	−	5.80234i	0.700213	−	0.404268i
$207$	1.87366	+	3.24527i	0.130228	+	0.225562i
$208$	−12.9196	+	31.0320i	−0.895815	+	2.15169i
$209$	14.0187			0.969694
$210$	−0.0840150	−	3.19763i	−0.00579758	−	0.220657i
$211$	−26.6701			−1.83604			−0.918022	−	0.396529i	$-0.870215\pi$
$211$	−26.6701			−1.83604			−0.918022	+	0.396529i	$0.870215\pi$
$212$	−15.8537	+	27.4594i	−1.08883	+	1.88592i
$213$	−7.25325	+	4.18766i	−0.496984	+	0.286934i
$214$	−23.8734	+	13.7833i	−1.63195	+	0.942207i
$215$	3.28225	+	1.89501i	0.223848	+	0.129238i
$216$		−	7.25298i		−	0.493503i
$217$	−11.8569	+	21.8423i	−0.804898	+	1.48275i
$218$	51.8836			3.51400
$219$	−2.95857	−	1.70813i	−0.199922	−	0.115425i
$220$	5.07233	+	8.78553i	0.341976	+	0.592321i
$221$	−9.48008	−	12.4010i	−0.637699	−	0.834182i
$222$	9.55049	−	16.5419i	0.640987	−	1.11022i
$223$			19.3807i			1.29782i	0.760863	+	0.648912i	$0.224776\pi$
$223$			19.3807i			1.29782i	−0.760863	+	0.648912i	$0.775224\pi$
$224$	−12.3415	+	22.7350i	−0.824600	+	1.51904i
$225$	4.78456			0.318970
$226$	11.7357	+	6.77561i	0.780647	+	0.450707i
$227$	−3.42959	+	1.98008i	−0.227630	+	0.131422i	−0.609478	−	0.792803i	$-0.708621\pi$
$227$	−3.42959	+	1.98008i	−0.227630	+	0.131422i	0.381848	+	0.924225i	$0.375288\pi$
$228$	12.7160	−	7.34161i	0.842140	−	0.486210i
$229$	−3.60857	−	2.08341i	−0.238461	−	0.137675i	0.376008	−	0.926616i	$-0.377296\pi$
$229$	−3.60857	−	2.08341i	−0.238461	−	0.137675i	−0.614469	+	0.788941i	$0.710630\pi$
$230$	−4.53052			−0.298734
$231$	12.0817	−	0.317436i	0.794916	−	0.0208858i
$232$			40.4394i			2.65497i
$233$	4.73376	−	8.19911i	0.310119	−	0.537142i	−0.668269	−	0.743920i	$-0.732964\pi$
$233$	4.73376	−	8.19911i	0.310119	−	0.537142i	0.978388	+	0.206778i	$0.0662978\pi$
$234$	7.46105	−	5.70368i	0.487744	−	0.372861i
$235$	−0.448818	−	0.777375i	−0.0292776	−	0.0507104i
$236$	28.7231	+	16.5833i	1.86972	+	1.07948i
$237$	5.86683			0.381092
$238$	−15.5910	−	25.4372i	−1.01062	−	1.64885i
$239$		−	1.82723i		−	0.118194i	−0.998252	−	0.0590968i	$-0.981178\pi$
$239$		−	1.82723i		−	0.118194i	0.998252	−	0.0590968i	$-0.0188221\pi$
$240$	3.74755	+	2.16365i	0.241903	+	0.139663i
$241$	13.3006	−	7.67909i	0.856765	−	0.494653i	−0.00616275	−	0.999981i	$-0.501962\pi$
$241$	13.3006	−	7.67909i	0.856765	−	0.494653i	0.862928	+	0.505328i	$0.168628\pi$
$242$	−22.2571	+	12.8502i	−1.43074	+	0.826039i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	23.0702			1.47692
$245$	2.72463	−	1.77008i	0.174070	−	0.113086i
$246$	−12.8984			−0.822373
$247$	10.2151	+	4.25285i	0.649969	+	0.270603i
$248$	−34.0656	−	59.0033i	−2.16317	−	3.74671i
$249$	−0.633331	+	0.365654i	−0.0401357	+	0.0231724i
$250$	−5.91479	+	10.2447i	−0.374084	+	0.647933i
$251$	20.7904			1.31228			0.656139	−	0.754640i	$-0.272189\pi$
$251$	20.7904			1.31228			0.656139	+	0.754640i	$0.272189\pi$
$252$	10.7928	−	6.61513i	0.679881	−	0.416714i
$253$		−	17.1178i		−	1.07619i
$254$	7.86544	+	4.54111i	0.493522	+	0.284935i
$255$	−1.74027	+	1.00474i	−0.108980	+	0.0629195i
$256$	9.14788	+	15.8446i	0.571743	+	0.990287i
$257$	−4.05332	+	7.02056i	−0.252839	+	0.437930i	−0.964306	−	0.264789i	$-0.914698\pi$
$257$	−4.05332	+	7.02056i	−0.252839	+	0.437930i	0.711467	+	0.702719i	$0.248031\pi$
$258$			21.2684i			1.32411i
$259$	19.3952	−	0.509593i	1.20516	−	0.0316646i
$260$	1.03081	+	7.94058i	0.0639279	+	0.492454i
$261$	2.78777	−	4.82857i	0.172559	−	0.298881i
$262$	44.6000	−	25.7498i	2.75540	−	1.59083i
$263$	1.88584	+	3.26637i	0.116286	+	0.201413i	0.918293	−	0.395901i	$-0.129568\pi$
$263$	1.88584	+	3.26637i	0.116286	+	0.201413i	−0.802007	+	0.597314i	$0.796234\pi$
$264$	−16.5659	+	28.6930i	−1.01956	+	1.76593i
$265$			3.07600i			0.188957i
$266$	18.5870	+	10.0898i	1.13964	+	0.618644i
$267$		−	3.14912i		−	0.192723i
$268$	23.4393	+	13.5327i	1.43178	+	0.826641i
$269$	−11.0337	−	19.1110i	−0.672738	−	1.16522i	−0.977125	−	0.212667i	$-0.931785\pi$
$269$	−11.0337	−	19.1110i	−0.672738	−	1.16522i	0.304387	−	0.952548i	$-0.401548\pi$
$270$	−0.604503	−	1.04703i	−0.0367889	−	0.0637202i
$271$	10.3882	+	5.99763i	0.631039	+	0.364330i	0.781154	−	0.624338i	$-0.214631\pi$
$271$	10.3882	+	5.99763i	0.631039	+	0.364330i	−0.150116	+	0.988668i	$0.547965\pi$
$272$	40.3615			2.44727
$273$	8.89990	+	3.43391i	0.538647	+	0.207830i
$274$	−8.15754			−0.492815
$275$	−18.9278	−	10.9280i	−1.14139	−	0.658982i
$276$	−8.96461	−	15.5272i	−0.539606	−	0.934625i
$277$	−14.7151	−	25.4874i	−0.884147	−	1.53139i	−0.846688	−	0.532089i	$-0.821407\pi$
$277$	−14.7151	−	25.4874i	−0.884147	−	1.53139i	−0.0374587	−	0.999298i	$-0.511926\pi$
$278$	−23.9108	−	13.8049i	−1.43407	−	0.827963i
$279$			9.39354i			0.562377i
$280$	0.233944	+	8.90396i	0.0139809	+	0.532114i
$281$		−	10.3189i		−	0.615572i	−0.951456	−	0.307786i	$-0.900412\pi$
$281$		−	10.3189i		−	0.615572i	0.951456	−	0.307786i	$-0.0995881\pi$
$282$	2.51862	−	4.36238i	0.149982	−	0.259776i
$283$	−5.49073	−	9.51022i	−0.326390	−	0.565324i	0.655403	−	0.755280i	$-0.272499\pi$
$283$	−5.49073	−	9.51022i	−0.326390	−	0.565324i	−0.981793	+	0.189956i	$0.939166\pi$
$284$	34.7036	−	20.0361i	2.05928	−	1.18892i
$285$	0.712225	−	1.23361i	0.0421886	−	0.0730728i
$286$	−42.5434	+	5.52277i	−2.51564	+	0.326568i
$287$	−6.84656	−	11.1704i	−0.404139	−	0.659365i
$288$			9.77746i			0.576142i
$289$	−0.871415	+	1.50934i	−0.0512597	+	0.0887844i
$290$	3.37044	+	5.83777i	0.197919	+	0.342805i
$291$	−1.70027	+	0.981652i	−0.0996717	+	0.0575455i
$292$	14.1555	+	8.17266i	0.828386	+	0.478269i
$293$			14.7635i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$293$			14.7635i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$294$	16.2472	+	8.27475i	0.947556	+	0.482593i
$295$	3.21756			0.187334
$296$	−26.5939	+	46.0619i	−1.54574	+	2.67730i
$297$	3.95602	−	2.28401i	0.229552	−	0.132532i
$298$	19.6830	+	34.0919i	1.14020	+	1.97489i
$299$	5.19303	−	12.4733i	0.300320	−	0.721349i
$300$	−22.8920			−1.32167
$301$	−18.4189	+	11.2894i	−1.06165	+	0.650709i
$302$	−8.70929			−0.501163
$303$	7.82608	−	13.5552i	0.449597	−	0.778724i
$304$	−24.7776	+	14.3054i	−1.42109	+	0.820469i
$305$	1.93824	−	1.11904i	0.110983	−	0.0640762i
$306$	−9.76582	−	5.63830i	−0.558275	−	0.322320i
$307$		−	12.8535i		−	0.733585i	−0.930303	−	0.366793i	$-0.880456\pi$
$307$		−	12.8535i		−	0.733585i	0.930303	−	0.366793i	$-0.119544\pi$
$308$	−57.8055	+	1.51879i	−3.29377	+	0.0865412i
$309$	4.45526			0.253451
$310$	−9.83532	−	5.67842i	−0.558608	−	0.322513i
$311$	6.19428	+	10.7288i	0.351245	+	0.608374i	0.986468	−	0.163955i	$-0.0524250\pi$
