LMFDB - Embedded newform 798.2.bc.b.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(31,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,28] 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	798.31
Dual form			798.2.bc.b.103.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.99811 - 1.73096i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.47235 - 0.942075i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(1.73096 + 2.99811i) q^{10} +(-0.833907 + 1.44437i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.376869 - 0.652756i) q^{13} +(-2.61215 - 0.420313i) q^{14} +(-2.99811 - 1.73096i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.71544i q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.186177 - 4.35492i) q^{19} -3.46192i q^{20} +(2.47235 - 0.942075i) q^{21} +(1.44437 - 0.833907i) q^{22} +0.179508 q^{23} -1.00000i q^{24} +(3.49245 + 6.04910i) q^{25} +(-0.652756 + 0.376869i) q^{26} +1.00000 q^{27} +(2.05203 + 1.67008i) q^{28} +(-6.09439 - 3.51860i) q^{29} +(1.73096 + 2.99811i) q^{30} +(1.13832 - 1.97162i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.833907 + 1.44437i) q^{33} +(-1.35772 + 2.35164i) q^{34} +(-9.04306 - 1.45509i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.60251 + 2.65726i) q^{37} +(-2.33869 + 3.67838i) q^{38} +(0.376869 - 0.652756i) q^{39} +(-1.73096 + 2.99811i) q^{40} +(-2.08627 - 3.61352i) q^{41} +(-2.61215 - 0.420313i) q^{42} +(-6.07440 - 10.5212i) q^{43} -1.66781 q^{44} +(-2.99811 - 1.73096i) q^{45} +(-0.155458 - 0.0897540i) q^{46} -1.39882i q^{47} +(-0.500000 + 0.866025i) q^{48} +(5.22499 - 4.65827i) q^{49} -6.98490i q^{50} -2.71544i q^{51} +0.753738 q^{52} +(-7.18923 + 4.15071i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(5.00029 - 2.88692i) q^{55} +(-0.942075 - 2.47235i) q^{56} +(0.186177 - 4.35492i) q^{57} +(3.51860 + 6.09439i) q^{58} +8.43918 q^{59} -3.46192i q^{60} +0.172034i q^{61} +(-1.97162 + 1.13832i) q^{62} +(2.47235 - 0.942075i) q^{63} -1.00000 q^{64} +(-2.25979 + 1.30469i) q^{65} +(1.44437 - 0.833907i) q^{66} +(0.393709 - 0.227308i) q^{67} +(2.35164 - 1.35772i) q^{68} +0.179508 q^{69} +(7.10398 + 5.78168i) q^{70} +(9.60367 - 5.54468i) q^{71} -1.00000i q^{72} +6.04386i q^{73} +5.31452 q^{74} +(3.49245 + 6.04910i) q^{75} +(3.86456 - 2.01623i) q^{76} +(-0.701003 + 4.35658i) q^{77} +(-0.652756 + 0.376869i) q^{78} +(-12.9200 - 7.45937i) q^{79} +(2.99811 - 1.73096i) q^{80} +1.00000 q^{81} +4.17254i q^{82} -8.65416i q^{83} +(2.05203 + 1.67008i) q^{84} +(-4.70032 + 8.14120i) q^{85} +12.1488i q^{86} +(-6.09439 - 3.51860i) q^{87} +(1.44437 + 0.833907i) q^{88} +14.3415 q^{89} +(1.73096 + 2.99811i) q^{90} +(0.316806 - 1.96888i) q^{91} +(0.0897540 + 0.155458i) q^{92} +(1.13832 - 1.97162i) q^{93} +(-0.699411 + 1.21141i) q^{94} +(-8.09638 + 12.7343i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-6.55154 - 11.3476i) q^{97} +(-6.85411 + 1.42168i) q^{98} +(-0.833907 + 1.44437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) $ 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.99811	−	1.73096i	−1.34080	−	0.774109i	−0.353872	−	0.935294i	$-0.615135\pi$
$5$	−2.99811	−	1.73096i	−1.34080	−	0.774109i	−0.986924	+	0.161185i	$0.948469\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	2.47235	−	0.942075i	0.934459	−	0.356071i
$7$	2.47235	−	0.942075i	0.934459	−	0.356071i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	1.73096	+	2.99811i	0.547378	+	0.948086i
$11$	−0.833907	+	1.44437i	−0.251432	+	0.435494i	−0.963920	−	0.266190i	$-0.914235\pi$
$11$	−0.833907	+	1.44437i	−0.251432	+	0.435494i	0.712488	+	0.701684i	$0.247568\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.376869	−	0.652756i	0.104525	−	0.181042i	−0.809019	−	0.587782i	$-0.800001\pi$
$13$	0.376869	−	0.652756i	0.104525	−	0.181042i	0.913544	+	0.406740i	$0.133335\pi$
$14$	−2.61215	−	0.420313i	−0.698127	−	0.112333i
$15$	−2.99811	−	1.73096i	−0.774109	−	0.446932i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	2.71544i		−	0.658591i	−0.944227	−	0.329296i	$-0.893189\pi$
$17$		−	2.71544i		−	0.658591i	0.944227	−	0.329296i	$-0.106811\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	0.186177	−	4.35492i	0.0427120	−	0.999087i
$19$	0.186177	−	4.35492i	0.0427120	−	0.999087i
$20$		−	3.46192i		−	0.774109i
$21$	2.47235	−	0.942075i	0.539510	−	0.205578i
$22$	1.44437	−	0.833907i	0.307941	−	0.177790i
$23$	0.179508			0.0374300			0.0187150	−	0.999825i	$-0.494042\pi$
$23$	0.179508			0.0374300			0.0187150	+	0.999825i	$0.494042\pi$
$24$		−	1.00000i		−	0.204124i
$25$	3.49245	+	6.04910i	0.698490	+	1.20982i
$26$	−0.652756	+	0.376869i	−0.128016	+	0.0739101i
$27$	1.00000			0.192450
$28$	2.05203	+	1.67008i	0.387798	+	0.315615i
$29$	−6.09439	−	3.51860i	−1.13170	−	0.653387i	−0.187338	−	0.982296i	$-0.559986\pi$
$29$	−6.09439	−	3.51860i	−1.13170	−	0.653387i	−0.944362	+	0.328908i	$0.893319\pi$
$30$	1.73096	+	2.99811i	0.316029	+	0.547378i
$31$	1.13832	−	1.97162i	0.204448	−	0.354114i	−0.745509	−	0.666496i	$-0.767793\pi$
$31$	1.13832	−	1.97162i	0.204448	−	0.354114i	0.949957	+	0.312382i	$0.101127\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.833907	+	1.44437i	−0.145165	+	0.251432i
$34$	−1.35772	+	2.35164i	−0.232847	+	0.403303i
$35$	−9.04306	−	1.45509i	−1.52856	−	0.245955i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.60251	+	2.65726i	−0.756648	+	0.436851i	−0.828091	−	0.560594i	$-0.810573\pi$
