LMFDB - Embedded newform 19.2.e.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,2,Mod(4,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("19.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	19.e (of order $9$, degree $6$, 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:	$0.151715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	19.4
Dual form			19.2.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826352 - 0.300767i) q^{2} +(0.0923963 + 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(-1.93969 + 1.62760i) q^{5} +(0.0812519 - 0.460802i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.41875 + 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +O(q^{10})$	\(q+(-0.826352 - 0.300767i) q^{2} +(0.0923963 + 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(-1.93969 + 1.62760i) q^{5} +(0.0812519 - 0.460802i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.41875 + 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +(2.09240 - 0.761570i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(0.326352 - 0.565258i) q^{12} +(-0.918748 + 5.21048i) q^{13} +(-1.26604 + 1.06234i) q^{14} +(-1.03209 - 0.866025i) q^{15} +(-0.00727396 - 0.0412527i) q^{16} +(-1.55303 - 0.565258i) q^{17} -2.38919 q^{18} +(-2.52094 - 3.55596i) q^{19} +3.10607 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.520945 + 2.95442i) q^{22} +(1.34730 + 1.13052i) q^{23} +(-1.15657 + 0.970481i) q^{24} +(0.245100 - 1.39003i) q^{25} +(2.32635 - 4.02936i) q^{26} +(1.52094 + 2.63435i) q^{27} +(-2.16637 + 0.788496i) q^{28} +(3.25877 - 1.18610i) q^{29} +(0.592396 + 1.02606i) q^{30} +(-0.971782 + 1.68317i) q^{31} +(0.979055 - 5.55250i) q^{32} +(1.39053 - 1.16679i) q^{33} +(1.11334 + 0.934204i) q^{34} +(0.826352 + 4.68647i) q^{35} +(-3.13176 - 1.13987i) q^{36} -0.837496 q^{37} +(1.01367 + 3.69669i) q^{38} -2.81521 q^{39} +(-6.75150 - 2.45734i) q^{40} +(-0.779715 - 4.42198i) q^{41} +(-0.673648 - 0.565258i) q^{42} +(3.67752 - 3.08580i) q^{43} +(-0.726682 + 4.12122i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(-0.773318 - 1.33943i) q^{46} +(-0.673648 + 0.245188i) q^{47} +(0.0209445 - 0.00762319i) q^{48} +(1.73396 + 3.00330i) q^{49} +(-0.620615 + 1.07494i) q^{50} +(0.152704 - 0.866025i) q^{51} +(4.97178 - 4.17182i) q^{52} +(-4.67752 - 3.92490i) q^{53} +(-0.464508 - 2.63435i) q^{54} +(8.11721 + 2.95442i) q^{55} +5.33275 q^{56} +(1.63041 - 1.64955i) q^{57} -3.04963 q^{58} +(10.1099 + 3.67972i) q^{59} +(0.286989 + 1.62760i) q^{60} +(3.36231 + 2.82131i) q^{61} +(1.30928 - 1.09861i) q^{62} +(0.886659 - 5.02849i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-6.69846 - 11.6021i) q^{65} +(-1.50000 + 0.545955i) q^{66} +(-13.3550 + 4.86084i) q^{67} +(1.01367 + 1.75573i) q^{68} +(-0.467911 + 0.810446i) q^{69} +(0.726682 - 4.12122i) q^{70} +(-10.5398 + 8.84397i) q^{71} +(5.90554 + 4.95534i) q^{72} +(-1.30541 - 7.40333i) q^{73} +(0.692066 + 0.251892i) q^{74} +0.751030 q^{75} +(-0.434945 + 5.32926i) q^{76} -6.41147 q^{77} +(2.32635 + 0.846723i) q^{78} +(-1.20914 - 6.85738i) q^{79} +(0.0812519 + 0.0681784i) q^{80} +(5.00387 - 4.19875i) q^{81} +(-0.685670 + 3.88863i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(-0.613341 - 1.06234i) q^{84} +(3.93242 - 1.43128i) q^{85} +(-3.96703 + 1.44388i) q^{86} +(0.922618 + 1.59802i) q^{87} +(4.84002 - 8.38316i) q^{88} +(-0.396459 + 2.24843i) q^{89} +(4.63429 - 3.88863i) q^{90} +(7.61721 + 6.39160i) q^{91} +(-0.374638 - 2.12467i) q^{92} +(-0.971782 - 0.353700i) q^{93} +0.630415 q^{94} +(10.6775 + 2.79439i) q^{95} +3.00000 q^{96} +(1.71301 + 0.623485i) q^{97} +(-0.529563 - 3.00330i) q^{98} +(-7.10014 - 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.826352	−	0.300767i	−0.584319	−	0.212675i	0.0329100	−	0.999458i	$-0.489523\pi$
$2$	−0.826352	−	0.300767i	−0.584319	−	0.212675i	−0.617229	+	0.786784i	$0.711745\pi$
$3$	0.0923963	+	0.524005i	0.0533450	+	0.302535i	0.999794	−	0.0203202i	$-0.00646857\pi$
$3$	0.0923963	+	0.524005i	0.0533450	+	0.302535i	−0.946449	+	0.322855i	$0.895357\pi$
$4$	−0.939693	−	0.788496i	−0.469846	−	0.394248i
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	−0.963561	−	0.267489i	$-0.913806\pi$
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	0.0961041	+	0.995371i	$0.469362\pi$
$6$	0.0812519	−	0.460802i	0.0331710	−	0.188122i
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	−0.631977	−	0.774987i	$-0.717756\pi$
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	0.987147	+	0.159814i	$0.0510895\pi$
$8$	1.41875	+	2.45734i	0.501603	+	0.868802i
$9$	2.55303	−	0.929228i	0.851011	−	0.309743i
$10$	2.09240	−	0.761570i	0.661674	−	0.240830i
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$	0.326352	−	0.565258i	0.0942097	−	0.163176i
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	0.541733	+	0.840551i	$0.317769\pi$
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	−0.796547	+	0.604576i	$0.793343\pi$
$14$	−1.26604	+	1.06234i	−0.338365	+	0.283922i
$15$	−1.03209	−	0.866025i	−0.266484	−	0.223607i
$16$	−0.00727396	−	0.0412527i	−0.00181849	−	0.0103132i
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	0.146748	−	0.989174i	$-0.453119\pi$
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	−0.523414	+	0.852079i	$0.675342\pi$
$18$	−2.38919			−0.563136
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$20$	3.10607			0.694538
$21$	0.939693	+	0.342020i	0.205058	+	0.0746349i
$22$	0.520945	+	2.95442i	0.111066	+	0.629885i
$23$	1.34730	+	1.13052i	0.280931	+	0.235729i	0.772354	−	0.635192i	$-0.219079\pi$
$23$	1.34730	+	1.13052i	0.280931	+	0.235729i	−0.491424	+	0.870921i	$0.663523\pi$
$24$	−1.15657	+	0.970481i	−0.236085	+	0.198099i
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$	2.32635	−	4.02936i	0.456235	−	0.790222i
$27$	1.52094	+	2.63435i	0.292706	+	0.506982i
$28$	−2.16637	+	0.788496i	−0.409406	+	0.149012i
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	−0.0212363	−	0.999774i	$-0.506760\pi$
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	0.626375	+	0.779522i	$0.284538\pi$
$30$	0.592396	+	1.02606i	0.108156	+	0.187332i
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	−0.940001	−	0.341172i	$-0.889176\pi$
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	0.765464	+	0.643479i	$0.222510\pi$
$32$	0.979055	−	5.55250i	0.173074	−	0.981553i
$33$	1.39053	−	1.16679i	0.242060	−	0.203113i
$34$	1.11334	+	0.934204i	0.190936	+	0.160215i
$35$	0.826352	+	4.68647i	0.139679	+	0.792159i
$36$	−3.13176	−	1.13987i	−0.521960	−	0.189978i
$37$	−0.837496			−0.137684			−0.0688418	−	0.997628i	$-0.521930\pi$
$37$	−0.837496			−0.137684			−0.0688418	+	0.997628i	$0.521930\pi$
$38$	1.01367	+	3.69669i	0.164439	+	0.599682i
$39$	−2.81521			−0.450794
$40$	−6.75150	−	2.45734i	−1.06751	−	0.388540i
$41$	−0.779715	−	4.42198i	−0.121771	−	0.690598i	−0.983173	−	0.182675i	$-0.941524\pi$
$41$	−0.779715	−	4.42198i	−0.121771	−	0.690598i	0.861402	−	0.507923i	$-0.169587\pi$
$42$	−0.673648	−	0.565258i	−0.103946	−	0.0872212i
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	−0.317768	−	0.948169i	$-0.602933\pi$
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	0.878584	+	0.477588i	$0.158489\pi$
$44$	−0.726682	+	4.12122i	−0.109551	+	0.621297i
$45$	−3.43969	+	5.95772i	−0.512759	+	0.888125i
$46$	−0.773318	−	1.33943i	−0.114020	−	0.197488i
$47$	−0.673648	+	0.245188i	−0.0982617	+	0.0357643i	−0.390683	−	0.920525i	$-0.627761\pi$
$47$	−0.673648	+	0.245188i	−0.0982617	+	0.0357643i	0.292422	+	0.956290i	$0.405539\pi$
$48$	0.0209445	−	0.00762319i	0.00302308	−	0.00110031i
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$	−0.620615	+	1.07494i	−0.0877682	+	0.152019i
$51$	0.152704	−	0.866025i	0.0213828	−	0.121268i
$52$	4.97178	−	4.17182i	0.689462	−	0.578527i
$53$	−4.67752	−	3.92490i	−0.642507	−	0.539127i	0.262280	−	0.964992i	$-0.415526\pi$
$53$	−4.67752	−	3.92490i	−0.642507	−	0.539127i	−0.904787	+	0.425865i	$0.859970\pi$
$54$	−0.464508	−	2.63435i	−0.0632115	−	0.358490i
$55$	8.11721	+	2.95442i	1.09452	+	0.398374i
$56$	5.33275			0.712618
$57$	1.63041	−	1.64955i	0.215954	−	0.218488i
$58$	−3.04963			−0.400436
$59$	10.1099	+	3.67972i	1.31620	+	0.479058i	0.902239	−	0.431236i	$-0.141922\pi$
$59$	10.1099	+	3.67972i	1.31620	+	0.479058i	0.413962	+	0.910294i	$0.364144\pi$
$60$	0.286989	+	1.62760i	0.0370501	+	0.210122i
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	0.832140	−	0.554565i	$-0.187115\pi$
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	−0.401640	+	0.915797i	$0.631560\pi$
$62$	1.30928	−	1.09861i	0.166278	−	0.139524i
$63$	0.886659	−	5.02849i	0.111709	−	0.633531i
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	−6.69846	−	11.6021i	−0.830842	−	1.43906i
$66$	−1.50000	+	0.545955i	−0.184637	+	0.0672025i
$67$	−13.3550	+	4.86084i	−1.63158	+	0.593846i	−0.985537	−	0.169458i	$-0.945798\pi$
$67$	−13.3550	+	4.86084i	−1.63158	+	0.593846i	−0.646040	+	0.763304i	$0.723576\pi$
$68$	1.01367	+	1.75573i	0.122926	+	0.212913i
$69$	−0.467911	+	0.810446i	−0.0563299	+	0.0975662i
$70$	0.726682	−	4.12122i	0.0868551	−	0.492580i
$71$	−10.5398	+	8.84397i	−1.25085	+	1.04959i	−0.254252	+	0.967138i	$0.581829\pi$
$71$	−10.5398	+	8.84397i	−1.25085	+	1.04959i	−0.996595	+	0.0824479i	$0.973726\pi$
$72$	5.90554	+	4.95534i	0.695975	+	0.583992i
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	−0.960782	−	0.277306i	$-0.910559\pi$
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	0.807995	−	0.589189i	$-0.200553\pi$
$74$	0.692066	+	0.251892i	0.0804511	+	0.0292818i
