LMFDB - Embedded newform 392.2.m.h.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(19,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,0,4,0,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9640188644209402576896.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Root			$1.01214 - 0.987711i$ of defining polynomial
Character	$\chi$	$=$	392.19
Dual form			392.2.m.h.227.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0345453 + 1.41379i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(-1.99761 + 0.0976797i) q^{4} +(1.92538 - 3.33486i) q^{5} +(-1.36145 - 2.23044i) q^{6} +(-0.207107 - 2.82083i) q^{8} +(0.207107 - 0.358719i) q^{9} +(4.78132 + 2.60689i) q^{10} +(2.12132 + 3.67423i) q^{11} +(3.10635 - 2.00186i) q^{12} +3.85077 q^{13} +7.11529i q^{15} +(3.98092 - 0.390252i) q^{16} +(0.274552 - 0.158513i) q^{17} +(0.514309 + 0.280414i) q^{18} +(2.53759 + 1.46508i) q^{19} +(-3.52043 + 6.84984i) q^{20} +(-5.12132 + 3.12603i) q^{22} +(2.55239 + 1.47363i) q^{23} +(2.93752 + 4.32258i) q^{24} +(-4.91421 - 8.51167i) q^{25} +(0.133026 + 5.44419i) q^{26} -4.77791i q^{27} +2.94725i q^{29} +(-10.0595 + 0.245800i) q^{30} +(-1.12786 - 1.95352i) q^{31} +(0.689257 + 5.61471i) q^{32} +(-6.78910 - 3.91969i) q^{33} +(0.233588 + 0.382683i) q^{34} +(-0.378680 + 0.736813i) q^{36} +(6.16203 + 3.55765i) q^{37} +(-1.98365 + 3.63823i) q^{38} +(-6.16203 + 3.55765i) q^{39} +(-9.80586 - 4.74052i) q^{40} -1.39942i q^{41} +5.41421 q^{43} +(-4.59648 - 7.13249i) q^{44} +(-0.797521 - 1.38135i) q^{45} +(-1.99523 + 3.65946i) q^{46} +(-3.85077 + 6.66973i) q^{47} +(-6.00974 + 4.30237i) q^{48} +(11.8640 - 7.24171i) q^{50} +(-0.292893 + 0.507306i) q^{51} +(-7.69235 + 0.376142i) q^{52} +(8.71442 - 5.03127i) q^{53} +(6.75497 - 0.165054i) q^{54} +16.3374 q^{55} -5.41421 q^{57} +(-4.16680 + 0.101814i) q^{58} +(-0.113723 + 0.0656581i) q^{59} +(-0.695020 - 14.2136i) q^{60} +(-0.797521 + 1.38135i) q^{61} +(2.72291 - 1.66205i) q^{62} +(-7.91421 + 1.16843i) q^{64} +(7.41421 - 12.8418i) q^{65} +(5.30709 - 9.73378i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-0.532965 + 0.343465i) q^{68} -5.44581 q^{69} -15.9570i q^{71} +(-1.05478 - 0.509921i) q^{72} +(-2.53759 + 1.46508i) q^{73} +(-4.81690 + 8.83472i) q^{74} +(15.7275 + 9.08028i) q^{75} +(-5.21222 - 2.67878i) q^{76} +(-5.24264 - 8.58892i) q^{78} +(-5.10479 - 2.94725i) q^{79} +(6.36336 - 14.0272i) q^{80} +(5.03553 + 8.72180i) q^{81} +(1.97848 - 0.0483433i) q^{82} -3.82683i q^{83} -1.22079i q^{85} +(0.187036 + 7.65457i) q^{86} +(-2.72291 - 4.71621i) q^{87} +(9.92507 - 6.74485i) q^{88} +(-8.38931 - 4.84357i) q^{89} +(1.92538 - 1.17525i) q^{90} +(-5.24264 - 2.69442i) q^{92} +(3.60963 + 2.08402i) q^{93} +(-9.56263 - 5.21378i) q^{94} +(9.77166 - 5.64167i) q^{95} +(-6.29027 - 8.34790i) q^{96} +16.6298i q^{97} +1.75736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 8 q^{9} - 4 q^{16} + 4 q^{18} - 48 q^{22} - 56 q^{25} - 8 q^{30} + 36 q^{32} - 40 q^{36} + 64 q^{43} + 48 q^{44} + 40 q^{46} + 88 q^{50} - 16 q^{51} - 64 q^{57} - 40 q^{58}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 8 * q^9 - 4 * q^16 + 4 * q^18 - 48 * q^22 - 56 * q^25 - 8 * q^30 + 36 * q^32 - 40 * q^36 + 64 * q^43 + 48 * q^44 + 40 * q^46 + 88 * q^50 - 16 * q^51 - 64 * q^57 - 40 * q^58 - 56 * q^60 - 104 * q^64 + 96 * q^65 + 16 * q^67 - 12 * q^72 + 8 * q^74 - 16 * q^78 + 24 * q^81 - 24 * q^86 - 24 * q^88 - 16 * q^92 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.0345453	+	1.41379i	0.0244272	+	0.999702i
$2$	0.0345453	+	1.41379i	0.0244272	+	0.999702i
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.884871	−	0.465837i	$-0.845753\pi$
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.0390089	+	0.999239i	$0.512420\pi$
$4$	−1.99761	+	0.0976797i	−0.998807	+	0.0488398i
$5$	1.92538	−	3.33486i	0.861058	−	1.49140i	−0.00985022	−	0.999951i	$-0.503135\pi$
$5$	1.92538	−	3.33486i	0.861058	−	1.49140i	0.870909	−	0.491445i	$-0.163531\pi$
$6$	−1.36145	−	2.23044i	−0.555811	−	0.910574i
$7$		0			0
$7$		0			0
$8$	−0.207107	−	2.82083i	−0.0732233	−	0.997316i
$9$	0.207107	−	0.358719i	0.0690356	−	0.119573i
$10$	4.78132	+	2.60689i	1.51198	+	0.824371i
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$	3.10635	−	2.00186i	0.896726	−	0.577888i
$13$	3.85077			1.06801			0.534006	−	0.845481i	$-0.320686\pi$
$13$	3.85077			1.06801			0.534006	+	0.845481i	$0.320686\pi$
$14$		0			0
$15$			7.11529i			1.83716i
$16$	3.98092	−	0.390252i	0.995229	−	0.0975631i
$17$	0.274552	−	0.158513i	0.0665886	−	0.0384450i	−0.466336	−	0.884608i	$-0.654426\pi$
$17$	0.274552	−	0.158513i	0.0665886	−	0.0384450i	0.532925	+	0.846163i	$0.321093\pi$
$18$	0.514309	+	0.280414i	0.121224	+	0.0660942i
$19$	2.53759	+	1.46508i	0.582162	+	0.336111i	0.761992	−	0.647586i	$-0.224221\pi$
$19$	2.53759	+	1.46508i	0.582162	+	0.336111i	−0.179830	+	0.983698i	$0.557555\pi$
$20$	−3.52043	+	6.84984i	−0.787191	+	1.53167i
$21$		0			0
$22$	−5.12132	+	3.12603i	−1.09187	+	0.666472i
$23$	2.55239	+	1.47363i	0.532211	+	0.307272i	0.741916	−	0.670492i	$-0.233917\pi$
$23$	2.55239	+	1.47363i	0.532211	+	0.307272i	−0.209705	+	0.977765i	$0.567250\pi$
$24$	2.93752	+	4.32258i	0.599620	+	0.882342i
$25$	−4.91421	−	8.51167i	−0.982843	−	1.70233i
$26$	0.133026	+	5.44419i	0.0260885	+	1.06769i
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$			2.94725i			0.547291i	0.961831	+	0.273645i	$0.0882295\pi$
$29$			2.94725i			0.547291i	−0.961831	+	0.273645i	$0.911771\pi$
$30$	−10.0595	+	0.245800i	−1.83661	+	0.0448767i
$31$	−1.12786	−	1.95352i	−0.202570	−	0.350862i	0.746785	−	0.665065i	$-0.231596\pi$
$31$	−1.12786	−	1.95352i	−0.202570	−	0.350862i	−0.949356	+	0.314203i	$0.898263\pi$
$32$	0.689257	+	5.61471i	0.121845	+	0.992549i
$33$	−6.78910	−	3.91969i	−1.18183	−	0.682330i
$34$	0.233588	+	0.382683i	0.0400601	+	0.0656297i
$35$		0			0
$36$	−0.378680	+	0.736813i	−0.0631133	+	0.122802i
$37$	6.16203	+	3.55765i	1.01303	+	0.584874i	0.912078	−	0.410018i	$-0.134477\pi$
$37$	6.16203	+	3.55765i	1.01303	+	0.584874i	0.100953	+	0.994891i	$0.467811\pi$
$38$	−1.98365	+	3.63823i	−0.321791	+	0.590199i
$39$	−6.16203	+	3.55765i	−0.986714	+	0.569679i
$40$	−9.80586	−	4.74052i	−1.55044	−	0.749542i
$41$		−	1.39942i		−	0.218552i	−0.994011	−	0.109276i	$-0.965147\pi$
$41$		−	1.39942i		−	0.218552i	0.994011	−	0.109276i	$-0.0348533\pi$
$42$		0			0
$43$	5.41421			0.825660			0.412830	−	0.910808i	$-0.364540\pi$
$43$	5.41421			0.825660			0.412830	+	0.910808i	$0.364540\pi$
$44$	−4.59648	−	7.13249i	−0.692945	−	1.07526i
$45$	−0.797521	−	1.38135i	−0.118887	−	0.205919i
$46$	−1.99523	+	3.65946i	−0.294180	+	0.539558i
$47$	−3.85077	+	6.66973i	−0.561692	+	0.972880i	0.435656	+	0.900113i	$0.356516\pi$
$47$	−3.85077	+	6.66973i	−0.561692	+	0.972880i	−0.997349	+	0.0727669i	$0.976817\pi$
$48$	−6.00974	+	4.30237i	−0.867432	+	0.620994i
$49$		0			0
$50$	11.8640	−	7.24171i	1.67782	−	1.02413i
$51$	−0.292893	+	0.507306i	−0.0410133	+	0.0710370i
$52$	−7.69235	+	0.376142i	−1.06674	+	0.0521615i
$53$	8.71442	−	5.03127i	1.19702	−	0.691099i	0.237129	−	0.971478i	$-0.423794\pi$
$53$	8.71442	−	5.03127i	1.19702	−	0.691099i	0.959889	+	0.280380i	$0.0904604\pi$
$54$	6.75497	−	0.165054i	0.919235	−	0.0224610i
$55$	16.3374			2.20294
$56$		0			0
$57$	−5.41421			−0.717130
$58$	−4.16680	+	0.101814i	−0.547128	+	0.0133688i
$59$	−0.113723	+	0.0656581i	−0.0148055	+	0.00854796i	−0.507384	−	0.861720i	$-0.669388\pi$
$59$	−0.113723	+	0.0656581i	−0.0148055	+	0.00854796i	0.492579	+	0.870268i	$0.336054\pi$
$60$	−0.695020	−	14.2136i	−0.0897266	−	1.83497i
$61$	−0.797521	+	1.38135i	−0.102112	+	0.176863i	−0.912555	−	0.408955i	$-0.865893\pi$
$61$	−0.797521	+	1.38135i	−0.102112	+	0.176863i	0.810443	+	0.585818i	$0.199227\pi$
$62$	2.72291	−	1.66205i	0.345809	−	0.211081i
$63$		0			0
$64$	−7.91421	+	1.16843i	−0.989277	+	0.146053i
$65$	7.41421	−	12.8418i	0.919620	−	1.59283i
$66$	5.30709	−	9.73378i	0.653258	−	1.19815i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−0.532965	+	0.343465i	−0.0646315	+	0.0416513i
$69$	−5.44581			−0.655599
$70$		0			0
$71$		−	15.9570i		−	1.89375i	−0.321597	−	0.946877i	$-0.604220\pi$
$71$		−	15.9570i		−	1.89375i	0.321597	−	0.946877i	$-0.395780\pi$
$72$	−1.05478	−	0.509921i	−0.124307	−	0.0600947i
$73$	−2.53759	+	1.46508i	−0.297002	+	0.171474i	−0.641095	−	0.767461i	$-0.721520\pi$
$73$	−2.53759	+	1.46508i	−0.297002	+	0.171474i	0.344093	+	0.938935i	$0.388186\pi$
$74$	−4.81690	+	8.83472i	−0.559954	+	1.02702i