$311$	6.19428	+	10.7288i	0.351245	+	0.608374i	−0.635223	+	0.772329i	$0.719092\pi$
$312$	−20.7757	+	15.8822i	−1.17619	+	0.899153i
$313$	−14.6067	+	25.2996i	−0.825622	+	1.43002i	0.0758211	+	0.997121i	$0.475842\pi$
$313$	−14.6067	+	25.2996i	−0.825622	+	1.43002i	−0.901443	+	0.432898i	$0.857491\pi$
$314$		−	54.0505i		−	3.05025i
$315$	0.585881	−	1.07928i	0.0330106	−	0.0608108i
$316$	−28.0702			−1.57907
$317$	8.51369	+	4.91538i	0.478176	+	0.276075i	0.719656	−	0.694331i	$-0.244299\pi$
$317$	8.51369	+	4.91538i	0.478176	+	0.276075i	−0.241480	+	0.970406i	$0.577633\pi$
$318$	−14.9489	+	8.63076i	−0.838293	+	0.483989i
$319$	−22.0570	+	12.7346i	−1.23496	+	0.713002i
$320$	−2.74219	−	1.58320i	−0.153293	−	0.0885038i
$321$	−10.5833			−0.590704
$322$	12.3203	−	22.6960i	0.686584	−	1.26480i
$323$		−	13.2861i		−	0.739258i
$324$	2.39228	−	4.14355i	0.132904	−	0.230197i
$325$	−10.4770	−	13.7051i	−0.581158	−	0.760220i
$326$	−10.6550	−	18.4550i	−0.590125	−	1.02213i
$327$	17.2504	+	9.95954i	0.953951	+	0.550764i
$328$	35.9163			1.98315
$329$	5.11483	−	0.134388i	0.281990	−	0.00740905i
$330$			5.52277i			0.304018i
$331$	−4.35183	−	2.51253i	−0.239198	−	0.138101i	0.375610	−	0.926778i	$-0.377433\pi$
$331$	−4.35183	−	2.51253i	−0.239198	−	0.138101i	−0.614808	+	0.788677i	$0.710767\pi$
$332$	3.03021	−	1.74949i	0.166304	−	0.0960157i
$333$	6.35076	−	3.66661i	0.348019	−	0.200929i
$334$	24.5158	−	42.4626i	1.34144	−	2.32345i
$335$	2.62567			0.143456
$336$	−21.0301	+	12.8898i	−1.14728	+	0.703196i
$337$	0.536185			0.0292078			0.0146039	−	0.999893i	$-0.495351\pi$
$337$	0.536185			0.0292078			0.0146039	+	0.999893i	$0.495351\pi$
$338$	−32.6757	−	8.88208i	−1.77732	−	0.483121i
$339$	2.60128	+	4.50556i	0.141282	+	0.244708i
$340$	8.32640	−	4.80725i	0.451563	−	0.260710i
$341$	21.4550	−	37.1611i	1.16185	−	2.01238i
$342$	7.99356			0.432242
$343$	1.45797	+	18.4628i	0.0787229	+	0.996897i
$344$		−	59.2229i		−	3.19309i
$345$	−1.50632	−	0.869676i	−0.0810977	−	0.0468218i
$346$	−19.4978	+	11.2571i	−1.04821	+	0.605184i
$347$	13.8050	+	23.9110i	0.741093	+	1.28361i	0.951998	+	0.306104i	$0.0990255\pi$
$347$	13.8050	+	23.9110i	0.741093	+	1.28361i	−0.210905	+	0.977507i	$0.567641\pi$
$348$	−13.3383	+	23.1026i	−0.715006	+	1.23843i
$349$		−	34.2310i		−	1.83234i	−0.400785	−	0.916172i	$-0.631263\pi$
$349$		−	34.2310i		−	1.83234i	0.400785	−	0.916172i	$-0.368737\pi$
$350$	−17.2305	−	28.1121i	−0.921011	−	1.50266i
$351$	3.57555	−	0.464160i	0.190849	−	0.0247750i
$352$	22.3318	−	38.6799i	1.19029	−	2.06164i
$353$	−15.6891	+	9.05813i	−0.835048	+	0.482115i	−0.855578	−	0.517674i	$-0.826798\pi$
$353$	−15.6891	+	9.05813i	−0.835048	+	0.482115i	0.0205296	+	0.999789i	$0.493465\pi$
$354$	9.02797	+	15.6369i	0.479831	+	0.831092i
$355$	1.94375	−	3.36667i	0.103163	−	0.178684i
$356$			15.0671i			0.798557i
$357$	−0.300847	−	11.4503i	−0.0159225	−	0.606014i
$358$			51.9100i			2.74353i
$359$	3.25320	+	1.87824i	0.171697	+	0.0991296i	0.583386	−	0.812195i	$-0.301728\pi$
$359$	3.25320	+	1.87824i	0.171697	+	0.0991296i	−0.411689	+	0.911325i	$0.635061\pi$
$360$	1.68327	+	2.91551i	0.0887162	+	0.153661i
$361$	−4.79099	−	8.29825i	−0.252158	−	0.436750i
$362$	−0.584528	−	0.337478i	−0.0307221	−	0.0177374i
$363$	−9.86683			−0.517874
$364$	−42.5821	−	16.4297i	−2.23191	−	0.861152i
$365$	1.58569			0.0829990
$366$	10.8768	+	6.27971i	0.568539	+	0.328246i
$367$	1.25697	+	2.17713i	0.0656132	+	0.113645i	0.896966	−	0.442100i	$-0.145766\pi$
$367$	1.25697	+	2.17713i	0.0656132	+	0.113645i	−0.831353	+	0.555745i	$0.812433\pi$
$368$	17.4678	+	30.2552i	0.910573	+	1.57716i
$369$	−4.28851	−	2.47597i	−0.223251	−	0.128894i
$370$			8.86591i			0.460917i
$371$	−15.4094	−	8.36488i	−0.800017	−	0.434283i
$372$		−	44.9439i		−	2.33023i
$373$	3.04474	−	5.27365i	0.157651	−	0.273059i	−0.776370	−	0.630277i	$-0.782941\pi$
$373$	3.04474	−	5.27365i	0.157651	−	0.273059i	0.934021	+	0.357218i	$0.116275\pi$
$374$	25.7559	+	44.6105i	1.33181	+	2.30675i
$375$	−3.93314	+	2.27080i	−0.203106	+	0.117264i
$376$	−7.01324	+	12.1473i	−0.361680	+	0.626449i
$377$	−19.9357	+	2.58795i	−1.02674	+	0.133286i
$378$	6.88906	−	0.181004i	0.354335	−	0.00930986i
$379$			2.67232i			0.137268i	0.997642	+	0.0686339i	$0.0218640\pi$
$379$			2.67232i			0.137268i	−0.997642	+	0.0686339i	$0.978136\pi$
$380$	−3.40768	+	5.90228i	−0.174810	+	0.302780i
$381$	1.74342	+	3.01969i	0.0893180	+	0.154703i
$382$	44.3013	−	25.5774i	2.26665	−	1.30865i
$383$	13.3898	+	7.73061i	0.684187	+	0.395016i	0.801431	−	0.598087i	$-0.204072\pi$
$383$	13.3898	+	7.73061i	0.684187	+	0.395016i	−0.117243	+	0.993103i	$0.537406\pi$
$384$			1.78605i			0.0911440i
$385$	−4.78286	+	2.93152i	−0.243757	+	0.149404i
$386$	63.8707			3.25093
$387$	−4.08266	+	7.07138i	−0.207533	+	0.359458i
$388$	8.13504	−	4.69677i	0.412994	−	0.238442i
$389$	4.69224	+	8.12719i	0.237906	+	0.412065i	0.960113	−	0.279612i	$-0.0902057\pi$
$389$	4.69224	+	8.12719i	0.237906	+	0.412065i	−0.722207	+	0.691677i	$0.756872\pi$
$390$	−1.67544	+	4.02429i	−0.0848392	+	0.203778i
$391$	−16.2232			−0.820444
$392$	−45.2412	−	23.0415i	−2.28503	−	1.16377i
$393$	19.7717			0.997349
$394$	27.8029	−	48.1560i	1.40069	−	2.42606i
$395$	−2.35831	+	1.36157i	−0.118660	+	0.0685082i
$396$	−18.9278	+	10.9280i	−0.951158	+	0.549152i
$397$	4.52648	+	2.61336i	0.227177	+	0.131161i	0.609269	−	0.792963i	$-0.291463\pi$
$397$	4.52648	+	2.61336i	0.227177	+	0.131161i	−0.382092	+	0.924124i	$0.624796\pi$
$398$			45.0186i			2.25658i
$399$	4.24303	+	6.92263i	0.212417	+	0.346565i
$400$	44.6057			2.23029
$401$	13.1585	+	7.59704i	0.657102	+	0.379378i	0.791172	−	0.611594i	$-0.209471\pi$
$401$	13.1585	+	7.59704i	0.657102	+	0.379378i	−0.134070	+	0.990972i	$0.542805\pi$
$402$	7.36722	+	12.7604i	0.367443	+	0.636431i
$403$	26.9072	−	20.5695i	1.34034	−	1.02464i
$404$	−37.4443	+	64.8555i	−1.86292	+	3.22668i
$405$		−	0.464160i		−	0.0230643i
$406$	−38.4103	+	1.00920i	−1.90627	+	0.0500857i
$407$	−33.4983			−1.66045
$408$	27.1935	+	15.7002i	1.34628	+	0.777274i
$409$	2.65415	−	1.53237i	0.131239	−	0.0757710i	−0.432943	−	0.901421i	$-0.642525\pi$
$409$	2.65415	−	1.53237i	0.131239	−	0.0757710i	0.564182	+	0.825650i	$0.309192\pi$
$410$	5.18483	−	2.99346i	0.256060	−	0.147837i
$411$	−2.71225	−	1.56592i	−0.133785	−	0.0772409i
$412$	−21.3164			−1.05018
$413$	−8.74986	+	16.1186i	−0.430552	+	0.793146i
$414$		−	9.76069i		−	0.479712i
$415$	0.169722	−	0.293967i	0.00833131	−	0.0144303i
$416$	28.0069	−	21.4102i	1.37315	−	1.04972i
$417$	−5.29996	−	9.17980i	−0.259540	−	0.449537i
$418$	−31.6227	−	18.2574i	−1.54672	−	0.892998i