$75$	0.751030			0.0867214
$76$	−0.434945	+	5.32926i	−0.0498916	+	0.611308i
$77$	−6.41147			−0.730655
$78$	2.32635	+	0.846723i	0.263407	+	0.0958725i
$79$	−1.20914	−	6.85738i	−0.136039	−	0.771515i	−0.974131	−	0.225986i	$-0.927440\pi$
$79$	−1.20914	−	6.85738i	−0.136039	−	0.771515i	0.838092	−	0.545529i	$-0.183671\pi$
$80$	0.0812519	+	0.0681784i	0.00908424	+	0.00762258i
$81$	5.00387	−	4.19875i	0.555986	−	0.466527i
$82$	−0.685670	+	3.88863i	−0.0757196	+	0.429427i
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	−0.926698	−	0.375807i	$-0.877366\pi$
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	0.788807	+	0.614641i	$0.210699\pi$
$84$	−0.613341	−	1.06234i	−0.0669210	−	0.115911i
$85$	3.93242	−	1.43128i	0.426531	−	0.155244i
$86$	−3.96703	+	1.44388i	−0.427776	+	0.155698i
$87$	0.922618	+	1.59802i	0.0989151	+	0.171326i
$88$	4.84002	−	8.38316i	0.515948	−	0.893648i
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	−0.998584	−	0.0532055i	$-0.983056\pi$
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	0.956559	+	0.291539i	$0.0941673\pi$
$90$	4.63429	−	3.88863i	0.488497	−	0.409897i
$91$	7.61721	+	6.39160i	0.798501	+	0.670022i
$92$	−0.374638	−	2.12467i	−0.0390587	−	0.221513i
$93$	−0.971782	−	0.353700i	−0.100769	−	0.0366769i
$94$	0.630415			0.0650223
$95$	10.6775	+	2.79439i	1.09549	+	0.286698i
$96$	3.00000			0.306186
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	0.427517	−	0.904007i	$-0.359388\pi$
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	−0.253587	+	0.967312i	$0.581611\pi$
$98$	−0.529563	−	3.00330i	−0.0534939	−	0.303379i
$99$	−7.10014	−	5.95772i	−0.713591	−	0.598774i
$100$	−1.32635	+	1.11294i	−0.132635	+	0.111294i
$101$	−1.37551	+	7.80093i	−0.136869	+	0.776222i	0.836671	+	0.547705i	$0.184499\pi$
$101$	−1.37551	+	7.80093i	−0.136869	+	0.776222i	−0.973540	+	0.228516i	$0.926613\pi$
$102$	−0.386659	+	0.669713i	−0.0382850	+	0.0663115i
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	0.866384	−	0.499379i	$-0.166439\pi$
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	−0.865667	+	0.500621i	$0.833105\pi$
$104$	−14.1074	+	5.13468i	−1.38335	+	0.503497i
$105$	−2.37939	+	0.866025i	−0.232204	+	0.0845154i
$106$	2.68479	+	4.65020i	0.260770	+	0.451667i
$107$	1.77719	−	3.07818i	0.171807	−	0.297579i	−0.767244	−	0.641355i	$-0.778373\pi$
$107$	1.77719	−	3.07818i	0.171807	−	0.297579i	0.939052	+	0.343776i	$0.111706\pi$
$108$	0.647956	−	3.67474i	0.0623496	−	0.353602i
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	−0.331055	−	0.943612i	$-0.607404\pi$
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	0.871789	+	0.489882i	$0.162960\pi$
$110$	−5.81908	−	4.88279i	−0.554827	−	0.465555i
$111$	−0.0773815	−	0.438852i	−0.00734473	−	0.0416540i
$112$	−0.0739780	−	0.0269258i	−0.00699026	−	0.00254425i
$113$	7.37733			0.694000			0.347000	−	0.937865i	$-0.387200\pi$
$113$	7.37733			0.694000			0.347000	+	0.937865i	$0.387200\pi$
$114$	−1.84343	+	0.872729i	−0.172653	+	0.0817386i
$115$	−4.45336			−0.415278
$116$	−3.99747	−	1.45496i	−0.371156	−	0.135090i
$117$	2.49613	+	14.1563i	0.230767	+	1.30875i
$118$	−7.24763	−	6.08148i	−0.667198	−	0.559846i
$119$	−2.37939	+	1.99654i	−0.218118	+	0.183023i
$120$	0.663848	−	3.76487i	0.0606008	−	0.343684i
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	−1.92989	−	3.34267i	−0.174724	−	0.302631i
$123$	2.24510	−	0.817150i	0.202434	−	0.0736799i
$124$	2.24035	−	0.815422i	0.201190	−	0.0732270i
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$	−2.24510	+	3.88863i	−0.200009	+	0.346426i
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	−0.985576	−	0.169233i	$-0.945871\pi$
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	0.984020	+	0.178060i	$0.0569822\pi$
$128$	−5.24170	+	4.39831i	−0.463305	+	0.388759i
$129$	1.95677	+	1.64192i	0.172284	+	0.144563i
$130$	2.04576	+	11.6021i	0.179425	+	1.01757i
$131$	2.85369	+	1.03866i	0.249328	+	0.0907481i	0.463661	−	0.886013i	$-0.346536\pi$
$131$	2.85369	+	1.03866i	0.249328	+	0.0907481i	−0.214333	+	0.976761i	$0.568758\pi$
$132$	−2.22668			−0.193808
$133$	−8.15657	+	0.761570i	−0.707265	+	0.0660365i
$134$	12.4979			1.07966
$135$	−7.23783	−	2.63435i	−0.622933	−	0.226729i
$136$	−0.814330	−	4.61830i	−0.0698282	−	0.396016i
$137$	14.9684	+	12.5600i	1.27883	+	1.07307i	0.993404	+	0.114671i	$0.0365813\pi$
$137$	14.9684	+	12.5600i	1.27883	+	1.07307i	0.285431	+	0.958399i	$0.407863\pi$
$138$	0.630415	−	0.528981i	0.0536645	−	0.0450298i
$139$	2.67365	−	15.1630i	0.226776	−	1.28611i	−0.632485	−	0.774573i	$-0.717965\pi$
$139$	2.67365	−	15.1630i	0.226776	−	1.28611i	0.859261	−	0.511537i	$-0.170924\pi$
$140$	2.91875	−	5.05542i	0.246679	−	0.427261i
$141$	−0.190722	−	0.330341i	−0.0160617	−	0.0278197i
$142$	11.3696	−	4.13819i	0.954114	−	0.347269i
$143$	16.9611	−	6.17334i	1.41836	−	0.516240i
$144$	−0.0569038	−	0.0985603i	−0.00474198	−	0.00821336i
$145$	−4.39053	+	7.60462i	−0.364614	+	0.631529i
$146$	−1.14796	+	6.51038i	−0.0950055	+	0.538803i
$147$	−1.41353	+	1.18610i	−0.116586	+	0.0978275i
$148$	0.786989	+	0.660362i	0.0646901	+	0.0542814i
$149$	−0.654048	−	3.70929i	−0.0535817	−	0.303877i	0.946226	−	0.323507i	$-0.104862\pi$
$149$	−0.654048	−	3.70929i	−0.0535817	−	0.303877i	−0.999807	+	0.0196306i	$0.993751\pi$
$150$	−0.620615	−	0.225885i	−0.0506730	−	0.0184435i
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$	5.16163	−	11.2398i	0.418663	−	0.911671i
$153$	−4.49020			−0.363011
$154$	5.29813	+	1.92836i	0.426936	+	0.155392i
$155$	−0.854570	−	4.84651i	−0.0686407	−	0.389281i
$156$	2.64543	+	2.21978i	0.211804	+	0.177725i
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	−0.902254	−	0.431205i	$-0.858088\pi$
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	0.267980	+	0.963425i	$0.413644\pi$
$158$	−1.06330	+	6.03028i	−0.0845916	+	0.479743i
$159$	1.62449	−	2.81369i	0.128830	−	0.223140i
$160$	7.13816	+	12.3636i	0.564321	+	0.977432i
$161$	3.10607	−	1.13052i	0.244792	−	0.0890971i
$162$	−5.39780	+	1.96464i	−0.424091	+	0.154357i
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	0.902905	−	0.429841i	$-0.141430\pi$
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	−0.823706	+	0.567018i	$0.808097\pi$
$164$	−2.75402	+	4.77011i	−0.215053	+	0.372483i
$165$	−0.798133	+	4.52644i	−0.0621346	+	0.352383i
$166$	1.69253	−	1.42020i	0.131366	−	0.110229i
$167$	−17.8157	−	14.9491i	−1.37862	−	1.15680i	−0.969720	−	0.244218i	$-0.921469\pi$
$167$	−17.8157	−	14.9491i	−1.37862	−	1.15680i	−0.408898	−	0.912580i	$-0.634087\pi$
$168$	0.492726	+	2.79439i	0.0380146	+	0.215592i
$169$	−14.0890	−	5.12797i	−1.08377	−	0.394460i
$170$	−3.68004			−0.282247
$171$	−9.74035	−	6.73595i	−0.744863	−	0.515111i
$172$	−5.88888			−0.449023
$173$	−0.842549	−	0.306663i	−0.0640578	−	0.0233151i	0.309793	−	0.950804i	$-0.399740\pi$
$173$	−0.842549	−	0.306663i	−0.0640578	−	0.0233151i	−0.373850	+	0.927489i	$0.621963\pi$
$174$	−0.281774	−	1.59802i	−0.0213613	−	0.121146i
$175$	−2.03209	−	1.70513i	−0.153611	−	0.128895i
$176$	−0.109470	+	0.0918566i	−0.00825164	+	0.00692395i
$177$	−0.994070	+	5.63765i	−0.0747189	+	0.423752i
$178$	1.00387	−	1.73875i	0.0752433	−	0.130325i
$179$	10.6591	+	18.4621i	0.796699	+	1.37992i	0.921755	+	0.387773i	$0.126755\pi$
$179$	10.6591	+	18.4621i	0.796699	+	1.37992i	−0.125056	+	0.992150i	$0.539911\pi$
$180$	7.92989	−	2.88624i	0.591059	−	0.215128i
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.288196	−	0.957571i	$-0.406945\pi$
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.836286	+	0.548294i	$0.184722\pi$
$182$	−4.37211	−	7.57272i	−0.324082	−	0.561327i
$183$	−1.16772	+	2.02255i	−0.0863202	+	0.149511i
$184$	−0.866592	+	4.91469i	−0.0638860	+	0.362316i
$185$	1.62449	−	1.36310i	0.119435	−	0.100217i
$186$	0.696652	+	0.584561i	0.0510810	+	0.0428621i
$187$	0.979055	+	5.55250i	0.0715956	+	0.406039i
$188$	0.826352	+	0.300767i	0.0602679	+	0.0219357i
$189$	5.71688			0.415842
$190$	−7.98293	−	5.52060i	−0.579142	−	0.400506i
$191$	18.9486			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$192$	−2.52094	−	0.917549i	−0.181934	−	0.0662184i
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	0.952833	+	0.303494i	$0.0981534\pi$
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	−0.791569	+	0.611080i	$0.790736\pi$
$194$	−1.22803	−	1.03044i	−0.0881671	−	0.0739810i
$195$	5.46064	−	4.58202i	0.391044	−	0.328125i
$196$	0.738703	−	4.18939i	0.0527645	−	0.299242i
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	−0.0743108	−	0.997235i	$-0.523676\pi$
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	0.900786	−	0.434263i	$-0.142991\pi$
$198$	4.07532	+	7.05866i	0.289621	+	0.501637i
$199$	−8.66550	+	3.15398i	−0.614281	+	0.223580i	−0.630375	−	0.776291i	$-0.717099\pi$
$199$	−8.66550	+	3.15398i	−0.614281	+	0.223580i	0.0160945	+	0.999870i	$0.494877\pi$
$200$	3.76352	−	1.36981i	0.266121	−	0.0968601i
$201$	−3.78106	−	6.54899i	−0.266695	−	0.461930i
$202$	3.48293	−	6.03260i	0.245058	−	0.424453i
$203$	1.13176	−	6.41852i	0.0794339	−	0.450492i
$204$	−0.826352	+	0.693392i	−0.0578562	+	0.0485471i
$205$	8.70961	+	7.30823i	0.608305	+	0.510429i
$206$	−0.00222152	−	0.0125989i	−0.000154781	−	0.000877805i
$207$	4.49020	+	1.63430i	0.312090	+	0.113592i
$208$	0.221629			0.0153672
$209$	−6.20574	+	13.5135i	−0.429260	+	0.934746i
$210$	2.22668			0.153656
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.177478	−	0.984125i	$-0.556794\pi$
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.768539	+	0.639803i	$0.779016\pi$
$212$	1.30066	+	7.37641i	0.0893297	+	0.506614i