$75$	15.7275	+	9.08028i	1.81606	+	1.04850i
$76$	−5.21222	−	2.67878i	−0.597883	−	0.307278i
$77$		0			0
$78$	−5.24264	−	8.58892i	−0.593612	−	0.972504i
$79$	−5.10479	−	2.94725i	−0.574334	−	0.331592i	0.184545	−	0.982824i	$-0.440919\pi$
$79$	−5.10479	−	2.94725i	−0.574334	−	0.331592i	−0.758878	+	0.651232i	$0.774252\pi$
$80$	6.36336	−	14.0272i	0.711445	−	1.56829i
$81$	5.03553	+	8.72180i	0.559504	+	0.969089i
$82$	1.97848	−	0.0483433i	0.218487	−	0.00533862i
$83$		−	3.82683i		−	0.420050i	−0.977696	−	0.210025i	$-0.932646\pi$
$83$		−	3.82683i		−	0.420050i	0.977696	−	0.210025i	$-0.0673545\pi$
$84$		0			0
$85$		−	1.22079i		−	0.132413i
$86$	0.187036	+	7.65457i	0.0201686	+	0.825413i
$87$	−2.72291	−	4.71621i	−0.291926	−	0.505631i
$88$	9.92507	−	6.74485i	1.05802	−	0.719004i
$89$	−8.38931	−	4.84357i	−0.889265	−	0.513417i	−0.0155628	−	0.999879i	$-0.504954\pi$
$89$	−8.38931	−	4.84357i	−0.889265	−	0.513417i	−0.873702	+	0.486462i	$0.838287\pi$
$90$	1.92538	−	1.17525i	0.202953	−	0.123882i
$91$		0			0
$92$	−5.24264	−	2.69442i	−0.546583	−	0.280912i
$93$	3.60963	+	2.08402i	0.374301	+	0.216103i
$94$	−9.56263	−	5.21378i	−0.986310	−	0.537760i
$95$	9.77166	−	5.64167i	1.00255	−	0.578823i
$96$	−6.29027	−	8.34790i	−0.641998	−	0.852004i
$97$			16.6298i			1.68850i	0.535947	+	0.844252i	$0.319955\pi$
$97$			16.6298i			1.68850i	−0.535947	+	0.844252i	$0.680045\pi$
$98$		0			0
$99$	1.75736			0.176621
$100$	10.6481	+	16.5230i	1.06481	+	1.65230i
$101$	−3.52043	−	6.09756i	−0.350295	−	0.606730i	0.636006	−	0.771684i	$-0.280585\pi$
$101$	−3.52043	−	6.09756i	−0.350295	−	0.606730i	−0.986301	+	0.164955i	$0.947252\pi$
$102$	−0.727343	−	0.396565i	−0.0720177	−	0.0392658i
$103$	2.72291	−	4.71621i	0.268296	−	0.464702i	−0.700126	−	0.714019i	$-0.746873\pi$
$103$	2.72291	−	4.71621i	0.268296	−	0.464702i	0.968422	+	0.249317i	$0.0802062\pi$
$104$	−0.797521	−	10.8624i	−0.0782033	−	1.06514i
$105$		0			0
$106$	7.41421	+	12.1466i	0.720132	+	1.17978i
$107$	−9.65685	+	16.7262i	−0.933563	+	1.61698i	−0.156387	+	0.987696i	$0.549985\pi$
$107$	−9.65685	+	16.7262i	−0.933563	+	1.61698i	−0.777176	+	0.629283i	$0.783349\pi$
$108$	0.466705	+	9.54442i	0.0449087	+	0.918412i
$109$	2.55239	−	1.47363i	0.244475	−	0.141148i	−0.372757	−	0.927929i	$-0.621587\pi$
$109$	2.55239	−	1.47363i	0.244475	−	0.141148i	0.617232	+	0.786781i	$0.288254\pi$
$110$	0.564381	+	23.0977i	0.0538116	+	2.20228i
$111$	−13.1474			−1.24789
$112$		0			0
$113$	1.41421			0.133038			0.0665190	−	0.997785i	$-0.478811\pi$
$113$	1.41421			0.133038			0.0665190	+	0.997785i	$0.478811\pi$
$114$	−0.187036	−	7.65457i	−0.0175175	−	0.716916i
$115$	9.82868	−	5.67459i	0.916530	−	0.529159i
$116$	−0.287887	−	5.88747i	−0.0267296	−	0.546638i
$117$	0.797521	−	1.38135i	0.0737308	−	0.127705i
$118$	−0.0967555	−	0.158513i	−0.00890706	−	0.0145923i
$119$		0			0
$120$	20.0711	−	1.47363i	1.83223	−	0.134523i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	−1.98049	−	1.07981i	−0.179305	−	0.0977613i
$123$	1.29289	+	2.23936i	0.116576	+	0.201916i
$124$	2.44386	+	3.79220i	0.219465	+	0.340550i
$125$	−18.5932			−1.66302
$126$		0			0
$127$			17.1778i			1.52429i	0.647408	+	0.762143i	$0.275853\pi$
$127$			17.1778i			1.52429i	−0.647408	+	0.762143i	$0.724147\pi$
$128$	−1.92531	−	11.1487i	−0.170175	−	0.985414i
$129$	−8.66386	+	5.00208i	−0.762810	+	0.440409i
$130$	18.4117	+	10.0385i	1.61482	+	0.880437i
$131$	−14.4019	−	8.31492i	−1.25830	−	0.726478i	−0.285553	−	0.958363i	$-0.592177\pi$
$131$	−14.4019	−	8.31492i	−1.25830	−	0.726478i	−0.972743	+	0.231885i	$0.925511\pi$
$132$	13.9449	+	7.16687i	1.21375	+	0.623796i
$133$		0			0
$134$	−2.41421	+	1.47363i	−0.208556	+	0.127302i
$135$	−15.9337	−	9.19932i	−1.37135	−	0.791751i
$136$	−0.504000	−	0.741637i	−0.0432176	−	0.0635948i
$137$	−5.77817	−	10.0081i	−0.493663	−	0.855049i	0.506311	−	0.862351i	$-0.331009\pi$
$137$	−5.77817	−	10.0081i	−0.493663	−	0.855049i	−0.999973	+	0.00730221i	$0.997676\pi$
$138$	−0.188127	−	7.69924i	−0.0160144	−	0.655403i
$139$		−	14.4650i		−	1.22691i	−0.789730	−	0.613455i	$-0.789779\pi$
$139$		−	14.4650i		−	1.22691i	0.789730	−	0.613455i	$-0.210221\pi$
$140$		0			0
$141$		−	14.2306i		−	1.19843i
$142$	22.5599	−	0.551241i	1.89319	−	0.0462591i
$143$	8.16872	+	14.1486i	0.683102	+	1.18317i
$144$	0.684484	−	1.50886i	0.0570403	−	0.125738i
$145$	9.82868	+	5.67459i	0.816228	+	0.471249i
$146$	−2.15897	−	3.53701i	−0.178678	−	0.292725i
$147$		0			0
$148$	−12.6569	−	6.50490i	−1.04039	−	0.534699i
$149$	−12.3241	−	7.11529i	−1.00963	−	0.582908i	−0.0985436	−	0.995133i	$-0.531418\pi$
$149$	−12.3241	−	7.11529i	−1.00963	−	0.582908i	−0.911082	+	0.412225i	$0.864752\pi$
$150$	−12.2943	+	22.5491i	−1.00383	+	1.84113i
$151$	−9.77166	+	5.64167i	−0.795206	+	0.459112i	−0.841792	−	0.539802i	$-0.818499\pi$
$151$	−9.77166	+	5.64167i	−0.795206	+	0.459112i	0.0465860	+	0.998914i	$0.485166\pi$
$152$	3.60718	−	7.46154i	0.292581	−	0.605210i
$153$		−	0.131316i		−	0.0106163i
$154$		0			0
$155$	−8.68629			−0.697700
$156$	11.9618	−	7.70871i	0.957713	−	0.617191i
$157$	0.797521	+	1.38135i	0.0636491	+	0.110243i	0.896094	−	0.443864i	$-0.146393\pi$
$157$	0.797521	+	1.38135i	0.0636491	+	0.110243i	−0.832445	+	0.554108i	$0.813060\pi$
$158$	3.99045	−	7.31892i	0.317463	−	0.582262i
$159$	−9.29658	+	16.1021i	−0.737267	+	1.27698i
$160$	20.0514	+	8.51189i	1.58520	+	0.672924i
$161$		0			0
$162$	−12.1569	+	7.42049i	−0.955133	+	0.583009i
$163$	1.29289	−	2.23936i	0.101267	−	0.175400i	−0.810940	−	0.585130i	$-0.801044\pi$
$163$	1.29289	−	2.23936i	0.101267	−	0.175400i	0.912207	+	0.409730i	$0.134377\pi$
$164$	0.136695	+	2.79550i	0.0106741	+	0.218291i
$165$	−26.1433	+	15.0938i	−2.03525	+	1.17505i
$166$	5.41035	−	0.132199i	0.419924	−	0.0102606i
$167$	−10.8916			−0.842819			−0.421409	−	0.906870i	$-0.638464\pi$
$167$	−10.8916			−0.842819			−0.421409	+	0.906870i	$0.638464\pi$
$168$		0			0
$169$	1.82843			0.140648
$170$	1.72594	−	0.0421726i	0.132374	−	0.00323449i
$171$	1.05110	−	0.606854i	0.0803798	−	0.0464073i
$172$	−10.8155	+	0.528859i	−0.824675	+	0.0403251i
$173$	10.0941	−	17.4835i	0.767440	−	1.32925i	−0.171506	−	0.985183i	$-0.554863\pi$
$173$	10.0941	−	17.4835i	0.767440	−	1.32925i	0.938947	−	0.344063i	$-0.111803\pi$
$174$	6.57368	−	4.01254i	0.498349	−	0.304190i
$175$		0			0
$176$	9.87868	+	13.7990i	0.744633	+	1.04014i
$177$	0.121320	−	0.210133i	0.00911900	−	0.0157946i
$178$	6.55799	−	12.0281i	0.491542	−	0.901541i
$179$	−6.82843	−	11.8272i	−0.510381	−	0.884005i	−0.999928	−	0.0120283i	$-0.996171\pi$
$179$	−6.82843	−	11.8272i	−0.510381	−	0.884005i	0.489547	−	0.871977i	$-0.337162\pi$
$180$	1.72807	+	2.68149i	0.128803	+	0.199867i
$181$	11.5523			0.858676			0.429338	−	0.903144i	$-0.358747\pi$
$181$	11.5523			0.858676			0.429338	+	0.903144i	$0.358747\pi$
$182$		0			0
$183$		−	2.94725i		−	0.217867i
$184$	3.62824	−	7.50508i	0.267477	−	0.553282i
$185$	23.7285	−	13.6997i	1.74456	−	1.00722i
$186$	−2.82168	+	5.17526i	−0.206895	+	0.379468i
$187$	1.16483	+	0.672512i	0.0851805	+	0.0491790i
$188$	7.04085	−	13.6997i	0.513507	−	0.999152i
$189$		0			0
$190$	8.31371	+	13.6202i	0.603140	+	0.988113i
$191$	8.71442	+	5.03127i	0.630553	+	0.364050i	0.780966	−	0.624573i	$-0.214727\pi$
$191$	8.71442	+	5.03127i	0.630553	+	0.364050i	−0.150413	+	0.988623i	$0.548060\pi$
$192$	11.5849	−	9.18151i	0.836067	−	0.662618i
$193$	3.29289	+	5.70346i	0.237028	+	0.410544i	0.959860	−	0.280479i	$-0.0904935\pi$
$193$	3.29289	+	5.70346i	0.237028	+	0.410544i	−0.722832	+	0.691023i	$0.757160\pi$
$194$	−23.5111	+	0.574482i	−1.68800	+	0.0412454i
$195$			27.3994i			1.96211i
$196$		0			0
$197$		−	1.72646i		−	0.123005i	−0.998107	−	0.0615026i	$-0.980411\pi$
$197$		−	1.72646i		−	0.123005i	0.998107	−	0.0615026i	$-0.0195892\pi$
$198$	0.0607085	+	2.48454i	0.00431436	+	0.176569i
$199$	4.97863	+	8.62325i	0.352926	+	0.611286i	0.986761	−	0.162183i	$-0.0518534\pi$
$199$	4.97863	+	8.62325i	0.352926	+	0.611286i	−0.633835	+	0.773469i	$0.718520\pi$
$200$	−22.9922	+	15.6250i	−1.62580	+	1.10485i
$201$	−3.20041	−	1.84776i	−0.225740	−	0.130331i
$202$	8.49906	−	5.18779i	0.597992	−	0.365012i
$203$		0			0
$204$	0.535534	−	1.04201i	0.0374949	−	0.0729553i
$205$	−4.66687	−	2.69442i	−0.325948	−	0.188186i
$206$	6.76180	+	3.68670i	0.471117	+	0.256864i
$207$	1.05724	−	0.610396i	0.0734830	−	0.0424254i
$208$	15.3296	−	1.50277i	1.06292	−	0.104198i
$209$			12.4316i			0.859910i
$210$		0			0
$211$	−14.9706			−1.03062			−0.515308	−	0.857005i	$-0.672322\pi$
