LMFDB - Embedded newform 361.2.c.j.292.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(68,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			292.3
Root			$0.951057 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	361.292
Dual form			361.2.c.j.68.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 1.01807i) q^{2} +(-0.587785 - 1.01807i) q^{3} +(0.309017 - 0.535233i) q^{4} +(-0.618034 - 1.07047i) q^{5} +(0.690983 - 1.19682i) q^{6} -4.23607 q^{7} +3.07768 q^{8} +(0.809017 - 1.40126i) q^{9} +(0.726543 - 1.25841i) q^{10} -3.61803 q^{11} -0.726543 q^{12} +(1.53884 - 2.66535i) q^{13} +(-2.48990 - 4.31263i) q^{14} +(-0.726543 + 1.25841i) q^{15} +(1.19098 + 2.06284i) q^{16} +(-1.23607 - 2.14093i) q^{17} +1.90211 q^{18} -0.763932 q^{20} +(2.48990 + 4.31263i) q^{21} +(-2.12663 - 3.68343i) q^{22} +(1.30902 - 2.26728i) q^{23} +(-1.80902 - 3.13331i) q^{24} +(1.73607 - 3.00696i) q^{25} +3.61803 q^{26} -5.42882 q^{27} +(-1.30902 + 2.26728i) q^{28} +(-1.31433 + 2.27648i) q^{29} -1.70820 q^{30} +1.17557 q^{31} +(1.67760 - 2.90569i) q^{32} +(2.12663 + 3.68343i) q^{33} +(1.45309 - 2.51682i) q^{34} +(2.61803 + 4.53457i) q^{35} +(-0.500000 - 0.866025i) q^{36} +6.43288 q^{37} -3.61803 q^{39} +(-1.90211 - 3.29456i) q^{40} +(4.61653 + 7.99606i) q^{41} +(-2.92705 + 5.06980i) q^{42} +(3.16312 + 5.47868i) q^{43} +(-1.11803 + 1.93649i) q^{44} -2.00000 q^{45} +3.07768 q^{46} +(1.26393 - 2.18919i) q^{47} +(1.40008 - 2.42502i) q^{48} +10.9443 q^{49} +4.08174 q^{50} +(-1.45309 + 2.51682i) q^{51} +(-0.951057 - 1.64728i) q^{52} +(0.224514 - 0.388870i) q^{53} +(-3.19098 - 5.52694i) q^{54} +(2.23607 + 3.87298i) q^{55} -13.0373 q^{56} -3.09017 q^{58} +(-1.40008 - 2.42502i) q^{59} +(0.449028 + 0.777739i) q^{60} +(0.263932 - 0.457144i) q^{61} +(0.690983 + 1.19682i) q^{62} +(-3.42705 + 5.93583i) q^{63} +8.70820 q^{64} -3.80423 q^{65} +(-2.50000 + 4.33013i) q^{66} +(-0.0857567 + 0.148535i) q^{67} -1.52786 q^{68} -3.07768 q^{69} +(-3.07768 + 5.33070i) q^{70} +(6.06961 + 10.5129i) q^{71} +(2.48990 - 4.31263i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(3.78115 + 6.54915i) q^{74} -4.08174 q^{75} +15.3262 q^{77} +(-2.12663 - 3.68343i) q^{78} +(-3.80423 - 6.58911i) q^{79} +(1.47214 - 2.54981i) q^{80} +(0.763932 + 1.32317i) q^{81} +(-5.42705 + 9.39993i) q^{82} +1.23607 q^{83} +3.07768 q^{84} +(-1.52786 + 2.64634i) q^{85} +(-3.71847 + 6.44058i) q^{86} +3.09017 q^{87} -11.1352 q^{88} +(-8.86978 + 15.3629i) q^{89} +(-1.17557 - 2.03615i) q^{90} +(-6.51864 + 11.2906i) q^{91} +(-0.809017 - 1.40126i) q^{92} +(-0.690983 - 1.19682i) q^{93} +2.97168 q^{94} -3.94427 q^{96} +(-7.83297 - 13.5671i) q^{97} +(6.43288 + 11.1421i) q^{98} +(-2.92705 + 5.06980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9} - 20 q^{11} + 14 q^{16} + 8 q^{17} - 24 q^{20} + 6 q^{23} - 10 q^{24} - 4 q^{25} + 20 q^{26} - 6 q^{28} + 40 q^{30} + 12 q^{35} - 4 q^{36} - 20 q^{39}+ \cdots - 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9 - 20 * q^11 + 14 * q^16 + 8 * q^17 - 24 * q^20 + 6 * q^23 - 10 * q^24 - 4 * q^25 + 20 * q^26 - 6 * q^28 + 40 * q^30 + 12 * q^35 - 4 * q^36 - 20 * q^39 - 10 * q^42 - 6 * q^43 - 16 * q^45 + 28 * q^47 + 16 * q^49 - 30 * q^54 + 20 * q^58 + 20 * q^61 + 10 * q^62 - 14 * q^63 + 16 * q^64 - 20 * q^66 - 48 * q^68 - 36 * q^73 - 10 * q^74 + 60 * q^77 - 24 * q^80 + 24 * q^81 - 30 * q^82 - 8 * q^83 - 48 * q^85 - 20 * q^87 - 2 * q^92 - 10 * q^93 + 40 * q^96 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.587785	+	1.01807i	0.415627	+	0.719887i	0.995494	−	0.0948241i	$-0.0302289\pi$
$2$	0.587785	+	1.01807i	0.415627	+	0.719887i	−0.579867	+	0.814711i	$0.696896\pi$
$3$	−0.587785	−	1.01807i	−0.339358	−	0.587785i	0.644954	−	0.764221i	$-0.276876\pi$
$3$	−0.587785	−	1.01807i	−0.339358	−	0.587785i	−0.984312	+	0.176436i	$0.943543\pi$
$4$	0.309017	−	0.535233i	0.154508	−	0.267617i
$5$	−0.618034	−	1.07047i	−0.276393	−	0.478727i	0.694092	−	0.719886i	$-0.255806\pi$
$5$	−0.618034	−	1.07047i	−0.276393	−	0.478727i	−0.970486	+	0.241159i	$0.922473\pi$
$6$	0.690983	−	1.19682i	0.282093	−	0.488599i
$7$	−4.23607			−1.60108			−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607			−1.60108			−0.800542	+	0.599277i	$0.795455\pi$
$8$	3.07768			1.08813
$9$	0.809017	−	1.40126i	0.269672	−	0.467086i
$10$	0.726543	−	1.25841i	0.229753	−	0.397944i
$11$	−3.61803			−1.09088			−0.545439	−	0.838150i	$-0.683637\pi$
$11$	−3.61803			−1.09088			−0.545439	+	0.838150i	$0.683637\pi$
$12$	−0.726543			−0.209735
$13$	1.53884	−	2.66535i	0.426798	−	0.739236i	−0.569789	−	0.821791i	$-0.692975\pi$
$13$	1.53884	−	2.66535i	0.426798	−	0.739236i	0.996586	+	0.0825557i	$0.0263082\pi$
$14$	−2.48990	−	4.31263i	−0.665453	−	1.15260i
$15$	−0.726543	+	1.25841i	−0.187592	+	0.324920i
$16$	1.19098	+	2.06284i	0.297746	+	0.515711i
$17$	−1.23607	−	2.14093i	−0.299791	−	0.519252i	0.676297	−	0.736629i	$-0.263583\pi$
$17$	−1.23607	−	2.14093i	−0.299791	−	0.519252i	−0.976088	+	0.217376i	$0.930250\pi$
$18$	1.90211			0.448332
$19$		0			0
$19$		0			0
$20$	−0.763932			−0.170820
$21$	2.48990	+	4.31263i	0.543340	+	0.941093i
$22$	−2.12663	−	3.68343i	−0.453398	−	0.785309i
$23$	1.30902	−	2.26728i	0.272949	−	0.472761i	−0.696667	−	0.717395i	$-0.745334\pi$
$23$	1.30902	−	2.26728i	0.272949	−	0.472761i	0.969616	+	0.244634i	$0.0786677\pi$
$24$	−1.80902	−	3.13331i	−0.369264	−	0.639584i
$25$	1.73607	−	3.00696i	0.347214	−	0.601392i
$26$	3.61803			0.709555
$27$	−5.42882			−1.04478
$28$	−1.30902	+	2.26728i	−0.247381	+	0.428476i
$29$	−1.31433	+	2.27648i	−0.244065	+	0.422732i	−0.961868	−	0.273513i	$-0.911814\pi$
$29$	−1.31433	+	2.27648i	−0.244065	+	0.422732i	0.717804	+	0.696246i	$0.245148\pi$
$30$	−1.70820			−0.311874
$31$	1.17557			0.211139			0.105569	−	0.994412i	$-0.466333\pi$
$31$	1.17557			0.211139			0.105569	+	0.994412i	$0.466333\pi$
$32$	1.67760	−	2.90569i	0.296560	−	0.513658i
$33$	2.12663	+	3.68343i	0.370198	+	0.641202i
$34$	1.45309	−	2.51682i	0.249202	−	0.431631i
$35$	2.61803	+	4.53457i	0.442529	+	0.766482i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	6.43288			1.05756			0.528780	−	0.848759i	$-0.322650\pi$
$37$	6.43288			1.05756			0.528780	+	0.848759i	$0.322650\pi$
$38$		0			0
$39$	−3.61803			−0.579349
$40$	−1.90211	−	3.29456i	−0.300750	−	0.520915i
$41$	4.61653	+	7.99606i	0.720980	+	1.24877i	0.960607	+	0.277909i	$0.0896414\pi$
$41$	4.61653	+	7.99606i	0.720980	+	1.24877i	−0.239627	+	0.970865i	$0.577025\pi$
$42$	−2.92705	+	5.06980i	−0.451654	+	0.782287i
$43$	3.16312	+	5.47868i	0.482371	+	0.835491i	0.999795	−	0.0202378i	$-0.00644234\pi$
$43$	3.16312	+	5.47868i	0.482371	+	0.835491i	−0.517424	+	0.855729i	$0.673109\pi$
$44$	−1.11803	+	1.93649i	−0.168550	+	0.291937i
$45$	−2.00000			−0.298142
$46$	3.07768			0.453780
$47$	1.26393	−	2.18919i	0.184363	−	0.319327i	−0.758998	−	0.651092i	$-0.774311\pi$
$47$	1.26393	−	2.18919i	0.184363	−	0.319327i	0.943362	+	0.331766i	$0.107644\pi$
$48$	1.40008	−	2.42502i	0.202085	−	0.350021i
$49$	10.9443			1.56347
$50$	4.08174			0.577245
$51$	−1.45309	+	2.51682i	−0.203473	+	0.352425i
$52$	−0.951057	−	1.64728i	−0.131888	−	0.228436i
$53$	0.224514	−	0.388870i	0.0308394	−	0.0534154i	−0.850194	−	0.526470i	$-0.823515\pi$
$53$	0.224514	−	0.388870i	0.0308394	−	0.0534154i	0.881033	+	0.473055i	$0.156849\pi$
$54$	−3.19098	−	5.52694i	−0.434238	−	0.752122i
$55$	2.23607	+	3.87298i	0.301511	+	0.522233i
$56$	−13.0373			−1.74218
$57$		0			0
$58$	−3.09017			−0.405759
$59$	−1.40008	−	2.42502i	−0.182275	−	0.315710i	0.760380	−	0.649479i	$-0.225013\pi$
$59$	−1.40008	−	2.42502i	−0.182275	−	0.315710i	−0.942655	+	0.333769i	$0.891680\pi$
$60$	0.449028	+	0.777739i	0.0579693	+	0.100406i
$61$	0.263932	−	0.457144i	0.0337930	−	0.0585312i	−0.848634	−	0.528980i	$-0.822575\pi$
$61$	0.263932	−	0.457144i	0.0337930	−	0.0585312i	0.882427	+	0.470449i	$0.155908\pi$
$62$	0.690983	+	1.19682i	0.0877549	+	0.151996i
$63$	−3.42705	+	5.93583i	−0.431768	+	0.747844i
$64$	8.70820			1.08853
$65$	−3.80423			−0.471856
$66$	−2.50000	+	4.33013i	−0.307729	+	0.533002i
$67$	−0.0857567	+	0.148535i	−0.0104768	+	0.0181464i	−0.871216	−	0.490899i	$-0.836668\pi$
$67$	−0.0857567	+	0.148535i	−0.0104768	+	0.0181464i	0.860739	+	0.509046i	$0.170002\pi$
$68$	−1.52786			−0.185281
$69$	−3.07768			−0.370510
$70$	−3.07768	+	5.33070i	−0.367854	+	0.637141i
$71$	6.06961	+	10.5129i	0.720330	+	1.24765i	0.960867	+	0.277009i	$0.0893431\pi$