$213$	−5.60813	−	4.70578i	−0.384262	−	0.322435i
$214$	−2.39440	+	2.00914i	−0.163678	+	0.137342i
$215$	−2.11081	+	11.9710i	−0.143956	+	0.816417i
$216$	−4.31567	+	7.47497i	−0.293644	+	0.508607i
$217$	1.82635	+	3.16333i	0.123981	+	0.214741i
$218$	−6.08987	+	2.21653i	−0.412458	+	0.150122i
$219$	3.75877	−	1.36808i	0.253994	−	0.0924463i
$220$	−5.29813	−	9.17664i	−0.357200	−	0.618689i
$221$	4.37211	−	7.57272i	0.294100	−	0.509396i
$222$	−0.0680482	+	0.385920i	−0.00456709	+	0.0259013i
$223$	−2.30928	+	1.93771i	−0.154641	+	0.129759i	−0.716825	−	0.697253i	$-0.754405\pi$
$223$	−2.30928	+	1.93771i	−0.154641	+	0.129759i	0.562185	+	0.827012i	$0.309961\pi$
$224$	−8.11721	−	6.81115i	−0.542354	−	0.455089i
$225$	−0.665907	−	3.77655i	−0.0443938	−	0.251770i
$226$	−6.09627	−	2.21886i	−0.405518	−	0.147596i
$227$	−13.7219			−0.910757			−0.455378	−	0.890298i	$-0.650496\pi$
$227$	−13.7219			−0.910757			−0.455378	+	0.890298i	$0.650496\pi$
$228$	−2.83275	+	0.264490i	−0.187603	+	0.0175163i
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	3.68004	+	1.33943i	0.242655	+	0.0883192i
$231$	−0.592396	−	3.35965i	−0.0389768	−	0.221048i
$232$	7.53802	+	6.32515i	0.494895	+	0.415266i
$233$	−18.5273	+	15.5463i	−1.21377	+	1.01847i	−0.214640	+	0.976693i	$0.568858\pi$
$233$	−18.5273	+	15.5463i	−1.21377	+	1.01847i	−0.999127	+	0.0417777i	$0.986698\pi$
$234$	2.19506	−	12.4488i	0.143496	−	0.813804i
$235$	0.907604	−	1.57202i	0.0592055	−	0.102547i
$236$	−6.59879	−	11.4294i	−0.429545	−	0.743993i
$237$	3.48158	−	1.26719i	0.226153	−	0.0823130i
$238$	2.56670	−	0.934204i	0.166375	−	0.0605554i
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	0.945665	+	0.325143i	$0.105413\pi$
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	−0.191250	+	0.981541i	$0.561254\pi$
$240$	−0.0282185	+	0.0488759i	−0.00182150	+	0.00315492i
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	−0.983098	−	0.183082i	$-0.941393\pi$
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	0.986427	+	0.164199i	$0.0525038\pi$
$242$	0.429892	−	0.360723i	0.0276345	−	0.0231881i
$243$	9.65317	+	8.09997i	0.619251	+	0.519613i
$244$	−0.934945	−	5.30234i	−0.0598537	−	0.339447i
$245$	−8.25150	−	3.00330i	−0.527169	−	0.191874i
$246$	−2.10101			−0.133956
$247$	20.8444	−	9.86830i	1.32629	−	0.627905i
$248$	−5.51485			−0.350193
$249$	−1.25624	−	0.457236i	−0.0796112	−	0.0289761i
$250$	1.38754	+	7.86911i	0.0877555	+	0.497686i
$251$	−12.4081	−	10.4116i	−0.783190	−	0.657175i	0.160859	−	0.986977i	$-0.448573\pi$
$251$	−12.4081	−	10.4116i	−0.783190	−	0.657175i	−0.944050	+	0.329802i	$0.893018\pi$
$252$	−4.79813	+	4.02611i	−0.302254	+	0.253621i
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$	0.0444153	−	0.0769295i	0.00278686	−	0.00482699i
$255$	1.11334	+	1.92836i	0.0697201	+	0.120759i
$256$	15.1300	−	5.50687i	0.945625	−	0.344179i
$257$	−14.4290	+	5.25173i	−0.900057	+	0.327594i	−0.750276	−	0.661125i	$-0.770079\pi$
$257$	−14.4290	+	5.25173i	−0.900057	+	0.327594i	−0.149782	+	0.988719i	$0.547857\pi$
$258$	−1.12314	−	1.94534i	−0.0699237	−	0.121111i
$259$	−0.786989	+	1.36310i	−0.0489011	+	0.0846992i
$260$	−2.85369	+	16.1841i	−0.176979	+	1.00370i
$261$	7.21760	−	6.05628i	0.446758	−	0.374874i
$262$	−2.04576	−	1.71660i	−0.126387	−	0.106052i
$263$	1.67453	+	9.49671i	0.103256	+	0.585592i	0.991903	+	0.127000i	$0.0405349\pi$
$263$	1.67453	+	9.49671i	0.103256	+	0.585592i	−0.888647	+	0.458592i	$0.848354\pi$
$264$	4.84002	+	1.76162i	0.297883	+	0.108420i
$265$	15.4611			0.949768
$266$	6.96926	+	1.82391i	0.427312	+	0.111831i
$267$	−1.21482			−0.0743459
$268$	16.3824	+	5.96270i	1.00071	+	0.364230i
$269$	−3.17412	−	18.0013i	−0.193529	−	1.09756i	−0.914498	−	0.404591i	$-0.867414\pi$
$269$	−3.17412	−	18.0013i	−0.193529	−	1.09756i	0.720969	−	0.692968i	$-0.243697\pi$
$270$	5.18866	+	4.35381i	0.315772	+	0.264964i
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	−0.0842129	−	0.996448i	$-0.526838\pi$
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	0.966686	+	0.255965i	$0.0823932\pi$
$272$	−0.0120217	+	0.0681784i	−0.000728923	+	0.00413393i
$273$	−2.64543	+	4.58202i	−0.160109	+	0.277316i
$274$	−8.59152	−	14.8809i	−0.519033	−	0.898991i
$275$	−4.52481	+	1.64690i	−0.272857	+	0.0993117i
$276$	1.07873	−	0.392624i	0.0649317	−	0.0236332i
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	0.581775	−	0.813350i	$-0.302358\pi$
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	−0.995269	+	0.0971571i	$0.969025\pi$
$278$	−6.76991	+	11.7258i	−0.406033	+	0.703269i
$279$	−0.916937	+	5.20021i	−0.0548956	+	0.311328i
$280$	−10.3439	+	8.67956i	−0.618166	+	0.518703i
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	0.891175	−	0.453661i	$-0.149882\pi$
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	−0.292018	+	0.956413i	$0.594327\pi$
$282$	0.0582480	+	0.330341i	0.00346862	+	0.0196715i
$283$	16.3293	+	5.94340i	0.970679	+	0.353298i	0.778209	−	0.628005i	$-0.216128\pi$
$283$	16.3293	+	5.94340i	0.970679	+	0.353298i	0.192469	+	0.981303i	$0.438350\pi$
$284$	16.8776			1.00150
$285$	−0.477711	+	5.85327i	−0.0282972	+	0.346718i
$286$	−15.8726			−0.938565
$287$	−7.92989	−	2.88624i	−0.468087	−	0.170370i
$288$	−2.65998	−	15.0855i	−0.156741	−	0.888921i
$289$	−10.9304	−	9.17166i	−0.642962	−	0.539509i
$290$	5.91534	−	4.96356i	0.347361	−	0.291470i
$291$	−0.168434	+	0.955234i	−0.00987375	+	0.0559968i
$292$	−4.61081	+	7.98617i	−0.269828	+	0.467355i
$293$	−7.80200	−	13.5135i	−0.455798	−	0.789465i	0.542936	−	0.839774i	$-0.317313\pi$
$293$	−7.80200	−	13.5135i	−0.455798	−	0.789465i	−0.998734	+	0.0503091i	$0.983979\pi$
$294$	1.52481	−	0.554987i	0.0889290	−	0.0323675i
$295$	−25.5993	+	9.31737i	−1.49045	+	0.542478i
$296$	−1.18820	−	2.05802i	−0.0690625	−	0.119620i
$297$	5.18866	−	8.98703i	0.301077	−	0.521480i
$298$	−0.575160	+	3.26189i	−0.0333181	+	0.188956i
$299$	−7.12836	+	5.98140i	−0.412243	+	0.345913i
$300$	−0.705737	−	0.592184i	−0.0407457	−	0.0341897i
$301$	−1.56670	−	8.88522i	−0.0903033	−	0.512136i
$302$	12.0617	+	4.39008i	0.694070	+	0.252621i
$303$	−4.21482			−0.242135
$304$	−0.128356	+	0.129862i	−0.00736170	+	0.00744807i
$305$	−11.1138			−0.636375
$306$	3.71048	+	1.35051i	0.212114	+	0.0772033i
$307$	3.73695	+	21.1933i	0.213279	+	1.20956i	0.883868	+	0.467736i	$0.154930\pi$
$307$	3.73695	+	21.1933i	0.213279	+	1.20956i	−0.670589	+	0.741829i	$0.733959\pi$
$308$	6.02481	+	5.05542i	0.343296	+	0.288059i
$309$	−0.00592979	+	0.00497568i	−0.000337334	+	0.000283057i
$310$	−0.751497	+	4.26195i	−0.0426821	+	0.242062i
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	−0.994997	−	0.0999083i	$-0.968145\pi$
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	0.584021	+	0.811738i	$0.301478\pi$
$312$	−3.99407	−	6.91793i	−0.226120	−	0.391651i
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.803634	−	0.595124i	$-0.797103\pi$
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.233081	+	0.972457i	$0.574881\pi$
$314$	8.57310	−	3.12035i	0.483808	−	0.176092i
$315$	6.46451	+	11.1969i	0.364234	+	0.630871i
$316$	−4.27079	+	7.39723i	−0.240251	+	0.416127i
$317$	4.92246	−	27.9166i	0.276473	−	1.56795i	−0.457772	−	0.889070i	$-0.651352\pi$
$317$	4.92246	−	27.9166i	0.276473	−	1.56795i	0.734245	−	0.678885i	$-0.237536\pi$
$318$	−2.18866	+	1.83651i	−0.122734	+	0.102986i
$319$	−9.06283	−	7.60462i	−0.507421	−	0.425777i
$320$	−2.21688	−	12.5726i	−0.123927	−	0.702827i
$321$	1.77719	+	0.646844i	0.0991930	+	0.0361033i
$322$	−2.90673			−0.161986
$323$	1.90508	+	6.94751i	0.106001	+	0.386570i
$324$	−8.01279			−0.445155
$325$	7.01754	+	2.55418i	0.389263	+	0.141680i
$326$	−0.308811	−	1.75135i	−0.0171035	−	0.0969985i
$327$	3.00387	+	2.52055i	0.166114	+	0.139387i
$328$	9.76011	−	8.18971i	0.538912	−	0.452201i
$329$	−0.233956	+	1.32683i	−0.0128984	+	0.0731504i
$330$	2.02094	−	3.50038i	0.111249	−	0.192690i
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	0.888567	−	0.458747i	$-0.151702\pi$
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	−0.841570	+	0.540148i	$0.818368\pi$
$332$	2.89615	−	1.05411i	0.158947	−	0.0578520i
$333$	−2.13816	+	0.778225i	−0.117170	+	0.0426465i
$334$	10.2258	+	17.7116i	0.559531	+	0.969136i
$335$	17.9932	−	31.1651i	0.983073	−	1.70273i
$336$	0.00727396	−	0.0412527i	0.000396827	−	0.00225052i
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.0672796	−	0.997734i	$-0.478568\pi$
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.994259	+	0.106997i	$0.0341236\pi$
$338$	10.1001	+	8.47502i	0.549375	+	0.460980i
$339$	0.681637	+	3.86576i	0.0370215	+	0.209959i
$340$	−4.82383	−	1.75573i	−0.261609	−	0.0952178i
$341$	6.63041			0.359057
$342$	6.02300	+	8.49584i	0.325687	+	0.459403i
$343$	19.6732			1.06225
$344$	12.8004	+	4.65895i	0.690149	+	0.251194i
$345$	−0.411474	−	2.33359i	−0.0221530	−	0.125636i
$346$	0.604007	+	0.506822i	0.0324716	+	0.0272469i
$347$	5.90033	−	4.95096i	0.316746	−	0.265782i	−0.470527	−	0.882385i	$-0.655936\pi$
$347$	5.90033	−	4.95096i	0.316746	−	0.265782i	0.787274	+	0.616604i	$0.211492\pi$
$348$	0.393056	−	2.22913i	0.0210700	−	0.119494i
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	0.382315	+	0.924032i	$0.375127\pi$
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	−0.991393	+	0.130921i	$0.958206\pi$
$350$	1.16637	+	2.02022i	0.0623453	+	0.107985i
$351$	−15.1236	+	5.50454i	−0.807238	+	0.293811i
$352$	−18.0744	+	6.57856i	−0.963371	+	0.350638i
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	0.977171	−	0.212454i	$-0.0681457\pi$
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	−0.672576	+	0.740028i	$0.734812\pi$