$211$	−14.9706			−1.03062			−0.515308	+	0.857005i	$0.672322\pi$
$212$	−16.9166	+	10.9018i	−1.16184	+	0.748736i
$213$	14.7424	+	25.5346i	1.01013	+	1.74960i
$214$	−23.9809	−	13.0750i	−1.63930	−	0.893786i
$215$	10.4244	−	18.0557i	0.710941	−	1.23139i
$216$	−13.4777	+	0.989538i	−0.917041	+	0.0673295i
$217$		0			0
$218$	2.17157	+	3.55765i	0.147077	+	0.240954i
$219$	2.70711	−	4.68885i	0.182929	−	0.316843i
$220$	−32.6359	+	1.59583i	−2.20031	+	0.107591i
$221$	1.05724	−	0.610396i	0.0711174	−	0.0410597i
$222$	−0.454179	−	18.5876i	−0.0304825	−	1.24752i
$223$	−5.44581			−0.364678			−0.182339	−	0.983236i	$-0.558367\pi$
$223$	−5.44581			−0.364678			−0.182339	+	0.983236i	$0.558367\pi$
$224$		0			0
$225$	−4.07107			−0.271405
$226$	0.0488544	+	1.99940i	0.00324975	+	0.132998i
$227$	−18.9279	+	10.9280i	−1.25629	+	0.725320i	−0.972351	−	0.233523i	$-0.924975\pi$
$227$	−18.9279	+	10.9280i	−1.25629	+	0.725320i	−0.283939	+	0.958842i	$0.591641\pi$
$228$	10.8155	−	0.528859i	0.716274	−	0.0350245i
$229$	−11.6891	+	20.2462i	−0.772440	+	1.33791i	0.163782	+	0.986497i	$0.447631\pi$
$229$	−11.6891	+	20.2462i	−0.772440	+	1.33791i	−0.936222	+	0.351409i	$0.885703\pi$
$230$	8.36223	+	13.6997i	0.551389	+	0.903330i
$231$		0			0
$232$	8.31371	−	0.610396i	0.545822	−	0.0400744i
$233$	−4.94975	+	8.57321i	−0.324269	+	0.561650i	−0.981364	−	0.192158i	$-0.938452\pi$
$233$	−4.94975	+	8.57321i	−0.324269	+	0.561650i	0.657095	+	0.753807i	$0.271785\pi$
$234$	1.98049	+	1.07981i	0.129468	+	0.0705893i
$235$	14.8284	+	25.6836i	0.967300	+	1.67541i
$236$	0.220761	−	0.142268i	0.0143703	−	0.00926085i
$237$	10.8916			0.707487
$238$		0			0
$239$		−	15.4514i		−	0.999467i	−0.866179	−	0.499733i	$-0.833431\pi$
$239$		−	15.4514i		−	0.999467i	0.866179	−	0.499733i	$-0.166569\pi$
$240$	2.77676	+	28.3254i	0.179239	+	1.82840i
$241$	−15.8883	+	9.17314i	−1.02346	+	0.590894i	−0.915104	−	0.403219i	$-0.867891\pi$
$241$	−15.8883	+	9.17314i	−1.02346	+	0.590894i	−0.108354	+	0.994112i	$0.534558\pi$
$242$	−8.69156	−	4.73885i	−0.558715	−	0.304625i
$243$	−3.70241	−	2.13759i	−0.237510	−	0.137126i
$244$	1.45821	−	2.83730i	0.0933522	−	0.181639i
$245$		0			0
$246$	−3.12132	+	1.90524i	−0.199008	+	0.121474i
$247$	9.77166	+	5.64167i	0.621756	+	0.358971i
$248$	−5.27696	+	3.58611i	−0.335088	+	0.227718i
$249$	3.53553	+	6.12372i	0.224055	+	0.388075i
$250$	−0.642306	−	26.2869i	−0.0406230	−	1.66253i
$251$			11.0322i			0.696344i	0.937431	+	0.348172i	$0.113197\pi$
$251$			11.0322i			0.696344i	−0.937431	+	0.348172i	$0.886803\pi$
$252$		0			0
$253$			12.5041i			0.786128i
$254$	−24.2859	+	0.593413i	−1.52383	+	0.0372341i
$255$	1.12786	+	1.95352i	0.0706296	+	0.122334i
$256$	15.6954	−	3.10712i	0.980963	−	0.194195i
$257$	13.3036	+	7.68087i	0.829859	+	0.479119i	0.853804	−	0.520594i	$-0.174289\pi$
$257$	13.3036	+	7.68087i	0.829859	+	0.479119i	−0.0239455	+	0.999713i	$0.507623\pi$
$258$	−7.37120	−	12.0761i	−0.458911	−	0.751825i
$259$		0			0
$260$	−13.5563	+	26.3772i	−0.840729	+	1.63584i
$261$	1.05724	+	0.610396i	0.0654413	+	0.0377825i
$262$	11.2580	−	20.6485i	0.695524	−	1.27567i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$	−9.65072	+	19.9627i	−0.593961	+	1.22862i
$265$		−	38.7485i		−	2.38030i
$266$		0			0
$267$	17.8995			1.09543
$268$	−2.16680	−	3.36229i	−0.132358	−	0.205384i
$269$	7.37120	+	12.7673i	0.449430	+	0.778435i	0.998349	−	0.0574403i	$-0.0182939\pi$
$269$	7.37120	+	12.7673i	0.449430	+	0.778435i	−0.548919	+	0.835875i	$0.684961\pi$
$270$	12.4555	−	22.8447i	0.758017	−	1.39028i
$271$	6.57368	−	11.3859i	0.399322	−	0.691647i	−0.594320	−	0.804229i	$-0.702579\pi$
$271$	6.57368	−	11.3859i	0.399322	−	0.691647i	0.993642	+	0.112582i	$0.0359121\pi$
$272$	1.03111	−	0.738170i	0.0625202	−	0.0447582i
$273$		0			0
$274$	13.9497	−	8.51487i	0.842735	−	0.514402i
$275$	20.8492	−	36.1119i	1.25726	−	2.17763i
$276$	10.8786	−	0.531945i	0.654816	−	0.0320193i
$277$	26.1433	−	15.0938i	1.57080	−	0.906900i	0.574725	−	0.818347i	$-0.305109\pi$
$277$	26.1433	−	15.0938i	1.57080	−	0.906900i	0.996071	−	0.0885530i	$-0.0282243\pi$
$278$	20.4506	−	0.499699i	1.22654	−	0.0299700i
$279$	−0.934353			−0.0559383
$280$		0			0
$281$	3.07107			0.183205			0.0916023	−	0.995796i	$-0.470801\pi$
$281$	3.07107			0.183205			0.0916023	+	0.995796i	$0.470801\pi$
$282$	20.1191	−	0.491600i	1.19807	−	0.0292743i
$283$	13.2370	−	7.64240i	0.786860	−	0.454294i	−0.0519961	−	0.998647i	$-0.516558\pi$
$283$	13.2370	−	7.64240i	0.786860	−	0.454294i	0.838856	+	0.544354i	$0.183225\pi$
$284$	1.55868	+	31.8760i	0.0924906	+	1.89149i
$285$	−10.4244	+	18.0557i	−0.617491	+	1.06953i
$286$	−19.7210	+	12.0376i	−1.16613	+	0.711800i
$287$		0			0
$288$	2.15685	+	0.915594i	0.127094	+	0.0539519i
$289$	−8.44975	+	14.6354i	−0.497044	+	0.860905i
$290$	−7.68316	+	14.0917i	−0.451171	+	0.827496i
$291$	−15.3640	−	26.6112i	−0.900651	−	1.55997i
$292$	4.92601	−	3.17452i	0.288273	−	0.185775i
$293$	−16.0638			−0.938455			−0.469228	−	0.883077i	$-0.655468\pi$
$293$	−16.0638			−0.938455			−0.469228	+	0.883077i	$0.655468\pi$
$294$		0			0
$295$			0.505668i			0.0294412i
$296$	8.75934	−	18.1189i	0.509126	−	1.05314i
$297$	17.5552	−	10.1355i	1.01865	−	0.588120i
$298$	9.63381	−	17.6694i	0.558071	−	1.02356i
$299$	9.82868	+	5.67459i	0.568407	+	0.328170i
$300$	−32.3044	−	16.6026i	−1.86510	−	0.958554i
$301$		0			0
$302$	−8.31371	−	13.6202i	−0.478400	−	0.783754i
$303$	11.2668	+	6.50490i	0.647262	+	0.373697i
$304$	10.6737	+	4.84205i	0.612177	+	0.277710i
$305$	3.07107	+	5.31925i	0.175849	+	0.304579i
$306$	0.185654	−	0.00453635i	0.0106131	−	0.000259326i
$307$			14.2024i			0.810575i	0.914189	+	0.405287i	$0.132829\pi$
$307$			14.2024i			0.810575i	−0.914189	+	0.405287i	$0.867171\pi$
$308$		0			0
$309$			10.0625i			0.572438i
$310$	−0.300070	−	12.2806i	−0.0170429	−	0.697492i
$311$	−13.1474	−	22.7719i	−0.745518	−	1.29127i	−0.949952	−	0.312395i	$-0.898869\pi$
$311$	−13.1474	−	22.7719i	−0.745518	−	1.29127i	0.204435	−	0.978880i	$-0.434464\pi$
$312$	11.3117	+	16.6452i	0.640401	+	0.942351i
$313$	13.7861	+	7.95943i	0.779238	+	0.449894i	0.836160	−	0.548485i	$-0.184795\pi$
$313$	13.7861	+	7.95943i	0.779238	+	0.449894i	−0.0569219	+	0.998379i	$0.518129\pi$
$314$	−1.92538	+	1.17525i	−0.108656	+	0.0663230i
$315$		0			0
$316$	10.4853	+	5.38883i	0.589843	+	0.303146i
$317$	7.21926	+	4.16804i	0.405474	+	0.234101i	0.688843	−	0.724910i	$-0.258119\pi$
$317$	7.21926	+	4.16804i	0.405474	+	0.234101i	−0.283369	+	0.959011i	$0.591452\pi$
$318$	−23.0862	−	12.5872i	−1.29461	−	0.705854i
$319$	−10.8289	+	6.25206i	−0.606302	+	0.350048i
$320$	−11.3414	+	28.6425i	−0.634001	+	1.60116i
$321$		−	35.6871i		−	1.99186i
$322$		0			0
$323$	0.928932			0.0516872
$324$	−10.9110	−	16.9309i	−0.606166	−	0.940606i
$325$	−18.9235	−	32.7765i	−1.04969	−	1.81811i
$326$	3.21065	+	1.75052i	0.177821	+	0.0969525i
$327$	−2.72291	+	4.71621i	−0.150577	+	0.260807i
$328$	−3.94753	+	0.289829i	−0.217966	+	0.0160031i
$329$		0			0
$330$	−22.2426	−	36.4397i	−1.22442	−	2.00594i
$331$	−5.53553	+	9.58783i	−0.304260	+	0.526995i	−0.977096	−	0.212797i	$-0.931743\pi$
$331$	−5.53553	+	9.58783i	−0.304260	+	0.526995i	0.672836	+	0.739792i	$0.265076\pi$
$332$	0.373804	+	7.64453i	0.0205152	+	0.419548i
$333$	2.55239	−	1.47363i	0.139870	−	0.0807542i
$334$	−0.376254	−	15.3985i	−0.0205877	−	0.842567i
$335$	7.70154			0.420780
$336$		0			0
$337$	−14.1421			−0.770371			−0.385186	−	0.922839i	$-0.625863\pi$
$337$	−14.1421			−0.770371			−0.385186	+	0.922839i	$0.625863\pi$
$338$	0.0631635	+	2.58501i	0.00343564	+	0.140606i
$339$	−2.26303	+	1.30656i	−0.122911	+	0.0709628i
$340$	0.119246	+	2.43867i	0.00646705	+	0.132255i
$341$	4.78512	−	8.28808i	0.259129	−	0.448824i
$342$	0.894276	+	1.46508i	0.0483569	+	0.0792222i
$343$		0			0
$344$	−1.12132	−	15.2726i	−0.0604575	−	0.823443i
$345$	−10.4853	+	18.1610i	−0.564509	+	0.977758i
$346$	25.0667	+	13.6670i	1.34760	+	0.734742i
$347$	−6.12132	−	10.6024i	−0.328610	−	0.569169i	0.653627	−	0.756817i	$-0.273247\pi$
$347$	−6.12132	−	10.6024i	−0.328610	−	0.569169i	−0.982236	+	0.187649i	$0.939913\pi$
$348$	5.89999	+	9.15519i	0.316273	+	0.490770i
$349$	14.7424			0.789142			0.394571	−	0.918865i	$-0.370893\pi$
$349$	14.7424			0.789142			0.394571	+	0.918865i	$0.370893\pi$
$350$		0			0
$351$		−	18.3986i		−	0.982046i
$352$	−19.1676	+	14.4431i	−1.02164	+	0.769819i
$353$	−4.09069	+	2.36176i	−0.217725	+	0.125704i	−0.604897	−	0.796304i	$-0.706786\pi$