$37$	−4.60251	+	2.65726i	−0.756648	+	0.436851i	0.0714429	+	0.997445i	$0.477240\pi$
$38$	−2.33869	+	3.67838i	−0.379386	+	0.596713i
$39$	0.376869	−	0.652756i	0.0603473	−	0.104525i
$40$	−1.73096	+	2.99811i	−0.273689	+	0.474043i
$41$	−2.08627	−	3.61352i	−0.325820	−	0.564338i	0.655858	−	0.754885i	$-0.272307\pi$
$41$	−2.08627	−	3.61352i	−0.325820	−	0.564338i	−0.981678	+	0.190547i	$0.938974\pi$
$42$	−2.61215	−	0.420313i	−0.403064	−	0.0648556i
$43$	−6.07440	−	10.5212i	−0.926338	−	1.60446i	−0.789395	−	0.613886i	$-0.789606\pi$
$43$	−6.07440	−	10.5212i	−0.926338	−	1.60446i	−0.136943	−	0.990579i	$-0.543728\pi$
$44$	−1.66781			−0.251432
$45$	−2.99811	−	1.73096i	−0.446932	−	0.258036i
$46$	−0.155458	−	0.0897540i	−0.0229211	−	0.0132335i
$47$		−	1.39882i		−	0.204039i	−0.994782	−	0.102020i	$-0.967470\pi$
$47$		−	1.39882i		−	0.204039i	0.994782	−	0.102020i	$-0.0325304\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	5.22499	−	4.65827i	0.746427	−	0.665467i
$50$		−	6.98490i		−	0.987814i
$51$		−	2.71544i		−	0.380238i
$52$	0.753738			0.104525
$53$	−7.18923	+	4.15071i	−0.987517	+	0.570143i	−0.904531	−	0.426407i	$-0.859779\pi$
$53$	−7.18923	+	4.15071i	−0.987517	+	0.570143i	−0.0829859	+	0.996551i	$0.526446\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	5.00029	−	2.88692i	0.674240	−	0.389272i
$56$	−0.942075	−	2.47235i	−0.125890	−	0.330381i
$57$	0.186177	−	4.35492i	0.0246598	−	0.576823i
$58$	3.51860	+	6.09439i	0.462015	+	0.800233i
$59$	8.43918			1.09869			0.549344	−	0.835596i	$-0.314878\pi$
$59$	8.43918			1.09869			0.549344	+	0.835596i	$0.314878\pi$
$60$		−	3.46192i		−	0.446932i
$61$			0.172034i			0.0220267i	0.999939	+	0.0110134i	$0.00350574\pi$
$61$			0.172034i			0.0220267i	−0.999939	+	0.0110134i	$0.996494\pi$
$62$	−1.97162	+	1.13832i	−0.250397	+	0.144567i
$63$	2.47235	−	0.942075i	0.311486	−	0.118690i
$64$	−1.00000			−0.125000
$65$	−2.25979	+	1.30469i	−0.280293	+	0.161827i
$66$	1.44437	−	0.833907i	0.177790	−	0.102647i
$67$	0.393709	−	0.227308i	0.0480992	−	0.0277701i	−0.475758	−	0.879576i	$-0.657826\pi$
$67$	0.393709	−	0.227308i	0.0480992	−	0.0277701i	0.523857	+	0.851806i	$0.324493\pi$
$68$	2.35164	−	1.35772i	0.285178	−	0.164648i
$69$	0.179508			0.0216102
$70$	7.10398	+	5.78168i	0.849088	+	0.691043i
$71$	9.60367	−	5.54468i	1.13975	−	0.658033i	0.193379	−	0.981124i	$-0.438055\pi$
$71$	9.60367	−	5.54468i	1.13975	−	0.658033i	0.946368	+	0.323091i	$0.104722\pi$
$72$		−	1.00000i		−	0.117851i
$73$			6.04386i			0.707380i	0.935363	+	0.353690i	$0.115073\pi$
$73$			6.04386i			0.707380i	−0.935363	+	0.353690i	$0.884927\pi$
$74$	5.31452			0.617801
$75$	3.49245	+	6.04910i	0.403273	+	0.698490i
$76$	3.86456	−	2.01623i	0.443296	−	0.231277i
$77$	−0.701003	+	4.35658i	−0.0798867	+	0.496479i
$78$	−0.652756	+	0.376869i	−0.0739101	+	0.0426720i
$79$	−12.9200	−	7.45937i	−1.45361	−	0.839244i	−0.454929	−	0.890528i	$-0.650336\pi$
$79$	−12.9200	−	7.45937i	−1.45361	−	0.839244i	−0.998684	+	0.0512833i	$0.983669\pi$
$80$	2.99811	−	1.73096i	0.335199	−	0.193527i
$81$	1.00000			0.111111
$82$			4.17254i			0.460780i
$83$		−	8.65416i		−	0.949918i	−0.880008	−	0.474959i	$-0.842463\pi$
$83$		−	8.65416i		−	0.949918i	0.880008	−	0.474959i	$-0.157537\pi$
$84$	2.05203	+	1.67008i	0.223895	+	0.182220i
$85$	−4.70032	+	8.14120i	−0.509822	+	0.883037i
$86$			12.1488i			1.31004i
$87$	−6.09439	−	3.51860i	−0.653387	−	0.377233i
$88$	1.44437	+	0.833907i	0.153970	+	0.0888948i
$89$	14.3415			1.52020			0.760098	−	0.649808i	$-0.225151\pi$
$89$	14.3415			1.52020			0.760098	+	0.649808i	$0.225151\pi$
$90$	1.73096	+	2.99811i	0.182459	+	0.316029i
$91$	0.316806	−	1.96888i	0.0332102	−	0.206395i
$92$	0.0897540	+	0.155458i	0.00935750	+	0.0162077i
$93$	1.13832	−	1.97162i	0.118038	−	0.204448i
$94$	−0.699411	+	1.21141i	−0.0721387	+	0.124948i
$95$	−8.09638	+	12.7343i	−0.830671	+	1.30651i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−6.55154	−	11.3476i	−0.665208	−	1.15217i	−0.979229	−	0.202758i	$-0.935010\pi$
$97$	−6.55154	−	11.3476i	−0.665208	−	1.15217i	0.314021	−	0.949416i	$-0.398324\pi$
$98$	−6.85411	+	1.42168i	−0.692370	+	0.143612i
$99$	−0.833907	+	1.44437i	−0.0838108	+	0.145165i
$100$	−3.49245	+	6.04910i	−0.349245	+	0.604910i
$101$	−5.62338	+	3.24666i	−0.559547	+	0.323055i	−0.752964	−	0.658062i	$-0.771376\pi$
$101$	−5.62338	+	3.24666i	−0.559547	+	0.323055i	0.193417	+	0.981117i	$0.438043\pi$
$102$	−1.35772	+	2.35164i	−0.134434	+	0.232847i
$103$	5.09047	+	8.81695i	0.501579	+	0.868760i	0.999998	+	0.00182371i	$0.000580506\pi$
$103$	5.09047	+	8.81695i	0.501579	+	0.868760i	−0.498420	+	0.866936i	$0.666086\pi$
$104$	−0.652756	−	0.376869i	−0.0640080	−	0.0369550i
$105$	−9.04306	−	1.45509i	−0.882513	−	0.142002i
$106$	8.30141			0.806304
$107$	−2.94290	+	1.69908i	−0.284501	+	0.164257i	−0.635459	−	0.772134i	$-0.719189\pi$
$107$	−2.94290	+	1.69908i	−0.284501	+	0.164257i	0.350958	+	0.936391i	$0.385856\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			3.20569i			0.307049i	0.988145	+	0.153525i	$0.0490624\pi$
$109$			3.20569i			0.307049i	−0.988145	+	0.153525i	$0.950938\pi$
$110$	−5.77384			−0.550514
$111$	−4.60251	+	2.65726i	−0.436851	+	0.252216i
$112$	−0.420313	+	2.61215i	−0.0397158	+	0.246825i
$113$		−	13.8494i		−	1.30284i	−0.758716	−	0.651421i	$-0.774173\pi$
$113$		−	13.8494i		−	1.30284i	0.758716	−	0.651421i	$-0.225827\pi$
$114$	−2.33869	+	3.67838i	−0.219039	+	0.344512i