$354$	2.51707	−	4.35970i	0.133781	−	0.231715i
$355$	6.04963	−	34.3092i	0.321081	−	1.82094i
$356$	2.14543	−	1.80023i	0.113708	−	0.0954120i
$357$	−1.26604	−	1.06234i	−0.0670062	−	0.0562249i
$358$	−3.25537	−	18.4621i	−0.172051	−	0.975752i
$359$	−9.75789	−	3.55158i	−0.515002	−	0.187445i	0.0714274	−	0.997446i	$-0.477245\pi$
$359$	−9.75789	−	3.55158i	−0.515002	−	0.187445i	−0.586429	+	0.810000i	$0.699467\pi$
$360$	−19.5202			−1.02881
$361$	−6.28968	+	17.9287i	−0.331036	+	0.943618i
$362$	−14.1575			−0.744099
$363$	−0.319078	−	0.116135i	−0.0167472	−	0.00609550i
$364$	−2.11809	−	12.0123i	−0.111018	−	0.629614i
$365$	14.5817	+	12.2355i	0.763242	+	0.640436i
$366$	1.57326	−	1.32012i	0.0822358	−	0.0690040i
$367$	−5.64930	+	32.0388i	−0.294891	+	1.67241i	0.372754	+	0.927930i	$0.378414\pi$
$367$	−5.64930	+	32.0388i	−0.294891	+	1.67241i	−0.667645	+	0.744480i	$0.732697\pi$
$368$	0.0368366	−	0.0638029i	0.00192024	−	0.00332596i
$369$	−6.09967	−	10.5649i	−0.317536	−	0.549989i
$370$	−1.75237	+	0.637812i	−0.0911016	+	0.0331583i
$371$	−10.7836	+	3.92490i	−0.559856	+	0.203771i
$372$	0.634285	+	1.09861i	0.0328862	+	0.0569605i
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	0.137183	+	0.990546i	$0.456195\pi$
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	−0.926429	+	0.376469i	$0.877138\pi$
$374$	0.860967	−	4.88279i	0.0445195	−	0.252483i
$375$	3.70368	−	3.10775i	0.191257	−	0.160484i
$376$	−1.55825	−	1.30753i	−0.0803605	−	0.0674305i
$377$	3.18614	+	18.0695i	0.164094	+	0.930626i
$378$	−4.72416	−	1.71945i	−0.242984	−	0.0884391i
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$	−7.83022	−	11.0450i	−0.401682	−	0.566599i
$381$	−0.0537486			−0.00275363
$382$	−15.6582	−	5.69913i	−0.801144	−	0.291593i
$383$	−4.07310	−	23.0997i	−0.208126	−	1.18034i	−0.892445	−	0.451157i	$-0.851012\pi$
$383$	−4.07310	−	23.0997i	−0.208126	−	1.18034i	0.684319	−	0.729183i	$-0.260100\pi$
$384$	−2.78905	−	2.34029i	−0.142328	−	0.119427i
$385$	12.4363	−	10.4353i	0.633812	−	0.531831i
$386$	1.97013	−	11.1732i	0.100277	−	0.568700i
$387$	6.52141	−	11.2954i	0.331502	−	0.574178i
$388$	−1.11809	−	1.93659i	−0.0567623	−	0.0983153i
$389$	−3.67365	+	1.33710i	−0.186261	+	0.0677936i	−0.433467	−	0.901169i	$-0.642710\pi$
$389$	−3.67365	+	1.33710i	−0.186261	+	0.0677936i	0.247206	+	0.968963i	$0.420488\pi$
$390$	−5.89053	+	2.14398i	−0.298279	+	0.108565i
$391$	−1.45336	−	2.51730i	−0.0734997	−	0.127305i
$392$	−4.92009	+	8.52185i	−0.248502	+	0.430418i
$393$	−0.280592	+	1.59132i	−0.0141540	+	0.0802714i
$394$	−15.6288	+	13.1141i	−0.787369	+	0.660681i
$395$	13.5064	+	11.3332i	0.679581	+	0.570236i
$396$	1.97431	+	11.1969i	0.0992127	+	0.562663i
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	0.122002	−	0.992530i	$-0.461069\pi$
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	−0.544527	+	0.838743i	$0.683291\pi$
$398$	8.10936			0.406486
$399$	−1.15270	−	4.20372i	−0.0577074	−	0.210449i
$400$	−0.0591253			−0.00295627
$401$	1.90508	+	0.693392i	0.0951350	+	0.0346263i	0.389149	−	0.921175i	$-0.372769\pi$
$401$	1.90508	+	0.693392i	0.0951350	+	0.0346263i	−0.294014	+	0.955801i	$0.594991\pi$
$402$	1.15476	+	6.54899i	0.0575943	+	0.326634i
$403$	−7.87733	−	6.60986i	−0.392398	−	0.329261i
$404$	7.44356	−	6.24589i	0.370331	−	0.310745i
$405$	−2.87211	+	16.2886i	−0.142716	+	0.809385i
$406$	−2.86571	+	4.96356i	−0.142223	+	0.246338i
$407$	1.42855	+	2.47432i	0.0708105	+	0.122647i
$408$	2.34477	−	0.853427i	0.116083	−	0.0422509i
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.541377	−	0.840780i	$-0.317903\pi$
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.955162	+	0.296084i	$0.0956808\pi$
$410$	−4.99912	−	8.65873i	−0.246889	−	0.427624i
$411$	−5.19846	+	9.00400i	−0.256421	+	0.444135i
$412$	0.00309887	−	0.0175745i	0.000152670	−	0.000865836i
$413$	15.4893	−	12.9971i	0.762180	−	0.639545i
$414$	−3.21894	−	2.70101i	−0.158202	−	0.132747i
$415$	−1.10472	−	6.26519i	−0.0542287	−	0.307546i
$416$	28.0317	+	10.2027i	1.37437	+	0.500228i
$417$	8.19253			0.401190
$418$	9.19253	−	9.30039i	0.449622	−	0.454897i
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$	2.91875	+	1.06234i	0.142420	+	0.0518368i
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	0.999862	−	0.0166178i	$-0.00528986\pi$
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	−0.945246	+	0.326357i	$0.894179\pi$
$422$	9.85117	+	8.26611i	0.479547	+	0.402388i
$423$	−1.49201	+	1.25195i	−0.0725440	+	0.0608717i
$424$	3.00862	−	17.0627i	0.146111	−	0.828639i
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$	3.21894	+	5.57537i	0.155958	+	0.270128i
$427$	7.75150	−	2.82131i	0.375121	−	0.136533i
$428$	−4.09714	+	1.49124i	−0.198043	+	0.0720817i
$429$	4.80200	+	8.31731i	0.231843	+	0.401564i
$430$	5.34477	−	9.25741i	0.257748	−	0.446432i
$431$	−2.43061	+	13.7847i	−0.117078	+	0.663984i	0.868622	+	0.495475i	$0.165006\pi$
$431$	−2.43061	+	13.7847i	−0.117078	+	0.663984i	−0.985700	+	0.168508i	$0.946105\pi$
$432$	0.0976108	−	0.0819052i	0.00469630	−	0.00394067i
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.0625499	−	0.998042i	$-0.519923\pi$
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.993741	+	0.111709i	$0.964368\pi$
$434$	−0.557781	−	3.16333i	−0.0267744	−	0.151845i
$435$	−4.39053	−	1.59802i	−0.210510	−	0.0766193i
$436$	−9.04013			−0.432944
$437$	0.623608	−	7.64090i	0.0298312	−	0.365514i
$438$	−3.51754			−0.168075
$439$	12.5376	+	4.56332i	0.598387	+	0.217795i	0.623414	−	0.781892i	$-0.285745\pi$
$439$	12.5376	+	4.56332i	0.598387	+	0.217795i	−0.0250271	+	0.999687i	$0.507967\pi$
$440$	4.25624	+	24.1384i	0.202908	+	1.15075i
$441$	7.21760	+	6.05628i	0.343695	+	0.288394i
$442$	−5.89053	+	4.94274i	−0.280184	+	0.235102i
$443$	5.88372	−	33.3682i	0.279544	−	1.58537i	−0.444603	−	0.895728i	$-0.646655\pi$
$443$	5.88372	−	33.3682i	0.279544	−	1.58537i	0.724147	−	0.689646i	$-0.242234\pi$
$444$	−0.273318	+	0.473401i	−0.0129711	+	0.0224666i
$445$	−2.89053	−	5.00654i	−0.137024	−	0.237333i
$446$	2.49108	−	0.906678i	0.117956	−	0.0429324i
$447$	1.88326	−	0.685449i	0.0890749	−	0.0324206i
$448$	4.73783	+	8.20616i	0.223841	+	0.387704i
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	−0.998022	−	0.0628725i	$-0.979974\pi$
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	0.553460	+	0.832876i	$0.313307\pi$
$450$	−0.585589	+	3.32104i	−0.0276049	+	0.156555i
$451$	−11.7344	+	9.84635i	−0.552552	+	0.463646i
$452$	−6.93242	−	5.81699i	−0.326074	−	0.273608i
$453$	−1.34864	−	7.64852i	−0.0633647	−	0.359359i
$454$	11.3391	+	4.12711i	0.532172	+	0.193695i
$455$	−25.1780			−1.18036
$456$	6.36665	+	1.66620i	0.298146	+	0.0780270i
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	−7.77941	−	2.83147i	−0.363508	−	0.132306i
$459$	−0.872989	−	4.95096i	−0.0407476	−	0.231091i
$460$	4.18479	+	3.51146i	0.195117	+	0.163723i
$461$	−10.6695	+	8.95280i	−0.496930	+	0.416973i	−0.856502	−	0.516144i	$-0.827367\pi$
$461$	−10.6695	+	8.95280i	−0.496930	+	0.416973i	0.359572	+	0.933117i	$0.382923\pi$
$462$	−0.520945	+	2.95442i	−0.0242365	+	0.137452i
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	−0.844816	−	0.535056i	$-0.820290\pi$
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	0.885781	+	0.464104i	$0.153624\pi$
$464$	−0.0726338	−	0.125805i	−0.00337194	−	0.00584037i
$465$	2.46064	−	0.895599i	0.114109	−	0.0415324i
$466$	19.9859	−	7.27428i	0.925830	−	0.336974i
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	−0.999933	−	0.0115724i	$-0.996316\pi$
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	0.489945	−	0.871754i	$-0.337017\pi$
$468$	8.81655	−	15.2707i	0.407545	−	0.705889i
$469$	−4.63816	+	26.3043i	−0.214170	+	1.21462i
$470$	−1.22281	+	1.02606i	−0.0564041	+	0.0473286i
$471$	−4.22874	−	3.54834i	−0.194850	−	0.163499i
$472$	5.30113	+	30.0642i	0.244004	+	1.38382i
$473$	−15.3897	−	5.60138i	−0.707617	−	0.257552i
$474$	−3.25814			−0.149651
$475$	−5.56077	+	2.63263i	−0.255146	+	0.120793i
$476$	3.81016			0.174638
$477$	−15.5890	−	5.67393i	−0.713771	−	0.259791i
$478$	−3.56196	−	20.2009i	−0.162920	−	0.923966i
$479$	−19.5012	−	16.3634i	−0.891032	−	0.747664i	0.0773851	−	0.997001i	$-0.475343\pi$
$479$	−19.5012	−	16.3634i	−0.891032	−	0.747664i	−0.968417	+	0.249337i	$0.919787\pi$
$480$	−5.81908	+	4.88279i	−0.265603	+	0.222868i
$481$	0.769448	−	4.36376i	0.0350838	−	0.198970i
$482$	−0.130882	+	0.226694i	−0.00596150	+	0.0103256i
$483$	0.879385	+	1.52314i	0.0400134	+	0.0693053i
$484$	0.735604	−	0.267738i	0.0334366	−	0.0121699i
$485$	−4.33750	+	1.57872i	−0.196956	+	0.0716860i
$486$	−5.54071	−	9.59679i	−0.251332	−	0.435319i
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	−0.489903	−	0.871777i	$-0.662968\pi$
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	0.999932	−	0.0116199i	$-0.00369881\pi$
$488$	−2.16267	+	12.2651i	−0.0978993	+	0.555214i
$489$	−0.824292	+	0.691663i	−0.0372758	+	0.0312781i
$490$	5.91534	+	4.96356i	0.267228	+	0.224231i
$491$	2.71482	+	15.3965i	0.122518	+	0.694835i	0.982751	+	0.184934i	$0.0592071\pi$
$491$	2.71482	+	15.3965i	0.122518	+	0.694835i	−0.860233	+	0.509902i	$0.829682\pi$
$492$	−2.75402	−	1.00238i	−0.124161	−	0.0451909i
$493$	−5.73143			−0.258131
$494$	−20.1928	+	1.88538i	−0.908519	+	0.0848274i
$495$	23.4688			1.05485
$496$	0.0765042	+	0.0278452i	0.00343514	+	0.00125029i
$497$	4.49020	+	25.4652i	0.201413	+	1.14227i
$498$	0.900578	+	0.755675i	0.0403559	+	0.0338626i
$499$	−21.9217	+	18.3945i	−0.981352	+	0.823452i	−0.984293	−	0.176544i	$-0.943508\pi$