$353$	−4.09069	+	2.36176i	−0.217725	+	0.125704i	0.387171	+	0.922008i	$0.373452\pi$
$354$	0.301275	+	0.164263i	0.0160126	+	0.00873046i
$355$	−53.2146	−	30.7235i	−2.82434	−	1.63063i
$356$	17.2317	+	8.85611i	0.913279	+	0.469373i
$357$		0			0
$358$	16.4853	−	10.0625i	0.871274	−	0.531822i
$359$	13.3813	+	7.72569i	0.706237	+	0.407746i	0.809666	−	0.586891i	$-0.199648\pi$
$359$	13.3813	+	7.72569i	0.706237	+	0.407746i	−0.103429	+	0.994637i	$0.532981\pi$
$360$	−3.73138	+	2.53576i	−0.196661	+	0.133646i
$361$	−5.20711	−	9.01897i	−0.274058	−	0.474683i
$362$	0.399078	+	16.3326i	0.0209751	+	0.858420i
$363$		−	12.9343i		−	0.678875i
$364$		0			0
$365$			11.2833i			0.590597i
$366$	4.16680	−	0.101814i	0.217802	−	0.00532188i
$367$	−15.2096	−	26.3437i	−0.793933	−	1.37513i	−0.923515	−	0.383563i	$-0.874697\pi$
$367$	−15.2096	−	26.3437i	−0.793933	−	1.37513i	0.129582	−	0.991569i	$-0.458637\pi$
$368$	10.7360	+	4.87030i	0.559651	+	0.253882i
$369$	−0.501998	−	0.289829i	−0.0261330	−	0.0150879i
$370$	20.1882	+	33.0740i	1.04953	+	1.71943i
$371$		0			0
$372$	−7.41421	−	3.81048i	−0.384409	−	0.197564i
$373$	−14.4385	−	8.33609i	−0.747598	−	0.431626i	0.0772271	−	0.997014i	$-0.475393\pi$
$373$	−14.4385	−	8.33609i	−0.747598	−	0.431626i	−0.824826	+	0.565387i	$0.808727\pi$
$374$	−0.910553	+	1.67005i	−0.0470836	+	0.0863564i
$375$	29.7529	−	17.1778i	1.53643	−	0.887060i
$376$	19.6117	+	9.48104i	1.01140	+	0.488947i
$377$			11.3492i			0.584513i
$378$		0			0
$379$	10.3848			0.533430			0.266715	−	0.963775i	$-0.414062\pi$
$379$	10.3848			0.533430			0.266715	+	0.963775i	$0.414062\pi$
$380$	−18.9689	+	12.2244i	−0.973085	+	0.627097i
$381$	−15.8703	−	27.4881i	−0.813058	−	1.40826i
$382$	−6.81213	+	12.4942i	−0.348539	+	0.639258i
$383$	16.9981	−	29.4416i	0.868563	−	1.50440i	0.00509839	−	0.999987i	$-0.498377\pi$
$383$	16.9981	−	29.4416i	0.868563	−	1.50440i	0.863465	−	0.504409i	$-0.168290\pi$
$384$	13.3809	+	16.0614i	0.682843	+	0.819632i
$385$		0			0
$386$	−7.94975	+	4.85249i	−0.404631	+	0.246985i
$387$	1.12132	−	1.94218i	0.0569999	−	0.0987268i
$388$	−1.62440	−	33.2200i	−0.0824662	−	1.68649i
$389$	−14.8764	+	8.58892i	−0.754266	+	0.435476i	−0.827233	−	0.561859i	$-0.810086\pi$
$389$	−14.8764	+	8.58892i	−0.754266	+	0.435476i	0.0729674	+	0.997334i	$0.476753\pi$
$390$	−38.7370	+	0.946519i	−1.96152	+	0.0479288i
$391$	0.934353			0.0472523
$392$		0			0
$393$	30.7279			1.55002
$394$	2.44085	−	0.0596410i	0.122968	−	0.00300467i
$395$	−19.6574	+	11.3492i	−0.989070	+	0.571040i
$396$	−3.51052	+	0.171658i	−0.176410	+	0.00862615i
$397$	−13.9449	+	24.1532i	−0.699873	+	1.21222i	0.268637	+	0.963241i	$0.413427\pi$
$397$	−13.9449	+	24.1532i	−0.699873	+	1.21222i	−0.968510	+	0.248974i	$0.919907\pi$
$398$	−12.0195	+	7.33664i	−0.602482	+	0.367753i
$399$		0			0
$400$	−22.8848	−	31.9665i	−1.14424	−	1.59832i
$401$	6.07107	−	10.5154i	0.303175	−	0.525114i	−0.673679	−	0.739024i	$-0.735287\pi$
$401$	6.07107	−	10.5154i	0.303175	−	0.525114i	0.976853	+	0.213911i	$0.0686201\pi$
$402$	2.50179	−	4.58855i	0.124778	−	0.228856i
$403$	−4.34315	−	7.52255i	−0.216347	−	0.374725i
$404$	7.62806	+	11.8367i	0.379510	+	0.588897i
$405$	38.7814			1.92706
$406$		0			0
$407$			30.1876i			1.49635i
$408$	1.49169	+	0.721137i	0.0738495	+	0.0357016i
$409$	−18.6063	+	10.7423i	−0.920021	+	0.531174i	−0.883642	−	0.468164i	$-0.844916\pi$
$409$	−18.6063	+	10.7423i	−0.920021	+	0.531174i	−0.0363790	+	0.999338i	$0.511582\pi$
$410$	3.64813	−	6.69106i	0.180168	−	0.330448i
$411$	18.4925	+	10.6767i	0.912170	+	0.526642i
$412$	−4.97863	+	9.68714i	−0.245280	+	0.477251i
$413$		0			0
$414$	0.899495	+	1.47363i	0.0442078	+	0.0724248i
$415$	−12.7620	−	7.36813i	−0.626461	−	0.361687i
$416$	2.65417	+	21.6209i	0.130131	+	1.06005i
$417$	13.3640	+	23.1471i	0.654436	+	1.13352i
$418$	−17.5757	+	0.429452i	−0.859654	+	0.0210052i
$419$			9.94977i			0.486078i	0.970017	+	0.243039i	$0.0781443\pi$
$419$			9.94977i			0.486078i	−0.970017	+	0.243039i	$0.921856\pi$
$420$		0			0
$421$		−	7.62096i		−	0.371423i	−0.982604	−	0.185712i	$-0.940541\pi$
$421$		−	7.62096i		−	0.371423i	0.982604	−	0.185712i	$-0.0594590\pi$
$422$	−0.517162	−	21.1653i	−0.0251751	−	1.03031i
$423$	1.59504	+	2.76269i	0.0775535	+	0.134327i
$424$	−15.9972	−	23.5399i	−0.776893	−	1.14320i
$425$	−2.69841	−	1.55793i	−0.130892	−	0.0755707i
$426$	−35.5913	+	21.7248i	−1.72440	+	1.05257i
$427$		0			0
$428$	17.6569	−	34.3557i	0.853476	−	1.66064i
$429$	−26.1433	−	15.0938i	−1.26221	−	0.728736i
$430$	25.8871	+	14.1143i	1.24839	+	0.680650i
$431$	16.3716	−	9.45215i	0.788592	−	0.455294i	−0.0508743	−	0.998705i	$-0.516201\pi$
$431$	16.3716	−	9.45215i	0.788592	−	0.455294i	0.839467	+	0.543411i	$0.182867\pi$
$432$	−1.86459	−	19.0205i	−0.0897102	−	0.915123i
$433$			18.1606i			0.872741i	0.899767	+	0.436371i	$0.143736\pi$
$433$			18.1606i			0.872741i	−0.899767	+	0.436371i	$0.856264\pi$
$434$		0			0
$435$	−20.9706			−1.00546
$436$	−4.95475	+	3.19305i	−0.237290	+	0.152919i
$437$	4.31795	+	7.47890i	0.206555	+	0.357764i
$438$	6.72257	+	3.66531i	0.321217	+	0.175135i
$439$	−19.7210	+	34.1578i	−0.941233	+	1.63026i	−0.178110	+	0.984011i	$0.556998\pi$
$439$	−19.7210	+	34.1578i	−0.941233	+	1.63026i	−0.763123	+	0.646253i	$0.776335\pi$
$440$	−3.38359	−	46.0852i	−0.161306	−	2.19703i
$441$		0			0
$442$	0.899495	+	1.47363i	0.0427846	+	0.0700932i
$443$	0.514719	−	0.891519i	0.0244550	−	0.0423573i	−0.853539	−	0.521029i	$-0.825548\pi$
$443$	0.514719	−	0.891519i	0.0244550	−	0.0423573i	0.877994	+	0.478672i	$0.158882\pi$
$444$	26.2633	−	1.28423i	1.24640	−	0.0609468i
$445$	−32.3053	+	18.6515i	−1.53142	+	0.884164i
$446$	−0.188127	−	7.69924i	−0.00890807	−	0.364570i
$447$	26.2947			1.24370
$448$		0			0
$449$	36.2843			1.71236			0.856180	−	0.516677i	$-0.172831\pi$
$449$	36.2843			1.71236			0.856180	+	0.516677i	$0.172831\pi$
$450$	−0.140636	−	5.75564i	−0.00662965	−	0.271324i
$451$	5.14179	−	2.96861i	0.242117	−	0.139787i
$452$	−2.82505	+	0.138140i	−0.132879	+	0.00649755i
$453$	10.4244	−	18.0557i	0.489783	−	0.848329i
$454$	−16.1038	−	26.3826i	−0.755791	−	1.23820i
$455$		0			0
$456$	1.12132	+	15.2726i	0.0525106	+	0.715205i
$457$	12.0208	−	20.8207i	0.562310	−	0.973950i	−0.434984	−	0.900438i	$-0.643246\pi$
$457$	12.0208	−	20.8207i	0.562310	−	0.973950i	0.997294	−	0.0735115i	$-0.0234206\pi$
$458$	−29.0277	−	15.8266i	−1.35638	−	0.739528i
$459$	−0.757359	−	1.31178i	−0.0353505	−	0.0612289i
$460$	−19.0796	+	12.2957i	−0.889592	+	0.573290i
$461$	25.6340			1.19389			0.596947	−	0.802280i	$-0.296380\pi$
$461$	25.6340			1.19389			0.596947	+	0.802280i	$0.296380\pi$
$462$		0			0
$463$			12.5041i			0.581116i	0.956857	+	0.290558i	$0.0938409\pi$
$463$			12.5041i			0.581116i	−0.956857	+	0.290558i	$0.906159\pi$
$464$	1.15017	+	11.7328i	0.0533954	+	0.544680i
$465$	13.8999	−	8.02509i	0.644590	−	0.372154i
$466$	−12.2917	−	6.70175i	−0.569403	−	0.310452i
$467$	−20.6419	−	11.9176i	−0.955191	−	0.551480i	−0.0605014	−	0.998168i	$-0.519270\pi$
$467$	−20.6419	−	11.9176i	−0.955191	−	0.551480i	−0.894690	+	0.446688i	$0.852603\pi$
$468$	−1.45821	+	2.83730i	−0.0674057	+	0.131154i
$469$		0			0
$470$	−35.7990	+	21.8516i	−1.65128	+	1.00794i
$471$	−2.55239	−	1.47363i	−0.117608	−	0.0679011i
$472$	0.208763	+	0.307196i	0.00960912	+	0.0141398i
$473$	11.4853	+	19.8931i	0.528094	+	0.914685i
$474$	0.376254	+	15.3985i	0.0172819	+	0.707276i
$475$		−	28.7988i		−	1.32138i
$476$		0			0
$477$		−	4.16804i		−	0.190842i
$478$	21.8450	−	0.533772i	0.999169	−	0.0244142i
$479$	−4.31795	−	7.47890i	−0.197292	−	0.341720i	0.750357	−	0.661032i	$-0.229881\pi$
$479$	−4.31795	−	7.47890i	−0.197292	−	0.341720i	−0.947649	+	0.319312i	$0.896548\pi$
$480$	−39.9503	+	4.90427i	−1.82347	+	0.223848i
$481$	23.7285	+	13.6997i	1.08193	+	0.624652i
$482$	−13.5178	−	22.1459i	−0.615718	−	1.00872i
$483$		0			0
$484$	6.39949	−	12.4518i	0.290886	−	0.565989i
$485$	55.4582	+	32.0188i	2.51823	+	1.45390i
$486$	2.89420	−	5.30828i	0.131284	−	0.240789i
$487$	20.6006	−	11.8937i	0.933500	−	0.538957i	0.0455832	−	0.998961i	$-0.485485\pi$
$487$	20.6006	−	11.8937i	0.933500	−	0.538957i	0.887917	+	0.460004i	$0.152152\pi$
$488$	4.06172	+	1.96359i	0.183865	+	0.0888874i
$489$			4.77791i			0.216065i
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	−2.80144	−	4.34708i	−0.126299	−	0.195981i
$493$	0.467177	+	0.809174i	0.0210406	+	0.0364434i
$494$	−7.63858	+	14.0100i	−0.343676	+	0.630339i
$495$	3.38359	−	5.86055i	0.152081	−	0.263412i
$496$	−5.25230	−	7.33664i	−0.235835	−	0.329425i