$419$	28.3394			1.38447			0.692236	−	0.721671i	$-0.256626\pi$
$419$	28.3394			1.38447			0.692236	+	0.721671i	$0.256626\pi$
$420$	−2.80318	+	5.16390i	−0.136781	+	0.251972i
$421$		−	20.3101i		−	0.989854i	−0.868934	−	0.494927i	$-0.835195\pi$
$421$		−	20.3101i		−	0.989854i	0.868934	−	0.494927i	$-0.164805\pi$
$422$	60.1611	+	34.7340i	2.92860	+	1.69083i
$423$	1.67480	−	0.966946i	0.0814316	−	0.0470145i
$424$	41.6261	−	24.0328i	2.02154	−	1.16714i
$425$	−10.3569	+	17.9387i	−0.502383	+	0.870152i
$426$	21.8154			1.05696
$427$	0.335072	+	12.7529i	0.0162152	+	0.617155i
$428$	50.6365			2.44761
$429$	−15.2051	−	6.33037i	−0.734109	−	0.305633i
$430$	−4.93596	−	8.54934i	−0.238033	−	0.412286i
$431$	−7.08307	+	4.08941i	−0.341180	+	0.196980i	−0.660794	−	0.750568i	$-0.729780\pi$
$431$	−7.08307	+	4.08941i	−0.341180	+	0.196980i	0.319614	+	0.947548i	$0.396447\pi$
$432$	−4.66143	+	8.07383i	−0.224273	+	0.388453i
$433$	−1.45603			−0.0699724			−0.0349862	−	0.999388i	$-0.511139\pi$
$433$	−1.45603			−0.0699724			−0.0349862	+	0.999388i	$0.511139\pi$
$434$	55.1927	−	33.8288i	2.64933	−	1.62383i
$435$			2.58795i			0.124083i
$436$	−82.5356	−	47.6520i	−3.95274	−	2.28212i
$437$	9.95933	−	5.75002i	0.476419	−	0.275061i
$438$	4.44921	+	7.70625i	0.212591	+	0.368219i
$439$	−10.7864	+	18.6826i	−0.514807	+	0.891672i	0.485045	+	0.874489i	$0.338803\pi$
$439$	−10.7864	+	18.6826i	−0.514807	+	0.891672i	−0.999852	+	0.0171831i	$0.994530\pi$
$440$		−	15.3784i		−	0.733139i
$441$	3.81351	+	5.87002i	0.181596	+	0.279525i
$442$	5.23415	+	40.3201i	0.248963	+	1.91783i
$443$	6.44696	−	11.1665i	0.306305	−	0.530535i	−0.671246	−	0.741234i	$-0.734241\pi$
$443$	6.44696	−	11.1665i	0.306305	−	0.530535i	0.977551	+	0.210699i	$0.0675741\pi$
$444$	−30.3856	+	17.5431i	−1.44203	+	0.832559i
$445$	0.730848	+	1.26587i	0.0346455	+	0.0600078i
$446$	25.2406	−	43.7179i	1.19518	−	2.07010i
$447$			15.1133i			0.714835i
$448$	15.3883	−	9.43182i	0.727028	−	0.445612i
$449$		−	3.89008i		−	0.183584i	−0.995778	−	0.0917921i	$-0.970740\pi$
$449$		−	3.89008i		−	0.183584i	0.995778	−	0.0917921i	$-0.0292595\pi$
$450$	−10.7928	−	6.23121i	−0.508776	−	0.293742i
$451$	11.3103	+	19.5900i	0.532581	+	0.922457i
$452$	−12.4460	−	21.5571i	−0.585410	−	1.01396i
$453$	−2.89569	−	1.67183i	−0.136052	−	0.0785494i
$454$	10.3151			0.484111
$455$	−4.37447	+	0.685145i	−0.205079	+	0.0321201i
$456$	−22.2585			−1.04235
$457$	10.6036	+	6.12199i	0.496016	+	0.286375i	0.727067	−	0.686567i	$-0.240883\pi$
$457$	10.6036	+	6.12199i	0.496016	+	0.286375i	−0.231051	+	0.972942i	$0.574216\pi$
$458$	5.42669	+	9.39930i	0.253573	+	0.439201i
$459$	−2.16465	−	3.74928i	−0.101037	−	0.175002i
$460$	7.20708	+	4.16101i	0.336032	+	0.194008i
$461$			30.7975i			1.43438i	0.696877	+	0.717190i	$0.254572\pi$
$461$			30.7975i			1.43438i	−0.696877	+	0.717190i	$0.745428\pi$
$462$	−27.6667	−	15.0186i	−1.28717	−	0.698730i
$463$		−	1.54997i		−	0.0720334i	−0.999351	−	0.0360167i	$-0.988533\pi$
$463$		−	1.54997i		−	0.0720334i	0.999351	−	0.0360167i	$-0.0114670\pi$
$464$	25.9900	−	45.0161i	1.20656	−	2.08982i
$465$	−2.18005	−	3.77596i	−0.101098	−	0.175106i
$466$	−21.3564	+	12.3301i	−0.989315	+	0.571181i
$467$	−6.53403	+	11.3173i	−0.302359	+	0.523701i	−0.976670	−	0.214747i	$-0.931107\pi$
$467$	−6.53403	+	11.3173i	−0.302359	+	0.523701i	0.674311	+	0.738447i	$0.264441\pi$
$468$	−17.1074	+	2.22080i	−0.790791	+	0.102656i
$469$	−7.14026	+	13.1535i	−0.329707	+	0.607372i
$470$			2.33809i			0.107848i
$471$	10.3755	−	17.9709i	0.478078	−	0.828056i
$472$	−25.1389	−	43.5418i	−1.15711	−	2.00418i
$473$	32.3022	−	18.6497i	1.48526	−	0.857514i
$474$	−13.2341	−	7.64072i	−0.607863	−	0.350950i
$475$		−	14.6832i		−	0.673712i
$476$	1.43942	+	54.7846i	0.0659757	+	2.51105i
$477$	−6.62702			−0.303430
$478$	−2.37971	+	4.12177i	−0.108845	+	0.188526i
$479$	−8.73629	+	5.04390i	−0.399171	+	0.230462i	−0.686126	−	0.727482i	$-0.740690\pi$
$479$	−8.73629	+	5.04390i	−0.399171	+	0.230462i	0.286955	+	0.957944i	$0.407357\pi$
$480$	−2.26915	−	3.93029i	−0.103572	−	0.179392i
$481$	−24.4093	−	10.1624i	−1.11297	−	0.463365i
$482$	−40.0037			−1.82212
$483$	8.45300	−	5.18103i	0.384625	−	0.235745i
$484$	47.2084			2.14584
$485$	0.455644	−	0.789198i	0.0206897	−	0.0358356i
$486$	2.25575	−	1.30236i	0.102323	−	0.0590762i
$487$	6.85704	−	3.95891i	0.310722	−	0.179396i	−0.336527	−	0.941674i	$-0.609252\pi$
$487$	6.85704	−	3.95891i	0.310722	−	0.179396i	0.647250	+	0.762278i	$0.275919\pi$
$488$	−30.2870	−	17.4862i	−1.37103	−	0.791564i
$489$		−	8.18130i		−	0.369971i
$490$	−8.45136	+	0.444412i	−0.381794	+	0.0200765i
$491$	8.55041			0.385874			0.192937	−	0.981211i	$-0.438199\pi$
$491$	8.55041			0.385874			0.192937	+	0.981211i	$0.438199\pi$
$492$	20.5186	+	11.8464i	0.925050	+	0.534078i
$493$	12.0691	+	20.9043i	0.543565	+	0.941483i
$494$	−17.5039	−	22.8971i	−0.787537	−	1.03019i
$495$	−1.06015	+	1.83623i	−0.0476500	+	0.0825323i
$496$			87.5747i			3.93222i
$497$	11.5797	+	18.8927i	0.519422	+	0.847452i
$498$	1.90485			0.0853583
$499$	18.7110	+	10.8028i	0.837619	+	0.483599i	0.856454	−	0.516223i	$-0.172663\pi$
$499$	18.7110	+	10.8028i	0.837619	+	0.483599i	−0.0188355	+	0.999823i	$0.505996\pi$
$500$	18.8183	−	10.8648i	0.841581	−	0.485887i
$501$	16.3022	−	9.41206i	0.728327	−	0.420500i
$502$	−46.8979	−	27.0765i	−2.09316	−	1.20849i
$503$	24.3890			1.08745			0.543725	−	0.839264i	$-0.317014\pi$
$503$	24.3890			1.08745			0.543725	+	0.839264i	$0.317014\pi$
$504$	−19.1830	+	0.504017i	−0.854477	+	0.0224507i
$505$			7.26511i			0.323293i
$506$	−22.2935	+	38.6135i	−0.991068	+	1.71658i
$507$	−9.15911	−	9.22554i	−0.406771	−	0.409721i
$508$	−8.34148	−	14.4479i	−0.370093	−	0.641021i
$509$	−19.7239	−	11.3876i	−0.874244	−	0.504745i	−0.00548797	−	0.999985i	$-0.501747\pi$
$509$	−19.7239	−	11.3876i	−0.874244	−	0.504745i	−0.868756	+	0.495240i	$0.835080\pi$
$510$	5.23415			0.231772
$511$	−4.31214	+	7.94365i	−0.190758	+	0.351406i
$512$		−	44.0832i		−	1.94822i
$513$	2.65773	+	1.53444i	0.117341	+	0.0677471i
$514$	18.2866	−	10.5578i	0.806586	−	0.465683i
$515$	−1.79090	+	1.03398i	−0.0789164	+	0.0455624i
$516$	19.5337	−	33.8334i	0.859924	−	1.48943i
$517$	−8.83406			−0.388522
$518$	−44.4144	−	24.1100i	−1.95146	−	1.05933i
$519$	−8.64360			−0.379412
$520$	4.66536	−	11.2059i	0.204589	−	0.491410i
$521$	5.05760	+	8.76002i	0.221577	+	0.383783i	0.955287	−	0.295680i	$-0.0955461\pi$
$521$	5.05760	+	8.76002i	0.221577	+	0.383783i	−0.733710	+	0.679463i	$0.762213\pi$
$522$	−12.5771	+	7.26137i	−0.550483	+	0.317821i