$71$	6.06961	+	10.5129i	0.720330	+	1.24765i	−0.240537	+	0.970640i	$0.577324\pi$
$72$	2.48990	−	4.31263i	0.293437	−	0.508248i
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	−0.999517	−	0.0310925i	$-0.990101\pi$
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	0.472831	−	0.881153i	$-0.343232\pi$
$74$	3.78115	+	6.54915i	0.439550	+	0.761323i
$75$	−4.08174			−0.471319
$76$		0			0
$77$	15.3262			1.74659
$78$	−2.12663	−	3.68343i	−0.240793	−	0.417066i
$79$	−3.80423	−	6.58911i	−0.428009	−	0.741333i	0.568687	−	0.822554i	$-0.307451\pi$
$79$	−3.80423	−	6.58911i	−0.428009	−	0.741333i	−0.996696	+	0.0812207i	$0.974118\pi$
$80$	1.47214	−	2.54981i	0.164590	−	0.285078i
$81$	0.763932	+	1.32317i	0.0848813	+	0.147019i
$82$	−5.42705	+	9.39993i	−0.599318	+	1.03805i
$83$	1.23607			0.135676			0.0678380	−	0.997696i	$-0.478390\pi$
$83$	1.23607			0.135676			0.0678380	+	0.997696i	$0.478390\pi$
$84$	3.07768			0.335803
$85$	−1.52786	+	2.64634i	−0.165720	+	0.287036i
$86$	−3.71847	+	6.44058i	−0.400973	+	0.694505i
$87$	3.09017			0.331301
$88$	−11.1352			−1.18701
$89$	−8.86978	+	15.3629i	−0.940195	+	1.62847i	−0.175097	+	0.984551i	$0.556024\pi$
$89$	−8.86978	+	15.3629i	−0.940195	+	1.62847i	−0.765098	+	0.643914i	$0.777310\pi$
$90$	−1.17557	−	2.03615i	−0.123916	−	0.214629i
$91$	−6.51864	+	11.2906i	−0.683339	+	1.18358i
$92$	−0.809017	−	1.40126i	−0.0843459	−	0.146091i
$93$	−0.690983	−	1.19682i	−0.0716516	−	0.124104i
$94$	2.97168			0.306506
$95$		0			0
$96$	−3.94427			−0.402561
$97$	−7.83297	−	13.5671i	−0.795317	−	1.37753i	−0.922638	−	0.385668i	$-0.873971\pi$
$97$	−7.83297	−	13.5671i	−0.795317	−	1.37753i	0.127320	−	0.991862i	$-0.459362\pi$
$98$	6.43288	+	11.1421i	0.649819	+	1.12552i
$99$	−2.92705	+	5.06980i	−0.294180	+	0.509534i
$100$	−1.07295	−	1.85840i	−0.107295	−	0.185840i
$101$	6.97214	−	12.0761i	0.693753	−	1.20162i	−0.276846	−	0.960914i	$-0.589289\pi$
$101$	6.97214	−	12.0761i	0.693753	−	1.20162i	0.970599	−	0.240702i	$-0.0773776\pi$
$102$	−3.41641			−0.338275
$103$	−1.00406			−0.0989327			−0.0494663	−	0.998776i	$-0.515752\pi$
$103$	−1.00406			−0.0989327			−0.0494663	+	0.998776i	$0.515752\pi$
$104$	4.73607	−	8.20311i	0.464410	−	0.804381i
$105$	3.07768	−	5.33070i	0.300351	−	0.520223i
$106$	0.527864			0.0512707
$107$	11.5842			1.11989			0.559943	−	0.828531i	$-0.310823\pi$
$107$	11.5842			1.11989			0.559943	+	0.828531i	$0.310823\pi$
$108$	−1.67760	+	2.90569i	−0.161427	+	0.279600i
$109$	−0.363271	−	0.629204i	−0.0347951	−	0.0602668i	0.848103	−	0.529831i	$-0.177745\pi$
$109$	−0.363271	−	0.629204i	−0.0347951	−	0.0602668i	−0.882899	+	0.469564i	$0.844411\pi$
$110$	−2.62866	+	4.55296i	−0.250632	+	0.434108i
$111$	−3.78115	−	6.54915i	−0.358891	−	0.621618i
$112$	−5.04508	−	8.73834i	−0.476716	−	0.825696i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−3.23607			−0.301765
$116$	0.812299	+	1.40694i	0.0754201	+	0.130631i
$117$	−2.48990	−	4.31263i	−0.230191	−	0.398703i
$118$	1.64590	−	2.85078i	0.151517	−	0.262435i
$119$	5.23607	+	9.06914i	0.479990	+	0.831366i
$120$	−2.23607	+	3.87298i	−0.204124	+	0.353553i
$121$	2.09017			0.190015
$122$	0.620541			0.0561812
$123$	5.42705	−	9.39993i	0.489341	−	0.847563i
$124$	0.363271	−	0.629204i	0.0326227	−	0.0565042i
$125$	−10.4721			−0.936656
$126$	−8.05748			−0.717817
$127$	7.97172	−	13.8074i	0.707376	−	1.22521i	−0.258451	−	0.966024i	$-0.583212\pi$
$127$	7.97172	−	13.8074i	0.707376	−	1.22521i	0.965827	−	0.259187i	$-0.0834546\pi$
$128$	1.76336	+	3.05422i	0.155860	+	0.269958i
$129$	3.71847	−	6.44058i	0.327393	−	0.567061i
$130$	−2.23607	−	3.87298i	−0.196116	−	0.339683i
$131$	2.54508	+	4.40822i	0.222365	+	0.385148i	0.955526	−	0.294908i	$-0.0952890\pi$
$131$	2.54508	+	4.40822i	0.222365	+	0.385148i	−0.733161	+	0.680056i	$0.761956\pi$
$132$	2.62866			0.228795
$133$		0			0
$134$	−0.201626			−0.0174178
$135$	3.35520	+	5.81137i	0.288769	+	0.500163i
$136$	−3.80423	−	6.58911i	−0.326210	−	0.565012i
$137$	2.35410	−	4.07742i	0.201125	−	0.348358i	−0.747767	−	0.663962i	$-0.768874\pi$
$137$	2.35410	−	4.07742i	0.201125	−	0.348358i	0.948891	+	0.315604i	$0.102207\pi$
$138$	−1.80902	−	3.13331i	−0.153994	−	0.266725i
$139$	0.454915	−	0.787936i	0.0385854	−	0.0668319i	−0.846088	−	0.533044i	$-0.821048\pi$
$139$	0.454915	−	0.787936i	0.0385854	−	0.0668319i	0.884673	+	0.466212i	$0.154382\pi$
$140$	3.23607			0.273498
$141$	−2.97168			−0.250261
$142$	−7.13525	+	12.3586i	−0.598777	+	1.03711i
$143$	−5.56758	+	9.64333i	−0.465585	+	0.806416i
$144$	3.85410			0.321175
$145$	3.24920			0.269831
$146$	5.29007	−	9.16267i	0.437809	−	0.758308i
$147$	−6.43288	−	11.1421i	−0.530575	−	0.918983i
$148$	1.98787	−	3.44309i	0.163402	−	0.283020i
$149$	11.5172	+	19.9484i	0.943528	+	1.63424i	0.758673	+	0.651472i	$0.225848\pi$
$149$	11.5172	+	19.9484i	0.943528	+	1.63424i	0.184855	+	0.982766i	$0.440819\pi$
$150$	−2.39919	−	4.15551i	−0.195893	−	0.339296i
$151$	2.45714			0.199959			0.0999797	−	0.994989i	$-0.468122\pi$
$151$	2.45714			0.199959			0.0999797	+	0.994989i	$0.468122\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	9.00854	+	15.6032i	0.725929	+	1.25735i
$155$	−0.726543	−	1.25841i	−0.0583573	−	0.101078i
$156$	−1.11803	+	1.93649i	−0.0895144	+	0.155043i
$157$	−7.78115	−	13.4774i	−0.621004	−	1.07561i	−0.989299	−	0.145901i	$-0.953392\pi$
$157$	−7.78115	−	13.4774i	−0.621004	−	1.07561i	0.368296	−	0.929709i	$-0.379941\pi$
$158$	4.47214	−	7.74597i	0.355784	−	0.616236i
$159$	−0.527864			−0.0418623
$160$	−4.14725			−0.327869
$161$	−5.54508	+	9.60437i	−0.437014	+	0.756930i
$162$	−0.898056	+	1.55548i	−0.0705579	+	0.122210i
$163$	6.52786			0.511302			0.255651	−	0.966769i	$-0.417710\pi$
$163$	6.52786			0.511302			0.255651	+	0.966769i	$0.417710\pi$
$164$	5.70634			0.445590
$165$	2.62866	−	4.55296i	0.204641	−	0.354448i
$166$	0.726543	+	1.25841i	0.0563906	+	0.0976714i
$167$	3.44095	−	5.95991i	0.266269	−	0.461192i	−0.701626	−	0.712545i	$-0.747542\pi$
$167$	3.44095	−	5.95991i	0.266269	−	0.461192i	0.967895	+	0.251354i	$0.0808757\pi$
$168$	7.66312	+	13.2729i	0.591222	+	1.02403i
$169$	1.76393	+	3.05522i	0.135687	+	0.235017i
$170$	−3.59222			−0.275511
$171$		0			0
$172$	3.90983			0.298122
$173$	7.77997	+	13.4753i	0.591500	+	1.02451i	0.994031	+	0.109101i	$0.0347973\pi$
$173$	7.77997	+	13.4753i	0.591500	+	1.02451i	−0.402531	+	0.915406i	$0.631869\pi$
$174$	1.81636	+	3.14602i	0.137698	+	0.238499i
$175$	−7.35410	+	12.7377i	−0.555918	+	0.962878i
$176$	−4.30902	−	7.46344i	−0.324804	−	0.562578i
$177$	−1.64590	+	2.85078i	−0.123713	+	0.214278i
$178$	−20.8541			−1.56308
$179$	18.2946			1.36740			0.683701	−	0.729762i	$-0.260369\pi$
$179$	18.2946			1.36740			0.683701	+	0.729762i	$0.260369\pi$
$180$	−0.618034	+	1.07047i	−0.0460655	+	0.0797878i
$181$	12.3107	−	21.3228i	0.915050	−	1.58491i	0.108221	−	0.994127i	$-0.465485\pi$
$181$	12.3107	−	21.3228i	0.915050	−	1.58491i	0.806829	−	0.590786i	$-0.201182\pi$
$182$	−15.3262			−1.13606
$183$	−0.620541			−0.0458717
$184$	4.02874	−	6.97798i	0.297003	−	0.514424i
$185$	−3.97574	−	6.88618i	−0.292302	−	0.506282i
$186$	0.812299	−	1.40694i	0.0595607	−	0.103162i
$187$	4.47214	+	7.74597i	0.327035	+	0.566441i
$188$	−0.781153	−	1.35300i	−0.0569714	−	0.0986774i
$189$	22.9969			1.67278
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	−5.11855	−	8.86560i	−0.369400	−	0.639819i
$193$	2.62866	+	4.55296i	0.189215	+	0.327730i	0.944989	−	0.327103i	$-0.106072\pi$
$193$	2.62866	+	4.55296i	0.189215	+	0.327730i	−0.755774	+	0.654833i	$0.772739\pi$
$194$	9.20820	−	15.9491i	0.661111	−	1.14508i
$195$	2.23607	+	3.87298i	0.160128	+	0.277350i
$196$	3.38197	−	5.85774i	0.241569	−	0.418410i
$197$	2.52786			0.180103			0.0900514	−	0.995937i	$-0.471297\pi$
$197$	2.52786			0.180103			0.0900514	+	0.995937i	$0.471297\pi$
$198$	−6.88191			−0.489076
$199$	9.47214	−	16.4062i	0.671462	−	1.16301i	−0.306028	−	0.952023i	$-0.599000\pi$
$199$	9.47214	−	16.4062i	0.671462	−	1.16301i	0.977490	−	0.210984i	$-0.0676666\pi$
$200$	5.34307	−	9.25446i	0.377812	−	0.654389i
$201$	0.201626			0.0142216
$202$	16.3925			1.15337
$203$	5.56758	−	9.64333i	0.390768	−	0.676829i
$204$	0.898056	+	1.55548i	0.0628765	+	0.108905i
$205$	5.70634	−	9.88367i	0.398548	−	0.690305i
$206$	−0.590170	−	1.02220i	−0.0411191	−	0.0712204i
$207$	−2.11803	−	3.66854i	−0.147214	−	0.254981i
$208$	7.33094			0.508309
$209$		0			0
$210$	7.23607			0.499336