$497$		0			0
$498$	−8.53553	+	5.21005i	−0.382486	+	0.233468i
$499$	20.3137	−	35.1844i	0.909366	−	1.57507i	0.0944202	−	0.995532i	$-0.469900\pi$
$499$	20.3137	−	35.1844i	0.909366	−	1.57507i	0.814946	−	0.579537i	$-0.196766\pi$
$500$	37.1419	−	1.81617i	1.66104	−	0.0812217i
$501$	17.4288	−	10.0625i	0.778663	−	0.449561i
$502$	−15.5972	+	0.381109i	−0.696136	+	0.0170097i
$503$	−34.9306			−1.55748			−0.778739	−	0.627348i	$-0.784140\pi$
$503$	−34.9306			−1.55748			−0.778739	+	0.627348i	$0.784140\pi$
$504$		0			0
$505$	−27.1127			−1.20650
$506$	−17.6782	+	0.431959i	−0.785893	+	0.0192029i
$507$	−2.92586	+	1.68925i	−0.129942	+	0.0750221i
$508$	−1.67793	−	34.3147i	−0.0744459	−	1.52247i
$509$	3.05325	−	5.28838i	0.135333	−	0.234403i	−0.790392	−	0.612602i	$-0.790123\pi$
$509$	3.05325	−	5.28838i	0.135333	−	0.234403i	0.925725	+	0.378198i	$0.123456\pi$
$510$	−2.72291	+	1.66205i	−0.120572	+	0.0735968i
$511$		0			0
$512$	4.93503	+	22.0827i	0.218100	+	0.975927i
$513$	7.00000	−	12.1244i	0.309058	−	0.535303i
$514$	−10.3996	+	19.0739i	−0.458705	+	0.841315i
$515$	−10.4853	−	18.1610i	−0.462037	−	0.800271i
$516$	16.8184	−	10.8385i	0.740390	−	0.477139i
$517$	−32.6749			−1.43704
$518$		0			0
$519$			37.3029i			1.63742i
$520$	−37.7601	−	18.2546i	−1.65589	−	0.800519i
$521$	−39.4561	+	22.7800i	−1.72860	+	0.998008i	−0.832759	+	0.553635i	$0.813240\pi$
$521$	−39.4561	+	22.7800i	−1.72860	+	0.998008i	−0.895842	+	0.444373i	$0.853427\pi$
$522$	−0.826450	+	1.51580i	−0.0361727	+	0.0663447i
$523$	3.47496	+	2.00627i	0.151950	+	0.0877281i	0.574047	−	0.818822i	$-0.305373\pi$
$523$	3.47496	+	2.00627i	0.151950	+	0.0877281i	−0.422097	+	0.906550i	$0.638706\pi$
$524$	29.5815	+	15.2032i	1.29228	+	0.664156i
$525$		0			0
$526$		0			0
$527$	−0.619315	−	0.357562i	−0.0269778	−	0.0155756i
$528$	−28.5565	−	12.9545i	−1.24276	−	0.563772i
$529$	−7.15685	−	12.3960i	−0.311168	−	0.538958i
$530$	54.7824	−	1.33858i	2.37959	−	0.0581442i
$531$			0.0543929i			0.00236045i
$532$		0			0
$533$		−	5.38883i		−	0.233416i
$534$	0.618343	+	25.3062i	0.0267583	+	1.09510i
$535$	37.1863	+	64.4086i	1.60770	+	2.78463i
$536$	4.67872	−	3.17955i	0.202090	−	0.137336i
$537$	21.8538	+	12.6173i	0.943060	+	0.544476i
$538$	−17.7956	+	10.8624i	−0.767225	+	0.468311i
$539$		0			0
$540$	32.7279	+	16.8203i	1.40839	+	0.723830i
$541$	6.59995	+	3.81048i	0.283754	+	0.163825i	0.635122	−	0.772412i	$-0.280950\pi$
$541$	6.59995	+	3.81048i	0.283754	+	0.163825i	−0.351368	+	0.936238i	$0.614283\pi$
$542$	16.3244	+	8.90048i	0.701194	+	0.382308i
$543$	−18.4861	+	10.6729i	−0.793314	+	0.458020i
$544$	1.07924	+	1.43227i	0.0462720	+	0.0614082i
$545$		−	11.3492i		−	0.486146i
$546$		0			0
$547$	37.4142			1.59972			0.799858	−	0.600189i	$-0.204908\pi$
$547$	37.4142			1.59972			0.799858	+	0.600189i	$0.204908\pi$
$548$	12.5201	+	19.4279i	0.534834	+	0.829918i
$549$	0.330344	+	0.572172i	0.0140987	+	0.0244197i
$550$	51.7750	+	28.2290i	2.20769	+	1.20369i
$551$	−4.31795	+	7.47890i	−0.183951	+	0.318612i
$552$	1.12786	+	15.3617i	0.0480051	+	0.653839i
$553$		0			0
$554$	22.2426	+	36.4397i	0.944999	+	1.54817i
$555$	−25.3137	+	43.8446i	−1.07451	+	1.86110i
$556$	1.41294	+	28.8956i	0.0599220	+	1.22545i
$557$	6.59995	−	3.81048i	0.279649	−	0.161455i	−0.353616	−	0.935391i	$-0.615048\pi$
$557$	6.59995	−	3.81048i	0.279649	−	0.161455i	0.633264	+	0.773936i	$0.281715\pi$
$558$	−0.0322775	−	1.32098i	−0.00136642	−	0.0559216i
$559$	20.8489			0.881814
$560$		0			0
$561$	−2.48528			−0.104929
$562$	0.106091	+	4.34185i	0.00447517	+	0.183150i
$563$	29.5332	−	17.0510i	1.24467	−	0.718613i	0.274632	−	0.961549i	$-0.411444\pi$
$563$	29.5332	−	17.0510i	1.24467	−	0.718613i	0.970042	+	0.242936i	$0.0781106\pi$
$564$	1.39004	+	28.4272i	0.0585312	+	1.19700i
$565$	2.72291	−	4.71621i	0.114553	−	0.198412i
$566$	11.2620	+	18.4504i	0.473379	+	0.775528i
$567$		0			0
$568$	−45.0122	+	3.30481i	−1.88867	+	0.138667i
$569$	−6.58579	+	11.4069i	−0.276091	+	0.478203i	−0.970410	−	0.241464i	$-0.922372\pi$
$569$	−6.58579	+	11.4069i	−0.276091	+	0.478203i	0.694319	+	0.719667i	$0.255706\pi$
$570$	−25.8871	−	14.1143i	−1.08429	−	0.591181i
$571$	17.1924	+	29.7781i	0.719479	+	1.24617i	0.961206	+	0.275830i	$0.0889527\pi$
$571$	17.1924	+	29.7781i	0.719479	+	1.24617i	−0.241727	+	0.970344i	$0.577714\pi$
$572$	−17.7000	−	27.4656i	−0.740073	−	1.14839i
$573$	−18.5932			−0.776740
$574$		0			0
$575$		−	28.9668i		−	1.20800i
$576$	−1.21995	+	3.08097i	−0.0508312	+	0.128374i
$577$	13.5311	−	7.81218i	0.563307	−	0.325225i	−0.191165	−	0.981558i	$-0.561227\pi$
$577$	13.5311	−	7.81218i	0.563307	−	0.325225i	0.754472	+	0.656333i	$0.227893\pi$
$578$	−20.9833	−	11.4406i	−0.872790	−	0.475866i
$579$	−10.5386	−	6.08447i	−0.437970	−	0.252862i
$580$	−20.1882	−	10.3756i	−0.838269	−	0.430823i
$581$		0			0
$582$	37.0919	−	22.6407i	1.53751	−	0.938488i
$583$	36.9722	+	21.3459i	1.53123	+	0.884056i
$584$	4.65829	+	6.85468i	0.192761	+	0.283649i
$585$	−3.07107	−	5.31925i	−0.126973	−	0.219924i
$586$	−0.554927	−	22.7108i	−0.0229238	−	0.938175i
$587$		−	20.6968i		−	0.854247i	−0.904193	−	0.427124i	$-0.859527\pi$
$587$		−	20.6968i		−	0.854247i	0.904193	−	0.427124i	$-0.140473\pi$
$588$		0			0
$589$		−	6.60963i		−	0.272345i
$590$	−0.714910	+	0.0174685i	−0.0294324	+	0.000719165i
$591$	1.59504	+	2.76269i	0.0656112	+	0.113642i
$592$	25.9189	+	11.7580i	1.06526	+	0.483249i
$593$	−36.8714	−	21.2877i	−1.51413	−	0.874181i	−0.999863	−	0.0165477i	$-0.994732\pi$
$593$	−36.8714	−	21.2877i	−1.51413	−	0.874181i	−0.514262	−	0.857633i	$-0.671934\pi$
$594$	14.9359	+	24.4692i	0.612827	+	1.00398i
$595$		0			0
$596$	25.3137	+	13.0098i	1.03689	+	0.532902i
$597$	−15.9337	−	9.19932i	−0.652122	−	0.376503i
$598$	−7.68316	+	14.0917i	−0.314188	+	0.576254i
$599$	−6.59995	+	3.81048i	−0.269667	+	0.155692i	−0.628736	−	0.777619i	$-0.716427\pi$
$599$	−6.59995	+	3.81048i	−0.269667	+	0.155692i	0.359070	+	0.933311i	$0.383094\pi$
$600$	22.3567	−	46.2453i	0.912708	−	1.88796i
$601$			20.2166i			0.824651i	0.911037	+	0.412325i	$0.135283\pi$
$601$			20.2166i			0.824651i	−0.911037	+	0.412325i	$0.864717\pi$
$602$		0			0
$603$	0.828427			0.0337362
$604$	18.9689	−	12.2244i	0.771834	−	0.497402i
$605$	13.4777	+	23.3441i	0.547946	+	0.949071i
$606$	−8.80736	+	16.1536i	−0.357774	+	0.656197i
$607$	17.9325	−	31.0600i	0.727857	−	1.26068i	−0.229931	−	0.973207i	$-0.573850\pi$
$607$	17.9325	−	31.0600i	0.727857	−	1.26068i	0.957787	−	0.287478i	$-0.0928167\pi$
$608$	−6.47692	+	15.2576i	−0.262674	+	0.618778i
$609$		0			0
$610$	−7.41421	+	4.52560i	−0.300193	+	0.183236i
$611$	−14.8284	+	25.6836i	−0.599894	+	1.03905i
$612$	0.0128269	+	0.262319i	0.000518498	+	0.0106036i
$613$	−26.5812	+	15.3467i	−1.07360	+	0.619845i	−0.929164	−	0.369668i	$-0.879471\pi$
$613$	−26.5812	+	15.3467i	−1.07360	+	0.619845i	−0.144440	+	0.989514i	$0.546138\pi$
$614$	−20.0793	+	0.490626i	−0.810333	+	0.0198001i
$615$	9.95727			0.401516
$616$		0			0
$617$	−23.1716			−0.932852			−0.466426	−	0.884560i	$-0.654459\pi$
$617$	−23.1716			−0.932852			−0.466426	+	0.884560i	$0.654459\pi$
$618$	−14.2263	+	0.347613i	−0.572267	+	0.0139831i
$619$	24.5522	−	14.1752i	0.986836	−	0.569750i	0.0825091	−	0.996590i	$-0.473707\pi$
$619$	24.5522	−	14.1752i	0.986836	−	0.569750i	0.904327	+	0.426840i	$0.140373\pi$
$620$	17.3519	−	0.848474i	0.696867	−	0.0340755i
$621$	7.04085	−	12.1951i	0.282540	−	0.489373i
$622$	31.7405	−	19.3743i	1.27268	−	0.776838i
$623$		0			0
$624$	−23.1421	+	16.5674i	−0.926427	+	0.663229i
$625$	−11.2279	+	19.4473i	−0.449117	+	0.777893i
$626$	−10.7767	+	19.7657i	−0.430725	+	0.789996i
$627$	−11.4853	−	19.8931i	−0.458678	−	0.794454i
$628$	−1.72807	−	2.68149i	−0.0689574	−	0.107003i
$629$	2.25573			0.0899418
$630$		0			0
$631$		−	32.6292i		−	1.29895i	−0.760383	−	0.649474i	$-0.774989\pi$
$631$		−	32.6292i		−	1.29895i	0.760383	−	0.649474i	$-0.225011\pi$
$632$	−7.25647	+	15.0102i	−0.288647	+	0.597072i
$633$	23.9560	−	13.8310i	0.952165	−	0.549733i
$634$	−5.64335	+	10.3505i	−0.224126	+	0.411072i
$635$	57.2858	+	33.0740i	2.27332	+	1.31250i
$636$	16.9981	−	33.0740i	0.674019	−	1.31147i
$637$		0			0
$638$	−9.21320	−	15.0938i	−0.364754	−	0.597570i
$639$	−5.72410	−	3.30481i	−0.226442	−	0.130736i
$640$	−40.8863	−	15.0449i	−1.61617	−	0.594700i
$641$	−11.0711	−	19.1757i	−0.437281	−	0.757393i	0.560198	−	0.828359i	$-0.310725\pi$
$641$	−11.0711	−	19.1757i	−0.437281	−	0.757393i	−0.997479	+	0.0709661i	$0.977392\pi$
$642$	50.4541	−	1.23282i	1.99126	−	0.0486555i