$523$	−8.30220	+	14.3798i	−0.363030	+	0.628786i	−0.988458	−	0.151496i	$-0.951591\pi$
$523$	−8.30220	+	14.3798i	−0.363030	+	0.628786i	0.625428	+	0.780282i	$0.284924\pi$
$524$	−94.5987			−4.13256
$525$	−0.332483	−	12.6544i	−0.0145108	−	0.552282i
$526$		−	9.82416i		−	0.428354i
$527$	−35.2190	−	20.3337i	−1.53417	−	0.885751i
$528$	36.8815	−	21.2935i	1.60506	−	0.926681i
$529$	4.47883	+	7.75756i	0.194732	+	0.337285i
$530$	4.00605	−	6.93868i	0.174012	−	0.301397i
$531$			6.93202i			0.300824i
$532$	−20.3010	−	33.1217i	−0.880161	−	1.43601i
$533$	2.29849	+	17.7059i	0.0995588	+	0.766928i
$534$	−4.10128	+	7.10363i	−0.177480	+	0.307404i
$535$	4.25423	−	2.45618i	0.183926	−	0.106190i
$536$	−20.5144	−	35.5320i	−0.886088	−	1.53475i
$537$	−9.96461	+	17.2592i	−0.430005	+	0.744790i
$538$			57.4795i			2.47812i
$539$	−1.67914	−	31.9320i	−0.0723255	−	1.37541i
$540$			2.22080i			0.0955680i
$541$	24.4034	+	14.0893i	1.04918	+	0.605746i	0.922421	−	0.386187i	$-0.126208\pi$
$541$	24.4034	+	14.0893i	1.04918	+	0.605746i	0.126763	+	0.991933i	$0.459541\pi$
$542$	−15.6221	−	27.0584i	−0.671029	−	1.16226i
$543$	−0.129564	−	0.224411i	−0.00556012	−	0.00963041i
$544$	−36.6585	−	21.1648i	−1.57172	−	0.907432i
$545$	−9.24564			−0.396040
$546$	−15.6038	−	19.3369i	−0.667780	−	0.827544i
$547$	−28.7280			−1.22832			−0.614160	−	0.789181i	$-0.710505\pi$
$547$	−28.7280			−1.22832			−0.614160	+	0.789181i	$0.710505\pi$
$548$	12.9769	+	7.49221i	0.554345	+	0.320051i
$549$	2.41090	+	4.17580i	0.102895	+	0.178219i
$550$	28.4643	+	49.3016i	1.21372	+	2.10223i
$551$	−14.8183	−	8.55534i	−0.631280	−	0.364470i
$552$			27.1792i			1.15682i
$553$	−0.407692	−	15.5168i	−0.0173368	−	0.659842i
$554$			76.6576i			3.25687i
$555$	−1.70189	+	2.94777i	−0.0722414	+	0.125126i
$556$	25.3579	+	43.9213i	1.07542	+	1.86268i
$557$	−23.6204	+	13.6373i	−1.00083	+	0.577829i	−0.908494	−	0.417898i	$-0.862767\pi$
$557$	−23.6204	+	13.6373i	−1.00083	+	0.577829i	−0.0923362	+	0.995728i	$0.529433\pi$
$558$	12.2338	−	21.1895i	0.517896	−	0.897023i
$559$	29.1955	−	3.79002i	1.23484	−	0.160301i
$560$	5.46208	−	10.0620i	0.230815	−	0.425198i
$561$			19.7763i			0.834958i
$562$	−13.4389	+	23.2768i	−0.566885	+	0.981873i
$563$	−4.35825	−	7.54871i	−0.183678	−	0.318140i	0.759452	−	0.650563i	$-0.225467\pi$
$563$	−4.35825	−	7.54871i	−0.183678	−	0.318140i	−0.943130	+	0.332423i	$0.892134\pi$
$564$	−8.01317	+	4.62641i	−0.337416	+	0.194807i
$565$	−2.09130	−	1.20741i	−0.0879816	−	0.0507962i
$566$			28.6036i			1.20230i
$567$	2.32524	+	1.26224i	0.0976510	+	0.0530090i
$568$	−60.7461			−2.54885
$569$	16.6405	−	28.8221i	0.697604	−	1.20829i	−0.271690	−	0.962385i	$-0.587583\pi$
$569$	16.6405	−	28.8221i	0.697604	−	1.20829i	0.969295	−	0.245902i	$-0.0790840\pi$
$570$	−3.21321	+	1.85515i	−0.134586	+	0.0777035i
$571$	−6.40807	−	11.0991i	−0.268169	−	0.464483i	0.700220	−	0.713927i	$-0.253085\pi$
$571$	−6.40807	−	11.0991i	−0.268169	−	0.464483i	−0.968389	+	0.249444i	$0.919752\pi$
$572$	72.7497	+	30.2880i	3.04182	+	1.26640i
$573$	19.6393			0.820443
$574$	0.896323	+	34.1142i	0.0374118	+	1.42390i
$575$	−17.9292			−0.747700
$576$	3.41090	−	5.90785i	0.142121	−	0.246161i
$577$	−19.9802	+	11.5356i	−0.831788	+	0.480233i	−0.854464	−	0.519510i	$-0.826115\pi$
$577$	−19.9802	+	11.5356i	−0.831788	+	0.480233i	0.0226765	+	0.999743i	$0.492781\pi$
$578$	3.93139	−	2.26979i	0.163524	−	0.0944109i
$579$	21.2359	+	12.2606i	0.882536	+	0.509532i
$580$		−	12.3822i		−	0.514142i
$581$	1.01111	+	1.64965i	0.0419477	+	0.0684389i
$582$	5.11385			0.211976
$583$	26.2166	+	15.1362i	1.08578	+	0.626877i
$584$	−12.3891	−	21.4585i	−0.512663	−	0.887958i
$585$	−1.32956	+	1.01639i	−0.0549704	+	0.0420227i
$586$	19.2273	−	33.3027i	0.794273	−	1.37572i
$587$		−	45.6950i		−	1.88603i	−0.332745	−	0.943017i	$-0.607975\pi$
$587$		−	45.6950i		−	1.88603i	0.332745	−	0.943017i	$-0.392025\pi$
$588$	−18.2459	−	28.0854i	−0.752450	−	1.15822i
$589$	28.8276			1.18782
$590$	−7.25803	−	4.19042i	−0.298808	−	0.172517i
$591$	18.4880	−	10.6740i	0.760494	−	0.439071i
$592$	59.2072	−	34.1833i	2.43340	−	1.40493i
$593$	21.0446	+	12.1501i	0.864197	+	0.498945i	0.865416	−	0.501055i	$-0.167054\pi$
$593$	21.0446	+	12.1501i	0.864197	+	0.498945i	−0.00121818	+	0.999999i	$0.500388\pi$
$594$	−11.8984			−0.488198
$595$	2.77832	+	4.53290i	0.113900	+	0.185831i
$596$		−	72.3105i		−	2.96195i
$597$	−8.64175	+	14.9679i	−0.353683	+	0.612597i
$598$	−27.9589	+	21.3735i	−1.14332	+	0.874026i
$599$	15.6357	+	27.0818i	0.638857	+	1.10653i	0.985684	+	0.168604i	$0.0539259\pi$
$599$	15.6357	+	27.0818i	0.638857	+	1.10653i	−0.346827	+	0.937929i	$0.612741\pi$
$600$	30.0531	+	17.3511i	1.22691	+	0.708358i
$601$	−16.1139			−0.657298			−0.328649	−	0.944452i	$-0.606593\pi$
$601$	−16.1139			−0.657298			−0.328649	+	0.944452i	$0.606593\pi$
$602$	56.2514	−	1.47796i	2.29264	−	0.0602371i
$603$			5.65682i			0.230364i
$604$	13.8546	+	7.99896i	0.563736	+	0.325473i
$605$	3.96621	−	2.28989i	0.161249	−	0.0930974i
$606$	−35.3074	+	20.3847i	−1.43426	+	0.828073i
$607$	2.70189	−	4.67982i	0.109667	−	0.189948i	−0.805969	−	0.591958i	$-0.798355\pi$
$607$	2.70189	−	4.67982i	0.109667	−	0.189948i	0.915635	+	0.402010i	$0.131688\pi$
$608$	30.0058			1.21690
$609$	−12.9645	−	7.03767i	−0.525348	−	0.285181i
$610$	−5.82958			−0.236033
$611$	−6.43715	−	2.67999i	−0.260419	−	0.108421i
$612$	10.3569	+	17.9387i	0.418652	+	0.725127i
$613$	15.1816	−	8.76508i	0.613178	−	0.354018i	−0.161030	−	0.986949i	$-0.551482\pi$
$613$	15.1816	−	8.76508i	0.613178	−	0.354018i	0.774208	+	0.632931i	$0.218148\pi$
$614$	−16.7398	+	28.9942i	−0.675564	+	1.17011i
$615$	2.29849			0.0926842
$616$	77.0394	+	41.8202i	3.10401	+	1.68498i
$617$		−	6.14240i		−	0.247284i	−0.992327	−	0.123642i	$-0.960543\pi$
$617$		−	6.14240i		−	0.247284i	0.992327	−	0.123642i	$-0.0394574\pi$
$618$	−10.0500	−	5.80234i	−0.404268	−	0.233404i
$619$	−2.55396	+	1.47453i	−0.102652	+	0.0592663i	−0.550447	−	0.834870i	$-0.685543\pi$
$619$	−2.55396	+	1.47453i	−0.102652	+	0.0592663i	0.447795	+	0.894136i	$0.352209\pi$
$620$	10.4306	+	18.0663i	0.418902	+	0.725560i
$621$	1.87366	−	3.24527i	0.0751872	−	0.130228i
$622$		−	32.2687i		−	1.29386i
$623$	−8.32891	+	0.218835i	−0.333691	+	0.00876745i
$624$	33.3344	−	4.32730i	1.33444	−	0.173231i
$625$	−10.9074	+	18.8921i	−0.436295	+	0.755685i
$626$	65.8984	−	38.0464i	2.63383	−	1.52064i
$627$	−7.00935	−	12.1406i	−0.279927	−	0.484847i
$628$	−49.6422	+	85.9828i	−1.98094	+	3.43109i
$629$			31.7477i			1.26586i
$630$	−2.72722	+	1.67157i	−0.108655	+	0.0665970i
$631$			16.2280i			0.646028i	0.946394	+	0.323014i	$0.104696\pi$