$211$	9.00854	+	15.6032i	0.620173	+	1.07417i	0.989453	+	0.144853i	$0.0462710\pi$
$211$	9.00854	+	15.6032i	0.620173	+	1.07417i	−0.369280	+	0.929318i	$0.620396\pi$
$212$	−0.138757	−	0.240335i	−0.00952989	−	0.0165063i
$213$	7.13525	−	12.3586i	0.488900	−	0.846799i
$214$	6.80902	+	11.7936i	0.465455	+	0.806191i
$215$	3.90983	−	6.77202i	0.266648	−	0.461848i
$216$	−16.7082			−1.13685
$217$	−4.97980			−0.338051
$218$	0.427051	−	0.739674i	0.0289235	−	0.0500970i
$219$	−5.29007	+	9.16267i	−0.357470	+	0.619156i
$220$	2.76393			0.186344
$221$	−7.60845			−0.511800
$222$	4.44501	−	7.69899i	0.298330	−	0.516722i
$223$	−6.79615	−	11.7713i	−0.455104	−	0.788263i	0.543590	−	0.839351i	$-0.317065\pi$
$223$	−6.79615	−	11.7713i	−0.455104	−	0.788263i	−0.998694	+	0.0510875i	$0.983731\pi$
$224$	−7.10642	+	12.3087i	−0.474818	+	0.822409i
$225$	−2.80902	−	4.86536i	−0.187268	−	0.324357i
$226$		0			0
$227$	−29.7073			−1.97174			−0.985870	−	0.167511i	$-0.946427\pi$
$227$	−29.7073			−1.97174			−0.985870	+	0.167511i	$0.946427\pi$
$228$		0			0
$229$	4.09017			0.270286			0.135143	−	0.990826i	$-0.456851\pi$
$229$	4.09017			0.270286			0.135143	+	0.990826i	$0.456851\pi$
$230$	−1.90211	−	3.29456i	−0.125422	−	0.217237i
$231$	−9.00854	−	15.6032i	−0.592718	−	1.02662i
$232$	−4.04508	+	7.00629i	−0.265573	+	0.459986i
$233$	−6.73607	−	11.6672i	−0.441294	−	0.764344i	0.556491	−	0.830853i	$-0.312147\pi$
$233$	−6.73607	−	11.6672i	−0.441294	−	0.764344i	−0.997786	+	0.0665089i	$0.978814\pi$
$234$	2.92705	−	5.06980i	0.191347	−	0.331423i
$235$	−3.12461			−0.203827
$236$	−1.73060			−0.112652
$237$	−4.47214	+	7.74597i	−0.290496	+	0.503155i
$238$	−6.15537	+	10.6614i	−0.398993	+	0.691076i
$239$	−15.8541			−1.02552			−0.512758	−	0.858533i	$-0.671376\pi$
$239$	−15.8541			−1.02552			−0.512758	+	0.858533i	$0.671376\pi$
$240$	−3.46120			−0.223419
$241$	−11.3269	+	19.6188i	−0.729631	+	1.26376i	0.227408	+	0.973800i	$0.426975\pi$
$241$	−11.3269	+	19.6188i	−0.729631	+	1.26376i	−0.957039	+	0.289959i	$0.906358\pi$
$242$	1.22857	+	2.12795i	0.0789755	+	0.136790i
$243$	−7.24518	+	12.5490i	−0.464779	+	0.805020i
$244$	−0.163119	−	0.282530i	−0.0104426	−	0.0180872i
$245$	−6.76393	−	11.7155i	−0.432132	−	0.748474i
$246$	12.7598			0.813533
$247$		0			0
$248$	3.61803			0.229745
$249$	−0.726543	−	1.25841i	−0.0460428	−	0.0797484i
$250$	−6.15537	−	10.6614i	−0.389300	−	0.674287i
$251$	−5.20820	+	9.02087i	−0.328739	+	0.569393i	−0.982262	−	0.187514i	$-0.939957\pi$
$251$	−5.20820	+	9.02087i	−0.328739	+	0.569393i	0.653523	+	0.756907i	$0.273290\pi$
$252$	2.11803	+	3.66854i	0.133424	+	0.231096i
$253$	−4.73607	+	8.20311i	−0.297754	+	0.515725i
$254$	18.7426			1.17602
$255$	3.59222			0.224954
$256$	6.63525	−	11.4926i	0.414703	−	0.718287i
$257$	−4.53077	+	7.84752i	−0.282622	+	0.489515i	−0.972030	−	0.234858i	$-0.924537\pi$
$257$	−4.53077	+	7.84752i	−0.282622	+	0.489515i	0.689408	+	0.724373i	$0.257871\pi$
$258$	8.74265			0.544293
$259$	−27.2501			−1.69324
$260$	−1.17557	+	2.03615i	−0.0729058	+	0.126277i
$261$	2.12663	+	3.68343i	0.131635	+	0.227998i
$262$	−2.99193	+	5.18217i	−0.184842	+	0.320155i
$263$	−5.94427	−	10.2958i	−0.366540	−	0.634865i	0.622482	−	0.782634i	$-0.286124\pi$
$263$	−5.94427	−	10.2958i	−0.366540	−	0.634865i	−0.989022	+	0.147769i	$0.952791\pi$
$264$	6.54508	+	11.3364i	0.402822	+	0.697708i
$265$	−0.555029			−0.0340952
$266$		0			0
$267$	20.8541			1.27625
$268$	0.0530006	+	0.0917997i	0.00323752	+	0.00560756i
$269$	3.85723	+	6.68091i	0.235179	+	0.407342i	0.959325	−	0.282305i	$-0.0910989\pi$
$269$	3.85723	+	6.68091i	0.235179	+	0.407342i	−0.724146	+	0.689647i	$0.757766\pi$
$270$	−3.94427	+	6.83168i	−0.240041	+	0.415763i
$271$	−7.13525	−	12.3586i	−0.433436	−	0.750733i	0.563731	−	0.825959i	$-0.309366\pi$
$271$	−7.13525	−	12.3586i	−0.433436	−	0.750733i	−0.997167	+	0.0752257i	$0.976032\pi$
$272$	2.94427	−	5.09963i	0.178523	−	0.309210i
$273$	15.3262			0.927586
$274$	5.53483			0.334371
$275$	−6.28115	+	10.8793i	−0.378768	+	0.656045i
$276$	−0.951057	+	1.64728i	−0.0572469	+	0.0991545i
$277$	−19.2361			−1.15578			−0.577892	−	0.816113i	$-0.696124\pi$
$277$	−19.2361			−1.15578			−0.577892	+	0.816113i	$0.696124\pi$
$278$	1.06957			0.0641485
$279$	0.951057	−	1.64728i	0.0569383	−	0.0986200i
$280$	8.05748	+	13.9560i	0.481527	+	0.834028i
$281$	2.21238	−	3.83196i	0.131980	−	0.228596i	−0.792460	−	0.609924i	$-0.791200\pi$
$281$	2.21238	−	3.83196i	0.131980	−	0.228596i	0.924440	+	0.381328i	$0.124533\pi$
$282$	−1.74671	−	3.02539i	−0.104015	−	0.180159i
$283$	0.454915	+	0.787936i	0.0270419	+	0.0468379i	0.879230	−	0.476398i	$-0.158058\pi$
$283$	0.454915	+	0.787936i	0.0270419	+	0.0468379i	−0.852188	+	0.523236i	$0.824725\pi$
$284$	7.50245			0.445189
$285$		0			0
$286$	−13.0902			−0.774038
$287$	−19.5559	−	33.8718i	−1.15435	−	1.99939i
$288$	−2.71441	−	4.70150i	−0.159948	−	0.277039i
$289$	5.44427	−	9.42976i	0.320251	−	0.554692i
$290$	1.90983	+	3.30792i	0.112149	+	0.194248i
$291$	−9.20820	+	15.9491i	−0.539794	+	0.934951i
$292$	−5.56231			−0.325509
$293$	24.7275			1.44459			0.722297	−	0.691583i	$-0.243086\pi$
$293$	24.7275			1.44459			0.722297	+	0.691583i	$0.243086\pi$
$294$	7.56231	−	13.0983i	0.441043	−	0.763908i
$295$	−1.73060	+	2.99749i	−0.100759	+	0.174520i
$296$	19.7984			1.15076
$297$	19.6417			1.13973
$298$	−13.5393	+	23.4508i	−0.784311	+	1.35847i
$299$	−4.02874	−	6.97798i	−0.232988	−	0.403547i
$300$	−1.26133	+	2.18468i	−0.0728228	+	0.126133i
$301$	−13.3992	−	23.2081i	−0.772316	−	1.33769i
$302$	1.44427	+	2.50155i	0.0831085	+	0.143948i
$303$	−16.3925			−0.941723
$304$		0			0
$305$	−0.652476			−0.0373607
$306$	−2.35114	−	4.07230i	−0.134406	−	0.232798i
$307$	13.7966	+	23.8964i	0.787412	+	1.36384i	0.927547	+	0.373705i	$0.121913\pi$
$307$	13.7966	+	23.8964i	0.787412	+	1.36384i	−0.140135	+	0.990132i	$0.544754\pi$
$308$	4.73607	−	8.20311i	0.269863	−	0.467416i
$309$	0.590170	+	1.02220i	0.0335736	+	0.0581512i
$310$	0.854102	−	1.47935i	0.0485097	−	0.0840213i
$311$	−5.52786			−0.313456			−0.156728	−	0.987642i	$-0.550095\pi$
$311$	−5.52786			−0.313456			−0.156728	+	0.987642i	$0.550095\pi$
$312$	−11.1352			−0.630405
$313$	−3.80902	+	6.59741i	−0.215298	+	0.372908i	−0.953365	−	0.301820i	$-0.902406\pi$
$313$	−3.80902	+	6.59741i	−0.215298	+	0.372908i	0.738066	+	0.674728i	$0.235739\pi$
$314$	9.14729	−	15.8436i	0.516212	−	0.894105i
$315$	8.47214			0.477351
$316$	−4.70228			−0.264524
$317$	−4.42477	+	7.66392i	−0.248520	+	0.430449i	−0.963115	−	0.269089i	$-0.913277\pi$
$317$	−4.42477	+	7.66392i	−0.248520	+	0.430449i	0.714596	+	0.699538i	$0.246611\pi$
$318$	−0.310271	−	0.537405i	−0.0173991	−	0.0301362i
$319$	4.75528	−	8.23639i	0.266245	−	0.461149i
$320$	−5.38197	−	9.32184i	−0.300861	−	0.521107i
$321$	−6.80902	−	11.7936i	−0.380042	−	0.658253i
$322$	−13.0373			−0.726539
$323$		0			0
$324$	0.944272			0.0524596
$325$	−5.34307	−	9.25446i	−0.296380	−	0.513345i
$326$	3.83698	+	6.64585i	0.212511	+	0.368079i
$327$	−0.427051	+	0.739674i	−0.0236160	+	0.0409041i
$328$	14.2082	+	24.6093i	0.784517	+	1.35882i
$329$	−5.35410	+	9.27358i	−0.295181	+	0.511269i
$330$	6.18034			0.340217
$331$	−24.2784			−1.33446			−0.667232	−	0.744850i	$-0.732521\pi$
$331$	−24.2784			−1.33446			−0.667232	+	0.744850i	$0.732521\pi$
$332$	0.381966	−	0.661585i	0.0209631	−	0.0363092i
$333$	5.20431	−	9.01413i	0.285194	−	0.493971i
$334$	8.09017			0.442674
$335$	0.212002			0.0115829
$336$	−5.93085	+	10.2725i	−0.323555	+	0.560413i
$337$	8.05748	+	13.9560i	0.438919	+	0.760230i	0.997606	−	0.0691484i	$-0.0220282\pi$
$337$	8.05748	+	13.9560i	0.438919	+	0.760230i	−0.558687	+	0.829378i	$0.688695\pi$
$338$	−2.07363	+	3.59163i	−0.112790	+	0.195359i
$339$		0			0
$340$	0.944272	+	1.63553i	0.0512103	+	0.0886989i
$341$	−4.25325			−0.230327
$342$		0			0
$343$	−16.7082			−0.902158
$344$	9.73508	+	16.8617i	0.524880	+	0.909119i
$345$	1.90211	+	3.29456i	0.102406	+	0.177373i
$346$	−9.14590	+	15.8412i	−0.491687	+	0.851626i
$347$	12.4164	+	21.5058i	0.666548	+	1.15449i	0.978863	+	0.204516i	$0.0655621\pi$
$347$	12.4164	+	21.5058i	0.666548	+	1.15449i	−0.312316	+	0.949978i	$0.601105\pi$
$348$	0.954915	−	1.65396i	0.0511888	−	0.0886616i
$349$	11.3820			0.609263			0.304631	−	0.952470i	$-0.401467\pi$
$349$	11.3820			0.609263			0.304631	+	0.952470i	$0.401467\pi$
$350$	−17.2905			−0.924218
$351$	−8.35410	+	14.4697i	−0.445909	+	0.772337i
$352$	−6.06961	+	10.5129i	−0.323511	+	0.560338i