$499$	−21.9217	+	18.3945i	−0.981352	+	0.823452i	0.00294090	+	0.999996i	$0.499064\pi$
$500$	−1.93552	+	10.9769i	−0.0865590	+	0.490900i
$501$	6.18732	−	10.7168i	0.276429	−	0.478789i
$502$	7.12196	+	12.3356i	0.317869	+	0.550565i
$503$	23.5351	−	8.56607i	1.04938	−	0.381942i	0.240950	−	0.970538i	$-0.422541\pi$
$503$	23.5351	−	8.56607i	1.04938	−	0.381942i	0.808428	+	0.588595i	$0.200319\pi$
$504$	13.6147	−	4.95534i	0.606446	−	0.220728i
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$	−2.63816	+	4.56942i	−0.117280	+	0.203135i
$507$	1.38532	−	7.85651i	0.0615240	−	0.348920i
$508$	0.0949225	−	0.0796494i	0.00421150	−	0.00353387i
$509$	25.6787	+	21.5470i	1.13819	+	0.955053i	0.999378	−	0.0352655i	$-0.0112277\pi$
$509$	25.6787	+	21.5470i	1.13819	+	0.955053i	0.138810	+	0.990319i	$0.455672\pi$
$510$	−0.340022	−	1.92836i	−0.0150564	−	0.0853893i
$511$	−13.2763	−	4.83218i	−0.587309	−	0.213763i
$512$	−0.473897			−0.0209435
$513$	5.53343	−	12.0495i	0.244307	−	0.531997i
$514$	13.5030			0.595591
$515$	−0.0346151	−	0.0125989i	−0.00152532	−	0.000555172i
$516$	−0.544111	−	3.08580i	−0.0239531	−	0.135845i
$517$	1.87346	+	1.57202i	0.0823945	+	0.0691372i
$518$	1.06031	−	0.889704i	0.0465872	−	0.0390913i
$519$	0.0828445	−	0.469834i	0.00363647	−	0.0206234i
$520$	19.0069	−	32.9209i	0.833506	−	1.44367i
$521$	13.7392	+	23.7969i	0.601924	+	1.04256i	0.992530	+	0.122005i	$0.0389323\pi$
$521$	13.7392	+	23.7969i	0.601924	+	1.04256i	−0.390606	+	0.920558i	$0.627734\pi$
$522$	−7.78581	+	2.83380i	−0.340776	+	0.124032i
$523$	9.73277	−	3.54244i	0.425584	−	0.154900i	−0.120343	−	0.992732i	$-0.538400\pi$
$523$	9.73277	−	3.54244i	0.425584	−	0.154900i	0.545928	+	0.837832i	$0.316177\pi$
$524$	−1.86262	−	3.22615i	−0.0813687	−	0.140935i
$525$	0.705737	−	1.22237i	0.0308009	−	0.0533487i
$526$	1.47255	−	8.35126i	0.0642064	−	0.364132i
$527$	2.46064	−	2.06472i	0.107187	−	0.0899406i
$528$	−0.0582480	−	0.0488759i	−0.00253492	−	0.00212705i
$529$	−3.45677	−	19.6043i	−0.150294	−	0.852361i
$530$	−12.7763	−	4.65020i	−0.554968	−	0.201992i
$531$	29.2303			1.26849
$532$	8.26517	+	5.71578i	0.358340	+	0.247811i
$533$	23.7570			1.02903
$534$	1.00387	+	0.365379i	0.0434417	+	0.0158115i
$535$	1.56283	+	8.86327i	0.0675672	+	0.383193i
$536$	−30.8922	−	25.9216i	−1.33434	−	1.11964i
$537$	−8.68938	+	7.29125i	−0.374974	+	0.314641i
$538$	−2.79127	+	15.8301i	−0.120340	+	0.682483i
$539$	5.91534	−	10.2457i	0.254792	−	0.441313i
$540$	4.72416	+	8.18248i	0.203295	+	0.352118i
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	−0.392509	−	0.919748i	$-0.628393\pi$
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	0.290524	+	0.956868i	$0.406170\pi$
$542$	−15.6710	+	5.70378i	−0.673128	+	0.244998i
$543$	4.28312	+	7.41858i	0.183806	+	0.318362i
$544$	−4.65910	+	8.06980i	−0.199757	+	0.345990i
$545$	−3.24035	+	18.3770i	−0.138801	+	0.787182i
$546$	3.56418	−	2.99070i	0.152533	−	0.127990i
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	0.759768	−	0.650194i	$-0.225312\pi$
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	−0.508384	+	0.861131i	$0.669757\pi$
$548$	−4.16220	−	23.6050i	−0.177800	−	1.00836i
$549$	11.2057	+	4.07855i	0.478249	+	0.174068i
$550$	4.23442			0.180556
$551$	−12.4329	−	8.59797i	−0.529659	−	0.366286i
$552$	−2.65539			−0.113021
$553$	−12.2973	−	4.47584i	−0.522933	−	0.190332i
$554$	2.10179	+	11.9198i	0.0892963	+	0.506425i
$555$	0.864370	+	0.725293i	0.0366905	+	0.0307870i
$556$	−14.4684	+	12.1404i	−0.613596	+	0.514868i
$557$	0.565360	−	3.20631i	0.0239551	−	0.135856i	−0.970485	−	0.241163i	$-0.922471\pi$
$557$	0.565360	−	3.20631i	0.0239551	−	0.135856i	0.994440	+	0.105307i	$0.0335824\pi$
$558$	2.32177	−	4.02142i	0.0982882	−	0.170240i
$559$	12.6998	+	21.9967i	0.537145	+	0.930362i
$560$	0.187319	−	0.0681784i	0.00791566	−	0.00288107i
$561$	−2.81908	+	1.02606i	−0.119022	+	0.0433203i
$562$	−5.76486	−	9.98503i	−0.243176	−	0.421193i
$563$	−2.62954	+	4.55449i	−0.110822	+	0.191949i	−0.916102	−	0.400946i	$-0.868682\pi$
$563$	−2.62954	+	4.55449i	−0.110822	+	0.191949i	0.805280	+	0.592895i	$0.202015\pi$
$564$	−0.0812519	+	0.460802i	−0.00342132	+	0.0194033i
$565$	−14.3097	+	12.0073i	−0.602015	+	0.505151i
$566$	−11.7062	−	9.82267i	−0.492048	−	0.412878i
$567$	−2.13176	−	12.0898i	−0.0895255	−	0.507724i
$568$	−36.6860	−	13.3526i	−1.53931	−	0.560264i
$569$	−29.9564			−1.25584			−0.627918	−	0.778280i	$-0.716093\pi$
$569$	−29.9564			−1.25584			−0.627918	+	0.778280i	$0.716093\pi$
$570$	2.15523	−	4.69318i	0.0902726	−	0.196576i
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	−20.8059	−	7.57272i	−0.869937	−	0.316631i
$573$	1.75078	+	9.92917i	0.0731399	+	0.414797i
$574$	5.68479	+	4.77011i	0.237279	+	0.199100i
$575$	1.90167	−	1.59569i	0.0793053	−	0.0665450i
$576$	−2.37867	+	13.4901i	−0.0991113	+	0.562088i
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$	6.27379	+	10.8665i	0.260955	+	0.451987i
$579$	−6.45084	+	2.34791i	−0.268088	+	0.0975759i
$580$	10.1220	−	3.68409i	0.420291	−	0.152974i
$581$	2.36097	+	4.08931i	0.0979494	+	0.169653i
$582$	0.426489	−	0.738700i	0.0176785	−	0.0306201i
$583$	−3.61721	+	20.5142i	−0.149810	+	0.849612i
$584$	16.3405	−	13.7113i	0.676174	−	0.567378i
$585$	−27.8824	−	23.3961i	−1.15279	−	0.967309i
$586$	2.38279	+	13.5135i	0.0984321	+	0.558236i
$587$	22.5872	+	8.22108i	0.932275	+	0.339320i	0.763111	−	0.646268i	$-0.223671\pi$
$587$	22.5872	+	8.22108i	0.932275	+	0.339320i	0.169164	+	0.985588i	$0.445893\pi$
$588$	2.26352			0.0933459
$589$	8.43511	−	0.787576i	0.347563	−	0.0324515i
$590$	23.9564			0.986268
$591$	11.6001	+	4.22210i	0.477166	+	0.173674i
$592$	0.00609191	+	0.0345490i	0.000250376	+	0.00141995i
$593$	−3.24897	−	2.72621i	−0.133419	−	0.111952i	0.573636	−	0.819110i	$-0.305532\pi$
$593$	−3.24897	−	2.72621i	−0.133419	−	0.111952i	−0.707055	+	0.707158i	$0.749977\pi$
$594$	−6.99067	+	5.86587i	−0.286831	+	0.240679i
$595$	1.36571	−	7.74535i	0.0559888	−	0.317529i
$596$	−2.31016	+	4.00131i	−0.0946276	+	0.163900i
$597$	−2.45336	−	4.24935i	−0.100409	−	0.173914i
$598$	7.68954	−	2.79876i	0.314449	−	0.114450i
$599$	24.6894	−	8.98622i	1.00878	−	0.367167i	0.215818	−	0.976434i	$-0.430758\pi$
$599$	24.6894	−	8.98622i	1.00878	−	0.367167i	0.792965	+	0.609267i	$0.208536\pi$
$600$	1.06552	+	1.84554i	0.0434998	+	0.0753438i
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	−0.00899659	−	0.999960i	$-0.502864\pi$
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	0.870489	−	0.492188i	$-0.163803\pi$
$602$	−1.37774	+	7.81353i	−0.0561523	+	0.318456i
$603$	−29.5790	+	24.8198i	−1.20455	+	1.01074i
$604$	13.7160	+	11.5091i	0.558096	+	0.468298i
$605$	−0.280592	−	1.59132i	−0.0114077	−	0.0646963i
$606$	3.48293	+	1.26768i	0.141484	+	0.0514960i
$607$	−22.0969			−0.896885			−0.448443	−	0.893812i	$-0.648021\pi$
$607$	−22.0969			−0.896885			−0.448443	+	0.893812i	$0.648021\pi$
$608$	−22.2126	+	10.5161i	−0.900840	+	0.426483i
$609$	3.46791			0.140527
$610$	9.18392	+	3.34267i	0.371846	+	0.135341i
$611$	−0.658633	−	3.73530i	−0.0266455	−	0.151114i
$612$	4.21941	+	3.54050i	0.170559	+	0.143116i
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	−0.524970	−	0.851121i	$-0.675924\pi$
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	0.747030	+	0.664790i	$0.231479\pi$
$614$	3.28622	−	18.6371i	0.132621	−	0.752131i
$615$	−3.02481	+	5.23913i	−0.121972	+	0.211262i
$616$	−9.09627	−	15.7552i	−0.366499	−	0.634795i
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.895995	−	0.444065i	$-0.146464\pi$
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.971811	−	0.235761i	$-0.0757583\pi$
$618$	0.00639661	−	0.00232818i	0.000257310	−	9.36530e-5i
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	−0.999279	−	0.0379684i	$-0.987911\pi$
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	0.466758	−	0.884385i	$-0.345422\pi$
$620$	−3.01842	+	5.22805i	−0.121223	+	0.209964i
$621$	−0.929015	+	5.26871i	−0.0372801	+	0.211426i
$622$	9.76470	−	8.19356i	0.391529	−	0.328532i
$623$	3.28699	+	2.75811i	0.131690	+	0.110501i
$624$	0.0204777	+	0.116135i	0.000819764	+	0.00464911i
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$	17.1643			0.686022
$627$	−7.65451	−	2.00324i	−0.305692	−	0.0800019i
$628$	12.7264			0.507838
$629$	1.30066	+	0.473401i	0.0518607	+	0.0188757i
$630$	−1.97431	−	11.1969i	−0.0786583	−	0.446093i
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.989138	−	0.146988i	$-0.0469579\pi$
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.0270071	+	0.999635i	$0.491402\pi$
$632$	15.1355	−	12.7002i	0.602057	−	0.505185i
$633$	1.35117	−	7.66285i	0.0537041	−	0.304571i
$634$	−12.4641	+	21.5884i	−0.495013	+	0.857387i
$635$	−0.127889	−	0.221510i	−0.00507511	−	0.00879035i
$636$	−3.74510	+	1.36310i	−0.148503	+	0.0540506i
$637$	−17.2417	+	6.27546i	−0.683141	+	0.248643i
$638$	5.20187	+	9.00990i	0.205944	+	0.356705i
$639$	−18.6905	+	32.3729i	−0.739384	+	1.28065i
$640$	3.00862	−	17.0627i	0.118926	−	0.674463i
$641$	−0.104256	+	0.0874810i	−0.00411786	+	0.00345529i	−0.644844	−	0.764314i	$-0.723078\pi$
$641$	−0.104256	+	0.0874810i	−0.00411786	+	0.00345529i	0.640726	+	0.767769i	$0.278633\pi$
$642$	−1.27403	−	1.06904i	−0.0502821	−	0.0421917i
$643$	8.36602	+	47.4461i	0.329924	+	1.87109i	0.472536	+	0.881311i	$0.343339\pi$
$643$	8.36602	+	47.4461i	0.329924	+	1.87109i	−0.142613	+	0.989779i	$0.545550\pi$
$644$	−3.81016	−	1.38678i	−0.150141	−	0.0546469i
$645$	−6.46791			−0.254674
$646$	0.515319	−	6.31407i	0.0202750	−	0.248424i
$647$	−36.9718			−1.45351			−0.726756	−	0.686895i	$-0.758973\pi$