$115$	−0.538185	−	0.310721i	−0.0501860	−	0.0289749i
$116$		−	7.03720i		−	0.653387i
$117$	0.376869	−	0.652756i	0.0348416	−	0.0603473i
$118$	−7.30854	−	4.21959i	−0.672806	−	0.388445i
$119$	−2.55815	−	6.71351i	−0.234505	−	0.615427i
$120$	−1.73096	+	2.99811i	−0.158014	+	0.273689i
$121$	4.10920	+	7.11734i	0.373563	+	0.647031i
$122$	0.0860172	−	0.148986i	0.00778763	−	0.0134886i
$123$	−2.08627	−	3.61352i	−0.188113	−	0.325820i
$124$	2.27664			0.204448
$125$		−	6.87157i		−	0.614612i
$126$	−2.61215	−	0.420313i	−0.232709	−	0.0374444i
$127$	8.41909	+	4.86076i	0.747073	+	0.431323i	0.824635	−	0.565664i	$-0.191380\pi$
$127$	8.41909	+	4.86076i	0.747073	+	0.431323i	−0.0775621	+	0.996988i	$0.524714\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.07440	−	10.5212i	−0.534822	−	0.926338i
$130$	2.60938			0.228858
$131$	5.90509	+	3.40930i	0.515930	+	0.297872i	0.735268	−	0.677777i	$-0.237056\pi$
$131$	5.90509	+	3.40930i	0.515930	+	0.297872i	−0.219338	+	0.975649i	$0.570390\pi$
$132$	−1.66781			−0.145165
$133$	−3.64237	−	10.9423i	−0.315833	−	0.948815i
$134$	−0.454616			−0.0392728
$135$	−2.99811	−	1.73096i	−0.258036	−	0.148977i
$136$	−2.71544			−0.232847
$137$	7.07999	+	12.2629i	0.604884	+	1.04769i	0.992070	+	0.125688i	$0.0401139\pi$
$137$	7.07999	+	12.2629i	0.604884	+	1.04769i	−0.387186	+	0.922002i	$0.626553\pi$
$138$	−0.155458	−	0.0897540i	−0.0132335	−	0.00764037i
$139$	12.9105	+	7.45388i	1.09505	+	0.632230i	0.934918	−	0.354865i	$-0.115473\pi$
$139$	12.9105	+	7.45388i	1.09505	+	0.632230i	0.160137	+	0.987095i	$0.448806\pi$
$140$	−3.26139	−	8.55907i	−0.275638	−	0.723373i
$141$		−	1.39882i		−	0.117802i
$142$	−11.0894			−0.930599
$143$	0.628548	+	1.08868i	0.0525618	+	0.0910397i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	12.1811	+	21.0983i	1.01159	+	1.75212i
$146$	3.02193	−	5.23414i	0.250097	−	0.433180i
$147$	5.22499	−	4.65827i	0.430950	−	0.384208i
$148$	−4.60251	−	2.65726i	−0.378324	−	0.218426i
$149$	−2.44641	+	4.23731i	−0.200418	+	0.347134i	−0.948663	−	0.316288i	$-0.897563\pi$
$149$	−2.44641	+	4.23731i	−0.200418	+	0.347134i	0.748245	+	0.663422i	$0.230897\pi$
$150$		−	6.98490i		−	0.570315i
$151$	−5.07321	−	2.92902i	−0.412852	−	0.238360i	0.279162	−	0.960244i	$-0.409943\pi$
$151$	−5.07321	−	2.92902i	−0.412852	−	0.238360i	−0.692014	+	0.721884i	$0.743277\pi$
$152$	−4.35492	−	0.186177i	−0.353231	−	0.0151010i
$153$		−	2.71544i		−	0.219530i
$154$	2.78538	−	3.42241i	0.224452	−	0.275786i
$155$	−6.82561	+	3.94077i	−0.548246	+	0.316530i
$156$	0.753738			0.0603473
$157$		−	5.42610i		−	0.433050i	−0.976277	−	0.216525i	$-0.930528\pi$
$157$		−	5.42610i		−	0.433050i	0.976277	−	0.216525i	$-0.0694723\pi$
$158$	7.45937	+	12.9200i	0.593435	+	1.02786i
$159$	−7.18923	+	4.15071i	−0.570143	+	0.329172i
$160$	−3.46192			−0.273689
$161$	0.443806	−	0.169110i	0.0349768	−	0.0133277i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	1.89504	+	3.28231i	0.148431	+	0.257091i	0.930648	−	0.365916i	$-0.119244\pi$
$163$	1.89504	+	3.28231i	0.148431	+	0.257091i	−0.782217	+	0.623007i	$0.785911\pi$
$164$	2.08627	−	3.61352i	0.162910	−	0.282169i
$165$	5.00029	−	2.88692i	0.389272	−	0.224747i
$166$	−4.32708	+	7.49472i	−0.335847	+	0.581703i
$167$	−6.08235	+	10.5349i	−0.470666	+	0.815217i	−0.999437	−	0.0335470i	$-0.989320\pi$
$167$	−6.08235	+	10.5349i	−0.470666	+	0.815217i	0.528771	+	0.848764i	$0.322653\pi$
$168$	−0.942075	−	2.47235i	−0.0726826	−	0.190746i
$169$	6.21594	+	10.7663i	0.478149	+	0.828179i
$170$	8.14120	−	4.70032i	0.624401	−	0.360498i
$171$	0.186177	−	4.35492i	0.0142373	−	0.333029i
$172$	6.07440	−	10.5212i	0.463169	−	0.802232i
$173$	4.79779	−	8.31002i	0.364769	−	0.631799i	−0.623970	−	0.781448i	$-0.714481\pi$
$173$	4.79779	−	8.31002i	0.364769	−	0.631799i	0.988739	+	0.149650i	$0.0478145\pi$
$174$	3.51860	+	6.09439i	0.266744	+	0.462015i
$175$	14.3333	+	11.6653i	1.08349	+	0.881816i
$176$	−0.833907	−	1.44437i	−0.0628581	−	0.108873i
$177$	8.43918			0.634327
$178$	−12.4201	−	7.17075i	−0.930927	−	0.537471i
$179$	13.2663	+	7.65932i	0.991572	+	0.572485i	0.905744	−	0.423825i	$-0.139313\pi$
$179$	13.2663	+	7.65932i	0.991572	+	0.572485i	0.0858285	+	0.996310i	$0.472646\pi$
$180$		−	3.46192i		−	0.258036i
$181$	−3.13405	+	5.42834i	−0.232952	+	0.403485i	−0.958676	−	0.284502i	$-0.908172\pi$
$181$	−3.13405	+	5.42834i	−0.232952	+	0.403485i	0.725723	+	0.687987i	$0.241505\pi$
$182$	−1.25880	+	1.54670i	−0.0933085	+	0.114649i
$183$			0.172034i			0.0127171i
$184$		−	0.179508i		−	0.0132335i
$185$	18.3985			1.35268
$186$	−1.97162	+	1.13832i	−0.144567	+	0.0834655i
$187$	3.92210	+	2.26443i	0.286812	+	0.165591i
$188$	1.21141	−	0.699411i	0.0883515	−	0.0510098i
$189$	2.47235	−	0.942075i	0.179837	−	0.0685258i
$190$	13.3788	−	6.98002i	0.970601	−	0.506384i
$191$	−8.25535	−	14.2987i	−0.597336	−	1.03462i	−0.993213	−	0.116313i	$-0.962892\pi$
$191$	−8.25535	−	14.2987i	−0.597336	−	1.03462i	0.395876	−	0.918304i	$-0.370441\pi$
$192$	−1.00000			−0.0721688
$193$		−	8.95031i		−	0.644257i	−0.946696	−	0.322129i	$-0.895602\pi$
$193$		−	8.95031i		−	0.644257i	0.946696	−	0.322129i	$-0.104398\pi$
$194$			13.1031i			0.940746i
$195$	−2.25979	+	1.30469i	−0.161827	+	0.0934309i
$196$	6.64667	+	2.19584i	0.474762	+	0.156846i
$197$	25.1014			1.78840			0.894200	−	0.447668i	$-0.147745\pi$
$197$	25.1014			1.78840			0.894200	+	0.447668i	$0.147745\pi$
$198$	1.44437	−	0.833907i	0.102647	−	0.0592632i