$353$	27.6180			1.46996			0.734980	−	0.678089i	$-0.237192\pi$
$353$	27.6180			1.46996			0.734980	+	0.678089i	$0.237192\pi$
$354$	−3.86974			−0.205674
$355$	7.50245	−	12.9946i	0.398189	−	0.689683i
$356$	5.48183	+	9.49480i	0.290536	+	0.503223i
$357$	6.15537	−	10.6614i	0.325777	−	0.564262i
$358$	10.7533	+	18.6252i	0.568329	+	0.984375i
$359$	18.8090	+	32.5782i	0.992702	+	1.71941i	0.600788	+	0.799408i	$0.294854\pi$
$359$	18.8090	+	32.5782i	0.992702	+	1.71941i	0.391914	+	0.920002i	$0.371813\pi$
$360$	−6.15537			−0.324416
$361$		0			0
$362$	28.9443			1.52128
$363$	−1.22857	−	2.12795i	−0.0644833	−	0.111688i
$364$	4.02874	+	6.97798i	0.211163	+	0.365746i
$365$	−5.56231	+	9.63420i	−0.291144	+	0.504277i
$366$	−0.364745	−	0.631757i	−0.0190655	−	0.0330225i
$367$	−10.7361	+	18.5954i	−0.560418	+	0.970673i	0.437042	+	0.899441i	$0.356026\pi$
$367$	−10.7361	+	18.5954i	−0.560418	+	0.970673i	−0.997460	+	0.0712315i	$0.977307\pi$
$368$	6.23607			0.325078
$369$	14.9394			0.777714
$370$	4.67376	−	8.09519i	0.242977	−	0.420849i
$371$	−0.951057	+	1.64728i	−0.0493764	+	0.0855224i
$372$	−0.854102			−0.0442831
$373$	−4.31877			−0.223617			−0.111809	−	0.993730i	$-0.535664\pi$
$373$	−4.31877			−0.223617			−0.111809	+	0.993730i	$0.535664\pi$
$374$	−5.25731	+	9.10593i	−0.271849	+	0.470856i
$375$	6.15537	+	10.6614i	0.317862	+	0.550553i
$376$	3.88998	−	6.73765i	0.200611	−	0.347468i
$377$	4.04508	+	7.00629i	0.208332	+	0.360842i
$378$	13.5172	+	23.4125i	0.695251	+	1.20421i
$379$	−7.95148			−0.408440			−0.204220	−	0.978925i	$-0.565466\pi$
$379$	−7.95148			−0.408440			−0.204220	+	0.978925i	$0.565466\pi$
$380$		0			0
$381$	−18.7426			−0.960215
$382$	−9.99235	−	17.3073i	−0.511253	−	0.885516i
$383$	−7.02067	−	12.1602i	−0.358739	−	0.621355i	0.629011	−	0.777396i	$-0.283460\pi$
$383$	−7.02067	−	12.1602i	−0.358739	−	0.621355i	−0.987750	+	0.156042i	$0.950127\pi$
$384$	2.07295	−	3.59045i	0.105785	−	0.183225i
$385$	−9.47214	−	16.4062i	−0.482745	−	0.836138i
$386$	−3.09017	+	5.35233i	−0.157286	+	0.272426i
$387$	10.2361			0.520329
$388$	−9.68208			−0.491533
$389$	−6.54508	+	11.3364i	−0.331849	+	0.574779i	−0.982874	−	0.184277i	$-0.941006\pi$
$389$	−6.54508	+	11.3364i	−0.331849	+	0.574779i	0.651025	+	0.759056i	$0.274339\pi$
$390$	−2.62866	+	4.55296i	−0.133107	+	0.230548i
$391$	−6.47214			−0.327310
$392$	33.6830			1.70125
$393$	2.99193	−	5.18217i	0.150923	−	0.261406i
$394$	1.48584	+	2.57355i	0.0748556	+	0.129654i
$395$	−4.70228	+	8.14459i	−0.236597	+	0.409799i
$396$	1.80902	+	3.13331i	0.0909065	+	0.157455i
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	0.620332	−	0.784339i	$-0.286998\pi$
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	−0.989424	+	0.145054i	$0.953665\pi$
$398$	22.2703			1.11631
$399$		0			0
$400$	8.27051			0.413525
$401$	3.80423	+	6.58911i	0.189974	+	0.329045i	0.945241	−	0.326372i	$-0.105826\pi$
$401$	3.80423	+	6.58911i	0.189974	+	0.329045i	−0.755267	+	0.655417i	$0.772493\pi$
$402$	0.118513	+	0.205270i	0.00591088	+	0.0102380i
$403$	1.80902	−	3.13331i	0.0901136	−	0.156081i
$404$	−4.30902	−	7.46344i	−0.214382	−	0.371320i
$405$	0.944272	−	1.63553i	0.0469212	−	0.0812700i
$406$	13.0902			0.649654
$407$	−23.2744			−1.15367
$408$	−4.47214	+	7.74597i	−0.221404	+	0.383482i
$409$	−10.9637	+	18.9896i	−0.542118	+	0.938975i	0.456665	+	0.889639i	$0.349044\pi$
$409$	−10.9637	+	18.9896i	−0.542118	+	0.938975i	−0.998782	+	0.0493363i	$0.984289\pi$
$410$	13.4164			0.662589
$411$	−5.53483			−0.273013
$412$	−0.310271	+	0.537405i	−0.0152859	+	0.0264760i
$413$	5.93085	+	10.2725i	0.291838	+	0.505479i
$414$	2.48990	−	4.31263i	0.122372	−	0.211954i
$415$	−0.763932	−	1.32317i	−0.0374999	−	0.0649518i
$416$	−5.16312	−	8.94278i	−0.253143	−	0.438456i
$417$	−1.06957			−0.0523770
$418$		0			0
$419$	−33.4164			−1.63250			−0.816249	−	0.577700i	$-0.803950\pi$
$419$	−33.4164			−1.63250			−0.816249	+	0.577700i	$0.803950\pi$
$420$	−1.90211	−	3.29456i	−0.0928136	−	0.160758i
$421$	7.07367	+	12.2520i	0.344749	+	0.597124i	0.985308	−	0.170786i	$-0.0546305\pi$
$421$	7.07367	+	12.2520i	0.344749	+	0.597124i	−0.640559	+	0.767909i	$0.721297\pi$
$422$	−10.5902	+	18.3427i	−0.515521	+	0.892909i
$423$	−2.04508	−	3.54219i	−0.0994354	−	0.172227i
$424$	0.690983	−	1.19682i	0.0335571	−	0.0581226i
$425$	−8.58359			−0.416365
$426$	16.7760			0.812799
$427$	−1.11803	+	1.93649i	−0.0541055	+	0.0937134i
$428$	3.57971	−	6.20024i	0.173032	−	0.299700i
$429$	13.0902			0.631999
$430$	9.19256			0.443305
$431$	7.97172	−	13.8074i	0.383984	−	0.665080i	−0.607643	−	0.794210i	$-0.707885\pi$
$431$	7.97172	−	13.8074i	0.383984	−	0.665080i	0.991628	+	0.129130i	$0.0412183\pi$
$432$	−6.46564	−	11.1988i	−0.311078	−	0.538803i
$433$	4.66953	−	8.08786i	0.224403	−	0.388678i	−0.731737	−	0.681587i	$-0.761290\pi$
$433$	4.66953	−	8.08786i	0.224403	−	0.388678i	0.956140	+	0.292909i	$0.0946234\pi$
$434$	−2.92705	−	5.06980i	−0.140503	−	0.243358i
$435$	−1.90983	−	3.30792i	−0.0915693	−	0.158603i
$436$	−0.449028			−0.0215045
$437$		0			0
$438$	−12.4377			−0.594296
$439$	5.79210	+	10.0322i	0.276442	+	0.478811i	0.970498	−	0.241110i	$-0.0775114\pi$
$439$	5.79210	+	10.0322i	0.276442	+	0.478811i	−0.694056	+	0.719921i	$0.744178\pi$
$440$	6.88191	+	11.9198i	0.328082	+	0.568255i
$441$	8.85410	−	15.3358i	0.421624	−	0.730274i
$442$	−4.47214	−	7.74597i	−0.212718	−	0.368438i
$443$	3.59017	−	6.21836i	0.170574	−	0.295443i	−0.768047	−	0.640394i	$-0.778771\pi$
$443$	3.59017	−	6.21836i	0.170574	−	0.295443i	0.938621	+	0.344951i	$0.112104\pi$
$444$	−4.67376			−0.221807
$445$	21.9273			1.03945
$446$	7.98936	−	13.8380i	0.378307	−	0.655247i
$447$	13.5393	−	23.4508i	0.640387	−	1.10918i
$448$	−36.8885			−1.74282
$449$	−34.9646			−1.65008			−0.825040	−	0.565074i	$-0.808848\pi$
$449$	−34.9646			−1.65008			−0.825040	+	0.565074i	$0.808848\pi$
$450$	3.30220	−	5.71957i	0.155667	−	0.269623i
$451$	−16.7027	−	28.9300i	−0.786502	−	1.36226i
$452$		0			0
$453$	−1.44427	−	2.50155i	−0.0678578	−	0.117533i
$454$	−17.4615	−	30.2442i	−0.819508	−	1.41943i
$455$	16.1150			0.755481
$456$		0			0
$457$	19.7082			0.921911			0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082			0.921911			0.460955	+	0.887423i	$0.347507\pi$
$458$	2.40414	+	4.16410i	0.112338	+	0.194575i
$459$	6.71040	+	11.6227i	0.313214	+	0.542503i
$460$	−1.00000	+	1.73205i	−0.0466252	+	0.0807573i
$461$	17.0902	+	29.6010i	0.795969	+	1.37866i	0.922222	+	0.386660i	$0.126371\pi$
$461$	17.0902	+	29.6010i	0.795969	+	1.37866i	−0.126254	+	0.991998i	$0.540295\pi$
$462$	10.5902	−	18.3427i	0.492699	−	0.853380i
$463$	16.8541			0.783277			0.391638	−	0.920119i	$-0.371908\pi$
$463$	16.8541			0.783277			0.391638	+	0.920119i	$0.371908\pi$
$464$	−6.26137			−0.290677
$465$	−0.854102	+	1.47935i	−0.0396080	+	0.0686031i
$466$	7.91872	−	13.7156i	0.366828	−	0.635364i
$467$	−0.236068			−0.0109239			−0.00546196	−	0.999985i	$-0.501739\pi$
$467$	−0.236068			−0.0109239			−0.00546196	+	0.999985i	$0.501739\pi$
$468$	−3.07768			−0.142266
$469$	0.363271	−	0.629204i	0.0167743	−	0.0290540i
$470$	−1.83660	−	3.18109i	−0.0847161	−	0.146733i
$471$	−9.14729	+	15.8436i	−0.421485	+	0.730034i
$472$	−4.30902	−	7.46344i	−0.198339	−	0.343533i
$473$	−11.4443	−	19.8221i	−0.526208	−	0.911419i
$474$	−10.5146			−0.482953
$475$		0			0
$476$	6.47214			0.296650
$477$	−0.363271	−	0.629204i	−0.0166330	−	0.0288093i
$478$	−9.31881	−	16.1406i	−0.426232	−	0.738256i
$479$	13.5451	−	23.4608i	0.618891	−	1.07195i	−0.370798	−	0.928714i	$-0.620916\pi$
$479$	13.5451	−	23.4608i	0.618891	−	1.07195i	0.989688	−	0.143237i	$-0.0457510\pi$
$480$	2.43769	+	4.22221i	0.111265	+	0.192717i
$481$	9.89919	−	17.1459i	0.451364	−	0.781786i
$482$	−26.6312			−1.21302
$483$	13.0373			0.593217
$484$	0.645898	−	1.11873i	0.0293590	−	0.0508513i
$485$	−9.68208	+	16.7699i	−0.439641	+	0.761480i
$486$	−17.0344			−0.772698
$487$	15.5599			0.705088			0.352544	−	0.935795i	$-0.385317\pi$
$487$	15.5599			0.705088			0.352544	+	0.935795i	$0.385317\pi$
$488$	0.812299	−	1.40694i	0.0367711	−	0.0636893i
$489$	−3.83698	−	6.64585i	−0.173514	−	0.300536i
$490$	7.95148	−	13.7724i	0.359211	−	0.622172i
$491$	8.13525	+	14.0907i	0.367139	+	0.635903i	0.989117	−	0.147131i	$-0.0470040\pi$
$491$	8.13525	+	14.0907i	0.367139	+	0.635903i	−0.621978	+	0.783035i	$0.713671\pi$
$492$	−3.35410	−	5.80948i	−0.151215	−	0.261911i
$493$	6.49839			0.292673
$494$		0			0
$495$	7.23607			0.325237