$647$	−36.9718			−1.45351			−0.726756	+	0.686895i	$0.758973\pi$
$648$	17.4170	+	6.33927i	0.684204	+	0.249030i
$649$	−6.37346	−	36.1457i	−0.250180	−	1.41884i
$650$	−5.03074	−	4.22130i	−0.197322	−	0.165573i
$651$	−1.48886	+	1.24930i	−0.0583529	+	0.0489639i
$652$	0.430770	−	2.44302i	0.0168702	−	0.0956759i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−1.72416	−	2.98632i	−0.0674198	−	0.116775i
$655$	−7.22580	+	2.62998i	−0.282336	+	0.102762i
$656$	−0.176747	+	0.0643307i	−0.00690081	+	0.00251169i
$657$	−10.2121	−	17.6879i	−0.398413	−	0.690072i
$658$	0.592396	−	1.02606i	0.0230940	−	0.0400000i
$659$	3.27760	−	18.5882i	0.127677	−	0.724093i	−0.852005	−	0.523534i	$-0.824613\pi$
$659$	3.27760	−	18.5882i	0.127677	−	0.724093i	0.979682	−	0.200559i	$-0.0642757\pi$
$660$	4.31908	−	3.62414i	0.168120	−	0.141069i
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	0.0604192	−	0.998173i	$-0.480756\pi$
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	−0.972517	+	0.232832i	$0.925201\pi$
$662$	−0.261135	−	1.48097i	−0.0101493	−	0.0575594i
$663$	4.37211	+	1.59132i	0.169799	+	0.0618017i
$664$	−7.12918			−0.276666
$665$	14.5817	−	14.7528i	0.565455	−	0.572090i
$666$	2.00093			0.0775346
$667$	5.73143	+	2.08607i	0.221922	+	0.0807729i
$668$	4.95394	+	28.0952i	0.191674	+	1.08703i
$669$	−1.22874	−	1.03104i	−0.0475059	−	0.0398622i
$670$	−24.2422	+	20.3416i	−0.936556	+	0.785864i
$671$	2.60014	−	14.7461i	0.100377	−	0.569267i
$672$	2.81908	−	4.88279i	0.108748	−	0.188358i
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	0.728134	−	0.685435i	$-0.240388\pi$
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	−0.957671	+	0.287865i	$0.907055\pi$
$674$	−21.0214	+	7.65117i	−0.809715	+	0.294712i
$675$	4.03462	−	1.46848i	0.155292	−	0.0565218i
$676$	9.19594	+	15.9278i	0.353690	+	0.612609i
$677$	−2.89053	+	5.00654i	−0.111092	+	0.192417i	−0.916211	−	0.400696i	$-0.868768\pi$
$677$	−2.89053	+	5.00654i	−0.111092	+	0.192417i	0.805119	+	0.593114i	$0.202102\pi$
$678$	0.599422	−	3.39949i	0.0230207	−	0.130557i
$679$	2.62449	−	2.20220i	0.100718	−	0.0845129i
$680$	9.09627	+	7.63267i	0.348826	+	0.292700i
$681$	−1.26786	−	7.19037i	−0.0485843	−	0.275535i
$682$	−5.47906	−	1.99421i	−0.209804	−	0.0763624i
$683$	21.0496			0.805442			0.402721	−	0.915323i	$-0.368065\pi$
$683$	21.0496			0.805442			0.402721	+	0.915323i	$0.368065\pi$
$684$	3.84167	+	14.0099i	0.146890	+	0.535684i
$685$	−49.4766			−1.89040
$686$	−16.2570	−	5.91707i	−0.620696	−	0.225915i
$687$	0.869833	+	4.93307i	0.0331862	+	0.188208i
$688$	−0.154048	−	0.129261i	−0.00587302	−	0.00492805i
$689$	24.7481	−	20.7661i	0.942827	−	0.791126i
$690$	−0.361844	+	2.05212i	−0.0137752	+	0.0781229i
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	−0.361744	−	0.932278i	$-0.617818\pi$
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	0.988248	−	0.152860i	$-0.0488483\pi$
$692$	0.549935	+	0.952515i	0.0209054	+	0.0362092i
$693$	−16.3687	+	5.95772i	−0.621796	+	0.226315i
$694$	−6.36484	+	2.31661i	−0.241606	+	0.0879374i
$695$	19.4932	+	33.7632i	0.739419	+	1.28071i
$696$	−2.61793	+	4.53438i	−0.0992322	+	0.171875i
$697$	−1.28864	+	7.30823i	−0.0488106	+	0.276819i
$698$	15.3302	−	12.8636i	0.580257	−	0.486894i
$699$	−9.85819	−	8.27201i	−0.372871	−	0.312876i
$700$	0.565055	+	3.20459i	0.0213571	+	0.121122i
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.0660380	−	0.997817i	$-0.521036\pi$
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.691973	+	0.721924i	$0.743258\pi$
$702$	14.1530			0.534171
$703$	2.11128	+	2.97810i	0.0796285	+	0.112321i
$704$	17.2003			0.648260
$705$	0.907604	+	0.330341i	0.0341823	+	0.0124414i
$706$	−1.74779	−	9.91220i	−0.0657789	−	0.373051i
$707$	11.4042	+	9.56926i	0.428899	+	0.359889i
$708$	5.37939	−	4.51384i	0.202170	−	0.169641i
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	0.889210	+	0.457499i	$0.151255\pi$
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	−0.992058	+	0.125781i	$0.959856\pi$
$710$	−15.3182	+	26.5319i	−0.574882	+	0.995725i
$711$	−9.45904	−	16.3835i	−0.354742	−	0.614431i
$712$	−6.08765	+	2.21572i	−0.228144	+	0.0830377i
$713$	−3.21213	+	1.16912i	−0.120295	+	0.0437839i
$714$	0.726682	+	1.25865i	0.0271954	+	0.0471038i
$715$	−22.8516	+	39.5802i	−0.854603	+	1.48022i
$716$	4.54101	−	25.7534i	0.169706	−	0.962448i
$717$	−9.50774	+	7.97794i	−0.355073	+	0.297942i
$718$	6.99525	+	5.86971i	0.261060	+	0.219056i
$719$	−6.13470	−	34.7916i	−0.228786	−	1.29751i	−0.855314	−	0.518109i	$-0.826636\pi$
$719$	−6.13470	−	34.7916i	−0.228786	−	1.29751i	0.626529	−	0.779398i	$-0.284475\pi$
$720$	0.270792	+	0.0985603i	0.0100918	+	0.00367313i
$721$	0.0273411			0.00101824
$722$	10.5899	−	12.9237i	0.394114	−	0.480971i
$723$	0.158385			0.00589040
$724$	−18.5577	−	6.75444i	−0.689691	−	0.251027i
$725$	−0.849985	−	4.82050i	−0.0315676	−	0.179029i
$726$	0.228741	+	0.191936i	0.00848937	+	0.00712343i
$727$	30.9647	−	25.9825i	1.14842	−	0.963637i	0.148737	−	0.988877i	$-0.452479\pi$
$727$	30.9647	−	25.9825i	1.14842	−	0.963637i	0.999681	+	0.0252396i	$0.00803487\pi$
$728$	−4.89945	+	27.7862i	−0.181586	+	1.02982i
$729$	6.44562	−	11.1641i	0.238727	−	0.413487i
$730$	−8.36959	−	14.4965i	−0.309772	−	0.536541i
$731$	−7.45558	+	2.71361i	−0.275755	+	0.100367i
$732$	2.69207	−	0.979832i	0.0995016	−	0.0362156i
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$	14.3045	−	24.7762i	0.527990	−	0.914505i
$735$	0.811337	−	4.60132i	0.0299266	−	0.169722i
$736$	7.59627	−	6.37402i	0.280002	−	0.234950i
$737$	37.1411	+	31.1651i	1.36811	+	1.14798i
$738$	1.86288	+	10.5649i	0.0685737	+	0.388901i
$739$	19.4290	+	7.07158i	0.714708	+	0.260132i	0.673677	−	0.739026i	$-0.264714\pi$
$739$	19.4290	+	7.07158i	0.714708	+	0.260132i	0.0410304	+	0.999158i	$0.486936\pi$
$740$	−2.60132			−0.0956264
$741$	7.09698	+	10.0108i	0.260714	+	0.367754i
$742$	10.0915			0.370471
$743$	−6.29978	−	2.29293i	−0.231117	−	0.0841196i	0.223866	−	0.974620i	$-0.428132\pi$
$743$	−6.29978	−	2.29293i	−0.231117	−	0.0841196i	−0.454982	+	0.890500i	$0.650354\pi$
$744$	−0.509552	−	2.88981i	−0.0186811	−	0.105946i
$745$	7.30587	+	6.13036i	0.267667	+	0.224599i
$746$	20.5367	−	17.2323i	0.751901	−	0.630920i
$747$	−1.18535	+	6.72243i	−0.0433695	+	0.245961i
$748$	3.45811	−	5.98962i	0.126441	−	0.219002i
$749$	−3.34002	−	5.78509i	−0.122042	−	0.211383i
$750$	−3.99525	+	1.45415i	−0.145886	+	0.0530982i
$751$	−10.0617	+	3.66214i	−0.367155	+	0.133633i	−0.519007	−	0.854770i	$-0.673698\pi$
$751$	−10.0617	+	3.66214i	−0.367155	+	0.133633i	0.151853	+	0.988403i	$0.451476\pi$
$752$	0.0150147	+	0.0260063i	0.000547531	+	0.000948352i
$753$	4.30928	−	7.46389i	0.157039	−	0.271999i
$754$	2.80184	−	15.8900i	0.102037	−	0.578681i
$755$	28.3123	−	23.7568i	1.03039	−	0.864599i
$756$	−5.37211	−	4.50774i	−0.195382	−	0.163945i
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	0.969301	−	0.245878i	$-0.0790764\pi$
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	−0.994940	+	0.100470i	$0.967965\pi$
$758$	−14.7585	−	5.37164i	−0.536052	−	0.195107i
$759$	3.19253			0.115882
$760$	8.28194	+	30.2029i	0.300417	+	1.09557i
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$	0.0444153	+	0.0161658i	0.00160900	+	0.000585627i
$763$	−2.40508	−	13.6399i	−0.0870697	−	0.493797i
$764$	−17.8059	−	14.9409i	−0.644194	−	0.540543i
$765$	8.70961	−	7.30823i	0.314897	−	0.264230i
$766$	−3.58182	+	20.3135i	−0.129417	+	0.733958i
$767$	−28.4616	+	49.2969i	−1.02769	+	1.78001i
$768$	4.28359	+	7.41939i	0.154571	+	0.267724i
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.677359	−	0.735652i	$-0.736876\pi$
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.0460191	+	0.998941i	$0.514654\pi$
$770$	−13.4153	+	4.88279i	−0.483455	+	0.175963i
$771$	−4.08512	−	7.07564i	−0.147122	−	0.254823i
$772$	7.91312	−	13.7059i	0.284800	−	0.493287i
$773$	3.11128	−	17.6450i	0.111905	−	0.634645i	−0.876331	−	0.481709i	$-0.840016\pi$
$773$	3.11128	−	17.6450i	0.111905	−	0.634645i	0.988236	−	0.152936i	$-0.0488727\pi$
$774$	−8.78627	+	7.37256i	−0.315816	+	0.265001i
$775$	2.10148	+	1.76335i	0.0754874	+	0.0633415i
$776$	0.898214	+	5.09403i	0.0322440	+	0.182865i
$777$	−0.786989	−	0.286441i	−0.0282331	−	0.0102760i
$778$	3.43788			0.123254
$779$	−13.7588	+	13.9202i	−0.492959	+	0.498743i
$780$	−8.74422			−0.313093
$781$	44.1070	+	16.0536i	1.57827	+	0.574444i
$782$	0.443868	+	2.51730i	0.0158727	+	0.0900184i
$783$	8.08100	+	6.78077i	0.288792	+	0.242325i
$784$	0.111281	−	0.0933762i	0.00397434	−	0.00333486i
$785$	4.56165	−	25.8704i	0.162812	−	0.923355i
$786$	0.710485	−	1.23060i	0.0253422	−	0.0438939i
$787$	−24.4158	−	42.2894i	−0.870330	−	1.50746i	−0.861656	−	0.507493i	$-0.830572\pi$
$787$	−24.4158	−	42.2894i	−0.870330	−	1.50746i	−0.00867371	−	0.999962i	$-0.502761\pi$
$788$	−26.7430	+	9.73367i	−0.952681	+	0.346748i
$789$	−4.82160	+	1.75492i	−0.171654	+	0.0624768i
$790$	−7.75237	−	13.4275i	−0.275817	−	0.477729i
$791$	6.93242	−	12.0073i	0.246488	−	0.426930i
$792$	4.56687	−	25.9000i	0.162277	−	0.920316i
$793$	−17.7895	+	14.9272i	−0.631724	+	0.530080i
$794$	6.03524	+	5.06417i	0.214183	+	0.179721i
$795$	1.42855	+	8.10170i	0.0506654	+	0.287338i
$796$	10.6298	+	3.86893i	0.376763	+	0.137131i
$797$	−28.5262			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$	−0.311804	+	3.82045i	−0.0110377	+	0.135242i
$799$	1.18479			0.0419149
$800$	−7.47818	−	2.72183i	−0.264394	−	0.0962314i
$801$	1.07713	+	6.10873i	0.0380586	+	0.215841i
$802$	−1.36571	−	1.14597i	−0.0482251	−	0.0404656i
$803$	−19.6459	+	16.4849i	−0.693289	+	0.581738i