$199$	−10.2769	+	5.93337i	−0.728510	+	0.420605i	−0.817877	−	0.575393i	$-0.804849\pi$
$199$	−10.2769	+	5.93337i	−0.728510	+	0.420605i	0.0893670	+	0.995999i	$0.471516\pi$
$200$	6.04910	−	3.49245i	0.427736	−	0.246954i
$201$	0.393709	−	0.227308i	0.0277701	−	0.0160331i
$202$	6.49332			0.456868
$203$	−18.3822	−	2.95782i	−1.29018	−	0.207598i
$204$	2.35164	−	1.35772i	0.164648	−	0.0950595i
$205$			14.4450i			1.00888i
$206$		−	10.1809i		−	0.709339i
$207$	0.179508			0.0124767
$208$	0.376869	+	0.652756i	0.0261312	+	0.0452605i
$209$	6.13486	+	3.90051i	0.424357	+	0.269804i
$210$	7.10398	+	5.78168i	0.490221	+	0.398974i
$211$	−0.506729	+	0.292560i	−0.0348846	+	0.0201407i	−0.517341	−	0.855779i	$-0.673078\pi$
$211$	−0.506729	+	0.292560i	−0.0348846	+	0.0201407i	0.482456	+	0.875920i	$0.339745\pi$
$212$	−7.18923	−	4.15071i	−0.493759	−	0.285072i
$213$	9.60367	−	5.54468i	0.658033	−	0.379915i
$214$	3.39817			0.232294
$215$			42.0582i			2.86835i
$216$		−	1.00000i		−	0.0680414i
$217$	0.956899	−	5.94692i	0.0649585	−	0.403703i
$218$	1.60284	−	2.77621i	0.108558	−	0.188028i
$219$			6.04386i			0.408406i
$220$	5.00029	+	2.88692i	0.337120	+	0.194636i
$221$	−1.77252	−	1.02337i	−0.119233	−	0.0688390i
$222$	5.31452			0.356687
$223$	11.6970	+	20.2599i	0.783291	+	1.35670i	0.930015	+	0.367523i	$0.119794\pi$
$223$	11.6970	+	20.2599i	0.783291	+	1.35670i	−0.146723	+	0.989178i	$0.546873\pi$
$224$	1.67008	−	2.05203i	0.111587	−	0.137107i
$225$	3.49245	+	6.04910i	0.232830	+	0.403273i
$226$	−6.92470	+	11.9939i	−0.460624	+	0.797825i
$227$	−13.4047	+	23.2177i	−0.889704	+	1.54101i	−0.0494792	+	0.998775i	$0.515756\pi$
$227$	−13.4047	+	23.2177i	−0.889704	+	1.54101i	−0.840225	+	0.542238i	$0.817577\pi$
$228$	3.86456	−	2.01623i	0.255937	−	0.133528i
$229$	20.4578	−	11.8113i	1.35189	−	0.780512i	0.363373	−	0.931644i	$-0.381625\pi$
$229$	20.4578	−	11.8113i	1.35189	−	0.780512i	0.988514	+	0.151131i	$0.0482916\pi$
$230$	0.310721	+	0.538185i	0.0204884	+	0.0354869i
$231$	−0.701003	+	4.35658i	−0.0461226	+	0.286642i
$232$	−3.51860	+	6.09439i	−0.231007	+	0.400116i
$233$	10.1683	−	17.6120i	0.666148	−	1.15380i	−0.312825	−	0.949811i	$-0.601275\pi$
$233$	10.1683	−	17.6120i	0.666148	−	1.15380i	0.978973	−	0.203991i	$-0.0653913\pi$
$234$	−0.652756	+	0.376869i	−0.0426720	+	0.0246367i
$235$	−2.42130	+	4.19382i	−0.157948	+	0.273575i
$236$	4.21959	+	7.30854i	0.274672	+	0.475746i
$237$	−12.9200	−	7.45937i	−0.839244	−	0.484538i
$238$	−1.14133	+	7.09315i	−0.0739817	+	0.459780i
$239$	−5.57170			−0.360404			−0.180202	−	0.983630i	$-0.557675\pi$
$239$	−5.57170			−0.360404			−0.180202	+	0.983630i	$0.557675\pi$
$240$	2.99811	−	1.73096i	0.193527	−	0.111733i
$241$	5.88826	+	10.1988i	0.379296	+	0.656960i	0.990960	−	0.134158i	$-0.0428329\pi$
$241$	5.88826	+	10.1988i	0.379296	+	0.656960i	−0.611664	+	0.791118i	$0.709500\pi$
$242$		−	8.21839i		−	0.528298i
$243$	1.00000			0.0641500
$244$	−0.148986	+	0.0860172i	−0.00953786	+	0.00550669i
$245$	−23.7284	+	4.92176i	−1.51595	+	0.314440i
$246$			4.17254i			0.266031i
$247$	−2.77254	−	1.76276i	−0.176412	−	0.112162i
$248$	−1.97162	−	1.13832i	−0.125198	−	0.0722833i
$249$		−	8.65416i		−	0.548435i
$250$	−3.43579	+	5.95095i	−0.217298	+	0.376371i
$251$	10.1039	+	5.83348i	0.637751	+	0.368206i	0.783748	−	0.621079i	$-0.213306\pi$
$251$	10.1039	+	5.83348i	0.637751	+	0.368206i	−0.145997	+	0.989285i	$0.546639\pi$
$252$	2.05203	+	1.67008i	0.129266	+	0.105205i
$253$	−0.149693	+	0.259276i	−0.00941112	+	0.0163005i
$254$	−4.86076	−	8.41909i	−0.304991	−	0.528261i
$255$	−4.70032	+	8.14120i	−0.294346	+	0.509822i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	18.2345			1.13744			0.568720	−	0.822531i	$-0.307439\pi$
$257$	18.2345			1.13744			0.568720	+	0.822531i	$0.307439\pi$
$258$			12.1488i			0.756352i
$259$	−8.87566	+	10.9056i	−0.551507	+	0.677640i
$260$	−2.25979	−	1.30469i	−0.140146	−	0.0809135i
$261$	−6.09439	−	3.51860i	−0.377233	−	0.217796i
$262$	−3.40930	−	5.90509i	−0.210627	−	0.364817i
$263$	19.1715			1.18217			0.591083	−	0.806611i	$-0.298700\pi$
$263$	19.1715			1.18217			0.591083	+	0.806611i	$0.298700\pi$
$264$	1.44437	+	0.833907i	0.0888948	+	0.0513234i
$265$	28.7388			1.76541
$266$	−2.31675	+	11.2975i	−0.142049	+	0.692692i
$267$	14.3415			0.877686
$268$	0.393709	+	0.227308i	0.0240496	+	0.0138850i
$269$	7.38072			0.450010			0.225005	−	0.974358i	$-0.427760\pi$
$269$	7.38072			0.450010			0.225005	+	0.974358i	$0.427760\pi$
$270$	1.73096	+	2.99811i	0.105343	+	0.182459i
$271$	−1.84564	−	1.06558i	−0.112115	−	0.0647296i	0.442894	−	0.896574i	$-0.353952\pi$
$271$	−1.84564	−	1.06558i	−0.112115	−	0.0647296i	−0.555009	+	0.831844i	$0.687285\pi$
$272$	2.35164	+	1.35772i	0.142589	+	0.0823239i
$273$	0.316806	−	1.96888i	0.0191739	−	0.119162i
$274$		−	14.1600i		−	0.855435i
$275$	−11.6495			−0.702492
$276$	0.0897540	+	0.155458i	0.00540256	+	0.00935750i
$277$	4.24474	−	7.35210i	0.255042	−	0.441745i	−0.709865	−	0.704338i	$-0.751244\pi$
$277$	4.24474	−	7.35210i	0.255042	−	0.441745i	0.964907	+	0.262592i	$0.0845775\pi$
$278$	−7.45388	−	12.9105i	−0.447054	−	0.774320i
$279$	1.13832	−	1.97162i	0.0681493	−	0.118038i
$280$	−1.45509	+	9.04306i	−0.0869582	+	0.540426i
$281$	19.9705	+	11.5299i	1.19134	+	0.687819i	0.958610	−	0.284723i	$-0.0919016\pi$
$281$	19.9705	+	11.5299i	1.19134	+	0.687819i	0.232728	+	0.972542i	$0.425235\pi$
$282$	−0.699411	+	1.21141i	−0.0416493	+	0.0721387i