$496$	1.40008	+	2.42502i	0.0628656	+	0.108886i
$497$	−25.7113	−	44.5332i	−1.15331	−	1.99759i
$498$	0.854102	−	1.47935i	0.0382732	−	0.0662912i
$499$	−10.7639	−	18.6437i	−0.481860	−	0.834606i	0.517923	−	0.855427i	$-0.326705\pi$
$499$	−10.7639	−	18.6437i	−0.481860	−	0.834606i	−0.999783	+	0.0208214i	$0.993372\pi$
$500$	−3.23607	+	5.60503i	−0.144721	+	0.250665i
$501$	−8.09017			−0.361442
$502$	−12.2452			−0.546531
$503$	14.2984	−	24.7655i	0.637533	−	1.10424i	−0.348439	−	0.937331i	$-0.613288\pi$
$503$	14.2984	−	24.7655i	0.637533	−	1.10424i	0.985972	−	0.166908i	$-0.0533784\pi$
$504$	−10.5474	+	18.2686i	−0.469818	+	0.813748i
$505$	−17.2361			−0.766995
$506$	−11.1352			−0.495018
$507$	2.07363	−	3.59163i	0.0920930	−	0.159510i
$508$	−4.92680	−	8.53346i	−0.218591	−	0.378611i
$509$	−6.20837	+	10.7532i	−0.275181	+	0.476628i	−0.970181	−	0.242382i	$-0.922071\pi$
$509$	−6.20837	+	10.7532i	−0.275181	+	0.476628i	0.695000	+	0.719010i	$0.255404\pi$
$510$	2.11146	+	3.65715i	0.0934969	+	0.161941i
$511$	19.0623	+	33.0169i	0.843267	+	1.46058i
$512$	22.6538			1.00117
$513$		0			0
$514$	−10.6525			−0.469861
$515$	0.620541	+	1.07481i	0.0273443	+	0.0473618i
$516$	−2.29814	−	3.98050i	−0.101170	−	0.175232i
$517$	−4.57295	+	7.92058i	−0.201118	+	0.348347i
$518$	−16.0172	−	27.7426i	−0.703756	−	1.21894i
$519$	9.14590	−	15.8412i	0.401460	−	0.695350i
$520$	−11.7082			−0.513439
$521$	2.97168			0.130192			0.0650959	−	0.997879i	$-0.479265\pi$
$521$	2.97168			0.130192			0.0650959	+	0.997879i	$0.479265\pi$
$522$	−2.50000	+	4.33013i	−0.109422	+	0.189525i
$523$	−4.06150	+	7.03472i	−0.177597	+	0.307607i	−0.941057	−	0.338248i	$-0.890166\pi$
$523$	−4.06150	+	7.03472i	−0.177597	+	0.307607i	0.763460	+	0.645855i	$0.223499\pi$
$524$	3.14590			0.137429
$525$	17.2905			0.754621
$526$	6.98791	−	12.1034i	0.304687	−	0.527734i
$527$	−1.45309	−	2.51682i	−0.0632974	−	0.109634i
$528$	−5.06555	+	8.77380i	−0.220450	+	0.381830i
$529$	8.07295	+	13.9828i	0.350998	+	0.607946i
$530$	−0.326238	−	0.565061i	−0.0141709	−	0.0245447i
$531$	−4.53077			−0.196619
$532$		0			0
$533$	28.4164			1.23085
$534$	12.2577	+	21.2310i	0.530444	+	0.918756i
$535$	−7.15942	−	12.4005i	−0.309529	−	0.536120i
$536$	−0.263932	+	0.457144i	−0.0114001	+	0.0197456i
$537$	−10.7533	−	18.6252i	−0.464039	−	0.803739i
$538$	−4.53444	+	7.85388i	−0.195494	+	0.338605i
$539$	−39.5967			−1.70555
$540$	4.14725			0.178469
$541$	3.35410	−	5.80948i	0.144204	−	0.249769i	−0.784872	−	0.619658i	$-0.787271\pi$
$541$	3.35410	−	5.80948i	0.144204	−	0.249769i	0.929076	+	0.369890i	$0.120604\pi$
$542$	8.38800	−	14.5284i	0.360295	−	0.624050i
$543$	−28.9443			−1.24212
$544$	−8.29451			−0.355624
$545$	−0.449028	+	0.777739i	−0.0192342	+	0.0333147i
$546$	9.00854	+	15.6032i	0.385530	+	0.667757i
$547$	−14.6291	+	25.3384i	−0.625496	+	1.08339i	0.362949	+	0.931809i	$0.381770\pi$
$547$	−14.6291	+	25.3384i	−0.625496	+	1.08339i	−0.988445	+	0.151582i	$0.951563\pi$
$548$	−1.45492	−	2.51999i	−0.0621509	−	0.107648i
$549$	−0.427051	−	0.739674i	−0.0182261	−	0.0315685i
$550$	−14.7679			−0.629704
$551$		0			0
$552$	−9.47214			−0.403161
$553$	16.1150	+	27.9119i	0.685278	+	1.18694i
$554$	−11.3067	−	19.5837i	−0.480375	−	0.832033i
$555$	−4.67376	+	8.09519i	−0.198390	+	0.343622i
$556$	−0.281153	−	0.486971i	−0.0119235	−	0.0206522i
$557$	−2.68034	+	4.64248i	−0.113570	+	0.196708i	−0.917207	−	0.398411i	$-0.869562\pi$
$557$	−2.68034	+	4.64248i	−0.113570	+	0.196708i	0.803637	+	0.595119i	$0.202895\pi$
$558$	2.23607			0.0946603
$559$	19.4702			0.823500
$560$	−6.23607	+	10.8012i	−0.263522	+	0.456433i
$561$	5.25731	−	9.10593i	0.221964	−	0.384453i
$562$	5.20163			0.219417
$563$	−18.1231			−0.763797			−0.381898	−	0.924204i	$-0.624730\pi$
$563$	−18.1231			−0.763797			−0.381898	+	0.924204i	$0.624730\pi$
$564$	−0.918300	+	1.59054i	−0.0386674	+	0.0669739i
$565$		0			0
$566$	−0.534785	+	0.926274i	−0.0224787	+	0.0389342i
$567$	−3.23607	−	5.60503i	−0.135902	−	0.235389i
$568$	18.6803	+	32.3553i	0.783810	+	1.35760i
$569$	18.3601			0.769695			0.384848	−	0.922980i	$-0.374254\pi$
$569$	18.3601			0.769695			0.384848	+	0.922980i	$0.374254\pi$
$570$		0			0
$571$	41.1033			1.72012			0.860060	−	0.510192i	$-0.170426\pi$
$571$	41.1033			1.72012			0.860060	+	0.510192i	$0.170426\pi$
$572$	3.44095	+	5.95991i	0.143874	+	0.249196i
$573$	9.99235	+	17.3073i	0.417436	+	0.723021i
$574$	22.9894	−	39.8187i	0.959557	−	1.66200i
$575$	−4.54508	−	7.87232i	−0.189543	−	0.328298i
$576$	7.04508	−	12.2024i	0.293545	−	0.508435i
$577$	−28.7082			−1.19514			−0.597569	−	0.801817i	$-0.703867\pi$
$577$	−28.7082			−1.19514			−0.597569	+	0.801817i	$0.703867\pi$
$578$	12.8003			0.532420
$579$	3.09017	−	5.35233i	0.128423	−	0.222435i
$580$	1.00406	−	1.73908i	0.0416912	−	0.0722113i
$581$	−5.23607			−0.217229
$582$	−21.6498			−0.897412
$583$	−0.812299	+	1.40694i	−0.0336420	+	0.0582696i
$584$	−13.8496	−	23.9882i	−0.573100	−	0.992638i
$585$	−3.07768	+	5.33070i	−0.127247	+	0.220397i
$586$	14.5344	+	25.1744i	0.600412	+	1.03994i
$587$	−19.5902	−	33.9312i	−0.808573	−	1.40049i	−0.913852	−	0.406047i	$-0.866907\pi$
$587$	−19.5902	−	33.9312i	−0.808573	−	1.40049i	0.105280	−	0.994443i	$-0.466426\pi$
$588$	−7.95148			−0.327913
$589$		0			0
$590$	−4.06888			−0.167513
$591$	−1.48584	−	2.57355i	−0.0611193	−	0.105862i
$592$	7.66145	+	13.2700i	0.314884	+	0.545395i
$593$	−15.3541	+	26.5941i	−0.630517	+	1.09209i	0.356929	+	0.934132i	$0.383824\pi$
$593$	−15.3541	+	26.5941i	−0.630517	+	1.09209i	−0.987446	+	0.157957i	$0.949509\pi$
$594$	11.5451	+	19.9967i	0.473701	+	0.820473i
$595$	6.47214	−	11.2101i	0.265332	−	0.459568i
$596$	14.2361			0.583132
$597$	−22.2703			−0.911464
$598$	4.73607	−	8.20311i	0.193672	−	0.335450i
$599$	10.3229	−	17.8797i	0.421781	−	0.730546i	−0.574333	−	0.818622i	$-0.694739\pi$
$599$	10.3229	−	17.8797i	0.421781	−	0.730546i	0.996114	+	0.0880760i	$0.0280718\pi$
$600$	−12.5623			−0.512854
$601$	41.2915			1.68431			0.842157	−	0.539233i	$-0.181286\pi$
$601$	41.2915			1.68431			0.842157	+	0.539233i	$0.181286\pi$
$602$	15.7517	−	27.2827i	0.641991	−	1.11196i
$603$	0.138757	+	0.240335i	0.00565063	+	0.00978718i
$604$	0.759299	−	1.31514i	0.0308954	−	0.0535124i
$605$	−1.29180	−	2.23746i	−0.0525190	−	0.0909655i
$606$	−9.63525	−	16.6888i	−0.391405	−	0.677934i
$607$	−1.51860			−0.0616380			−0.0308190	−	0.999525i	$-0.509812\pi$
$607$	−1.51860			−0.0616380			−0.0308190	+	0.999525i	$0.509812\pi$
$608$		0			0
$609$	−13.0902			−0.530440
$610$	−0.383516	−	0.664269i	−0.0155281	−	0.0268955i
$611$	−3.88998	−	6.73765i	−0.157372	−	0.272576i
$612$	−1.23607	+	2.14093i	−0.0499651	+	0.0865421i
$613$	12.2639	+	21.2418i	0.495336	+	0.857946i	0.999986	−	0.00537770i	$-0.00171178\pi$
$613$	12.2639	+	21.2418i	0.495336	+	0.857946i	−0.504650	+	0.863324i	$0.668378\pi$
$614$	−16.2188	+	28.0919i	−0.654539	+	1.13370i
$615$	−13.4164			−0.541002
$616$	47.1693			1.90051
$617$	−8.63525	+	14.9567i	−0.347642	+	0.602134i	−0.985830	−	0.167747i	$-0.946351\pi$
$617$	−8.63525	+	14.9567i	−0.347642	+	0.602134i	0.638188	+	0.769881i	$0.279684\pi$
$618$	−0.693786	+	1.20167i	−0.0279082	+	0.0483384i
$619$	36.7771			1.47820			0.739098	−	0.673598i	$-0.235252\pi$
$619$	36.7771			1.47820			0.739098	+	0.673598i	$0.235252\pi$
$620$	−0.898056			−0.0360668
$621$	−7.10642	+	12.3087i	−0.285171	+	0.493931i
$622$	−3.24920	−	5.62777i	−0.130281	−	0.225653i
$623$	37.5730	−	65.0783i	1.50533	−	2.60731i
$624$	−4.30902	−	7.46344i	−0.172499	−	0.298777i
$625$	−2.20820	−	3.82472i	−0.0883282	−	0.152989i
$626$	−8.95554			−0.357935
$627$		0			0
$628$	−9.61803			−0.383801
$629$	−7.95148	−	13.7724i	−0.317046	−	0.549140i
$630$	4.97980	+	8.62526i	0.198400	+	0.343639i
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	−0.502379	−	0.864647i	$-0.667542\pi$
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	0.999996	+	0.00274930i	$0.000875132\pi$
$632$	−11.7082	−	20.2792i	−0.465727	−	0.806663i
$633$	10.5902	−	18.3427i	0.420921	−	0.729057i
$634$	−10.4033			−0.413166
$635$	−19.7072			−0.782056
$636$	−0.163119	+	0.282530i	−0.00646809	+	0.0112031i
$637$	16.8415	−	29.1703i	0.667285	−	1.15577i
$638$	11.1803			0.442634
$639$	19.6417			0.777013
$640$	2.17963	−	3.77523i	0.0861573	−	0.149229i
$641$	−14.4576	−	25.0413i	−0.571041	−	0.989072i	−0.996459	−	0.0840753i	$-0.973206\pi$
$641$	−14.4576	−	25.0413i	−0.571041	−	0.989072i	0.425418	−	0.904997i	$-0.360127\pi$
$642$	8.00448	−	13.8642i	0.315912	−	0.547175i