$643$			25.0263i			0.986942i	0.869762	+	0.493471i	$0.164272\pi$
$643$			25.0263i			0.986942i	−0.869762	+	0.493471i	$0.835728\pi$
$644$		0			0
$645$			38.5237i			1.51687i
$646$	0.0320902	+	1.31332i	0.00126257	+	0.0516717i
$647$	−16.5309	−	28.6324i	−0.649898	−	1.12566i	−0.983147	−	0.182818i	$-0.941478\pi$
$647$	−16.5309	−	28.6324i	−0.649898	−	1.12566i	0.333248	−	0.942839i	$-0.391855\pi$
$648$	23.5599	−	16.0108i	0.925519	−	0.628962i
$649$	−0.482487	−	0.278564i	−0.0189393	−	0.0109346i
$650$	45.6854	−	27.8862i	1.79193	−	1.09379i
$651$		0			0
$652$	−2.36396	+	4.59966i	−0.0925799	+	0.180137i
$653$	23.5909	+	13.6202i	0.923182	+	0.532999i	0.884649	−	0.466258i	$-0.154398\pi$
$653$	23.5909	+	13.6202i	0.923182	+	0.532999i	0.0385332	+	0.999257i	$0.487731\pi$
$654$	−6.76180	−	3.68670i	−0.264407	−	0.144161i
$655$	−55.4582	+	32.0188i	−2.16693	+	1.25108i
$656$	−0.546126	−	5.57097i	−0.0213226	−	0.217510i
$657$			1.21371i			0.0473513i
$658$		0			0
$659$	−33.6985			−1.31271			−0.656353	−	0.754454i	$-0.727902\pi$
$659$	−33.6985			−1.31271			−0.656353	+	0.754454i	$0.727902\pi$
$660$	50.7498	−	32.7053i	1.97543	−	1.27305i
$661$	6.90402	+	11.9581i	0.268535	+	0.465117i	0.968484	−	0.249077i	$-0.0801271\pi$
$661$	6.90402	+	11.9581i	0.268535	+	0.465117i	−0.699949	+	0.714193i	$0.746794\pi$
$662$	−13.7464	−	7.49488i	−0.534270	−	0.291297i
$663$	−1.12786	+	1.95352i	−0.0438026	+	0.0758684i
$664$	−10.7949	+	0.792563i	−0.418922	+	0.0307574i
$665$		0			0
$666$	2.17157	+	3.55765i	0.0841467	+	0.137856i
$667$	−4.34315	+	7.52255i	−0.168167	+	0.291274i
$668$	21.7572	−	1.06389i	0.841813	−	0.0411631i
$669$	8.71442	−	5.03127i	0.336919	−	0.194520i
$670$	0.266052	+	10.8884i	0.0102785	+	0.420654i
$671$	−6.76719			−0.261244
$672$		0			0
$673$	−10.1005			−0.389346			−0.194673	−	0.980868i	$-0.562365\pi$
$673$	−10.1005			−0.389346			−0.194673	+	0.980868i	$0.562365\pi$
$674$	−0.488544	−	19.9940i	−0.0188180	−	0.770141i
$675$	−40.6680	+	23.4797i	−1.56531	+	0.903733i
$676$	−3.65249	+	0.178600i	−0.140480	+	0.00686924i
$677$	−16.0071	+	27.7251i	−0.615202	+	1.06556i	0.375147	+	0.926966i	$0.377592\pi$
$677$	−16.0071	+	27.7251i	−0.615202	+	1.06556i	−0.990349	+	0.138596i	$0.955741\pi$
$678$	−1.92538	−	3.15432i	−0.0739440	−	0.121141i
$679$		0			0
$680$	−3.44365	+	0.252834i	−0.132058	+	0.00969575i
$681$	20.1924	−	34.9742i	0.773774	−	1.34022i
$682$	11.8829	+	6.47885i	0.455020	+	0.248088i
$683$	8.51472	+	14.7479i	0.325807	+	0.564314i	0.981675	−	0.190561i	$-0.0610308\pi$
$683$	8.51472	+	14.7479i	0.325807	+	0.564314i	−0.655869	+	0.754875i	$0.727697\pi$
$684$	−2.04042	+	1.31493i	−0.0780174	+	0.0502777i
$685$	−44.5008			−1.70029
$686$		0			0
$687$		−	43.1974i		−	1.64808i
$688$	21.5535	−	2.11291i	0.821721	−	0.0805539i
$689$	33.5572	−	19.3743i	1.27843	−	0.738101i
$690$	−26.0381	−	14.1966i	−0.991255	−	0.540456i
$691$	27.6584	+	15.9686i	1.05218	+	0.607474i	0.923257	−	0.384182i	$-0.125516\pi$
$691$	27.6584	+	15.9686i	1.05218	+	0.607474i	0.128918	+	0.991655i	$0.458850\pi$
$692$	−18.4563	+	35.9113i	−0.701604	+	1.36514i
$693$		0			0
$694$	14.7782	−	9.02054i	0.560972	−	0.342415i
$695$	−48.2390	−	27.8508i	−1.82981	−	1.05644i
$696$	−12.7397	+	8.65762i	−0.482898	+	0.328166i
$697$	−0.221825	−	0.384213i	−0.00840224	−	0.0145531i
$698$	0.509280	+	20.8427i	0.0192765	+	0.788907i
$699$		−	18.2919i		−	0.691862i
$700$		0			0
$701$		−	8.84175i		−	0.333948i	−0.985961	−	0.166974i	$-0.946600\pi$
$701$		−	8.84175i		−	0.333948i	0.985961	−	0.166974i	$-0.0533997\pi$
$702$	26.0118	−	0.635586i	0.981753	−	0.0239886i
$703$	10.4244	+	18.0557i	0.393165	+	0.680982i
$704$	−21.0817	−	26.6001i	−0.794545	−	1.00253i
$705$	−47.4571	−	27.3994i	−1.78734	−	1.03192i
$706$	−3.48035	−	5.70179i	−0.130985	−	0.214590i
$707$		0			0
$708$	−0.221825	+	0.431615i	−0.00833671	+	0.0162211i
$709$	−41.0197	−	23.6827i	−1.54053	−	0.889424i	−0.998805	−	0.0488663i	$-0.984439\pi$
$709$	−41.0197	−	23.6827i	−1.54053	−	0.889424i	−0.541722	−	0.840558i	$-0.682227\pi$
$710$	41.5983	−	76.2957i	1.56115	−	2.86333i
$711$	−2.11447	+	1.22079i	−0.0792989	+	0.0457833i
$712$	−11.9254	+	24.6680i	−0.446924	+	0.924472i
$713$		−	6.64820i		−	0.248977i
$714$		0			0
$715$	62.9117			2.35276
$716$	14.7958	+	22.9591i	0.552946	+	0.858023i
$717$	14.2752	+	24.7254i	0.533118	+	0.923387i
$718$	−10.4603	+	19.1852i	−0.390373	+	0.715987i
$719$	−7.70154	+	13.3395i	−0.287219	+	0.497478i	−0.973145	−	0.230194i	$-0.926064\pi$
$719$	−7.70154	+	13.3395i	−0.287219	+	0.497478i	0.685926	+	0.727671i	$0.259397\pi$
$720$	−3.71394	−	5.18779i	−0.138410	−	0.193338i
$721$		0			0
$722$	12.5711	−	7.67333i	0.467847	−	0.285572i
$723$	16.9497	−	29.3578i	0.630368	−	1.09183i
$724$	−23.0770	+	1.12843i	−0.857652	+	0.0419376i
$725$	25.0860	−	14.4834i	0.931672	−	0.537901i
$726$	18.2864	−	0.446819i	0.678673	−	0.0165830i
$727$	−27.6161			−1.02422			−0.512112	−	0.858919i	$-0.671137\pi$
$727$	−27.6161			−1.02422			−0.512112	+	0.858919i	$0.671137\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	−15.9523	+	0.389786i	−0.590421	+	0.0144266i
$731$	1.48648	−	0.858221i	0.0549796	−	0.0317425i
$732$	0.287887	+	5.88747i	0.0106406	+	0.217607i
$733$	17.3285	−	30.0138i	0.640041	−	1.10858i	−0.345382	−	0.938462i	$-0.612251\pi$
$733$	17.3285	−	30.0138i	0.640041	−	1.10858i	0.985423	−	0.170122i	$-0.0544162\pi$
$734$	36.7191	−	22.4132i	1.35533	−	0.827287i
$735$		0			0
$736$	−6.51472	+	15.3467i	−0.240136	+	0.565685i
$737$	−4.24264	+	7.34847i	−0.156280	+	0.270684i
$738$	0.392416	−	0.719733i	0.0144450	−	0.0264937i
$739$	7.87868	+	13.6463i	0.289822	+	0.501986i	0.973767	−	0.227547i	$-0.0730706\pi$
$739$	7.87868	+	13.6463i	0.289822	+	0.501986i	−0.683945	+	0.729533i	$0.739737\pi$
$740$	−46.0623	+	29.6845i	−1.69328	+	1.09122i
$741$	−20.8489			−0.765903
$742$		0			0
$743$			38.0181i			1.39475i	0.716708	+	0.697374i	$0.245648\pi$
$743$			38.0181i			1.39475i	−0.716708	+	0.697374i	$0.754352\pi$
$744$	5.13110	−	10.6138i	0.188115	−	0.389120i
$745$	−47.4571	+	27.3994i	−1.73869	+	1.00383i
$746$	11.2867	−	20.7010i	0.413236	−	0.757919i
$747$	−1.37276	−	0.792563i	−0.0502267	−	0.0289984i
$748$	−2.39256	−	1.22964i	−0.0874807	−	0.0449601i
$749$		0			0
$750$	25.3137	+	41.4710i	0.924326	+	1.51431i
$751$	−38.9052	−	22.4619i	−1.41967	−	0.819648i	−0.423402	−	0.905942i	$-0.639164\pi$
$751$	−38.9052	−	22.4619i	−1.41967	−	0.819648i	−0.996270	+	0.0862936i	$0.972498\pi$
$752$	−12.7267	+	28.0544i	−0.464096	+	1.02304i
$753$	−10.1924	−	17.6537i	−0.371431	−	0.643338i
$754$	−16.0454	+	0.392061i	−0.584338	+	0.0142780i
$755$			43.4495i			1.58129i
$756$		0			0
$757$		−	43.9126i		−	1.59603i	−0.602638	−	0.798015i	$-0.705884\pi$
$757$		−	43.9126i		−	1.59603i	0.602638	−	0.798015i	$-0.294116\pi$
$758$	0.358745	+	14.6819i	0.0130302	+	0.533271i
$759$	−11.5523	−	20.0092i	−0.419322	−	0.726287i
$760$	−17.9380	−	26.3958i	−0.650679	−	0.957476i
$761$	−38.1304	−	22.0146i	−1.38223	−	0.798028i	−0.389803	−	0.920898i	$-0.627457\pi$
$761$	−38.1304	−	22.0146i	−1.38223	−	0.798028i	−0.992423	+	0.122870i	$0.960790\pi$
$762$	38.3142	−	23.3868i	1.38798	−	0.847215i
$763$		0			0
$764$	−17.8995	−	9.19932i	−0.647581	−	0.332820i
$765$	−0.437922	−	0.252834i	−0.0158331	−	0.00914124i
$766$	42.2115	+	23.0147i	1.52516	+	0.831556i
$767$	−0.437922	+	0.252834i	−0.0158124	+	0.00912931i
$768$	−22.2453	+	19.4727i	−0.802707	+	0.702661i
$769$			8.15640i			0.294127i	0.989127	+	0.147064i	$0.0469822\pi$
$769$			8.15640i			0.294127i	−0.989127	+	0.147064i	$0.953018\pi$
$770$		0			0
$771$	−28.3848			−1.02225
$772$	−7.13504	−	11.0717i	−0.256796	−	0.398478i
$773$	0.330344	+	0.572172i	0.0118816	+	0.0205796i	0.871905	−	0.489675i	$-0.162885\pi$
$773$	0.330344	+	0.572172i	0.0118816	+	0.0205796i	−0.860023	+	0.510255i	$0.829551\pi$
$774$	2.78458	+	1.51822i	0.100090	+	0.0545713i
$775$	−11.0851	+	19.2000i	−0.398190	+	0.689685i
$776$	46.9100	−	3.44415i	1.68397	−	0.123638i
$777$		0			0
$778$	−12.6569	−	20.7355i	−0.453770	−	0.743403i
$779$	2.05025	−	3.55114i	0.0734579	−	0.127233i
$780$	−2.67636	−	54.7333i	−0.0958291	−	1.95977i
$781$	58.6299	−	33.8500i	2.09794	−	1.21125i
$782$	0.0322775	+	1.32098i	0.00115424	+	0.0472382i
$783$	14.0817			0.503239
$784$		0			0
$785$	6.14214			0.219222
$786$	1.06150	+	43.4429i	0.0378626	+	1.54956i
$787$	−8.93841	+	5.16059i	−0.318620	+	0.183955i	−0.650777	−	0.759269i	$-0.725557\pi$
$787$	−8.93841	+	5.16059i	−0.318620	+	0.183955i	0.332157	+	0.943224i	$0.392224\pi$
$788$	0.168640	+	3.44880i	0.00600755	+	0.122858i