$283$		−	21.7372i		−	1.29214i	−0.763276	−	0.646072i	$-0.776411\pi$
$283$		−	21.7372i		−	1.29214i	0.763276	−	0.646072i	$-0.223589\pi$
$284$	9.60367	+	5.54468i	0.569873	+	0.329016i
$285$	−8.09638	+	12.7343i	−0.479588	+	0.754313i
$286$		−	1.25710i		−	0.0743336i
$287$	−8.56219	−	6.96846i	−0.505410	−	0.411335i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	9.62638			0.566257
$290$		−	24.3622i		−	1.43060i
$291$	−6.55154	−	11.3476i	−0.384058	−	0.665208i
$292$	−5.23414	+	3.02193i	−0.306305	+	0.176845i
$293$	−24.9558			−1.45793			−0.728966	−	0.684549i	$-0.759999\pi$
$293$	−24.9558			−1.45793			−0.728966	+	0.684549i	$0.759999\pi$
$294$	−6.85411	+	1.42168i	−0.399740	+	0.0829143i
$295$	−25.3016	−	14.6079i	−1.47312	−	0.850504i
$296$	2.65726	+	4.60251i	0.154450	+	0.267516i
$297$	−0.833907	+	1.44437i	−0.0483882	+	0.0838108i
$298$	4.23731	−	2.44641i	0.245461	−	0.141717i
$299$	0.0676510	−	0.117175i	0.00391236	−	0.00677640i
$300$	−3.49245	+	6.04910i	−0.201637	+	0.349245i
$301$	−24.9298	−	20.2895i	−1.43693	−	1.16946i
$302$	2.92902	+	5.07321i	0.168546	+	0.291930i
$303$	−5.62338	+	3.24666i	−0.323055	+	0.186516i
$304$	3.67838	+	2.33869i	0.210970	+	0.134133i
$305$	0.297785	−	0.515778i	0.0170511	−	0.0295334i
$306$	−1.35772	+	2.35164i	−0.0776157	+	0.134434i
$307$	1.13626	+	1.96806i	0.0648499	+	0.112323i	0.896627	−	0.442786i	$-0.146010\pi$
$307$	1.13626	+	1.96806i	0.0648499	+	0.112323i	−0.831777	+	0.555109i	$0.812676\pi$
$308$	−4.12341	+	1.57121i	−0.234953	+	0.0895278i
$309$	5.09047	+	8.81695i	0.289587	+	0.501579i
$310$	7.88154			0.447641
$311$	−0.188708	−	0.108951i	−0.0107007	−	0.00617803i	0.494640	−	0.869098i	$-0.335300\pi$
$311$	−0.188708	−	0.108951i	−0.0107007	−	0.00617803i	−0.505341	+	0.862920i	$0.668633\pi$
$312$	−0.652756	−	0.376869i	−0.0369550	−	0.0213360i
$313$		−	21.4129i		−	1.21033i	−0.796100	−	0.605165i	$-0.793107\pi$
$313$		−	21.4129i		−	1.21033i	0.796100	−	0.605165i	$-0.206893\pi$
$314$	−2.71305	+	4.69914i	−0.153106	+	0.265188i
$315$	−9.04306	−	1.45509i	−0.509519	−	0.0819850i
$316$		−	14.9187i		−	0.839244i
$317$		−	22.4697i		−	1.26202i	−0.775774	−	0.631011i	$-0.782640\pi$
$317$		−	22.4697i		−	1.26202i	0.775774	−	0.631011i	$-0.217360\pi$
$318$	8.30141			0.465520
$319$	10.1643	−	5.86837i	0.569092	−	0.328566i
$320$	2.99811	+	1.73096i	0.167600	+	0.0967636i
$321$	−2.94290	+	1.69908i	−0.164257	+	0.0948336i
$322$	−0.468902	−	0.0754495i	−0.0261309	−	0.00420463i
$323$	−11.8255	−	0.505553i	−0.657990	−	0.0281297i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	5.26479			0.292038
$326$		−	3.79009i		−	0.209914i
$327$			3.20569i			0.177275i
$328$	−3.61352	+	2.08627i	−0.199523	+	0.115195i
$329$	−1.31779	−	3.45837i	−0.0726523	−	0.190666i
$330$	−5.77384			−0.317840
$331$	−29.9763	+	17.3068i	−1.64764	+	0.951268i	−0.669639	+	0.742687i	$0.733551\pi$
$331$	−29.9763	+	17.3068i	−1.64764	+	0.951268i	−0.978005	+	0.208581i	$0.933115\pi$
$332$	7.49472	−	4.32708i	0.411326	−	0.237479i
$333$	−4.60251	+	2.65726i	−0.252216	+	0.145617i
$334$	10.5349	−	6.08235i	0.576446	−	0.332811i
$335$	−1.57385			−0.0859884
$336$	−0.420313	+	2.61215i	−0.0229299	+	0.142505i
$337$	−21.0211	+	12.1365i	−1.14509	+	0.661118i	−0.947686	−	0.319204i	$-0.896585\pi$
$337$	−21.0211	+	12.1365i	−1.14509	+	0.661118i	−0.197404	+	0.980322i	$0.563251\pi$
$338$		−	12.4319i		−	0.676205i
$339$		−	13.8494i		−	0.752196i
$340$	−9.40065			−0.509822
$341$	1.89850	+	3.28830i	0.102810	+	0.178072i
$342$	−2.33869	+	3.67838i	−0.126462	+	0.198904i
$343$	8.52955	−	16.4392i	0.460552	−	0.887633i
$344$	−10.5212	+	6.07440i	−0.567264	+	0.327510i
$345$	−0.538185	−	0.310721i	−0.0289749	−	0.0167287i
$346$	−8.31002	+	4.79779i	−0.446749	+	0.257931i
$347$	−19.6708			−1.05598			−0.527992	−	0.849249i	$-0.677055\pi$
$347$	−19.6708			−1.05598			−0.527992	+	0.849249i	$0.677055\pi$
$348$		−	7.03720i		−	0.377233i
$349$		−	24.4588i		−	1.30925i	−0.755954	−	0.654625i	$-0.772827\pi$
$349$		−	24.4588i		−	1.30925i	0.755954	−	0.654625i	$-0.227173\pi$
$350$	−6.58030	−	17.2691i	−0.351732	−	0.923072i
$351$	0.376869	−	0.652756i	0.0201158	−	0.0348416i
$352$			1.66781i			0.0888948i
$353$	−12.4164	−	7.16862i	−0.660859	−	0.381547i	0.131745	−	0.991284i	$-0.457942\pi$
$353$	−12.4164	−	7.16862i	−0.660859	−	0.381547i	−0.792604	+	0.609736i	$0.791275\pi$
$354$	−7.30854	−	4.21959i	−0.388445	−	0.224269i
$355$	−38.3905			−2.03756
$356$	7.17075	+	12.4201i	0.380049	+	0.658265i
$357$	−2.55815	−	6.71351i	−0.135392	−	0.355317i
$358$	−7.65932	−	13.2663i	−0.404808	−	0.701148i
$359$	−7.73185	+	13.3920i	−0.408071	+	0.706800i	−0.994674	−	0.103075i	$-0.967132\pi$
$359$	−7.73185	+	13.3920i	−0.408071	+	0.706800i	0.586602	+	0.809875i	$0.300465\pi$
$360$	−1.73096	+	2.99811i	−0.0912296	+	0.158014i
$361$	−18.9307	−	1.62157i	−0.996351	−	0.0853459i
$362$	5.42834	−	3.13405i	0.285307	−	0.164722i
$363$	4.10920	+	7.11734i	0.215677	+	0.373563i
$364$	1.86350	−	0.710078i	0.0976740	−	0.0372182i
$365$	10.4617	−	18.1202i	0.547590	−	0.948453i
$366$	0.0860172	−	0.148986i	0.00449619	−	0.00778763i
$367$	24.5784	−	14.1903i	1.28298	−	0.740729i	0.305588	−	0.952164i	$-0.401147\pi$
$367$	24.5784	−	14.1903i	1.28298	−	0.740729i	0.977392	+	0.211435i	$0.0678136\pi$
$368$	−0.0897540	+	0.155458i	−0.00467875	+	0.00810383i
$369$	−2.08627	−	3.61352i	−0.108607	−	0.188113i
$370$	−15.9335	−	9.19923i	−0.828345	−	0.478245i