$643$	−3.85410	−	6.67550i	−0.151991	−	0.263256i	0.779968	−	0.625819i	$-0.215235\pi$
$643$	−3.85410	−	6.67550i	−0.151991	−	0.263256i	−0.931959	+	0.362563i	$0.881902\pi$
$644$	3.42705	+	5.93583i	0.135045	+	0.233904i
$645$	−9.19256			−0.361957
$646$		0			0
$647$	−32.1246			−1.26295			−0.631474	−	0.775397i	$-0.717550\pi$
$647$	−32.1246			−1.26295			−0.631474	+	0.775397i	$0.717550\pi$
$648$	2.35114	+	4.07230i	0.0923615	+	0.159975i
$649$	5.06555	+	8.77380i	0.198840	+	0.344402i
$650$	6.28115	−	10.8793i	0.246367	−	0.426720i
$651$	2.92705	+	5.06980i	0.114720	+	0.198701i
$652$	2.01722	−	3.49393i	0.0790005	−	0.136833i
$653$	19.7426			0.772589			0.386295	−	0.922375i	$-0.373755\pi$
$653$	19.7426			0.772589			0.386295	+	0.922375i	$0.373755\pi$
$654$	−1.00406			−0.0392617
$655$	3.14590	−	5.44886i	0.122920	−	0.212904i
$656$	−10.9964	+	19.0463i	−0.429338	+	0.743634i
$657$	−14.5623			−0.568130
$658$	−12.5882			−0.490741
$659$	−9.33905	+	16.1757i	−0.363798	+	0.630116i	−0.988582	−	0.150681i	$-0.951853\pi$
$659$	−9.33905	+	16.1757i	−0.363798	+	0.630116i	0.624785	+	0.780797i	$0.285187\pi$
$660$	−1.62460	−	2.81389i	−0.0632374	−	0.109530i
$661$	−2.52265	+	4.36937i	−0.0981199	+	0.169949i	−0.910906	−	0.412613i	$-0.864616\pi$
$661$	−2.52265	+	4.36937i	−0.0981199	+	0.169949i	0.812787	+	0.582562i	$0.197950\pi$
$662$	−14.2705	−	24.7172i	−0.554639	−	0.960663i
$663$	4.47214	+	7.74597i	0.173683	+	0.300828i
$664$	3.80423			0.147633
$665$		0			0
$666$	12.2361			0.474138
$667$	3.44095	+	5.95991i	0.133234	+	0.230769i
$668$	−2.12663	−	3.68343i	−0.0822817	−	0.142516i
$669$	−7.98936	+	13.8380i	−0.308886	+	0.535007i
$670$	0.124612	+	0.215834i	0.00481417	+	0.00833839i
$671$	−0.954915	+	1.65396i	−0.0368641	+	0.0638505i
$672$	16.7082			0.644533
$673$	−28.2542			−1.08912			−0.544559	−	0.838722i	$-0.683303\pi$
$673$	−28.2542			−1.08912			−0.544559	+	0.838722i	$0.683303\pi$
$674$	−9.47214	+	16.4062i	−0.364853	+	0.631944i
$675$	−9.42481	+	16.3242i	−0.362761	+	0.628321i
$676$	2.18034			0.0838592
$677$	−11.6902			−0.449291			−0.224645	−	0.974441i	$-0.572122\pi$
$677$	−11.6902			−0.449291			−0.224645	+	0.974441i	$0.572122\pi$
$678$		0			0
$679$	33.1810	+	57.4711i	1.27337	+	2.20554i
$680$	−4.70228	+	8.14459i	−0.180324	+	0.312331i
$681$	17.4615	+	30.2442i	0.669126	+	1.15896i
$682$	−2.50000	−	4.33013i	−0.0957299	−	0.165809i
$683$	32.7445			1.25293			0.626466	−	0.779449i	$-0.284501\pi$
$683$	32.7445			1.25293			0.626466	+	0.779449i	$0.284501\pi$
$684$		0			0
$685$	−5.81966			−0.222358
$686$	−9.82084	−	17.0102i	−0.374961	−	0.649452i
$687$	−2.40414	−	4.16410i	−0.0917237	−	0.158870i
$688$	−7.53444	+	13.0500i	−0.287248	+	0.497528i
$689$	−0.690983	−	1.19682i	−0.0263244	−	0.0455951i
$690$	−2.23607	+	3.87298i	−0.0851257	+	0.147442i
$691$	46.3050			1.76152			0.880762	−	0.473560i	$-0.157031\pi$
$691$	46.3050			1.76152			0.880762	+	0.473560i	$0.157031\pi$
$692$	9.61657			0.365567
$693$	12.3992	−	21.4760i	0.471006	−	0.815807i
$694$	−14.5964	+	25.2816i	−0.554070	+	0.959678i
$695$	−1.12461			−0.0426590
$696$	9.51057			0.360497
$697$	11.4127	−	19.7673i	0.432286	−	0.748741i
$698$	6.69015	+	11.5877i	0.253226	+	0.438600i
$699$	−7.91872	+	13.7156i	−0.299514	+	0.518773i
$700$	4.54508	+	7.87232i	0.171788	+	0.297546i
$701$	16.8713	+	29.2220i	0.637221	+	1.10370i	0.986040	+	0.166509i	$0.0532495\pi$
$701$	16.8713	+	29.2220i	0.637221	+	1.10370i	−0.348819	+	0.937190i	$0.613417\pi$
$702$	−19.6417			−0.741327
$703$		0			0
$704$	−31.5066			−1.18745
$705$	1.83660	+	3.18109i	0.0691704	+	0.119807i
$706$	16.2335	+	28.1172i	0.610955	+	1.05820i
$707$	−29.5344	+	51.1552i	−1.11076	+	1.92389i
$708$	1.01722	+	1.76188i	0.0382295	+	0.0662154i
$709$	−6.70820	+	11.6190i	−0.251932	+	0.436359i	−0.964058	−	0.265693i	$-0.914399\pi$
$709$	−6.70820	+	11.6190i	−0.251932	+	0.436359i	0.712126	+	0.702052i	$0.247733\pi$
$710$	17.6393			0.661992
$711$	−12.3107			−0.461689
$712$	−27.2984	+	47.2822i	−1.02305	+	1.77197i
$713$	1.53884	−	2.66535i	0.0576301	−	0.0998182i
$714$	14.4721			0.541606
$715$	13.7638			0.514738
$716$	5.65334	−	9.79187i	0.211275	−	0.365939i
$717$	9.31881	+	16.1406i	0.348017	+	0.602784i
$718$	−22.1113	+	38.2979i	−0.825187	+	1.42927i
$719$	−6.19098	−	10.7231i	−0.230885	−	0.399904i	0.727184	−	0.686443i	$-0.240829\pi$
$719$	−6.19098	−	10.7231i	−0.230885	−	0.399904i	−0.958069	+	0.286539i	$0.907495\pi$
$720$	−2.38197	−	4.12569i	−0.0887706	−	0.153755i
$721$	4.25325			0.158399
$722$		0			0
$723$	26.6312			0.990425
$724$	−7.60845	−	13.1782i	−0.282766	−	0.489765i
$725$	4.56352	+	7.90426i	0.169485	+	0.293557i
$726$	1.44427	−	2.50155i	0.0536020	−	0.0928413i
$727$	9.52786	+	16.5027i	0.353369	+	0.612053i	0.986837	−	0.161716i	$-0.0517027\pi$
$727$	9.52786	+	16.5027i	0.353369	+	0.612053i	−0.633468	+	0.773768i	$0.718369\pi$
$728$	−20.0623	+	34.7489i	−0.743559	+	1.28788i
$729$	21.6180			0.800668
$730$	−13.0778			−0.484030
$731$	7.81966	−	13.5440i	0.289221	−	0.500945i
$732$	−0.191758	+	0.332134i	−0.00708757	+	0.0122760i
$733$	35.1803			1.29942			0.649708	−	0.760184i	$-0.274891\pi$
$733$	35.1803			1.29942			0.649708	+	0.760184i	$0.274891\pi$
$734$	−25.2420			−0.931700
$735$	−7.95148	+	13.7724i	−0.293295	+	0.508001i
$736$	−4.39201	−	7.60719i	−0.161892	−	0.280405i
$737$	0.310271	−	0.537405i	0.0114290	−	0.0197956i
$738$	8.78115	+	15.2094i	0.323239	+	0.559866i
$739$	−5.26393	−	9.11740i	−0.193637	−	0.335389i	0.752816	−	0.658231i	$-0.228695\pi$
$739$	−5.26393	−	9.11740i	−0.193637	−	0.335389i	−0.946453	+	0.322842i	$0.895362\pi$
$740$	−4.91428			−0.180653
$741$		0			0
$742$	−2.23607			−0.0820886
$743$	−2.15938	−	3.74016i	−0.0792201	−	0.137213i	0.823694	−	0.567035i	$-0.191910\pi$
$743$	−2.15938	−	3.74016i	−0.0792201	−	0.137213i	−0.902914	+	0.429822i	$0.858576\pi$
$744$	−2.12663	−	3.68343i	−0.0779659	−	0.135041i
$745$	14.2361	−	24.6576i	0.521569	−	0.903384i
$746$	−2.53851	−	4.39682i	−0.0929414	−	0.160979i
$747$	1.00000	−	1.73205i	0.0365881	−	0.0633724i
$748$	5.52786			0.202119
$749$	−49.0714			−1.79303
$750$	−7.23607	+	12.5332i	−0.264224	+	0.457649i
$751$	−22.1316	+	38.3330i	−0.807592	+	1.39879i	0.106934	+	0.994266i	$0.465897\pi$
$751$	−22.1316	+	38.3330i	−0.807592	+	1.39879i	−0.914527	+	0.404525i	$0.867437\pi$
$752$	6.02129			0.219574
$753$	12.2452			0.446241
$754$	−4.75528	+	8.23639i	−0.173177	+	0.299952i
$755$	−1.51860	−	2.63029i	−0.0552674	−	0.0957260i
$756$	7.10642	−	12.3087i	0.258458	−	0.447663i
$757$	1.86475	+	3.22983i	0.0677753	+	0.117390i	0.897922	−	0.440155i	$-0.145077\pi$
$757$	1.86475	+	3.22983i	0.0677753	+	0.117390i	−0.830146	+	0.557545i	$0.811743\pi$
$758$	−4.67376	−	8.09519i	−0.169759	−	0.294031i
$759$	11.1352			0.404181
$760$		0			0
$761$	−6.05573			−0.219520			−0.109760	−	0.993958i	$-0.535008\pi$
$761$	−6.05573			−0.219520			−0.109760	+	0.993958i	$0.535008\pi$
$762$	−11.0167	−	19.0814i	−0.399091	−	0.691246i
$763$	1.53884	+	2.66535i	0.0557098	+	0.0964922i
$764$	−5.25329	+	9.09896i	−0.190057	+	0.329189i
$765$	2.47214	+	4.28187i	0.0893803	+	0.154811i
$766$	8.25329	−	14.2951i	0.298203	−	0.516504i
$767$	−8.61803			−0.311179
$768$	−15.6004			−0.562932
$769$	18.0795	−	31.3147i	0.651964	−	1.12924i	−0.330681	−	0.943743i	$-0.607278\pi$
$769$	18.0795	−	31.3147i	0.651964	−	1.12924i	0.982646	−	0.185493i	$-0.0593882\pi$
$770$	11.1352	−	19.2867i	0.401283	−	0.695043i
$771$	10.6525			0.383640
$772$	3.24920			0.116941
$773$	−18.5191	+	32.0760i	−0.666086	+	1.15369i	0.312904	+	0.949785i	$0.398698\pi$
$773$	−18.5191	+	32.0760i	−0.666086	+	1.15369i	−0.978990	+	0.203910i	$0.934635\pi$
$774$	6.01661	+	10.4211i	0.216263	+	0.374578i
$775$	2.04087	−	3.53489i	0.0733102	−	0.126977i
$776$	−24.1074	−	41.7552i	−0.865405	−	1.49893i
$777$	16.0172	+	27.7426i	0.574615	+	0.995262i
$778$	−15.3884			−0.551702
$779$		0			0
$780$	2.76393			0.0989646
$781$	−21.9601	−	38.0359i	−0.785793	−	1.36103i
$782$	−3.80423	−	6.58911i	−0.136039	−	0.235626i
$783$	7.13525	−	12.3586i	0.254993	−	0.441661i
$784$	13.0344	+	22.5763i	0.465516	+	0.806297i
$785$	−9.61803	+	16.6589i	−0.343282	+	0.594582i
$786$	7.03444			0.250910
$787$	14.3188			0.510412			0.255206	−	0.966887i	$-0.417857\pi$
$787$	14.3188			0.510412			0.255206	+	0.966887i	$0.417857\pi$
$788$	0.781153	−	1.35300i	0.0278274	−	0.0481985i
$789$	−6.98791	+	12.1034i	−0.248776	+	0.430893i
$790$	−11.0557			−0.393345
$791$		0			0
$792$	−9.00854	+	15.6032i	−0.320104	+	0.554437i