$789$		0			0
$790$	−16.7245	−	27.3994i	−0.595029	−	0.974826i
$791$		0			0
$792$	−0.363961	−	4.95722i	−0.0129328	−	0.176147i
$793$	−3.07107	+	5.31925i	−0.109057	+	0.188892i
$794$	−34.6294	−	18.8808i	−1.22895	−	0.670053i
$795$	35.7990	+	62.0057i	1.26966	+	2.19911i
$796$	−10.7877	−	16.7396i	−0.382360	−	0.593319i
$797$	−8.36223			−0.296205			−0.148103	−	0.988972i	$-0.547317\pi$
$797$	−8.36223			−0.296205			−0.148103	+	0.988972i	$0.547317\pi$
$798$		0			0
$799$			2.44158i			0.0863770i
$800$	44.4034	−	33.4586i	1.56990	−	1.18294i
$801$	−3.47496	+	2.00627i	−0.122782	+	0.0708881i
$802$	15.0763	+	8.21997i	0.532363	+	0.290257i
$803$	−10.7661	−	6.21579i	−0.379926	−	0.219350i
$804$	6.57368	+	3.37849i	0.231836	+	0.119150i
$805$		0			0
$806$	10.4853	−	6.40017i	0.369328	−	0.225436i
$807$	−23.5909	−	13.6202i	−0.830438	−	0.479454i
$808$	−16.4711	+	11.1934i	−0.579451	+	0.393782i
$809$	10.4645	+	18.1250i	0.367911	+	0.637241i	0.989239	−	0.146310i	$-0.0467398\pi$
$809$	10.4645	+	18.1250i	0.367911	+	0.637241i	−0.621328	+	0.783551i	$0.713406\pi$
$810$	1.33971	+	54.8288i	0.0470727	+	1.92649i
$811$			30.8548i			1.08346i	0.840553	+	0.541729i	$0.182230\pi$
$811$			30.8548i			1.08346i	−0.840553	+	0.541729i	$0.817770\pi$
$812$		0			0
$813$			24.2931i			0.851997i
$814$	−42.6790	+	1.04284i	−1.49590	+	0.0365515i
$815$	−4.97863	−	8.62325i	−0.174394	−	0.302059i
$816$	−0.968006	+	2.13385i	−0.0338870	+	0.0746995i
$817$	13.7390	+	7.93223i	0.480668	+	0.277514i
$818$	−15.8302	−	25.9343i	−0.553489	−	0.906771i
$819$		0			0
$820$	9.58579	+	4.92655i	0.334750	+	0.172042i
$821$	−27.6384	−	15.9570i	−0.964588	−	0.556905i	−0.0670056	−	0.997753i	$-0.521345\pi$
$821$	−27.6384	−	15.9570i	−0.964588	−	0.556905i	−0.897582	+	0.440848i	$0.854678\pi$
$822$	−14.4558	+	26.5134i	−0.504203	+	0.924762i
$823$	−18.9240	+	10.9258i	−0.659649	+	0.380849i	−0.792143	−	0.610335i	$-0.791035\pi$
$823$	−18.9240	+	10.9258i	−0.659649	+	0.380849i	0.132494	+	0.991184i	$0.457701\pi$
$824$	−13.8676	−	6.70411i	−0.483100	−	0.233549i
$825$			77.0488i			2.68249i
$826$		0			0
$827$	9.65685			0.335802			0.167901	−	0.985804i	$-0.446301\pi$
$827$	9.65685			0.335802			0.167901	+	0.985804i	$0.446301\pi$
$828$	−2.05233	+	1.32261i	−0.0713233	+	0.0459637i
$829$	−20.9857	−	36.3483i	−0.728864	−	1.26243i	−0.957364	−	0.288886i	$-0.906715\pi$
$829$	−20.9857	−	36.3483i	−0.728864	−	1.26243i	0.228499	−	0.973544i	$-0.426618\pi$
$830$	9.97613	−	18.2973i	0.346277	−	0.635109i
$831$	−27.8897	+	48.3064i	−0.967484	+	1.67573i
$832$	−30.4758	+	4.49935i	−1.05656	+	0.155987i
$833$		0			0
$834$	−32.2635	+	19.6935i	−1.11719	+	0.681929i
$835$	−20.9706	+	36.3221i	−0.725716	+	1.25698i
$836$	−1.21431	−	24.8335i	−0.0419979	−	0.858884i
$837$	−9.33374	+	5.38883i	−0.322621	+	0.186265i
$838$	−14.0669	+	0.343718i	−0.485933	+	0.0118735i
$839$	9.95727			0.343763			0.171882	−	0.985118i	$-0.445015\pi$
$839$	9.95727			0.343763			0.171882	+	0.985118i	$0.445015\pi$
$840$		0			0
$841$	20.3137			0.700473
$842$	10.7745	−	0.263268i	0.371312	−	0.00907282i
$843$	−4.91434	+	2.83730i	−0.169259	+	0.0977217i
$844$	29.9054	−	1.46232i	1.02939	−	0.0503351i
$845$	3.52043	−	6.09756i	0.121106	−	0.209762i
$846$	−3.85077	+	2.35049i	−0.132392	+	0.0808116i
$847$		0			0
$848$	32.7279	−	23.4299i	1.12388	−	0.804586i
$849$	−14.1213	+	24.4588i	−0.484642	+	0.839425i
$850$	2.10937	−	3.86881i	0.0723508	−	0.132699i
$851$	10.4853	+	18.1610i	0.359431	+	0.622552i
$852$	−31.9438	−	49.5682i	−1.09438	−	1.69818i
$853$	13.8080			0.472778			0.236389	−	0.971658i	$-0.424036\pi$
$853$	13.8080			0.472778			0.236389	+	0.971658i	$0.424036\pi$
$854$		0			0
$855$		−	4.67371i		−	0.159838i
$856$	49.1817	+	23.7763i	1.68100	+	0.812657i
$857$	31.1139	−	17.9636i	1.06283	−	0.613625i	0.136616	−	0.990624i	$-0.456378\pi$
$857$	31.1139	−	17.9636i	1.06283	−	0.613625i	0.926213	+	0.377000i	$0.123044\pi$
$858$	20.4364	−	37.4825i	0.697687	−	1.27963i
$859$	28.9174	+	16.6955i	0.986650	+	0.569643i	0.904271	−	0.426958i	$-0.140415\pi$
$859$	28.9174	+	16.6955i	0.986650	+	0.569643i	0.0823789	+	0.996601i	$0.473748\pi$
$860$	−19.0603	+	37.0865i	−0.649952	+	1.26464i
$861$		0			0
$862$	13.9289	+	22.8195i	0.474421	+	0.777236i
$863$	15.3144	+	8.84175i	0.521307	+	0.300977i	0.737469	−	0.675381i	$-0.236021\pi$
$863$	15.3144	+	8.84175i	0.521307	+	0.300977i	−0.216162	+	0.976357i	$0.569354\pi$
$864$	26.8266	−	3.29321i	0.912658	−	0.112037i
$865$	−38.8701	−	67.3249i	−1.32162	−	2.28912i
$866$	−25.6753	+	0.627362i	−0.872481	+	0.0213186i
$867$		−	31.2262i		−	1.06050i
$868$		0			0
$869$		−	25.0083i		−	0.848347i
$870$	−0.724434	−	29.6480i	−0.0245606	−	1.00516i
$871$	3.85077	+	6.66973i	0.130478	+	0.225995i
$872$	−4.68547	−	6.89468i	−0.158670	−	0.233483i
$873$	5.96544	+	3.44415i	0.201900	+	0.116567i
$874$	−10.4244	+	6.36304i	−0.352612	+	0.215233i
$875$		0			0
$876$	−4.94975	+	9.63093i	−0.167236	+	0.325399i
$877$	−12.7620	−	7.36813i	−0.430941	−	0.248804i	0.268806	−	0.963194i	$-0.413371\pi$
$877$	−12.7620	−	7.36813i	−0.430941	−	0.248804i	−0.699748	+	0.714390i	$0.746704\pi$
$878$	−48.9733	−	26.7014i	−1.65277	−	0.901130i
$879$	25.7053	−	14.8410i	0.867020	−	0.500574i
$880$	65.0380	−	6.37572i	2.19243	−	0.214926i
$881$		−	21.2220i		−	0.714988i	−0.933915	−	0.357494i	$-0.883631\pi$
$881$		−	21.2220i		−	0.714988i	0.933915	−	0.357494i	$-0.116369\pi$
$882$		0			0
$883$	−2.34315			−0.0788531			−0.0394266	−	0.999222i	$-0.512553\pi$
$883$	−2.34315			−0.0788531			−0.0394266	+	0.999222i	$0.512553\pi$
$884$	−2.05233	+	1.32261i	−0.0690272	+	0.0444840i
$885$	−0.467177	−	0.809174i	−0.0157040	−	0.0272001i
$886$	1.27820	+	0.696907i	0.0429421	+	0.0234131i
$887$	−6.10650	+	10.5768i	−0.205036	+	0.355133i	−0.950144	−	0.311811i	$-0.899065\pi$
$887$	−6.10650	+	10.5768i	−0.205036	+	0.355133i	0.745108	+	0.666944i	$0.232398\pi$
$888$	2.72291	+	37.0865i	0.0913747	+	1.24454i
$889$		0			0
$890$	−27.4853	−	45.0286i	−0.921309	−	1.50936i
$891$	−21.3640	+	37.0035i	−0.715720	+	1.23966i
$892$	10.8786	−	0.531945i	0.364243	−	0.0178108i
$893$	−19.5433	+	11.2833i	−0.653992	+	0.377582i
$894$	0.908358	+	37.1752i	0.0303800	+	1.24333i
$895$	−52.5894			−1.75787
$896$		0			0
$897$	−20.9706			−0.700187
$898$	1.25345	+	51.2984i	0.0418282	+	1.71185i
$899$	5.75751	−	3.32410i	0.192024	−	0.110865i
$900$	8.13242	−	0.397660i	0.271081	−	0.0132553i
$901$	1.59504	−	2.76269i	0.0531385	−	0.0920386i
$902$	4.37462	+	7.16687i	0.145659	+	0.238631i
$903$		0			0
$904$	−0.292893	−	3.98926i	−0.00974148	−	0.132681i
$905$	22.2426	−	38.5254i	0.739370	−	1.28063i
$906$	25.8871	+	14.1143i	0.860040	+	0.468915i
$907$	−1.51472	−	2.62357i	−0.0502954	−	0.0871142i	0.839782	−	0.542924i	$-0.182683\pi$
$907$	−1.51472	−	2.62357i	−0.0502954	−	0.0871142i	−0.890077	+	0.455810i	$0.849350\pi$
$908$	36.7432	−	23.6789i	1.21937	−	0.785811i
$909$	−2.91642			−0.0967314
$910$		0			0
$911$			14.7363i			0.488234i	0.969746	+	0.244117i	$0.0784981\pi$
$911$			14.7363i			0.488234i	−0.969746	+	0.244117i	$0.921502\pi$
$912$	−21.5535	+	2.11291i	−0.713709	+	0.0699654i
$913$	14.0607	−	8.11794i	0.465341	−	0.268665i
$914$	29.8513	+	16.2757i	0.987395	+	0.538351i
$915$	−9.82868	−	5.67459i	−0.324926	−	0.187596i
$916$	21.3727	−	41.5858i	0.706175	−	1.37403i
$917$		0			0
$918$	1.82843	−	1.11606i	0.0603471	−	0.0368356i
$919$	13.8192	+	7.97852i	0.455854	+	0.263187i	0.710299	−	0.703900i	$-0.248560\pi$
$919$	13.8192	+	7.97852i	0.455854	+	0.263187i	−0.254446	+	0.967087i	$0.581893\pi$
$920$	−18.0427	−	26.5498i	−0.594849	−	0.875322i
$921$	−13.1213	−	22.7268i	−0.432362	−	0.748873i
$922$	0.885534	+	36.2412i	0.0291635	+	1.19354i
$923$		−	61.4469i		−	2.02255i
$924$		0			0
$925$		−	69.9322i		−	2.29936i
$926$	−17.6782	+	0.431959i	−0.580943	+	0.0141950i
$927$	−1.12786	−	1.95352i	−0.0370439	−	0.0641620i
$928$	−16.5480	+	2.03141i	−0.543213	+	0.0666845i
$929$	−6.67538	−	3.85403i	−0.219012	−	0.126447i	0.386481	−	0.922297i	$-0.373691\pi$
$929$	−6.67538	−	3.85403i	−0.219012	−	0.126447i	−0.605493	+	0.795851i	$0.707024\pi$
$930$	11.8260	+	19.3743i	0.387789	+	0.635307i
$931$		0			0
$932$	9.05025	−	17.6095i	0.296451	−	0.576817i
$933$	42.0769	+	24.2931i	1.37754	+	0.795322i
$934$	16.1359	−	29.5950i	0.527983	−	0.968377i
$935$	4.48547	−	2.58969i	0.146691	−	0.0846919i
$936$	−4.06172	−	1.96359i	−0.132761	−	0.0641819i
$937$		−	17.9749i		−	0.587213i	−0.955926	−	0.293606i	$-0.905144\pi$
$937$		−	17.9749i		−	0.587213i	0.955926	−	0.293606i	$-0.0948555\pi$