$371$	−13.8640	+	17.0348i	−0.719783	+	0.884401i
$372$	2.27664			0.118038
$373$	−27.5861	+	15.9268i	−1.42835	+	0.824660i	−0.996991	−	0.0775196i	$-0.975300\pi$
$373$	−27.5861	+	15.9268i	−1.42835	+	0.824660i	−0.431361	+	0.902179i	$0.641967\pi$
$374$	−2.26443	−	3.92210i	−0.117091	−	0.202807i
$375$		−	6.87157i		−	0.354846i
$376$	−1.39882			−0.0721387
$377$	−4.59357	+	2.65210i	−0.236581	+	0.136590i
$378$	−2.61215	−	0.420313i	−0.134355	−	0.0216185i
$379$		−	27.1879i		−	1.39655i	−0.715829	−	0.698275i	$-0.753951\pi$
$379$		−	27.1879i		−	1.39655i	0.715829	−	0.698275i	$-0.246049\pi$
$380$	−15.0764	−	0.644530i	−0.773403	−	0.0330637i
$381$	8.41909	+	4.86076i	0.431323	+	0.249024i
$382$			16.5107i			0.844761i
$383$	−8.28398	+	14.3483i	−0.423292	+	0.733162i	−0.996259	−	0.0864155i	$-0.972459\pi$
$383$	−8.28398	+	14.3483i	−0.423292	+	0.733162i	0.572968	+	0.819578i	$0.305792\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	9.64276	−	11.8481i	0.491441	−	0.603836i
$386$	−4.47515	+	7.75119i	−0.227779	+	0.394525i
$387$	−6.07440	−	10.5212i	−0.308779	−	0.534822i
$388$	6.55154	−	11.3476i	0.332604	−	0.576087i
$389$	−11.3635	−	19.6822i	−0.576152	−	0.997925i	−0.995915	−	0.0902912i	$-0.971220\pi$
$389$	−11.3635	−	19.6822i	−0.576152	−	0.997925i	0.419763	−	0.907634i	$-0.362113\pi$
$390$	2.60938			0.132131
$391$		−	0.487443i		−	0.0246511i
$392$	−4.65827	−	5.22499i	−0.235278	−	0.263902i
$393$	5.90509	+	3.40930i	0.297872	+	0.171977i
$394$	−21.7384	−	12.5507i	−1.09517	−	0.632295i
$395$	25.8237	+	44.7280i	1.29933	+	2.25051i
$396$	−1.66781			−0.0838108
$397$	11.8577	+	6.84602i	0.595119	+	0.343592i	0.767119	−	0.641505i	$-0.221690\pi$
$397$	11.8577	+	6.84602i	0.595119	+	0.343592i	−0.172000	+	0.985097i	$0.555023\pi$
$398$	11.8667			0.594826
$399$	−3.64237	−	10.9423i	−0.182346	−	0.547798i
$400$	−6.98490			−0.349245
$401$	27.7981	+	16.0492i	1.38817	+	0.801461i	0.993109	−	0.117193i	$-0.0373897\pi$
$401$	27.7981	+	16.0492i	1.38817	+	0.801461i	0.395062	+	0.918654i	$0.370723\pi$
$402$	−0.454616			−0.0226742
$403$	−0.857994	−	1.48609i	−0.0427397	−	0.0740274i
$404$	−5.62338	−	3.24666i	−0.279774	−	0.161527i
$405$	−2.99811	−	1.73096i	−0.148977	−	0.0860121i
$406$	14.4406	+	11.7527i	0.716673	+	0.583275i
$407$		−	8.86364i		−	0.439354i
$408$	−2.71544			−0.134434
$409$	−12.9097	−	22.3602i	−0.638342	−	1.10564i	−0.985797	−	0.167943i	$-0.946287\pi$
$409$	−12.9097	−	22.3602i	−0.638342	−	1.10564i	0.347455	−	0.937697i	$-0.387046\pi$
$410$	7.22250	−	12.5097i	0.356694	−	0.617812i
$411$	7.07999	+	12.2629i	0.349230	+	0.604884i
$412$	−5.09047	+	8.81695i	−0.250789	+	0.434380i
$413$	20.8646	−	7.95034i	1.02668	−	0.391210i
$414$	−0.155458	−	0.0897540i	−0.00764037	−	0.00441117i
$415$	−14.9800	+	25.9461i	−0.735340	+	1.27365i
$416$		−	0.753738i		−	0.0369550i
$417$	12.9105	+	7.45388i	0.632230	+	0.365018i
$418$	−3.36269	−	6.44537i	−0.164475	−	0.315253i
$419$			3.39479i			0.165846i	0.996556	+	0.0829231i	$0.0264256\pi$
$419$			3.39479i			0.165846i	−0.996556	+	0.0829231i	$0.973574\pi$
$420$	−3.26139	−	8.55907i	−0.159139	−	0.417640i
$421$	−24.6109	+	14.2091i	−1.19946	+	0.692511i	−0.960436	−	0.278502i	$-0.910162\pi$
$421$	−24.6109	+	14.2091i	−1.19946	+	0.692511i	−0.239028	+	0.971013i	$0.576829\pi$
$422$	0.585120			0.0284832
$423$		−	1.39882i		−	0.0680130i
$424$	4.15071	+	7.18923i	0.201576	+	0.349140i
$425$	16.4260	−	9.48355i	0.796777	−	0.460020i
$426$	−11.0894			−0.537282
$427$	0.162069	+	0.425329i	0.00784308	+	0.0205831i
$428$	−2.94290	−	1.69908i	−0.142250	−	0.0821283i
$429$	0.628548	+	1.08868i	0.0303466	+	0.0525618i
$430$	21.0291	−	36.4235i	1.01411	−	1.75650i
$431$	−22.5823	+	13.0379i	−1.08775	+	0.628013i	−0.932976	−	0.359938i	$-0.882798\pi$
$431$	−22.5823	+	13.0379i	−1.08775	+	0.628013i	−0.154773	+	0.987950i	$0.549465\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	13.9183	−	24.1073i	0.668873	−	1.15852i	−0.309347	−	0.950949i	$-0.600110\pi$
$433$	13.9183	−	24.1073i	0.668873	−	1.15852i	0.978220	−	0.207572i	$-0.0665563\pi$
$434$	−3.80216	+	4.67173i	−0.182509	+	0.224250i
$435$	12.1811	+	21.0983i	0.584040	+	1.01159i
$436$	−2.77621	+	1.60284i	−0.132956	+	0.0767623i
$437$	0.0334203	−	0.781743i	0.00159871	−	0.0373958i
$438$	3.02193	−	5.23414i	0.144393	−	0.250097i
$439$	11.3884	−	19.7254i	0.543541	−	0.941441i	−0.455156	−	0.890412i	$-0.650417\pi$
$439$	11.3884	−	19.7254i	0.543541	−	0.941441i	0.998697	−	0.0510290i	$-0.0162501\pi$
$440$	−2.88692	−	5.00029i	−0.137629	−	0.238380i
$441$	5.22499	−	4.65827i	0.248809	−	0.221822i
$442$	1.02337	+	1.77252i	0.0486766	+	0.0843103i
$443$	19.2591			0.915025			0.457513	−	0.889203i	$-0.348740\pi$
$443$	19.2591			0.915025			0.457513	+	0.889203i	$0.348740\pi$
$444$	−4.60251	−	2.65726i	−0.218426	−	0.126108i
$445$	−42.9974	−	24.8246i	−2.03827	−	1.17680i
$446$		−	23.3941i		−	1.10774i
$447$	−2.44641	+	4.23731i	−0.115711	+	0.200418i
$448$	−2.47235	+	0.942075i	−0.116807	+	0.0445088i
$449$			17.6814i			0.834438i	0.908806	+	0.417219i	$0.136995\pi$
$449$			17.6814i			0.834438i	−0.908806	+	0.417219i	$0.863005\pi$
$450$		−	6.98490i		−	0.329271i
$451$	6.95902			0.327687
$452$	11.9939	−	6.92470i	0.564147	−	0.325711i
$453$	−5.07321	−	2.92902i	−0.238360	−	0.137617i
$454$	23.2177	−	13.4047i	1.08966	−	0.629116i
$455$	−4.35787	+	5.35454i	−0.204300	+	0.251025i
$456$	−4.35492	−	0.186177i	−0.203938	−	0.00871854i
$457$	12.2550	+	21.2263i	0.573266	+	0.992926i	0.996228	+	0.0867787i	$0.0276573\pi$