$804$	−1.61081	+	9.13538i	−0.0568091	+	0.322180i
$805$	−4.18479	+	7.24827i	−0.147495	+	0.255468i
$806$	4.52141	+	7.83131i	0.159260	+	0.275846i
$807$	9.13950	−	3.32651i	0.321726	−	0.117099i
$808$	−21.1211	+	7.68745i	−0.743037	+	0.270443i
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	0.966459	−	0.256822i	$-0.0826755\pi$
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	−0.705644	+	0.708567i	$0.749342\pi$
$810$	7.27244	−	12.5962i	0.255528	−	0.442587i
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	−0.999638	−	0.0269103i	$-0.991433\pi$
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	0.948556	+	0.316609i	$0.102544\pi$
$812$	−6.12449	+	5.13905i	−0.214927	+	0.180345i
$813$	7.72984	+	6.48610i	0.271097	+	0.227478i
$814$	−0.436289	−	2.47432i	−0.0152919	−	0.0867248i
$815$	−4.81180	−	1.75135i	−0.168550	−	0.0613472i
$816$	−0.0368366			−0.00128954
$817$	−20.2438	−	5.29796i	−0.708241	−	0.185352i
$818$	−28.3233			−0.990299
$819$	25.3862	+	9.23984i	0.887067	+	0.322866i
$820$	−2.42185	−	13.7350i	−0.0845746	−	0.479646i
$821$	4.80999	+	4.03606i	0.167870	+	0.140860i	0.722852	−	0.691002i	$-0.242831\pi$
$821$	4.80999	+	4.03606i	0.167870	+	0.140860i	−0.554983	+	0.831862i	$0.687275\pi$
$822$	7.00387	−	5.87695i	0.244288	−	0.204982i
$823$	1.91472	−	10.8589i	0.0667428	−	0.378517i	−0.933080	−	0.359670i	$-0.882889\pi$
$823$	1.91472	−	10.8589i	0.0667428	−	0.378517i	0.999822	−	0.0188472i	$-0.00599961\pi$
$824$	−0.0206398	+	0.0357492i	−0.000719023	+	0.00124538i
$825$	−1.28106	−	2.21886i	−0.0446008	−	0.0772508i
$826$	−16.7087	+	6.08148i	−0.581371	+	0.211602i
$827$	−31.8892	+	11.6067i	−1.10890	+	0.403606i	−0.830589	−	0.556886i	$-0.811996\pi$
$827$	−31.8892	+	11.6067i	−1.10890	+	0.403606i	−0.278309	+	0.960492i	$0.589774\pi$
$828$	−2.93077	−	5.07624i	−0.101851	−	0.176412i
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	−0.633206	−	0.773983i	$-0.718262\pi$
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	0.986892	+	0.161381i	$0.0515949\pi$
$830$	−0.971477	+	5.50952i	−0.0337205	+	0.191238i
$831$	5.61019	−	4.70750i	0.194615	−	0.163302i
$832$	−20.4349	−	17.1470i	−0.708454	−	0.594464i
$833$	−0.995252	−	5.64436i	−0.0344834	−	0.195565i
$834$	−6.76991	−	2.46405i	−0.234423	−	0.0853230i
$835$	58.8881			2.03791
$836$	16.4868	−	7.80531i	0.570208	−	0.269952i
$837$	−5.91210			−0.204352
$838$	19.2126	+	6.99281i	0.663688	+	0.241563i
$839$	2.74526	+	15.5692i	0.0947770	+	0.537507i	0.994815	+	0.101697i	$0.0324271\pi$
$839$	2.74526	+	15.5692i	0.0947770	+	0.537507i	−0.900038	+	0.435810i	$0.856462\pi$
$840$	−5.50387	−	4.61830i	−0.189902	−	0.159346i
$841$	−13.0025	+	10.9104i	−0.448363	+	0.376221i
$842$	0.985452	−	5.58878i	0.0339609	−	0.192602i
$843$	−3.48814	+	6.04164i	−0.120138	+	0.208085i
$844$	8.96926	+	15.5352i	0.308734	+	0.534744i
$845$	35.6746	−	12.9845i	1.22724	−	0.446680i
$846$	1.60947	−	0.585799i	0.0553347	−	0.0201402i
$847$	0.599670	+	1.03866i	0.0206049	+	0.0356888i
$848$	−0.127889	+	0.221510i	−0.00439172	+	0.00760668i
$849$	−1.60560	+	9.10581i	−0.0551040	+	0.312511i
$850$	1.57145	−	1.31860i	0.0539003	−	0.0452278i
$851$	−1.12836	−	0.946803i	−0.0386795	−	0.0324560i
$852$	1.55943	+	8.84397i	0.0534252	+	0.302989i
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.995115	−	0.0987227i	$-0.0314757\pi$
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.698845	+	0.715274i	$0.253698\pi$
$854$	−7.25402			−0.248228
$855$	29.8567	−	2.78768i	1.02108	−	0.0953368i
$856$	10.0855			0.344716
$857$	21.6386	+	7.87581i	0.739161	+	0.269033i	0.684038	−	0.729447i	$-0.260222\pi$
$857$	21.6386	+	7.87581i	0.739161	+	0.269033i	0.0551238	+	0.998480i	$0.482445\pi$
$858$	−1.46657	−	8.31731i	−0.0500678	−	0.283948i
$859$	6.82501	+	5.72686i	0.232866	+	0.195398i	0.751753	−	0.659445i	$-0.229209\pi$
$859$	6.82501	+	5.72686i	0.232866	+	0.195398i	−0.518886	+	0.854843i	$0.673653\pi$
$860$	11.4226	−	9.58471i	0.389508	−	0.326836i
$861$	0.779715	−	4.42198i	0.0265726	−	0.150701i
$862$	6.15451	−	10.6599i	0.209624	−	0.363079i
$863$	−14.8849	−	25.7814i	−0.506688	−	0.877609i	−0.999970	−	0.00773998i	$-0.997536\pi$
$863$	−14.8849	−	25.7814i	−0.506688	−	0.877609i	0.493282	−	0.869869i	$-0.335797\pi$
$864$	16.1163	−	5.86587i	0.548289	−	0.199561i
$865$	2.13341	−	0.776497i	0.0725380	−	0.0264017i
$866$	12.6160	+	21.8516i	0.428710	+	0.742548i
$867$	3.79607	−	6.57499i	0.128921	−	0.223298i
$868$	0.778066	−	4.41263i	0.0264093	−	0.149775i
$869$	−18.1971	+	15.2692i	−0.617295	+	0.517972i
$870$	3.14749	+	2.64106i	0.106710	+	0.0895402i
$871$	−13.0574	−	74.0520i	−0.442432	−	2.50916i
$872$	19.6501	+	7.15204i	0.665435	+	0.242199i
$873$	4.95273			0.167625
$874$	−2.81345	+	6.12651i	−0.0951665	+	0.207232i
$875$	−17.0770			−0.577307
$876$	−4.61081	−	1.67820i	−0.155785	−	0.0567011i
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	−0.965930	−	0.258802i	$-0.916672\pi$
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	0.819162	−	0.573562i	$-0.194439\pi$
$878$	−8.98798	−	7.54181i	−0.303330	−	0.254524i
$879$	6.36025	−	5.33688i	0.214526	−	0.180009i
$880$	0.0628336	−	0.356347i	0.00211812	−	0.0120125i
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	−0.985095	−	0.172014i	$-0.944973\pi$
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$882$	−4.14274	−	7.17544i	−0.139493	−	0.241610i
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	−0.168460	−	0.985708i	$-0.553880\pi$
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	0.504553	+	0.863381i	$0.331657\pi$
$884$	−10.0795	+	3.66864i	−0.339010	+	0.123390i
$885$	−7.24763	−	12.5533i	−0.243626	−	0.421973i
$886$	−14.8981	+	25.8043i	−0.500512	+	0.866912i
$887$	−9.78312	+	55.4828i	−0.328485	+	1.86293i	0.155474	+	0.987840i	$0.450310\pi$
$887$	−9.78312	+	55.4828i	−0.328485	+	1.86293i	−0.483959	+	0.875091i	$0.660802\pi$
$888$	0.968626	−	0.812774i	0.0325050	−	0.0272749i
$889$	0.145430	+	0.122030i	0.00487756	+	0.00409275i
$890$	0.882789	+	5.00654i	0.0295911	+	0.167820i
$891$	−20.9402	−	7.62159i	−0.701522	−	0.255333i
$892$	3.69789			0.123815
$893$	2.57011	+	1.77736i	0.0860054	+	0.0594771i
$894$	−1.76239			−0.0589432
$895$	−50.7242	−	18.4621i	−1.69552	−	0.617120i
$896$	2.23308	+	12.6644i	0.0746019	+	0.423088i
$897$	−3.79292	−	3.18264i	−0.126642	−	0.106265i
$898$	12.6917	−	10.6496i	0.423526	−	0.355381i
$899$	−1.17041	+	6.63771i	−0.0390353	+	0.221380i
$900$	−2.35204	+	4.07386i	−0.0784015	+	0.135795i
$901$	5.04576	+	8.73951i	0.168099	+	0.291155i
$902$	12.6582	−	4.60722i	0.421473	−	0.153404i
$903$	4.51114	−	1.64192i	0.150121	−	0.0546398i
$904$	10.4666	+	18.1286i	0.348113	+	0.602949i
$905$	−20.3824	+	35.3033i	−0.677533	+	1.17352i
$906$	−1.18597	+	6.72600i	−0.0394014	+	0.223456i
$907$	−4.53777	+	3.80764i	−0.150674	+	0.126431i	−0.715009	−	0.699116i	$-0.753577\pi$
$907$	−4.53777	+	3.80764i	−0.150674	+	0.126431i	0.564334	+	0.825546i	$0.309133\pi$
$908$	12.8944	+	10.8197i	0.427916	+	0.359064i
$909$	3.73711	+	21.1942i	0.123952	+	0.702968i
$910$	20.8059	+	7.57272i	0.689708	+	0.251033i
$911$	−34.0591			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$911$	−34.0591			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$912$	−0.0799077	−	0.0552603i	−0.00264601	−	0.00182985i
$913$	8.57129			0.283668
$914$	−11.7995	−	4.29466i	−0.390292	−	0.142055i
$915$	−1.02687	−	5.82369i	−0.0339474	−	0.192525i
$916$	−8.84642	−	7.42303i	−0.292294	−	0.245264i
$917$	4.37211	−	3.66864i	0.144380	−	0.121149i
$918$	−0.767693	+	4.35381i	−0.0253377	+	0.143697i
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	−0.809637	−	0.586931i	$-0.800336\pi$
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	0.913116	+	0.407700i	$0.133669\pi$
$920$	−6.31820	−	10.9434i	−0.208305	−	0.360795i
$921$	−10.7601	+	3.91636i	−0.354558	+	0.129048i
$922$	11.5095	−	4.18911i	0.379045	−	0.137961i
$923$	−36.3979	−	63.0429i	−1.19805	−	2.07508i
$924$	−2.09240	+	3.62414i	−0.0688348	+	0.119225i
$925$	−0.205270	+	1.16415i	−0.00674924	+	0.0382769i
$926$	−1.18757	+	0.996487i	−0.0390259	+	0.0327466i
$927$	0.0302779	+	0.0254062i	0.000994456	+	0.000834448i
$928$	−3.39528	−	19.2556i	−0.111455	−	0.632095i
$929$	−26.6152	−	9.68712i	−0.873215	−	0.317824i	−0.133747	−	0.991016i	$-0.542701\pi$
$929$	−26.6152	−	9.68712i	−0.873215	−	0.317824i	−0.739468	+	0.673191i	$0.764923\pi$
$930$	−2.30272			−0.0755091
$931$	6.30840	−	13.7370i	0.206749	−	0.450213i
$932$	29.6682			0.971814
$933$	−7.24763	−	2.63792i	−0.237277	−	0.0863616i
$934$	3.36588	+	19.0888i	0.110135	+	0.624606i
$935$	−10.9363	−	9.17664i	−0.357655	−	0.300108i
$936$	−31.2454	+	26.2180i	−1.02129	+	0.856962i
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	0.873441	+	0.486930i	$0.161883\pi$
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	−0.987306	+	0.158830i	$0.949228\pi$
$938$	11.7442	−	20.3416i	0.383462	−	0.664176i
$939$	−5.19278	−	8.99416i	−0.169460	−	0.293513i
$940$	−2.09240	+	0.761570i	−0.0682464	+	0.0248397i
$941$	−5.06980	+	1.84526i	−0.165271	+	0.0601537i	−0.423331	−	0.905975i	$-0.639139\pi$
$941$	−5.06980	+	1.84526i	−0.165271	+	0.0601537i	0.258060	+	0.966129i	$0.416917\pi$
$942$	2.42720	+	4.20404i	0.0790826	+	0.136975i
$943$	3.94862	−	6.83920i	0.128585	−	0.222715i
$944$	0.0782589	−	0.443828i	0.00254711	−	0.0144454i
$945$	−11.0890	+	9.30477i	−0.360725	+	0.302684i
$946$	11.0326	+	9.25741i	0.358699	+	0.300984i
$947$	1.15358	+	6.54228i	0.0374863	+	0.212596i	0.997797	−	0.0663359i	$-0.0211309\pi$
$947$	1.15358	+	6.54228i	0.0374863	+	0.212596i	−0.960311	+	0.278931i	$0.910020\pi$
$948$	−4.27079	−	1.55444i	−0.138709	−	0.0504859i