$793$	−0.812299	−	1.40694i	−0.0288456	−	0.0499620i
$794$	8.64527	−	14.9740i	0.306809	−	0.531409i
$795$	0.326238	+	0.565061i	0.0115705	+	0.0200406i
$796$	−5.85410	−	10.1396i	−0.207493	−	0.359389i
$797$	−12.8658			−0.455729			−0.227864	−	0.973693i	$-0.573174\pi$
$797$	−12.8658			−0.455729			−0.227864	+	0.973693i	$0.573174\pi$
$798$		0			0
$799$	−6.24922			−0.221082
$800$	−5.82485	−	10.0889i	−0.205940	−	0.356698i
$801$	14.3516	+	24.8577i	0.507089	+	0.878304i
$802$	−4.47214	+	7.74597i	−0.157917	+	0.273520i
$803$	16.2812	+	28.1998i	0.574549	+	0.995149i
$804$	0.0623059	−	0.107917i	0.00219736	−	0.00380594i
$805$	13.7082			0.483151
$806$	4.25325			0.149814
$807$	4.53444	−	7.85388i	0.159620	−	0.276470i
$808$	21.4580	−	37.1664i	0.754891	−	1.30751i
$809$	−0.729490			−0.0256475			−0.0128238	−	0.999918i	$-0.504082\pi$
$809$	−0.729490			−0.0256475			−0.0128238	+	0.999918i	$0.504082\pi$
$810$	2.22012			0.0780069
$811$	−16.0620	+	27.8201i	−0.564012	+	0.976897i	0.433129	+	0.901332i	$0.357409\pi$
$811$	−16.0620	+	27.8201i	−0.564012	+	0.976897i	−0.997141	+	0.0755650i	$0.975924\pi$
$812$	−3.44095	−	5.95991i	−0.120754	−	0.209152i
$813$	−8.38800	+	14.5284i	−0.294180	+	0.509534i
$814$	−13.6803	−	23.6950i	−0.479496	−	0.830511i
$815$	−4.03444	−	6.98786i	−0.141320	−	0.244774i
$816$	−6.92240			−0.242332
$817$		0			0
$818$	−25.7771			−0.901275
$819$	10.5474	+	18.2686i	0.368555	+	0.638356i
$820$	−3.52671	−	6.10844i	−0.123158	−	0.213316i
$821$	9.51722	−	16.4843i	0.332153	−	0.575306i	−0.650781	−	0.759266i	$-0.725558\pi$
$821$	9.51722	−	16.4843i	0.332153	−	0.575306i	0.982934	+	0.183960i	$0.0588915\pi$
$822$	−3.25329	−	5.63486i	−0.113471	−	0.196538i
$823$	19.3607	−	33.5337i	0.674871	−	1.16891i	−0.301636	−	0.953423i	$-0.597533\pi$
$823$	19.3607	−	33.5337i	0.674871	−	1.16891i	0.976507	−	0.215487i	$-0.0691340\pi$
$824$	−3.09017			−0.107651
$825$	14.7679			0.514151
$826$	−6.97214	+	12.0761i	−0.242592	+	0.420181i
$827$	7.86572	−	13.6238i	0.273518	−	0.473747i	−0.696242	−	0.717807i	$-0.745146\pi$
$827$	7.86572	−	13.6238i	0.273518	−	0.473747i	0.969760	+	0.244060i	$0.0784794\pi$
$828$	−2.61803			−0.0909830
$829$	−11.6902			−0.406017			−0.203009	−	0.979177i	$-0.565072\pi$
$829$	−11.6902			−0.406017			−0.203009	+	0.979177i	$0.565072\pi$
$830$	0.898056	−	1.55548i	0.0311720	−	0.0539914i
$831$	11.3067	+	19.5837i	0.392224	+	0.679352i
$832$	13.4005	−	23.2104i	0.464580	−	0.804677i
$833$	−13.5279	−	23.4309i	−0.468713	−	0.811834i
$834$	−0.628677	−	1.08890i	−0.0217693	−	0.0377055i
$835$	−8.50651			−0.294380
$836$		0			0
$837$	−6.38197			−0.220593
$838$	−19.6417	−	34.0204i	−0.678510	−	1.17521i
$839$	11.8087	+	20.4533i	0.407682	+	0.706126i	0.994630	−	0.103499i	$-0.0330039\pi$
$839$	11.8087	+	20.4533i	0.407682	+	0.706126i	−0.586948	+	0.809625i	$0.699671\pi$
$840$	9.47214	−	16.4062i	0.326820	−	0.566068i
$841$	11.0451	+	19.1306i	0.380865	+	0.659678i
$842$	−8.31559	+	14.4030i	−0.286574	+	0.496361i
$843$	−5.20163			−0.179154
$844$	11.1352			0.383288
$845$	2.18034	−	3.77646i	0.0750060	−	0.129914i
$846$	2.40414	−	4.16410i	0.0826561	−	0.143165i
$847$	−8.85410			−0.304231
$848$	1.06957			0.0367292
$849$	0.534785	−	0.926274i	0.0183538	−	0.0317897i
$850$	−5.04531	−	8.73873i	−0.173053	−	0.299736i
$851$	8.42075	−	14.5852i	0.288660	−	0.499973i
$852$	−4.40983	−	7.63805i	−0.151078	−	0.261675i
$853$	11.1525	+	19.3167i	0.381853	+	0.661390i	0.991327	−	0.131417i	$-0.0419526\pi$
$853$	11.1525	+	19.3167i	0.381853	+	0.661390i	−0.609474	+	0.792806i	$0.708619\pi$
$854$	−2.62866			−0.0899507
$855$		0			0
$856$	35.6525			1.21858
$857$	10.5271	+	18.2335i	0.359600	+	0.622846i	0.987894	−	0.155130i	$-0.0495798\pi$
$857$	10.5271	+	18.2335i	0.359600	+	0.622846i	−0.628294	+	0.777976i	$0.716246\pi$
$858$	7.69421	+	13.3268i	0.262676	+	0.454968i
$859$	−10.5279	+	18.2348i	−0.359206	+	0.622163i	−0.987828	−	0.155548i	$-0.950286\pi$
$859$	−10.5279	+	18.2348i	−0.359206	+	0.622163i	0.628622	+	0.777711i	$0.283619\pi$
$860$	−2.41641	−	4.18534i	−0.0823988	−	0.142719i
$861$	−22.9894	+	39.8187i	−0.783475	+	1.35702i
$862$	18.7426			0.638377
$863$	27.1846			0.925375			0.462687	−	0.886521i	$-0.346885\pi$
$863$	27.1846			0.925375			0.462687	+	0.886521i	$0.346885\pi$
$864$	−9.10739	+	15.7745i	−0.309840	+	0.536658i
$865$	9.61657	−	16.6564i	0.326973	−	0.566334i
$866$	10.9787			0.373072
$867$	−12.8003			−0.434719
$868$	−1.53884	+	2.66535i	−0.0522317	+	0.0904679i
$869$	13.7638	+	23.8396i	0.466906	+	0.808704i
$870$	2.24514	−	3.88870i	0.0761174	−	0.131839i
$871$	0.263932	+	0.457144i	0.00894300	+	0.0154897i
$872$	−1.11803	−	1.93649i	−0.0378614	−	0.0655779i
$873$	−25.3480			−0.857900
$874$		0			0
$875$	44.3607			1.49966
$876$	3.26944	+	5.66284i	0.110464	+	0.191330i
$877$	−20.6457	−	35.7595i	−0.697157	−	1.20751i	−0.969448	−	0.245296i	$-0.921115\pi$
$877$	−20.6457	−	35.7595i	−0.697157	−	1.20751i	0.272291	−	0.962215i	$-0.412219\pi$
$878$	−6.80902	+	11.7936i	−0.229793	+	0.398013i
$879$	−14.5344	−	25.1744i	−0.490235	−	0.849111i
$880$	−5.32624	+	9.22531i	−0.179547	+	0.310985i
$881$	−55.5755			−1.87238			−0.936192	−	0.351488i	$-0.885676\pi$
$881$	−55.5755			−1.87238			−0.936192	+	0.351488i	$0.885676\pi$
$882$	20.8172			0.700953
$883$	−21.5172	+	37.2689i	−0.724112	+	1.25420i	0.235226	+	0.971941i	$0.424417\pi$
$883$	−21.5172	+	37.2689i	−0.724112	+	1.25420i	−0.959338	+	0.282258i	$0.908916\pi$
$884$	−2.35114	+	4.07230i	−0.0790774	+	0.136966i
$885$	4.06888			0.136774
$886$	8.44100			0.283581
$887$	−13.3148	+	23.0619i	−0.447067	+	0.774343i	−0.998194	−	0.0600789i	$-0.980865\pi$
$887$	−13.3148	+	23.0619i	−0.447067	+	0.774343i	0.551127	+	0.834422i	$0.314198\pi$
$888$	−11.6372	−	20.1562i	−0.390519	−	0.676398i
$889$	−33.7688	+	58.4892i	−1.13257	+	1.96167i
$890$	12.8885	+	22.3236i	0.432025	+	0.748289i
$891$	−2.76393	−	4.78727i	−0.0925952	−	0.160380i
$892$	−8.40051			−0.281270
$893$		0			0
$894$	31.8328			1.06465
$895$	−11.3067	−	19.5837i	−0.377941	−	0.654612i
$896$	−7.46969	−	12.9379i	−0.249545	−	0.432225i
$897$	−4.73607	+	8.20311i	−0.158133	+	0.273894i
$898$	−20.5517	−	35.5965i	−0.685818	−	1.18787i
$899$	−1.54508	+	2.67617i	−0.0515315	+	0.0892551i
$900$	−3.47214			−0.115738
$901$	−1.11006			−0.0369814
$902$	19.6353	−	34.0093i	0.653782	−	1.13238i
$903$	−15.7517	+	27.2827i	−0.524183	+	0.907912i
$904$		0			0
$905$	−30.4338			−1.01165
$906$	1.69784	−	2.94075i	0.0564071	−	0.0976999i
$907$	−6.32688	−	10.9585i	−0.210081	−	0.363870i	0.741659	−	0.670777i	$-0.234039\pi$
$907$	−6.32688	−	10.9585i	−0.210081	−	0.363870i	−0.951740	+	0.306907i	$0.900706\pi$
$908$	−9.18005	+	15.9003i	−0.304651	+	0.527670i
$909$	−11.2812	−	19.5395i	−0.374172	−	0.648085i
$910$	9.47214	+	16.4062i	0.313998	+	0.543861i
$911$	18.3601			0.608297			0.304149	−	0.952625i	$-0.401628\pi$
$911$	18.3601			0.608297			0.304149	+	0.952625i	$0.401628\pi$
$912$		0			0
$913$	−4.47214			−0.148006
$914$	11.5842	+	20.0644i	0.383171	+	0.663672i
$915$	0.383516	+	0.664269i	0.0126786	+	0.0219600i
$916$	1.26393	−	2.18919i	0.0417615	−	0.0723330i
$917$	−10.7812	−	18.6735i	−0.356025	−	0.616653i
$918$	−7.88854	+	13.6634i	−0.260361	+	0.450958i
$919$	−2.63932			−0.0870631			−0.0435316	−	0.999052i	$-0.513861\pi$
$919$	−2.63932			−0.0870631			−0.0435316	+	0.999052i	$0.513861\pi$
$920$	−9.95959			−0.328358
$921$	16.2188	−	28.0919i	0.534429	−	0.925658i
$922$	−20.0907	+	34.7981i	−0.661652	+	1.14601i
$923$	37.3607			1.22974
$924$	−11.1352			−0.366320
$925$	11.1679	−	19.3434i	0.367199	−	0.636007i
$926$	9.90659	+	17.1587i	0.325551	+	0.563871i
$927$	−0.812299	+	1.40694i	−0.0266794	+	0.0462101i
$928$	4.40983	+	7.63805i	0.144760	+	0.250731i
$929$	10.7533	+	18.6252i	0.352804	+	0.611074i	0.986740	−	0.162311i	$-0.0518949\pi$
$929$	10.7533	+	18.6252i	0.352804	+	0.611074i	−0.633936	+	0.773386i	$0.718562\pi$
$930$	−2.00811			−0.0658487
$931$		0			0
$932$	−8.32624			−0.272735
$933$	3.24920	+	5.62777i	0.106374	+	0.184245i
$934$	−0.138757	−	0.240335i	−0.00454028	−	0.00786399i
$935$	5.52786	−	9.57454i	0.180780	−	0.313121i
$936$	−7.66312	−	13.2729i	−0.250477	−	0.433839i
$937$	20.8992	−	36.1985i	0.682747	−	1.18255i	−0.291393	−	0.956604i	$-0.594119\pi$
$937$	20.8992	−	36.1985i	0.682747	−	1.18255i	0.974139	−	0.225948i	$-0.0725481\pi$
$938$	0.854102			0.0278874
$939$	8.95554			0.292253
$940$	−0.965558	+	1.67240i	−0.0314930	+	0.0545475i