$457$	12.2550	+	21.2263i	0.573266	+	0.992926i	−0.422961	+	0.906148i	$0.639009\pi$
$458$	−23.6226			−1.10381
$459$		−	2.71544i		−	0.126746i
$460$		−	0.621443i		−	0.0289749i
$461$	−8.66536	+	5.00295i	−0.403586	+	0.233011i	−0.688030	−	0.725682i	$-0.741524\pi$
$461$	−8.66536	+	5.00295i	−0.403586	+	0.233011i	0.284444	+	0.958693i	$0.408191\pi$
$462$	2.78538	−	3.42241i	0.129588	−	0.159225i
$463$	−0.788739			−0.0366558			−0.0183279	−	0.999832i	$-0.505834\pi$
$463$	−0.788739			−0.0366558			−0.0183279	+	0.999832i	$0.505834\pi$
$464$	6.09439	−	3.51860i	0.282925	−	0.163347i
$465$	−6.82561	+	3.94077i	−0.316530	+	0.182749i
$466$	−17.6120	+	10.1683i	−0.815861	+	0.471038i
$467$	1.14251	−	0.659631i	0.0528693	−	0.0305241i	−0.473332	−	0.880884i	$-0.656949\pi$
$467$	1.14251	−	0.659631i	0.0528693	−	0.0305241i	0.526202	+	0.850360i	$0.323616\pi$
$468$	0.753738			0.0348416
$469$	0.759244	−	0.932888i	0.0350586	−	0.0430767i
$470$	4.19382	−	2.42130i	0.193447	−	0.111686i
$471$		−	5.42610i		−	0.250021i
$472$		−	8.43918i		−	0.388445i
$473$	20.2620			0.931646
$474$	7.45937	+	12.9200i	0.342620	+	0.593435i
$475$	26.9936	−	14.0831i	1.23855	−	0.646179i
$476$	4.53500	−	5.57218i	0.207861	−	0.255400i
$477$	−7.18923	+	4.15071i	−0.329172	+	0.190048i
$478$	4.82524	+	2.78585i	0.220701	+	0.127422i
$479$	−8.68664	+	5.01524i	−0.396903	+	0.229152i	−0.685147	−	0.728405i	$-0.740262\pi$
$479$	−8.68664	+	5.01524i	−0.396903	+	0.229152i	0.288244	+	0.957557i	$0.406929\pi$
$480$	−3.46192			−0.158014
$481$			4.00576i			0.182647i
$482$		−	11.7765i		−	0.536406i
$483$	0.443806	−	0.169110i	0.0201939	−	0.00769477i
$484$	−4.10920	+	7.11734i	−0.186782	+	0.323515i
$485$			45.3618i			2.05977i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−13.6501	−	7.88090i	−0.618546	−	0.357118i	0.157757	−	0.987478i	$-0.449574\pi$
$487$	−13.6501	−	7.88090i	−0.618546	−	0.357118i	−0.776303	+	0.630360i	$0.782907\pi$
$488$	0.172034			0.00778763
$489$	1.89504	+	3.28231i	0.0856968	+	0.148431i
$490$	23.0103	+	7.60183i	1.03950	+	0.343416i
$491$	9.86382	+	17.0846i	0.445148	+	0.771019i	0.998063	−	0.0622190i	$-0.0198177\pi$
$491$	9.86382	+	17.0846i	0.445148	+	0.771019i	−0.552915	+	0.833238i	$0.686484\pi$
$492$	2.08627	−	3.61352i	0.0940563	−	0.162910i
$493$	−9.55455	+	16.5490i	−0.430315	+	0.745328i
$494$	1.51971	+	2.91287i	0.0683748	+	0.131056i
$495$	5.00029	−	2.88692i	0.224747	−	0.129757i
$496$	1.13832	+	1.97162i	0.0511120	+	0.0885286i
$497$	18.5201	−	22.7558i	0.830740	−	1.02073i
$498$	−4.32708	+	7.49472i	−0.193901	+	0.335847i
$499$	1.50082	−	2.59949i	0.0671858	−	0.116369i	−0.830476	−	0.557055i	$-0.811931\pi$
$499$	1.50082	−	2.59949i	0.0671858	−	0.116369i	0.897662	+	0.440686i	$0.145265\pi$
$500$	5.95095	−	3.43579i	0.266135	−	0.153653i
$501$	−6.08235	+	10.5349i	−0.271739	+	0.470666i
$502$	−5.83348	−	10.1039i	−0.260361	−	0.450958i
$503$	6.00756	+	3.46847i	0.267864	+	0.154651i	0.627916	−	0.778281i	$-0.283908\pi$
$503$	6.00756	+	3.46847i	0.267864	+	0.154651i	−0.360053	+	0.932932i	$0.617241\pi$
$504$	−0.942075	−	2.47235i	−0.0419633	−	0.110127i
$505$	22.4794			1.00032
$506$	0.259276	−	0.149693i	0.0115262	−	0.00665467i
$507$	6.21594	+	10.7663i	0.276060	+	0.478149i
$508$			9.72153i			0.431323i
$509$	9.36696			0.415183			0.207592	−	0.978216i	$-0.433437\pi$
$509$	9.36696			0.415183			0.207592	+	0.978216i	$0.433437\pi$
$510$	8.14120	−	4.70032i	0.360498	−	0.208134i
$511$	5.69377	+	14.9425i	0.251877	+	0.661018i
$512$			1.00000i			0.0441942i
$513$	0.186177	−	4.35492i	0.00821992	−	0.192274i
$514$	−15.7916	−	9.11727i	−0.696537	−	0.402146i
$515$		−	35.2456i		−	1.55311i
$516$	6.07440	−	10.5212i	0.267411	−	0.463169i
$517$	2.02041	+	1.16649i	0.0888577	+	0.0513020i
$518$	13.1393	−	5.00668i	0.577309	−	0.219981i
$519$	4.79779	−	8.31002i	0.210600	−	0.364769i
$520$	1.30469	+	2.25979i	0.0572145	+	0.0990984i
$521$	4.52031	−	7.82940i	0.198038	−	0.343012i	−0.749854	−	0.661603i	$-0.769876\pi$
$521$	4.52031	−	7.82940i	0.198038	−	0.343012i	0.947892	+	0.318591i	$0.103210\pi$
$522$	3.51860	+	6.09439i	0.154005	+	0.266744i
$523$	−11.9726			−0.523527			−0.261763	−	0.965132i	$-0.584304\pi$
$523$	−11.9726			−0.523527			−0.261763	+	0.965132i	$0.584304\pi$
$524$			6.81861i			0.297872i
$525$	14.3333	+	11.6653i	0.625554	+	0.509116i
$526$	−16.6030	−	9.58576i	−0.723926	−	0.417959i
$527$	−5.35383	−	3.09104i	−0.233217	−	0.134648i
$528$	−0.833907	−	1.44437i	−0.0362912	−	0.0628581i
$529$	−22.9678			−0.998599
$530$	−24.8886	−	14.3694i	−1.08109	−	0.624168i
$531$	8.43918			0.366229
$532$	7.65510	−	8.62551i	0.331891	−	0.373963i
$533$	−3.14500			−0.136225
$534$	−12.4201	−	7.17075i	−0.537471	−	0.310309i
$535$	11.7642			0.508610
$536$	−0.227308	−	0.393709i	−0.00981821	−	0.0170056i
$537$	13.2663	+	7.65932i	0.572485	+	0.330524i
$538$	−6.39189	−	3.69036i	−0.275574	−	0.159103i
$539$	2.37111	+	11.4314i	0.102131	+	0.492385i
$540$		−	3.46192i		−	0.148977i
$541$	19.9442			0.857467			0.428734	−	0.903431i	$-0.358960\pi$
$541$	19.9442			0.857467			0.428734	+	0.903431i	$0.358960\pi$
$542$	1.06558	+	1.84564i	0.0457707	+	0.0792772i
$543$	−3.13405	+	5.42834i	−0.134495	+	0.232952i
$544$	−1.35772	−	2.35164i	−0.0582118	−	0.100826i
$545$	5.54892	−	9.61101i	0.237689	−	0.411690i
$546$	−1.25880	+	1.54670i	−0.0538717	+	0.0661925i
$547$	−16.6959	−	9.63940i	−0.713866	−	0.412151i	0.0986247	−	0.995125i	$-0.468556\pi$