$631$			16.2280i			0.646028i	−0.946394	+	0.323014i	$0.895304\pi$
$632$	36.8511	+	21.2760i	1.46586	+	0.846314i
$633$	13.3350	+	23.0970i	0.530020	+	0.918022i
$634$	−12.8032	−	22.1758i	−0.508479	−	0.880712i
$635$	−1.40162	−	0.809225i	−0.0556216	−	0.0321131i
$636$	31.7073			1.25728
$637$	8.46368	−	23.7774i	0.335343	−	0.942096i
$638$	66.3402			2.62643
$639$	7.25325	+	4.18766i	0.286934	+	0.165661i
$640$	−0.414507	−	0.717947i	−0.0163848	−	0.0283793i
$641$	1.40622	+	2.43564i	0.0555422	+	0.0962018i	0.892460	−	0.451127i	$-0.148978\pi$
$641$	1.40622	+	2.43564i	0.0555422	+	0.0962018i	−0.836917	+	0.547329i	$0.815645\pi$
$642$	23.8734	+	13.7833i	0.942207	+	0.543983i
$643$		−	29.0689i		−	1.14637i	−0.819428	−	0.573183i	$-0.805708\pi$
$643$		−	29.0689i		−	1.14637i	0.819428	−	0.573183i	$-0.194292\pi$
$644$	−40.4439	+	24.7889i	−1.59371	+	0.976821i
$645$		−	3.79002i		−	0.149232i
$646$	−17.3033	+	29.9701i	−0.680788	+	1.17916i
$647$	−18.7051	−	32.3982i	−0.735373	−	1.27370i	−0.954559	−	0.298021i	$-0.903674\pi$
$647$	−18.7051	−	32.3982i	−0.735373	−	1.27370i	0.219186	−	0.975683i	$-0.429660\pi$
$648$	−6.28127	+	3.62649i	−0.246751	+	0.142462i
$649$	15.8328	−	27.4232i	0.621492	−	1.07646i
$650$	5.78456	+	44.5600i	0.226889	+	1.74779i
$651$	24.8444	−	0.652766i	0.973729	−	0.0255839i
$652$			39.1439i			1.53299i
$653$	−3.77665	+	6.54135i	−0.147792	+	0.255983i	−0.930411	−	0.366518i	$-0.880550\pi$
$653$	−3.77665	+	6.54135i	−0.147792	+	0.255983i	0.782619	+	0.622501i	$0.213883\pi$
$654$	−25.9418	−	44.9325i	−1.01440	−	1.75700i
$655$	−7.94771	+	4.58861i	−0.310543	+	0.179292i
$656$	−39.9812	−	23.0831i	−1.56100	−	0.901245i
$657$			3.41627i			0.133281i
$658$	−11.7128	−	6.35820i	−0.456613	−	0.247869i
$659$	−35.1269			−1.36835			−0.684175	−	0.729318i	$-0.739837\pi$
$659$	−35.1269			−1.36835			−0.684175	+	0.729318i	$0.739837\pi$
$660$	5.07233	−	8.78553i	0.197440	−	0.341976i
$661$	13.8292	−	7.98429i	0.537893	−	0.310553i	−0.206331	−	0.978482i	$-0.566152\pi$
$661$	13.8292	−	7.98429i	0.537893	−	0.310553i	0.744225	+	0.667929i	$0.232819\pi$
$662$	6.54444	+	11.3353i	0.254357	+	0.440559i
$663$	−5.99954	+	14.4105i	−0.233003	+	0.559657i
$664$	−5.30416			−0.205841
$665$	−3.31219	−	1.79800i	−0.128441	−	0.0697233i
$666$	−19.1010			−0.740148
$667$	−10.4467	+	18.0941i	−0.404496	+	0.700608i
$668$	−77.9986	+	45.0325i	−3.01786	+	1.74236i
$669$	16.7841	−	9.69033i	0.648912	−	0.374650i
$670$	−5.92286	−	3.41957i	−0.228820	−	0.132109i
$671$		−	22.0261i		−	0.850308i
$672$	25.8598	−	0.679445i	0.997563	−	0.0262102i
$673$	14.9364			0.575757			0.287879	−	0.957667i	$-0.407050\pi$
$673$	14.9364			0.575757			0.287879	+	0.957667i	$0.407050\pi$
$674$	−1.20950	−	0.698305i	−0.0465882	−	0.0268977i
$675$	−2.39228	−	4.14355i	−0.0920788	−	0.159485i
$676$	43.8223	+	44.1401i	1.68547	+	1.69770i
$677$	−1.99065	+	3.44790i	−0.0765068	+	0.132514i	−0.901741	−	0.432278i	$-0.857710\pi$
$677$	−1.99065	+	3.44790i	−0.0765068	+	0.132514i	0.825234	+	0.564791i	$0.191043\pi$
$678$		−	13.5512i		−	0.520431i
$679$	2.71447	+	4.42873i	0.104172	+	0.169959i
$680$	−14.5748			−0.558917
$681$	3.42959	+	1.98008i	0.131422	+	0.0758767i
$682$	−96.7941	+	55.8841i	−3.70644	+	2.13991i
$683$	−2.56232	+	1.47935i	−0.0980443	+	0.0566059i	−0.548220	−	0.836334i	$-0.684695\pi$
$683$	−2.56232	+	1.47935i	−0.0980443	+	0.0566059i	0.450176	+	0.892940i	$0.351361\pi$
$684$	−12.7160	−	7.34161i	−0.486210	−	0.280713i
$685$	1.45367			0.0555419
$686$	20.7564	−	43.5463i	0.792481	−	1.66260i
$687$			4.16682i			0.158974i
$688$	−38.0621	+	65.9255i	−1.45110	+	2.51338i
$689$	14.5115	+	18.9827i	0.552844	+	0.723182i
$690$	2.26526	+	3.92355i	0.0862370	+	0.149367i
$691$	−18.1762	−	10.4941i	−0.691457	−	0.399213i	0.112701	−	0.993629i	$-0.464050\pi$
$691$	−18.1762	−	10.4941i	−0.691457	−	0.399213i	−0.804158	+	0.594416i	$0.797383\pi$
$692$	41.3558			1.57211
$693$	−6.31575	−	10.3043i	−0.239915	−	0.391429i
$694$		−	71.9164i		−	2.72991i
$695$	4.26089	+	2.46003i	0.161625	+	0.0933142i
$696$	35.0215	−	20.2197i	1.32749	−	0.766425i
$697$	18.5662	−	10.7192i	0.703246	−	0.406019i
$698$	−44.5811	+	77.2167i	−1.68742	+	2.92269i
$699$	−9.46752			−0.358095
$700$	1.59079	+	60.5456i	0.0601260	+	2.28841i
$701$	−16.0616			−0.606639			−0.303319	−	0.952889i	$-0.598095\pi$
$701$	−16.0616			−0.606639			−0.303319	+	0.952889i	$0.598095\pi$
$702$	−8.67006	−	3.60962i	−0.327230	−	0.136236i
$703$	−11.2524	−	19.4897i	−0.424392	−	0.735068i
$704$	−26.9872	+	15.5811i	−1.01712	+	0.587234i
$705$	−0.448818	+	0.777375i	−0.0169035	+	0.0292776i
$706$	47.1877			1.77593
$707$	−36.3951	−	19.7568i	−1.36878	−	0.743029i
$708$		−	33.1666i		−	1.24648i
$709$	21.4558	+	12.3875i	0.805788	+	0.465222i	0.845491	−	0.533990i	$-0.179308\pi$
$709$	21.4558	+	12.3875i	0.805788	+	0.465222i	−0.0397031	+	0.999212i	$0.512641\pi$
$710$	−8.76922	+	5.06291i	−0.329103	+	0.190008i
$711$	−2.93341	−	5.08082i	−0.110012	−	0.190546i
$712$	11.4203	−	19.7805i	0.427992	−	0.741304i
$713$		−	35.2005i		−	1.31827i
$714$	−14.2338	+	26.2208i	−0.532685	+	0.981290i
$715$	7.58121	−	0.984155i	0.283521	−	0.0368053i
$716$	47.6762	−	82.5776i	1.78174	−	3.08607i
$717$	−1.58243	+	0.913614i	−0.0590968	+	0.0341195i
$718$	−4.89228	−	8.47367i	−0.182578	−	0.316235i
$719$	15.8716	−	27.4904i	0.591911	−	1.02522i	−0.402063	−	0.915612i	$-0.631707\pi$
$719$	15.8716	−	27.4904i	0.591911	−	1.02522i	0.993975	−	0.109609i	$-0.0349598\pi$
$720$		−	4.32730i		−	0.161269i
$721$	−0.309600	−	11.7834i	−0.0115301	−	0.438838i
$722$			24.9584i			0.928855i
$723$	−13.3006	−	7.67909i	−0.494653	−	0.285588i
$724$	0.619906	+	1.07371i	0.0230386	+	0.0399041i
$725$	13.3383	+	23.1026i	0.495371	+	0.858007i
$726$	22.2571	+	12.8502i	0.826039	+	0.476914i
$727$	36.4008			1.35003			0.675016	−	0.737803i	$-0.264137\pi$
$727$	36.4008			1.35003			0.675016	+	0.737803i	$0.264137\pi$
$728$	43.4496	+	53.8447i	1.61035	+	1.99562i
$729$	1.00000			0.0370370
$730$	−3.57693	−	2.06514i	−0.132388	−	0.0764344i
$731$	−17.6751	−	30.6141i	−0.653736	−	1.13230i
$732$	−11.5351	−	19.9794i	−0.426349	−	0.738458i
$733$	14.2104	+	8.20439i	0.524874	+	0.303036i	0.738927	−	0.673786i	$-0.235333\pi$
$733$	14.2104	+	8.20439i	0.524874	+	0.303036i	−0.214053	+	0.976822i	$0.568666\pi$
$734$		−	6.54810i		−	0.241695i
$735$	−2.89525	−	1.47456i	−0.106793	−	0.0543899i
$736$		−	36.6392i		−	1.35054i
$737$	12.9203	−	22.3785i	0.475924	−	0.824324i
$738$	6.44921	+	11.1704i	0.237399	+	0.411186i
$739$	−32.8322	+	18.9557i	−1.20775	+	0.697296i	−0.962268	−	0.272104i	$-0.912280\pi$