$941$	−7.27794	+	12.6058i	−0.237254	+	0.410936i	−0.959925	−	0.280256i	$-0.909581\pi$
$941$	−7.27794	+	12.6058i	−0.237254	+	0.410936i	0.722671	+	0.691192i	$0.242914\pi$
$942$	−21.5066			−0.700722
$943$	24.1724			0.787163
$944$	3.33495	−	5.77631i	0.108543	−	0.188003i
$945$	−14.2128	−	24.6174i	−0.462344	−	0.800803i
$946$	13.4535	−	23.3022i	0.437413	−	0.757621i
$947$	2.90983	+	5.03997i	0.0945568	+	0.163777i	0.909424	−	0.415871i	$-0.136523\pi$
$947$	2.90983	+	5.03997i	0.0945568	+	0.163777i	−0.814867	+	0.579648i	$0.803190\pi$
$948$	2.76393	+	4.78727i	0.0897683	+	0.155483i
$949$	−27.6992			−0.899153
$950$		0			0
$951$	10.4033			0.337349
$952$	16.1150	+	27.9119i	0.522289	+	0.904631i
$953$	−18.6579	−	32.3164i	−0.604387	−	1.04683i	−0.992148	−	0.125069i	$-0.960085\pi$
$953$	−18.6579	−	32.3164i	−0.604387	−	1.04683i	0.387761	−	0.921760i	$-0.373249\pi$
$954$	0.427051	−	0.739674i	0.0138263	−	0.0239478i
$955$	10.5066	+	18.1979i	0.339985	+	0.588871i
$956$	−4.89919	+	8.48564i	−0.158451	+	0.274445i
$957$	−11.1803			−0.361409
$958$	31.8464			1.02891
$959$	−9.97214	+	17.2722i	−0.322017	+	0.557750i
$960$	−6.32688	+	10.9585i	−0.204199	+	0.353683i
$961$	−29.6180			−0.955420
$962$	23.2744			0.750396
$963$	9.37181	−	16.2324i	0.302002	−	0.523083i
$964$	7.00042	+	12.1251i	0.225468	+	0.390523i
$965$	3.24920	−	5.62777i	0.104595	−	0.181164i
$966$	7.66312	+	13.2729i	0.246557	+	0.427049i
$967$	−16.8541	−	29.1922i	−0.541991	−	0.938757i	−0.998790	−	0.0491863i	$-0.984337\pi$
$967$	−16.8541	−	29.1922i	−0.541991	−	0.938757i	0.456798	−	0.889570i	$-0.348996\pi$
$968$	6.43288			0.206761
$969$		0			0
$970$	−22.7639			−0.730906
$971$	8.53926	+	14.7904i	0.274038	+	0.474648i	0.969892	−	0.243536i	$-0.0783072\pi$
$971$	8.53926	+	14.7904i	0.274038	+	0.474648i	−0.695854	+	0.718183i	$0.744974\pi$
$972$	4.47777	+	7.75572i	0.143624	+	0.248765i
$973$	−1.92705	+	3.33775i	−0.0617784	+	0.107003i
$974$	9.14590	+	15.8412i	0.293053	+	0.507584i
$975$	−6.28115	+	10.8793i	−0.201158	+	0.348416i
$976$	1.25735			0.0402469
$977$	−28.2542			−0.903931			−0.451966	−	0.892035i	$-0.649277\pi$
$977$	−28.2542			−0.903931			−0.451966	+	0.892035i	$0.649277\pi$
$978$	4.51064	−	7.81266i	0.144234	−	0.249821i
$979$	32.0912	−	55.5835i	1.02564	−	1.77646i
$980$	−8.36068			−0.267072
$981$	−1.17557			−0.0375331
$982$	−9.56357	+	16.5646i	−0.305186	+	0.528597i
$983$	10.8046	+	18.7142i	0.344615	+	0.596890i	0.985284	−	0.170927i	$-0.0546762\pi$
$983$	10.8046	+	18.7142i	0.344615	+	0.596890i	−0.640669	+	0.767817i	$0.721343\pi$
$984$	16.7027	−	28.9300i	0.532464	−	0.922255i
$985$	−1.56231	−	2.70599i	−0.0497792	−	0.0862201i
$986$	3.81966	+	6.61585i	0.121643	+	0.210691i
$987$	12.5882			0.400688
$988$		0			0
$989$	16.5623			0.526651
$990$	4.25325	+	7.36685i	0.135177	+	0.234134i
$991$	−10.5271	−	18.2335i	−0.334405	−	0.579207i	0.648965	−	0.760818i	$-0.275202\pi$
$991$	−10.5271	−	18.2335i	−0.334405	−	0.579207i	−0.983370	+	0.181611i	$0.941869\pi$
$992$	1.97214	−	3.41584i	0.0626154	−	0.108453i
$993$	14.2705	+	24.7172i	0.452861	+	0.784378i
$994$	30.2254	−	52.3520i	0.958692	−	1.66050i
$995$	−23.4164			−0.742350
$996$	−0.898056			−0.0284560
$997$	−3.56231	+	6.17009i	−0.112819	+	0.195409i	−0.916906	−	0.399103i	$-0.869321\pi$
$997$	−3.56231	+	6.17009i	−0.112819	+	0.195409i	0.804087	+	0.594512i	$0.202655\pi$
$998$	12.6538	−	21.9170i	0.400548	−	0.693769i
$999$	−34.9230			−1.10491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.j.292.3		8
19.2	odd	18		361.2.e.m.28.3		24
19.3	odd	18		361.2.e.m.234.3		24
19.4	even	9		361.2.e.m.245.2		24
19.5	even	9		361.2.e.m.99.3		24
19.6	even	9		361.2.e.m.62.3		24
19.7	even	3		361.2.a.i.1.2	✓	4
19.8	odd	6	inner	361.2.c.j.68.2		8
19.9	even	9		361.2.e.m.54.2		24
19.10	odd	18		361.2.e.m.54.3		24
19.11	even	3	inner	361.2.c.j.68.3		8
19.12	odd	6		361.2.a.i.1.3	yes	4
19.13	odd	18		361.2.e.m.62.2		24
19.14	odd	18		361.2.e.m.99.2		24
19.15	odd	18		361.2.e.m.245.3		24
19.16	even	9		361.2.e.m.234.2		24
19.17	even	9		361.2.e.m.28.2		24
19.18	odd	2	inner	361.2.c.j.292.2		8
57.26	odd	6		3249.2.a.bc.1.3		4
57.50	even	6		3249.2.a.bc.1.2		4
76.7	odd	6		5776.2.a.bu.1.2		4
76.31	even	6		5776.2.a.bu.1.3		4
95.64	even	6		9025.2.a.bj.1.3		4
95.69	odd	6		9025.2.a.bj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.2	✓	4	19.7	even	3
361.2.a.i.1.3	yes	4	19.12	odd	6
361.2.c.j.68.2		8	19.8	odd	6	inner
361.2.c.j.68.3		8	19.11	even	3	inner
361.2.c.j.292.2		8	19.18	odd	2	inner
361.2.c.j.292.3		8	1.1	even	1	trivial
361.2.e.m.28.2		24	19.17	even	9
361.2.e.m.28.3		24	19.2	odd	18
361.2.e.m.54.2		24	19.9	even	9
361.2.e.m.54.3		24	19.10	odd	18
361.2.e.m.62.2		24	19.13	odd	18
361.2.e.m.62.3		24	19.6	even	9
361.2.e.m.99.2		24	19.14	odd	18
361.2.e.m.99.3		24	19.5	even	9
361.2.e.m.234.2		24	19.16	even	9
361.2.e.m.234.3		24	19.3	odd	18
361.2.e.m.245.2		24	19.4	even	9
361.2.e.m.245.3		24	19.15	odd	18
3249.2.a.bc.1.2		4	57.50	even	6
3249.2.a.bc.1.3		4	57.26	odd	6
5776.2.a.bu.1.2		4	76.7	odd	6
5776.2.a.bu.1.3		4	76.31	even	6
9025.2.a.bj.1.2		4	95.69	odd	6
9025.2.a.bj.1.3		4	95.64	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 1.01807i) q^{2} +(-0.587785 - 1.01807i) q^{3} +(0.309017 - 0.535233i) q^{4} +(-0.618034 - 1.07047i) q^{5} +(0.690983 - 1.19682i) q^{6} -4.23607 q^{7} +3.07768 q^{8} +(0.809017 - 1.40126i) q^{9} +(0.726543 - 1.25841i) q^{10} -3.61803 q^{11} -0.726543 q^{12} +(1.53884 - 2.66535i) q^{13} +(-2.48990 - 4.31263i) q^{14} +(-0.726543 + 1.25841i) q^{15} +(1.19098 + 2.06284i) q^{16} +(-1.23607 - 2.14093i) q^{17} +1.90211 q^{18} -0.763932 q^{20} +(2.48990 + 4.31263i) q^{21} +(-2.12663 - 3.68343i) q^{22} +(1.30902 - 2.26728i) q^{23} +(-1.80902 - 3.13331i) q^{24} +(1.73607 - 3.00696i) q^{25} +3.61803 q^{26} -5.42882 q^{27} +(-1.30902 + 2.26728i) q^{28} +(-1.31433 + 2.27648i) q^{29} -1.70820 q^{30} +1.17557 q^{31} +(1.67760 - 2.90569i) q^{32} +(2.12663 + 3.68343i) q^{33} +(1.45309 - 2.51682i) q^{34} +(2.61803 + 4.53457i) q^{35} +(-0.500000 - 0.866025i) q^{36} +6.43288 q^{37} -3.61803 q^{39} +(-1.90211 - 3.29456i) q^{40} +(4.61653 + 7.99606i) q^{41} +(-2.92705 + 5.06980i) q^{42} +(3.16312 + 5.47868i) q^{43} +(-1.11803 + 1.93649i) q^{44} -2.00000 q^{45} +3.07768 q^{46} +(1.26393 - 2.18919i) q^{47} +(1.40008 - 2.42502i) q^{48} +10.9443 q^{49} +4.08174 q^{50} +(-1.45309 + 2.51682i) q^{51} +(-0.951057 - 1.64728i) q^{52} +(0.224514 - 0.388870i) q^{53} +(-3.19098 - 5.52694i) q^{54} +(2.23607 + 3.87298i) q^{55} -13.0373 q^{56} -3.09017 q^{58} +(-1.40008 - 2.42502i) q^{59} +(0.449028 + 0.777739i) q^{60} +(0.263932 - 0.457144i) q^{61} +(0.690983 + 1.19682i) q^{62} +(-3.42705 + 5.93583i) q^{63} +8.70820 q^{64} -3.80423 q^{65} +(-2.50000 + 4.33013i) q^{66} +(-0.0857567 + 0.148535i) q^{67} -1.52786 q^{68} -3.07768 q^{69} +(-3.07768 + 5.33070i) q^{70} +(6.06961 + 10.5129i) q^{71} +(2.48990 - 4.31263i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(3.78115 + 6.54915i) q^{74} -4.08174 q^{75} +15.3262 q^{77} +(-2.12663 - 3.68343i) q^{78} +(-3.80423 - 6.58911i) q^{79} +(1.47214 - 2.54981i) q^{80} +(0.763932 + 1.32317i) q^{81} +(-5.42705 + 9.39993i) q^{82} +1.23607 q^{83} +3.07768 q^{84} +(-1.52786 + 2.64634i) q^{85} +(-3.71847 + 6.44058i) q^{86} +3.09017 q^{87} -11.1352 q^{88} +(-8.86978 + 15.3629i) q^{89} +(-1.17557 - 2.03615i) q^{90} +(-6.51864 + 11.2906i) q^{91} +(-0.809017 - 1.40126i) q^{92} +(-0.690983 - 1.19682i) q^{93} +2.97168 q^{94} -3.94427 q^{96} +(-7.83297 - 13.5671i) q^{97} +(6.43288 + 11.1421i) q^{98} +(-2.92705 + 5.06980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} + 10 q^{6} - 16 q^{7} + 2 q^{9} - 20 q^{11} + 14 q^{16} + 8 q^{17} - 24 q^{20} + 6 q^{23} - 10 q^{24} - 4 q^{25} + 20 q^{26} - 6 q^{28} + 40 q^{30} + 12 q^{35} - 4 q^{36} - 20 q^{39}+ \cdots - 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 + 10 * q^6 - 16 * q^7 + 2 * q^9 - 20 * q^11 + 14 * q^16 + 8 * q^17 - 24 * q^20 + 6 * q^23 - 10 * q^24 - 4 * q^25 + 20 * q^26 - 6 * q^28 + 40 * q^30 + 12 * q^35 - 4 * q^36 - 20 * q^39 - 10 * q^42 - 6 * q^43 - 16 * q^45 + 28 * q^47 + 16 * q^49 - 30 * q^54 + 20 * q^58 + 20 * q^61 + 10 * q^62 - 14 * q^63 + 16 * q^64 - 20 * q^66 - 48 * q^68 - 36 * q^73 - 10 * q^74 + 60 * q^77 - 24 * q^80 + 24 * q^81 - 30 * q^82 - 8 * q^83 - 48 * q^85 - 20 * q^87 - 2 * q^92 - 10 * q^93 + 40 * q^96 - 10 * q^99

Introduction

L-functions

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