$949$	39.7743			1.29113
$950$	5.38696	−	0.502975i	0.174776	−	0.0163187i
$951$	15.0833			0.489109
$952$	−8.28194	−	3.01438i	−0.268419	−	0.0976966i
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	−0.997693	−	0.0678799i	$-0.978377\pi$
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	0.914309	−	0.405018i	$-0.132735\pi$
$954$	11.1755	+	9.37732i	0.361819	+	0.303602i
$955$	−36.7545	+	30.8407i	−1.18935	+	0.997981i
$956$	4.96868	−	28.1788i	0.160699	−	0.911368i
$957$	3.14749	−	5.45161i	0.101744	−	0.176226i
$958$	11.1932	+	19.3873i	0.361637	+	0.626374i
$959$	34.5082	−	12.5600i	1.11433	−	0.405582i
$960$	6.38326	−	2.32332i	0.206019	−	0.0749847i
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$	−1.94831	+	3.37457i	−0.0628161	+	0.108801i
$963$	1.67689	−	9.51011i	0.0540370	−	0.306459i
$964$	−0.279715	+	0.234709i	−0.00900901	+	0.00755946i
$965$	−25.0253	−	20.9987i	−0.805592	−	0.675972i
$966$	−0.268571	−	1.52314i	−0.00864112	−	0.0490062i
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	0.000850519	−	1.00000i	$-0.499729\pi$
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	−0.642136	+	0.766591i	$0.721951\pi$
$968$	−1.81076			−0.0582002
$969$	−3.46451	+	1.64019i	−0.111296	+	0.0526906i
$970$	4.05913			0.130331
$971$	35.3387	+	12.8622i	1.13407	+	0.412769i	0.839770	−	0.542943i	$-0.182690\pi$
$971$	35.3387	+	12.8622i	1.13407	+	0.412769i	0.294304	+	0.955712i	$0.404912\pi$
$972$	−2.68422	−	15.2230i	−0.0860964	−	0.488277i
$973$	−22.1668	−	18.6002i	−0.710636	−	0.596295i
$974$	−15.1643	+	12.7244i	−0.485896	+	0.407715i
$975$	−0.690007	+	3.91322i	−0.0220979	+	0.125323i
$976$	0.0919294	−	0.159226i	0.00294259	−	0.00509671i
$977$	23.0107	+	39.8558i	0.736179	+	1.27510i	0.954204	+	0.299156i	$0.0967050\pi$
$977$	23.0107	+	39.8558i	0.736179	+	1.27510i	−0.218026	+	0.975943i	$0.569962\pi$
$978$	0.889185	−	0.323637i	0.0284330	−	0.0103488i
$979$	7.31908	−	2.66393i	0.233919	−	0.0851395i
$980$	5.38578	+	9.32845i	0.172042	+	0.297986i
$981$	10.0111	−	17.3398i	0.319631	−	0.553618i
$982$	2.38737	−	13.5395i	0.0761842	−	0.432062i
$983$	46.4195	−	38.9506i	1.48055	−	1.24233i	0.574961	−	0.818181i	$-0.305017\pi$
$983$	46.4195	−	38.9506i	1.48055	−	1.24233i	0.905592	−	0.424150i	$-0.139427\pi$
$984$	5.19325	+	4.35765i	0.165555	+	0.138917i
$985$	10.2010	+	57.8527i	0.325031	+	1.84334i
$986$	4.73618	+	1.72383i	0.150831	+	0.0548979i
$987$	−0.716881			−0.0228186
$988$	−27.3684	−	7.16252i	−0.870705	−	0.227870i
$989$	8.44326			0.268480
$990$	−19.3935	−	7.05866i	−0.616367	−	0.224339i
$991$	7.27554	+	41.2616i	0.231115	+	1.31072i	0.850643	+	0.525744i	$0.176213\pi$
$991$	7.27554	+	41.2616i	0.231115	+	1.31072i	−0.619528	+	0.784975i	$0.712676\pi$
$992$	8.39440	+	7.04374i	0.266522	+	0.223639i
$993$	−0.697033	+	0.584880i	−0.0221197	+	0.0185606i
$994$	3.94862	−	22.3937i	0.125242	−	0.710285i
$995$	11.6750	−	20.2217i	0.370122	−	0.641070i
$996$	0.819955	+	1.42020i	0.0259813	+	0.0450009i
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.790885	−	0.611965i	$-0.790379\pi$
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.212490	+	0.977163i	$0.568157\pi$
$998$	23.6475	−	8.60700i	0.748550	−	0.272450i
$999$	−1.27379	−	2.20626i	−0.0403008	−	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.2.e.a.4.1	✓	6
3.2	odd	2		171.2.u.c.118.1		6
4.3	odd	2		304.2.u.b.289.1		6
5.2	odd	4		475.2.u.a.99.2		12
5.3	odd	4		475.2.u.a.99.1		12
5.4	even	2		475.2.l.a.251.1		6
7.2	even	3		931.2.x.a.802.1		6
7.3	odd	6		931.2.v.a.422.1		6
7.4	even	3		931.2.v.b.422.1		6
7.5	odd	6		931.2.x.b.802.1		6
7.6	odd	2		931.2.w.a.99.1		6
19.2	odd	18		361.2.e.b.54.1		6
19.3	odd	18		361.2.e.a.245.1		6
19.4	even	9		361.2.c.i.292.1		6
19.5	even	9	inner	19.2.e.a.5.1	yes	6
19.6	even	9		361.2.c.i.68.1		6
19.7	even	3		361.2.e.f.234.1		6
19.8	odd	6		361.2.e.a.28.1		6
19.9	even	9		361.2.a.g.1.3		3
19.10	odd	18		361.2.a.h.1.1		3
19.11	even	3		361.2.e.g.28.1		6
19.12	odd	6		361.2.e.b.234.1		6
19.13	odd	18		361.2.c.h.68.3		6
19.14	odd	18		361.2.e.h.62.1		6
19.15	odd	18		361.2.c.h.292.3		6
19.16	even	9		361.2.e.g.245.1		6
19.17	even	9		361.2.e.f.54.1		6
19.18	odd	2		361.2.e.h.99.1		6
57.5	odd	18		171.2.u.c.100.1		6
57.29	even	18		3249.2.a.s.1.3		3
57.47	odd	18		3249.2.a.z.1.1		3
76.43	odd	18		304.2.u.b.81.1		6
76.47	odd	18		5776.2.a.br.1.1		3
76.67	even	18		5776.2.a.bi.1.3		3
95.9	even	18		9025.2.a.bd.1.1		3
95.24	even	18		475.2.l.a.176.1		6
95.29	odd	18		9025.2.a.x.1.3		3
95.43	odd	36		475.2.u.a.24.2		12
95.62	odd	36		475.2.u.a.24.1		12
133.5	odd	18		931.2.v.a.214.1		6
133.24	odd	18		931.2.x.b.765.1		6
133.62	odd	18		931.2.w.a.442.1		6
133.81	even	9		931.2.x.a.765.1		6
133.100	even	9		931.2.v.b.214.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	1.1	even	1	trivial
19.2.e.a.5.1	yes	6	19.5	even	9	inner
171.2.u.c.100.1		6	57.5	odd	18
171.2.u.c.118.1		6	3.2	odd	2
304.2.u.b.81.1		6	76.43	odd	18
304.2.u.b.289.1		6	4.3	odd	2
361.2.a.g.1.3		3	19.9	even	9
361.2.a.h.1.1		3	19.10	odd	18
361.2.c.h.68.3		6	19.13	odd	18
361.2.c.h.292.3		6	19.15	odd	18
361.2.c.i.68.1		6	19.6	even	9
361.2.c.i.292.1		6	19.4	even	9
361.2.e.a.28.1		6	19.8	odd	6
361.2.e.a.245.1		6	19.3	odd	18
361.2.e.b.54.1		6	19.2	odd	18
361.2.e.b.234.1		6	19.12	odd	6
361.2.e.f.54.1		6	19.17	even	9
361.2.e.f.234.1		6	19.7	even	3
361.2.e.g.28.1		6	19.11	even	3
361.2.e.g.245.1		6	19.16	even	9
361.2.e.h.62.1		6	19.14	odd	18
361.2.e.h.99.1		6	19.18	odd	2
475.2.l.a.176.1		6	95.24	even	18
475.2.l.a.251.1		6	5.4	even	2
475.2.u.a.24.1		12	95.62	odd	36
475.2.u.a.24.2		12	95.43	odd	36
475.2.u.a.99.1		12	5.3	odd	4
475.2.u.a.99.2		12	5.2	odd	4
931.2.v.a.214.1		6	133.5	odd	18
931.2.v.a.422.1		6	7.3	odd	6
931.2.v.b.214.1		6	133.100	even	9
931.2.v.b.422.1		6	7.4	even	3
931.2.w.a.99.1		6	7.6	odd	2
931.2.w.a.442.1		6	133.62	odd	18
931.2.x.a.765.1		6	133.81	even	9
931.2.x.a.802.1		6	7.2	even	3
931.2.x.b.765.1		6	133.24	odd	18
931.2.x.b.802.1		6	7.5	odd	6
3249.2.a.s.1.3		3	57.29	even	18
3249.2.a.z.1.1		3	57.47	odd	18
5776.2.a.bi.1.3		3	76.67	even	18
5776.2.a.br.1.1		3	76.47	odd	18
9025.2.a.x.1.3		3	95.29	odd	18
9025.2.a.bd.1.1		3	95.9	even	18

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.826352 - 0.300767i) q^{2} +(0.0923963 + 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(-1.93969 + 1.62760i) q^{5} +(0.0812519 - 0.460802i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.41875 + 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +O(q^{10})\)	\(q+(-0.826352 - 0.300767i) q^{2} +(0.0923963 + 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(-1.93969 + 1.62760i) q^{5} +(0.0812519 - 0.460802i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.41875 + 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +(2.09240 - 0.761570i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(0.326352 - 0.565258i) q^{12} +(-0.918748 + 5.21048i) q^{13} +(-1.26604 + 1.06234i) q^{14} +(-1.03209 - 0.866025i) q^{15} +(-0.00727396 - 0.0412527i) q^{16} +(-1.55303 - 0.565258i) q^{17} -2.38919 q^{18} +(-2.52094 - 3.55596i) q^{19} +3.10607 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.520945 + 2.95442i) q^{22} +(1.34730 + 1.13052i) q^{23} +(-1.15657 + 0.970481i) q^{24} +(0.245100 - 1.39003i) q^{25} +(2.32635 - 4.02936i) q^{26} +(1.52094 + 2.63435i) q^{27} +(-2.16637 + 0.788496i) q^{28} +(3.25877 - 1.18610i) q^{29} +(0.592396 + 1.02606i) q^{30} +(-0.971782 + 1.68317i) q^{31} +(0.979055 - 5.55250i) q^{32} +(1.39053 - 1.16679i) q^{33} +(1.11334 + 0.934204i) q^{34} +(0.826352 + 4.68647i) q^{35} +(-3.13176 - 1.13987i) q^{36} -0.837496 q^{37} +(1.01367 + 3.69669i) q^{38} -2.81521 q^{39} +(-6.75150 - 2.45734i) q^{40} +(-0.779715 - 4.42198i) q^{41} +(-0.673648 - 0.565258i) q^{42} +(3.67752 - 3.08580i) q^{43} +(-0.726682 + 4.12122i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(-0.773318 - 1.33943i) q^{46} +(-0.673648 + 0.245188i) q^{47} +(0.0209445 - 0.00762319i) q^{48} +(1.73396 + 3.00330i) q^{49} +(-0.620615 + 1.07494i) q^{50} +(0.152704 - 0.866025i) q^{51} +(4.97178 - 4.17182i) q^{52} +(-4.67752 - 3.92490i) q^{53} +(-0.464508 - 2.63435i) q^{54} +(8.11721 + 2.95442i) q^{55} +5.33275 q^{56} +(1.63041 - 1.64955i) q^{57} -3.04963 q^{58} +(10.1099 + 3.67972i) q^{59} +(0.286989 + 1.62760i) q^{60} +(3.36231 + 2.82131i) q^{61} +(1.30928 - 1.09861i) q^{62} +(0.886659 - 5.02849i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-6.69846 - 11.6021i) q^{65} +(-1.50000 + 0.545955i) q^{66} +(-13.3550 + 4.86084i) q^{67} +(1.01367 + 1.75573i) q^{68} +(-0.467911 + 0.810446i) q^{69} +(0.726682 - 4.12122i) q^{70} +(-10.5398 + 8.84397i) q^{71} +(5.90554 + 4.95534i) q^{72} +(-1.30541 - 7.40333i) q^{73} +(0.692066 + 0.251892i) q^{74} +0.751030 q^{75} +(-0.434945 + 5.32926i) q^{76} -6.41147 q^{77} +(2.32635 + 0.846723i) q^{78} +(-1.20914 - 6.85738i) q^{79} +(0.0812519 + 0.0681784i) q^{80} +(5.00387 - 4.19875i) q^{81} +(-0.685670 + 3.88863i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(-0.613341 - 1.06234i) q^{84} +(3.93242 - 1.43128i) q^{85} +(-3.96703 + 1.44388i) q^{86} +(0.922618 + 1.59802i) q^{87} +(4.84002 - 8.38316i) q^{88} +(-0.396459 + 2.24843i) q^{89} +(4.63429 - 3.88863i) q^{90} +(7.61721 + 6.39160i) q^{91} +(-0.374638 - 2.12467i) q^{92} +(-0.971782 - 0.353700i) q^{93} +0.630415 q^{94} +(10.6775 + 2.79439i) q^{95} +3.00000 q^{96} +(1.71301 + 0.623485i) q^{97} +(-0.529563 - 3.00330i) q^{98} +(-7.10014 - 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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