$739$	−32.8322	+	18.9557i	−1.20775	+	0.697296i	−0.245485	+	0.969400i	$0.578947\pi$
$740$	8.14281	−	14.1038i	0.299336	−	0.518464i
$741$	−1.42445	−	10.9729i	−0.0523285	−	0.403100i
$742$	23.8658	+	38.9377i	0.876140	+	1.42945i
$743$			33.6517i			1.23456i	0.786743	+	0.617280i	$0.211766\pi$
$743$			33.6517i			1.23456i	−0.786743	+	0.617280i	$0.788234\pi$
$744$	−34.0656	+	59.0033i	−1.24890	+	2.16317i
$745$	−3.50750	−	6.07517i	−0.128505	−	0.222577i
$746$	−13.7364	+	7.93070i	−0.502924	+	0.290363i
$747$	0.633331	+	0.365654i	0.0231724	+	0.0133786i
$748$		−	94.6210i		−	3.45969i
$749$	0.735446	+	27.9912i	0.0268726	+	1.02278i
$750$	11.8296			0.431955
$751$	−2.85330	+	4.94206i	−0.104118	+	0.180338i	−0.913378	−	0.407113i	$-0.866535\pi$
$751$	−2.85330	+	4.94206i	−0.104118	+	0.180338i	0.809259	+	0.587452i	$0.199869\pi$
$752$	15.6139	−	9.01471i	0.569381	−	0.328732i
$753$	−10.3952	−	18.0050i	−0.378822	−	0.656139i
$754$	48.3403	+	20.1256i	1.76045	+	0.732932i
$755$	1.55199			0.0564828
$756$	−11.1253	−	6.03925i	−0.404622	−	0.219645i
$757$	10.4161			0.378578			0.189289	−	0.981921i	$-0.439382\pi$
$757$	10.4161			0.378578			0.189289	+	0.981921i	$0.439382\pi$
$758$	3.48032	−	6.02809i	0.126411	−	0.218950i
$759$	−14.8244	+	8.55890i	−0.538093	+	0.310668i
$760$	8.94735	−	5.16576i	0.324555	−	0.187382i
$761$	44.7324	+	25.8262i	1.62155	+	0.936201i	0.986507	+	0.163722i	$0.0523500\pi$
$761$	44.7324	+	25.8262i	1.62155	+	0.936201i	0.635041	+	0.772479i	$0.280983\pi$
$762$		−	9.08223i		−	0.329014i
$763$	25.1426	−	46.3167i	0.910224	−	1.67678i
$764$	−93.9652			−3.39954
$765$	1.74027	+	1.00474i	0.0629195	+	0.0363266i
$766$	−20.1361	−	34.8767i	−0.727546	−	1.26015i
$767$	19.8563	−	15.1794i	0.716970	−	0.548096i
$768$	9.14788	−	15.8446i	0.330096	−	0.571743i
$769$			0.362142i			0.0130592i	0.999979	+	0.00652958i	$0.00207845\pi$
$769$			0.362142i			0.0130592i	−0.999979	+	0.00652958i	$0.997922\pi$
$770$	14.6068	−	0.383782i	0.526393	−	0.0138306i
$771$	8.10664			0.291954
$772$	−101.605	−	58.6614i	−3.65683	−	2.11127i
$773$	−11.6446	+	6.72303i	−0.418828	+	0.241811i	−0.694576	−	0.719420i	$-0.744408\pi$
$773$	−11.6446	+	6.72303i	−0.418828	+	0.241811i	0.275748	+	0.961230i	$0.411075\pi$
$774$	18.4189	−	10.6342i	0.662055	−	0.382238i
$775$	−38.9226	−	22.4720i	−1.39814	−	0.807216i
$776$	−14.2398			−0.511179
$777$	−10.1389	−	16.5419i	−0.363732	−	0.593438i
$778$		−	24.4439i		−	0.876356i
$779$	−7.59845	+	13.1609i	−0.272243	+	0.471538i
$780$	6.36134	−	4.86299i	0.227772	−	0.174123i
$781$	−19.1293	−	33.1330i	−0.684502	−	1.18559i
$782$	36.5956	+	21.1285i	1.30866	+	0.755552i
$783$	−5.57555			−0.199254
$784$	35.5528	+	54.7254i	1.26974	+	1.95448i
$785$			9.63179i			0.343773i
$786$	−44.6000	−	25.7498i	−1.59083	−	0.918466i
$787$	−15.0347	+	8.68027i	−0.535928	+	0.309418i	−0.743427	−	0.668817i	$-0.766801\pi$
$787$	−15.0347	+	8.68027i	−0.535928	+	0.309418i	0.207499	+	0.978235i	$0.433468\pi$
$788$	−88.4568	+	51.0706i	−3.15114	+	1.81931i
$789$	1.88584	−	3.26637i	0.0671376	−	0.116286i
$790$	7.09303			0.252359
$791$	11.7357	−	7.19307i	0.417273	−	0.255756i
$792$	33.1318			1.17729
$793$	6.68205	−	16.0498i	0.237287	−	0.569946i
$794$	−6.80707	−	11.7902i	−0.241574	−	0.418418i
$795$	2.66389	−	1.53800i	0.0944785	−	0.0545472i
$796$	41.3469	−	71.6150i	1.46550	−	2.53833i
$797$	−35.1519			−1.24514			−0.622572	−	0.782563i	$-0.713912\pi$
$797$	−35.1519			−1.24514			−0.622572	+	0.782563i	$0.713912\pi$
$798$	−0.555480	−	21.1417i	−0.0196638	−	0.748407i
$799$			8.37240i			0.296194i
$800$	−40.5134	−	23.3904i	−1.43236	−	0.826975i
$801$	−2.72722	+	1.57456i	−0.0963615	+	0.0556343i
$802$	−19.7881	−	34.2741i	−0.698744	−	1.21026i
$803$	7.80279	−	13.5148i	0.275355	−	0.476928i
$804$		−	27.0654i		−	0.954523i
$805$	−2.19548	+	4.04442i	−0.0773804	+	0.142547i
$806$	−87.4848	+	11.3568i	−3.08152	+	0.400028i
$807$	−11.0337	+	19.1110i	−0.388405	+	0.672738i
$808$	98.3154	−	56.7624i	3.45872	−	1.99689i
$809$	−0.0546871	−	0.0947209i	−0.00192270	−	0.00333021i	0.865062	−	0.501664i	$-0.167279\pi$
$809$	−0.0546871	−	0.0947209i	−0.00192270	−	0.00333021i	−0.866985	+	0.498334i	$0.833945\pi$
$810$	−0.604503	+	1.04703i	−0.0212401	+	0.0367889i
$811$			11.0787i			0.389026i	0.980900	+	0.194513i	$0.0623127\pi$
$811$			11.0787i			0.389026i	−0.980900	+	0.194513i	$0.937687\pi$
$812$	62.0294	+	33.6721i	2.17681	+	1.18166i
$813$		−	11.9953i		−	0.420692i
$814$	75.5639	+	43.6268i	2.64851	+	1.52912i
$815$	1.89872	+	3.28867i	0.0665091	+	0.115197i
$816$	−20.1807	−	34.9540i	−0.706467	−	1.22364i
$817$	21.7012	+	12.5292i	0.759229	+	0.438341i
$818$	−7.98280			−0.279112
$819$	−1.47610	−	9.42450i	−0.0515790	−	0.329319i
$820$	−10.9973			−0.384041
$821$	−3.52286	−	2.03392i	−0.122949	−	0.0709845i	0.437264	−	0.899333i	$-0.355947\pi$
$821$	−3.52286	−	2.03392i	−0.122949	−	0.0709845i	−0.560213	+	0.828349i	$0.689281\pi$
$822$	4.07877	+	7.06464i	0.142263	+	0.246407i
$823$	14.4821	+	25.0836i	0.504813	+	0.874361i	0.999985	+	0.00556599i	$0.00177172\pi$
$823$	14.4821	+	25.0836i	0.504813	+	0.874361i	−0.495172	+	0.868795i	$0.664895\pi$
$824$	27.9847	+	16.1569i	0.974892	+	0.562854i
$825$			21.8560i			0.760927i
$826$	40.7297	−	24.9642i	1.41717	−	0.868614i
$827$		−	38.1072i		−	1.32512i	−0.749009	−	0.662559i	$-0.769470\pi$
$827$		−	38.1072i		−	1.32512i	0.749009	−	0.662559i	$-0.230530\pi$
$828$	−8.96461	+	15.5272i	−0.311542	+	0.539606i
$829$	−4.76233	−	8.24859i	−0.165402	−	0.286485i	0.771396	−	0.636356i	$-0.219559\pi$
$829$	−4.76233	−	8.24859i	−0.165402	−	0.286485i	−0.936798	+	0.349870i	$0.886226\pi$
$830$	−0.765700	+	0.442077i	−0.0265778	+	0.0153447i
$831$	−14.7151	+	25.4874i	−0.510462	+	0.884147i
$832$	−24.3917	+	3.16641i	−0.845630	+	0.109775i
$833$	−30.2633	+	1.59138i	−1.04856	+	0.0551382i
$834$			27.6098i			0.956049i
$835$	−4.36870	+	7.56682i	−0.151185	+	0.261860i
$836$	33.5366	+	58.0872i	1.15989	+	2.00899i
$837$	8.13504	−	4.69677i	0.281188	−	0.162344i
$838$	−63.9268	−	36.9081i	−2.20831	−	1.27497i
$839$			16.0315i			0.553468i	0.960947	+	0.276734i	$0.0892521\pi$
$839$			16.0315i			0.553468i	−0.960947	+	0.276734i	$0.910748\pi$
$840$	7.59409	−	4.65458i	0.262021	−	0.160598i
$841$	2.08675			0.0719570
$842$	−26.4511	+	45.8146i	−0.911564	+	1.57887i
$843$	−8.93640	+	5.15944i	−0.307786	+	0.177700i
$844$	−63.8023	−	110.509i	−2.19616	−	3.80387i
$845$	5.82279	+	1.58278i	0.200310	+	0.0544494i
$846$	−5.03724			−0.173184
$847$	0.685655	+	26.0962i	0.0235594	+	0.896675i
$848$	−61.7828			−2.12163
$849$	−5.49073	+	9.51022i	−0.188441	+	0.326390i