$938$		0			0
$939$	−29.4142			−0.959897
$940$	−32.1302	−	49.8574i	−1.04797	−	1.62617i
$941$	−22.1136	−	38.3019i	−0.720882	−	1.24860i	−0.960647	−	0.277774i	$-0.910403\pi$
$941$	−22.1136	−	38.3019i	−0.720882	−	1.24860i	0.239764	−	0.970831i	$-0.422930\pi$
$942$	1.99523	−	3.65946i	0.0650080	−	0.119232i
$943$	2.06222	−	3.57187i	0.0671550	−	0.116316i
$944$	−0.427099	+	0.305760i	−0.0139009	+	0.00995165i
$945$		0			0
$946$	−27.7279	+	16.9250i	−0.901513	+	0.550279i
$947$	12.6066	−	21.8353i	0.409660	−	0.709551i	−0.585192	−	0.810895i	$-0.698981\pi$
$947$	12.6066	−	21.8353i	0.409660	−	0.709551i	0.994851	+	0.101344i	$0.0323142\pi$
$948$	−21.7572	+	1.06389i	−0.706643	+	0.0345535i
$949$	−9.77166	+	5.64167i	−0.317201	+	0.183136i
$950$	40.7155	−	0.994862i	1.32098	−	0.0322776i
$951$	−15.4031			−0.499479
$952$		0			0
$953$	5.37258			0.174035			0.0870175	−	0.996207i	$-0.472266\pi$
$953$	5.37258			0.174035			0.0870175	+	0.996207i	$0.472266\pi$
$954$	5.89274	−	0.143986i	0.190785	−	0.00466173i
$955$	33.5572	−	19.3743i	1.08589	−	0.626937i
$956$	1.50929	+	30.8659i	0.0488138	+	0.998274i
$957$	11.5523	−	20.0092i	0.373433	−	0.646805i
$958$	10.4244	−	6.36304i	0.336799	−	0.205580i
$959$		0			0
$960$	−8.31371	−	56.3120i	−0.268324	−	1.81746i
$961$	12.9558	−	22.4402i	0.417930	−	0.723877i
$962$	−18.5488	+	34.0205i	−0.598037	+	1.09686i
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$	30.8427	−	19.8763i	0.993377	−	0.640174i
$965$	25.3603			0.816378
$966$		0			0
$967$		−	8.84175i		−	0.284332i	−0.989843	−	0.142166i	$-0.954593\pi$
$967$		−	8.84175i		−	0.284332i	0.989843	−	0.142166i	$-0.0454066\pi$
$968$	17.8253	+	8.61740i	0.572926	+	0.276974i
$969$	−1.48648	+	0.858221i	−0.0477527	+	0.0275700i
$970$	−43.3521	+	79.5125i	−1.39195	+	2.55299i
$971$	25.7170	+	14.8477i	0.825299	+	0.476486i	0.852240	−	0.523151i	$-0.175243\pi$
$971$	25.7170	+	14.8477i	0.825299	+	0.476486i	−0.0269416	+	0.999637i	$0.508577\pi$
$972$	7.60478	+	3.90842i	0.243924	+	0.125363i
$973$		0			0
$974$	17.5269	+	28.7140i	0.561598	+	0.920056i
$975$	60.5630	+	34.9661i	1.93957	+	1.11981i
$976$	−2.63579	+	5.81026i	−0.0843696	+	0.185982i
$977$	−1.87868	−	3.25397i	−0.0601043	−	0.104104i	0.834408	−	0.551148i	$-0.185810\pi$
$977$	−1.87868	−	3.25397i	−0.0601043	−	0.104104i	−0.894512	+	0.447044i	$0.852477\pi$
$978$	−6.75497	+	0.165054i	−0.216000	+	0.00527785i
$979$		−	41.0990i		−	1.31353i
$980$		0			0
$981$		−	1.22079i		−	0.0389769i
$982$	−0.898177	−	36.7586i	−0.0286620	−	1.17301i
$983$	1.12786	+	1.95352i	0.0359733	+	0.0623076i	0.883452	−	0.468523i	$-0.155214\pi$
$983$	1.12786	+	1.95352i	0.0359733	+	0.0623076i	−0.847478	+	0.530830i	$0.821880\pi$
$984$	6.04909	−	4.11082i	0.192838	−	0.131048i
$985$	−5.75751	−	3.32410i	−0.183450	−	0.105915i
$986$	−1.12786	+	0.688444i	−0.0359185	+	0.0219245i
$987$		0			0
$988$	−20.0711	−	10.3154i	−0.638546	−	0.328176i
$989$	13.8192	+	7.97852i	0.439425	+	0.253702i
$990$	8.40249	+	4.58124i	0.267049	+	0.145601i
$991$	31.2481	−	18.0411i	0.992627	−	0.573093i	0.0865685	−	0.996246i	$-0.472410\pi$
$991$	31.2481	−	18.0411i	0.992627	−	0.573093i	0.906059	+	0.423152i	$0.139077\pi$
$992$	10.1910	−	7.67910i	0.323566	−	0.243812i
$993$		−	20.4567i		−	0.649173i
$994$		0			0
$995$	38.3431			1.21556
$996$	−7.66079	−	11.8875i	−0.242742	−	0.376669i
$997$	5.11547	+	8.86025i	0.162008	+	0.280607i	0.935589	−	0.353091i	$-0.114869\pi$
$997$	5.11547	+	8.86025i	0.162008	+	0.280607i	−0.773580	+	0.633698i	$0.781536\pi$
$998$	50.4451	+	27.5039i	1.59681	+	0.870621i
$999$	16.9981	−	29.4416i	0.537797	−	0.931491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.m.h.19.5		16
4.3	odd	2		1568.2.q.h.1391.8		16
7.2	even	3		392.2.e.d.195.5	✓	8
7.3	odd	6	inner	392.2.m.h.227.1		16
7.4	even	3	inner	392.2.m.h.227.2		16
7.5	odd	6		392.2.e.d.195.6	yes	8
7.6	odd	2	inner	392.2.m.h.19.6		16
8.3	odd	2	inner	392.2.m.h.19.1		16
8.5	even	2		1568.2.q.h.1391.7		16
28.3	even	6		1568.2.q.h.815.7		16
28.11	odd	6		1568.2.q.h.815.2		16
28.19	even	6		1568.2.e.d.783.2		8
28.23	odd	6		1568.2.e.d.783.7		8
28.27	even	2		1568.2.q.h.1391.1		16
56.3	even	6	inner	392.2.m.h.227.5		16
56.5	odd	6		1568.2.e.d.783.1		8
56.11	odd	6	inner	392.2.m.h.227.6		16
56.13	odd	2		1568.2.q.h.1391.2		16
56.19	even	6		392.2.e.d.195.8	yes	8
56.27	even	2	inner	392.2.m.h.19.2		16
56.37	even	6		1568.2.e.d.783.8		8
56.45	odd	6		1568.2.q.h.815.8		16
56.51	odd	6		392.2.e.d.195.7	yes	8
56.53	even	6		1568.2.q.h.815.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.5	✓	8	7.2	even	3
392.2.e.d.195.6	yes	8	7.5	odd	6
392.2.e.d.195.7	yes	8	56.51	odd	6
392.2.e.d.195.8	yes	8	56.19	even	6
392.2.m.h.19.1		16	8.3	odd	2	inner
392.2.m.h.19.2		16	56.27	even	2	inner
392.2.m.h.19.5		16	1.1	even	1	trivial
392.2.m.h.19.6		16	7.6	odd	2	inner
392.2.m.h.227.1		16	7.3	odd	6	inner
392.2.m.h.227.2		16	7.4	even	3	inner
392.2.m.h.227.5		16	56.3	even	6	inner
392.2.m.h.227.6		16	56.11	odd	6	inner
1568.2.e.d.783.1		8	56.5	odd	6
1568.2.e.d.783.2		8	28.19	even	6
1568.2.e.d.783.7		8	28.23	odd	6
1568.2.e.d.783.8		8	56.37	even	6
1568.2.q.h.815.1		16	56.53	even	6
1568.2.q.h.815.2		16	28.11	odd	6
1568.2.q.h.815.7		16	28.3	even	6
1568.2.q.h.815.8		16	56.45	odd	6
1568.2.q.h.1391.1		16	28.27	even	2
1568.2.q.h.1391.2		16	56.13	odd	2
1568.2.q.h.1391.7		16	8.5	even	2
1568.2.q.h.1391.8		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0345453 + 1.41379i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(-1.99761 + 0.0976797i) q^{4} +(1.92538 - 3.33486i) q^{5} +(-1.36145 - 2.23044i) q^{6} +(-0.207107 - 2.82083i) q^{8} +(0.207107 - 0.358719i) q^{9} +(4.78132 + 2.60689i) q^{10} +(2.12132 + 3.67423i) q^{11} +(3.10635 - 2.00186i) q^{12} +3.85077 q^{13} +7.11529i q^{15} +(3.98092 - 0.390252i) q^{16} +(0.274552 - 0.158513i) q^{17} +(0.514309 + 0.280414i) q^{18} +(2.53759 + 1.46508i) q^{19} +(-3.52043 + 6.84984i) q^{20} +(-5.12132 + 3.12603i) q^{22} +(2.55239 + 1.47363i) q^{23} +(2.93752 + 4.32258i) q^{24} +(-4.91421 - 8.51167i) q^{25} +(0.133026 + 5.44419i) q^{26} -4.77791i q^{27} +2.94725i q^{29} +(-10.0595 + 0.245800i) q^{30} +(-1.12786 - 1.95352i) q^{31} +(0.689257 + 5.61471i) q^{32} +(-6.78910 - 3.91969i) q^{33} +(0.233588 + 0.382683i) q^{34} +(-0.378680 + 0.736813i) q^{36} +(6.16203 + 3.55765i) q^{37} +(-1.98365 + 3.63823i) q^{38} +(-6.16203 + 3.55765i) q^{39} +(-9.80586 - 4.74052i) q^{40} -1.39942i q^{41} +5.41421 q^{43} +(-4.59648 - 7.13249i) q^{44} +(-0.797521 - 1.38135i) q^{45} +(-1.99523 + 3.65946i) q^{46} +(-3.85077 + 6.66973i) q^{47} +(-6.00974 + 4.30237i) q^{48} +(11.8640 - 7.24171i) q^{50} +(-0.292893 + 0.507306i) q^{51} +(-7.69235 + 0.376142i) q^{52} +(8.71442 - 5.03127i) q^{53} +(6.75497 - 0.165054i) q^{54} +16.3374 q^{55} -5.41421 q^{57} +(-4.16680 + 0.101814i) q^{58} +(-0.113723 + 0.0656581i) q^{59} +(-0.695020 - 14.2136i) q^{60} +(-0.797521 + 1.38135i) q^{61} +(2.72291 - 1.66205i) q^{62} +(-7.91421 + 1.16843i) q^{64} +(7.41421 - 12.8418i) q^{65} +(5.30709 - 9.73378i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-0.532965 + 0.343465i) q^{68} -5.44581 q^{69} -15.9570i q^{71} +(-1.05478 - 0.509921i) q^{72} +(-2.53759 + 1.46508i) q^{73} +(-4.81690 + 8.83472i) q^{74} +(15.7275 + 9.08028i) q^{75} +(-5.21222 - 2.67878i) q^{76} +(-5.24264 - 8.58892i) q^{78} +(-5.10479 - 2.94725i) q^{79} +(6.36336 - 14.0272i) q^{80} +(5.03553 + 8.72180i) q^{81} +(1.97848 - 0.0483433i) q^{82} -3.82683i q^{83} -1.22079i q^{85} +(0.187036 + 7.65457i) q^{86} +(-2.72291 - 4.71621i) q^{87} +(9.92507 - 6.74485i) q^{88} +(-8.38931 - 4.84357i) q^{89} +(1.92538 - 1.17525i) q^{90} +(-5.24264 - 2.69442i) q^{92} +(3.60963 + 2.08402i) q^{93} +(-9.56263 - 5.21378i) q^{94} +(9.77166 - 5.64167i) q^{95} +(-6.29027 - 8.34790i) q^{96} +16.6298i q^{97} +1.75736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 8 q^{9} - 4 q^{16} + 4 q^{18} - 48 q^{22} - 56 q^{25} - 8 q^{30} + 36 q^{32} - 40 q^{36} + 64 q^{43} + 48 q^{44} + 40 q^{46} + 88 q^{50} - 16 q^{51} - 64 q^{57} - 40 q^{58}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 8 * q^9 - 4 * q^16 + 4 * q^18 - 48 * q^22 - 56 * q^25 - 8 * q^30 + 36 * q^32 - 40 * q^36 + 64 * q^43 + 48 * q^44 + 40 * q^46 + 88 * q^50 - 16 * q^51 - 64 * q^57 - 40 * q^58 - 56 * q^60 - 104 * q^64 + 96 * q^65 + 16 * q^67 - 12 * q^72 + 8 * q^74 - 16 * q^78 + 24 * q^81 - 24 * q^86 - 24 * q^88 - 16 * q^92 + 96 * q^99

Introduction

L-functions

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