$850$	46.7251	−	26.9768i	1.60266	−	0.925295i
$851$	−23.7983	+	13.7399i	−0.815794	+	0.470999i
$852$	−34.7036	−	20.0361i	−1.18892	−	0.686426i
$853$		−	51.0076i		−	1.74647i	−0.487303	−	0.873233i	$-0.662019\pi$
$853$		−	51.0076i		−	1.74647i	0.487303	−	0.873233i	$-0.337981\pi$
$854$	15.8530	−	29.2037i	0.542478	−	0.999331i
$855$	−1.42445			−0.0487152
$856$	−66.4767	−	38.3804i	−2.27213	−	1.31181i
$857$	−11.5139	−	19.9427i	−0.393308	−	0.681229i	0.599576	−	0.800318i	$-0.295336\pi$
$857$	−11.5139	−	19.9427i	−0.393308	−	0.681229i	−0.992884	+	0.119089i	$0.962003\pi$
$858$	26.0545	+	34.0822i	0.889487	+	1.16355i
$859$	10.4701	−	18.1347i	0.357234	−	0.618748i	−0.630264	−	0.776381i	$-0.717053\pi$
$859$	10.4701	−	18.1347i	0.357234	−	0.618748i	0.987498	+	0.157634i	$0.0503865\pi$
$860$			18.1335i			0.618349i
$861$	−6.25053	+	11.5145i	−0.213017	+	0.392412i
$862$	21.3035			0.725602
$863$	−9.14389	−	5.27923i	−0.311262	−	0.179707i	0.336229	−	0.941780i	$-0.390848\pi$
$863$	−9.14389	−	5.27923i	−0.311262	−	0.179707i	−0.647491	+	0.762073i	$0.724182\pi$
$864$	8.46753	−	4.88873i	0.288071	−	0.166318i
$865$	3.47451	−	2.00601i	0.118137	−	0.0682063i
$866$	3.28444	+	1.89627i	0.111610	+	0.0644380i
$867$	1.74283			0.0591896
$868$	−118.869	+	3.12320i	−4.03469	+	0.106008i
$869$			26.7998i			0.909121i
$870$	3.37044	−	5.83777i	0.114268	−	0.197919i
$871$	16.2036	−	12.3870i	0.549039	−	0.419718i
$872$	72.2363	+	125.117i	2.44623	+	4.23700i
$873$	1.70027	+	0.981652i	0.0575455	+	0.0332239i
$874$	−29.9544			−1.01322
$875$	6.27922	+	10.2447i	0.212276	+	0.346335i
$876$		−	16.3453i		−	0.552257i
$877$	32.2429	+	18.6154i	1.08877	+	0.628599i	0.933248	−	0.359234i	$-0.116962\pi$
$877$	32.2429	+	18.6154i	1.08877	+	0.628599i	0.155518	+	0.987833i	$0.450295\pi$
$878$	48.6629	−	28.0956i	1.64229	−	0.948179i
$879$	12.7855	−	7.38173i	0.431245	−	0.248980i
$880$	−9.88360	+	17.1189i	−0.333176	+	0.577078i
$881$	−9.90917			−0.333848			−0.166924	−	0.985970i	$-0.553384\pi$
$881$	−9.90917			−0.333848			−0.166924	+	0.985970i	$0.553384\pi$
$882$	−0.957455	−	18.2079i	−0.0322392	−	0.613091i
$883$	7.93329			0.266977			0.133488	−	0.991050i	$-0.457382\pi$
$883$	7.93329			0.266977			0.133488	+	0.991050i	$0.457382\pi$
$884$	28.7052	−	68.9478i	0.965459	−	2.31897i
$885$	−1.60878	−	2.78649i	−0.0540786	−	0.0936669i
$886$	−29.0855	+	16.7925i	−0.977147	+	0.564156i
$887$	2.18406	−	3.78291i	0.0733337	−	0.127018i	−0.827027	−	0.562163i	$-0.809970\pi$
$887$	2.18406	−	3.78291i	0.0733337	−	0.127018i	0.900360	+	0.435145i	$0.143303\pi$
$888$	53.1877			1.78486
$889$	7.86544	−	4.82090i	0.263798	−	0.161688i
$890$		−	3.80730i		−	0.127621i
$891$	−3.95602	−	2.28401i	−0.132532	−	0.0765173i
$892$	−80.3046	+	46.3639i	−2.68880	+	1.55238i
$893$	−2.96744	−	5.13976i	−0.0993016	−	0.171995i
$894$	19.6830	−	34.0919i	0.658297	−	1.14020i
$895$		−	9.25034i		−	0.309205i
$896$	4.72382	−	0.124114i	0.157812	−	0.00414637i
$897$	−13.3987	+	1.73935i	−0.447369	+	0.0580753i
$898$	−5.06628	+	8.77505i	−0.169064	+	0.292827i
$899$	−45.3573	+	26.1871i	−1.51275	+	0.873388i
$900$	11.4460	+	19.8250i	0.381533	+	0.660834i
$901$	14.3452	−	24.8466i	0.477907	−	0.827759i
$902$		−	58.9202i		−	1.96183i
$903$	18.9864	+	10.3066i	0.631826	+	0.342982i
$904$			37.7341i			1.25502i
$905$	0.104163	+	0.0601384i	0.00346249	+	0.00199907i
$906$	4.35465	+	7.54247i	0.144673	+	0.250582i
$907$	14.4157	+	24.9687i	0.478664	+	0.829071i	0.999701	−	0.0244635i	$-0.00778776\pi$
$907$	14.4157	+	24.9687i	0.478664	+	0.829071i	−0.521036	+	0.853534i	$0.674454\pi$
$908$	−16.4091	−	9.47378i	−0.544554	−	0.314398i
$909$	−15.6522			−0.519149
$910$	10.7600	+	4.15162i	0.356692	+	0.137625i
$911$	48.3751			1.60274			0.801369	−	0.598171i	$-0.204106\pi$
$911$	48.3751			1.60274			0.801369	+	0.598171i	$0.204106\pi$
$912$	24.7776	+	14.3054i	0.820469	+	0.473698i
$913$	−1.67031	−	2.89307i	−0.0552793	−	0.0957466i
$914$	−15.9461	−	27.6194i	−0.527449	−	0.913568i
$915$	−1.93824	−	1.11904i	−0.0640762	−	0.0369944i
$916$		−	19.9364i		−	0.658716i
$917$	−1.37395	−	52.2929i	−0.0453719	−	1.72686i
$918$			11.2766i			0.372183i
$919$	15.5584	−	26.9479i	0.513224	−	0.888930i	−0.486658	−	0.873592i	$-0.661784\pi$
$919$	15.5584	−	26.9479i	0.513224	−	0.888930i	0.999882	−	0.0153377i	$-0.00488233\pi$
$920$	−6.30774	−	10.9253i	−0.207960	−	0.360198i
$921$	−11.1314	+	6.42673i	−0.366793	+	0.211768i
$922$	40.1093	−	69.4714i	1.32093	−	2.28792i
$923$	−3.88749	−	29.9464i	−0.127958	−	0.985698i
$924$	30.2181	+	49.3016i	0.994101	+	1.62190i
$925$			35.0862i			1.15363i
$926$	−2.01862	+	3.49636i	−0.0663360	+	0.114897i
$927$	−2.22763	−	3.85837i	−0.0731649	−	0.126725i
$928$	−47.2111	+	27.2574i	−1.54978	+	0.894766i
$929$	−46.0689	−	26.5979i	−1.51147	−	0.872649i	−0.999910	−	0.0134024i	$-0.995734\pi$
$929$	−46.0689	−	26.5979i	−1.51147	−	0.872649i	−0.511562	−	0.859246i	$-0.670933\pi$
$930$			11.3568i			0.372406i
$931$	18.0144	−	11.7032i	0.590397	−	0.383557i
$932$	45.2979			1.48378
$933$	6.19428	−	10.7288i	0.202791	−	0.351245i
$934$	29.4783	−	17.0193i	0.964559	−	0.556888i
$935$	−4.58969	−	7.94958i	−0.150099	−	0.259979i
$936$	24.1423	+	10.0512i	0.789114	+	0.328533i
$937$	12.7179			0.415474			0.207737	−	0.978185i	$-0.433390\pi$
$937$	12.7179			0.415474			0.207737	+	0.978185i	$0.433390\pi$
$938$	33.2372	−	20.3718i	1.08523	−	0.665164i
$939$	29.2135			0.953346
$940$	2.14739	−	3.71939i	0.0700403	−	0.121313i
$941$	−46.7431	+	26.9871i	−1.52378	+	0.879755i	−0.524177	+	0.851609i	$0.675627\pi$
$941$	−46.7431	+	26.9871i	−1.52378	+	0.879755i	−0.999604	+	0.0281461i	$0.991040\pi$
$942$	−46.8091	+	27.0253i	−1.52512	+	0.880531i
$943$	16.0704	+	9.27823i	0.523323	+	0.302141i
$944$			64.6262i			2.10340i
$945$	−1.22763	+	0.0322549i	−0.0399347	+	0.00104925i
$946$	−97.1544			−3.15876
$947$	18.3509	+	10.5949i	0.596324	+	0.344288i	0.767594	−	0.640936i	$-0.221454\pi$
$947$	18.3509	+	10.5949i	0.596324	+	0.344288i	−0.171270	+	0.985224i	$0.554787\pi$
$948$	14.0351	+	24.3095i	0.455838	+	0.789535i
$949$	9.78568	−	7.48077i	0.317657	−	0.242836i
$950$	−19.1228	+	33.1217i	−0.620426	+	1.07461i
$951$		−	9.83076i		−	0.318784i
$952$	39.6347	−	73.0134i	1.28457	−	2.36638i
$953$	25.8117			0.836122			0.418061	−	0.908419i	$-0.362710\pi$
$953$	25.8117			0.836122			0.418061	+	0.908419i	$0.362710\pi$
$954$	14.9489	+	8.63076i	0.483989	+	0.279431i
$955$	−7.89449	+	4.55788i	−0.255460	+	0.147490i
$956$	7.57120	−	4.37124i	0.244870	−	0.141376i
$957$	22.0570	+	12.7346i	0.713002	+	0.411652i
$958$	26.2759			0.848935
$959$	−3.95312	+	7.28227i	−0.127653	+	0.235157i
$960$			3.16641i			0.102195i
$961$	28.6193	−	49.5701i	0.923203	−	1.59903i
$962$	41.8263	+	54.7135i	1.34854	+	1.76404i
$963$	5.29167	+	9.16544i	0.170522	+	0.295352i
$964$	63.6373	+	36.7410i	2.04962	+	1.18335i
$965$	−11.3817			−0.366391
$966$	−25.8154	+	0.678280i	−0.830598	+	0.0218233i
$967$			40.3935i			1.29897i	0.760375	+	0.649484i	$0.225015\pi$
$967$			40.3935i			1.29897i	−0.760375	+	0.649484i	$0.774985\pi$
$968$	−61.9762	−	35.7820i	−1.99199	−	1.15008i
$969$	−11.5061	+	6.64305i	−0.369629	+	0.213405i
$970$	−2.05564	+	1.18682i	−0.0660026	+	0.0381066i
$971$	−7.28924	+	12.6253i	−0.233923	+	0.405166i	−0.958959	−	0.283544i	$-0.908490\pi$
$971$	−7.28924	+	12.6253i	−0.233923	+	0.405166i	0.725036	+	0.688711i	$0.241823\pi$
$972$	−4.78456			−0.153465
$973$	−23.9108	+	14.6554i	−0.766545	+	0.469832i
$974$	−20.6237			−0.660826
$975$	−6.63044	+	15.9259i	−0.212344	+	0.510036i
$976$	22.4765	+	38.9304i	0.719455	+	1.24613i
$977$	−6.97255	+	4.02560i	−0.223071	+	0.128790i	−0.607372	−	0.794418i	$-0.707776\pi$
$977$	−6.97255	+	4.02560i	−0.223071	+	0.128790i	0.384300	+	0.923208i	$0.374443\pi$
$978$	−10.6550	+	18.4550i	−0.340709	+	0.590125i
$979$	14.3852			0.459754
$980$	13.8525	+	7.05511i	0.442501	+	0.225367i
$981$		−	19.9191i		−	0.635967i
$982$	−19.2876	−	11.1357i	−0.615492	−	0.355354i
$983$	−37.8895	+	21.8755i	−1.20849	+	0.697720i	−0.962428	−	0.271535i	$-0.912469\pi$
$983$	−37.8895	+	21.8755i	−1.20849	+	0.697720i	−0.246058	+	0.969255i	$0.579135\pi$
$984$	−17.9582	−	31.1045i	−0.572486	−	0.991574i
$985$	−4.95446	+	8.58138i	−0.157862	+	0.273426i
$986$		−	62.8733i		−	2.00229i
$987$	−2.67380	−	4.36238i	−0.0851080	−	0.138856i
$988$	6.81536	+	52.5006i	0.216826	+	1.67027i
$989$	15.2990	−	26.4986i	0.486480	−	0.842608i
$990$	4.78286	−	2.76138i	0.152009	−	0.0877625i
$991$	−11.3285	−	19.6216i	−0.359862	−	0.623300i	0.628075	−	0.778153i	$-0.283843\pi$
$991$	−11.3285	−	19.6216i	−0.359862	−	0.623300i	−0.987938	+	0.154853i	$0.950510\pi$
$992$	45.9225	−	79.5401i	1.45804	−	2.52540i
$993$			5.02506i			0.159466i
$994$	−1.51597	−	57.6981i	−0.0480837	−	1.83007i
$995$		−	8.02231i		−	0.254324i
$996$	−3.03021	−	1.74949i	−0.0960157	−	0.0554347i
$997$	22.8932	+	39.6521i	0.725033	+	1.25579i	0.958960	+	0.283540i	$0.0915090\pi$
$997$	22.8932	+	39.6521i	0.725033	+	1.25579i	−0.233927	+	0.972254i	$0.575158\pi$
$998$	−28.1382	−	48.7368i	−0.890700	−	1.54274i
$999$	−6.35076	−	3.66661i	−0.200929	−	0.116006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.c.142.1	yes	16
3.2	odd	2		819.2.dl.f.415.8		16
7.2	even	3		1911.2.c.n.883.8		8
7.4	even	3	inner	273.2.bj.c.25.8	yes	16
7.5	odd	6		1911.2.c.k.883.8		8
13.12	even	2	inner	273.2.bj.c.142.8	yes	16
21.11	odd	6		819.2.dl.f.298.1		16
39.38	odd	2		819.2.dl.f.415.1		16
91.12	odd	6		1911.2.c.k.883.1		8
91.25	even	6	inner	273.2.bj.c.25.1	✓	16
91.51	even	6		1911.2.c.n.883.1		8
273.116	odd	6		819.2.dl.f.298.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.c.25.1	✓	16	91.25	even	6	inner
273.2.bj.c.25.8	yes	16	7.4	even	3	inner
273.2.bj.c.142.1	yes	16	1.1	even	1	trivial
273.2.bj.c.142.8	yes	16	13.12	even	2	inner
819.2.dl.f.298.1		16	21.11	odd	6
819.2.dl.f.298.8		16	273.116	odd	6
819.2.dl.f.415.1		16	39.38	odd	2
819.2.dl.f.415.8		16	3.2	odd	2
1911.2.c.k.883.1		8	91.12	odd	6
1911.2.c.k.883.8		8	7.5	odd	6
1911.2.c.n.883.1		8	91.51	even	6
1911.2.c.n.883.8		8	7.2	even	3

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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25575 - 1.30236i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.39228 + 4.14355i) q^{4} +(0.401974 + 0.232080i) q^{5} +2.60472i q^{6} +(-2.25575 + 1.38260i) q^{7} -7.25298i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.25575 - 1.30236i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.39228 + 4.14355i) q^{4} +(0.401974 + 0.232080i) q^{5} +2.60472i q^{6} +(-2.25575 + 1.38260i) q^{7} -7.25298i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.604503 - 1.04703i) q^{10} +(3.95602 - 2.28401i) q^{11} +(2.39228 - 4.14355i) q^{12} +(3.57555 - 0.464160i) q^{13} +(6.88906 - 0.181004i) q^{14} -0.464160i q^{15} +(-4.66143 + 8.07383i) q^{16} +(-2.16465 - 3.74928i) q^{17} +(2.25575 - 1.30236i) q^{18} +(2.65773 + 1.53444i) q^{19} +2.22080i q^{20} +(2.32524 + 1.26224i) q^{21} -11.8984 q^{22} +(1.87366 - 3.24527i) q^{23} +(-6.28127 + 3.62649i) q^{24} +(-2.39228 - 4.14355i) q^{25} +(-8.67006 - 3.60962i) q^{26} +1.00000 q^{27} +(-11.1253 - 6.03925i) q^{28} -5.57555 q^{29} +(-0.604503 + 1.04703i) q^{30} +(8.13504 - 4.69677i) q^{31} +(8.46753 - 4.88873i) q^{32} +(-3.95602 - 2.28401i) q^{33} +11.2766i q^{34} +(-1.22763 + 0.0322549i) q^{35} -4.78456 q^{36} +(-6.35076 - 3.66661i) q^{37} +(-3.99678 - 6.92263i) q^{38} +(-2.18975 - 2.86444i) q^{39} +(1.68327 - 2.91551i) q^{40} +4.95194i q^{41} +(-3.60128 - 5.87560i) q^{42} +8.16532 q^{43} +(18.9278 + 10.9280i) q^{44} +(-0.401974 + 0.232080i) q^{45} +(-8.45300 + 4.88034i) q^{46} +(-1.67480 - 0.966946i) q^{47} +9.32286 q^{48} +(3.17683 - 6.23761i) q^{49} +12.4624i q^{50} +(-2.16465 + 3.74928i) q^{51} +(10.4770 + 13.7051i) q^{52} +(3.31351 + 5.73917i) q^{53} +(-2.25575 - 1.30236i) q^{54} +2.12029 q^{55} +(10.0280 + 16.3609i) q^{56} -3.06888i q^{57} +(12.5771 + 7.26137i) q^{58} +(6.00330 - 3.46601i) q^{59} +(1.92327 - 1.11040i) q^{60} +(2.41090 - 4.17580i) q^{61} -24.4675 q^{62} +(-0.0694910 - 2.64484i) q^{63} -6.82180 q^{64} +(1.54500 + 0.643233i) q^{65} +(5.94921 + 10.3043i) q^{66} +(4.89895 - 2.82841i) q^{67} +(10.3569 - 17.9387i) q^{68} -3.74731 q^{69} +(2.81123 + 1.52605i) q^{70} -8.37533i q^{71} +(6.28127 + 3.62649i) q^{72} +(2.95857 - 1.70813i) q^{73} +(9.55049 + 16.5419i) q^{74} +(-2.39228 + 4.14355i) q^{75} +14.6832i q^{76} +(-5.76593 + 10.6218i) q^{77} +(1.20901 + 9.31330i) q^{78} +(-2.93341 + 5.08082i) q^{79} +(-3.74755 + 2.16365i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.44921 - 11.1704i) q^{82} -0.731307i q^{83} +(0.332483 + 12.6544i) q^{84} -2.00949i q^{85} +(-18.4189 - 10.6342i) q^{86} +(2.78777 + 4.82857i) q^{87} +(-16.5659 - 28.6930i) q^{88} +(2.72722 + 1.57456i) q^{89} +1.20901 q^{90} +(-7.42381 + 5.99059i) q^{91} +17.9292 q^{92} +(-8.13504 - 4.69677i) q^{93} +(2.51862 + 4.36238i) q^{94} +(0.712225 + 1.23361i) q^{95} +(-8.46753 - 4.88873i) q^{96} -1.96330i q^{97} +(-15.2897 + 9.93311i) q^{98} +4.56802i 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	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

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