$547$	−16.6959	−	9.63940i	−0.713866	−	0.412151i	−0.812491	+	0.582974i	$0.801889\pi$
$548$	−7.07999	+	12.2629i	−0.302442	+	0.523845i
$549$			0.172034i			0.00734225i
$550$	10.0888	+	5.82476i	0.430187	+	0.248369i
$551$	−16.4579	+	25.8855i	−0.701128	+	1.10276i
$552$		−	0.179508i		−	0.00764037i
$553$	−38.9700	−	6.27053i	−1.65717	−	0.266650i
$554$	−7.35210	+	4.24474i	−0.312361	+	0.180342i
$555$	18.3985			0.780971
$556$			14.9078i			0.632230i
$557$	10.7137	+	18.5567i	0.453955	+	0.786272i	0.998627	−	0.0523762i	$-0.0166795\pi$
$557$	10.7137	+	18.5567i	0.453955	+	0.786272i	−0.544673	+	0.838649i	$0.683346\pi$
$558$	−1.97162	+	1.13832i	−0.0834655	+	0.0481889i
$559$	−9.15702			−0.387301
$560$	5.78168	−	7.10398i	0.244320	−	0.300198i
$561$	3.92210	+	2.26443i	0.165591	+	0.0956042i
$562$	−11.5299	−	19.9705i	−0.486362	−	0.842403i
$563$	6.85177	−	11.8676i	0.288768	−	0.500160i	−0.684748	−	0.728780i	$-0.740088\pi$
$563$	6.85177	−	11.8676i	0.288768	−	0.500160i	0.973516	+	0.228620i	$0.0734212\pi$
$564$	1.21141	−	0.699411i	0.0510098	−	0.0294505i
$565$	−23.9728	+	41.5221i	−1.00854	+	1.74685i
$566$	−10.8686	+	18.8250i	−0.456842	+	0.791273i
$567$	2.47235	−	0.942075i	0.103829	−	0.0395634i
$568$	−5.54468	−	9.60367i	−0.232650	−	0.402961i
$569$	17.8423	−	10.3012i	0.747988	−	0.431851i	−0.0769788	−	0.997033i	$-0.524527\pi$
$569$	17.8423	−	10.3012i	0.747988	−	0.431851i	0.824966	+	0.565182i	$0.191194\pi$
$570$	13.3788	−	6.98002i	0.560377	−	0.292361i
$571$	−18.6332	+	32.2737i	−0.779776	+	1.35061i	0.152294	+	0.988335i	$0.451334\pi$
$571$	−18.6332	+	32.2737i	−0.779776	+	1.35061i	−0.932070	+	0.362277i	$0.881999\pi$
$572$	−0.628548	+	1.08868i	−0.0262809	+	0.0455198i
$573$	−8.25535	−	14.2987i	−0.344872	−	0.597336i
$574$	3.93084	+	10.3160i	0.164070	+	0.430580i
$575$	0.626923	+	1.08586i	0.0261445	+	0.0452836i
$576$	−1.00000			−0.0416667
$577$	−13.2699	−	7.66139i	−0.552434	−	0.318948i	0.197669	−	0.980269i	$-0.436663\pi$
$577$	−13.2699	−	7.66139i	−0.552434	−	0.318948i	−0.750103	+	0.661321i	$0.769996\pi$
$578$	−8.33669	−	4.81319i	−0.346760	−	0.200202i
$579$		−	8.95031i		−	0.371962i
$580$	−12.1811	+	21.0983i	−0.505793	+	0.876059i
$581$	−8.15287	−	21.3961i	−0.338238	−	0.887659i
$582$			13.1031i			0.543140i
$583$		−	13.8452i		−	0.573410i
$584$	6.04386			0.250097
$585$	−2.25979	+	1.30469i	−0.0934309	+	0.0539423i
$586$	21.6123	+	12.4779i	0.892798	+	0.515457i
$587$	34.2667	−	19.7839i	1.41434	−	0.816568i	0.418545	−	0.908196i	$-0.362540\pi$
$587$	34.2667	−	19.7839i	1.41434	−	0.816568i	0.995793	+	0.0916279i	$0.0292070\pi$
$588$	6.64667	+	2.19584i	0.274104	+	0.0905549i
$589$	−8.37434	−	5.32436i	−0.345059	−	0.219386i
$590$	14.6079	+	25.3016i	0.601397	+	1.04165i
$591$	25.1014			1.03253
$592$		−	5.31452i		−	0.218426i
$593$		−	16.8852i		−	0.693393i	−0.937977	−	0.346697i	$-0.887303\pi$
$593$		−	16.8852i		−	0.693393i	0.937977	−	0.346697i	$-0.112697\pi$
$594$	1.44437	−	0.833907i	0.0592632	−	0.0342156i
$595$	−3.95121	+	24.5559i	−0.161984	+	1.00669i
$596$	−4.89283			−0.200418
$597$	−10.2769	+	5.93337i	−0.420605	+	0.242837i
$598$	−0.117175	+	0.0676510i	−0.00479164	+	0.00276646i
$599$	−31.7884	+	18.3530i	−1.29884	+	0.749884i	−0.980203	−	0.197993i	$-0.936558\pi$
$599$	−31.7884	+	18.3530i	−1.29884	+	0.749884i	−0.318635	+	0.947878i	$0.603224\pi$
$600$	6.04910	−	3.49245i	0.246954	−	0.142579i
$601$	20.0026			0.815921			0.407961	−	0.913000i	$-0.366240\pi$
$601$	20.0026			0.815921			0.407961	+	0.913000i	$0.366240\pi$
$602$	11.4451	+	30.0361i	0.466467	+	1.22418i
$603$	0.393709	−	0.227308i	0.0160331	−	0.00925670i
$604$		−	5.85804i		−	0.238360i
$605$		−	28.4514i		−	1.15672i
$606$	6.49332			0.263773
$607$	−16.1450	−	27.9639i	−0.655304	−	1.13502i	−0.981817	−	0.189828i	$-0.939207\pi$
$607$	−16.1450	−	27.9639i	−0.655304	−	1.13502i	0.326513	−	0.945193i	$-0.394126\pi$
$608$	−2.01623	−	3.86456i	−0.0817688	−	0.156729i
$609$	−18.3822	−	2.95782i	−0.744885	−	0.119857i
$610$	−0.515778	+	0.297785i	−0.0208833	+	0.0120570i
$611$	−0.913089	−	0.527172i	−0.0369396	−	0.0213271i
$612$	2.35164	−	1.35772i	0.0950595	−	0.0548826i
$613$	19.5552			0.789828			0.394914	−	0.918718i	$-0.370774\pi$
$613$	19.5552			0.789828			0.394914	+	0.918718i	$0.370774\pi$
$614$		−	2.27253i		−	0.0917117i
$615$			14.4450i			0.582479i
$616$	4.35658	+	0.701003i	0.175532	+	0.0282442i
$617$	−19.7457	+	34.2005i	−0.794931	+	1.37686i	0.127953	+	0.991780i	$0.459159\pi$
$617$	−19.7457	+	34.2005i	−0.794931	+	1.37686i	−0.922883	+	0.385080i	$0.874174\pi$
$618$		−	10.1809i		−	0.409537i
$619$	31.3247	+	18.0853i	1.25904	+	0.726910i	0.972889	−	0.231273i	$-0.0742892\pi$
$619$	31.3247	+	18.0853i	1.25904	+	0.726910i	0.286156	+	0.958183i	$0.407622\pi$
$620$	−6.82561	−	3.94077i	−0.274123	−	0.158265i
$621$	0.179508			0.00720341
$622$	0.108951	+	0.188708i	0.00436853	+	0.00756652i
$623$	35.4572	−	13.5108i	1.42056	−	0.541298i
$624$	0.376869	+	0.652756i	0.0150868	+	0.0261312i
$625$	5.56783	−	9.64377i	0.222713	−	0.385751i
$626$	−10.7065	+	18.5441i	−0.427916	+	0.741172i
$627$	6.13486	+	3.90051i	0.245003	+	0.155771i
$628$	4.69914	−	2.71305i	0.187516	−	0.108262i
$629$	7.21564	+	12.4978i	0.287706	+	0.498322i
$630$	7.10398	+	5.78168i	0.283029	+	0.230348i
$631$	5.48283	−	9.49653i	0.218268	−	0.378051i	−0.736011	−	0.676970i	$-0.763293\pi$
$631$	5.48283	−	9.49653i	0.218268	−	0.378051i	0.954279	+	0.298919i	$0.0966260\pi$
$632$	−7.45937	+	12.9200i	−0.296718	+	0.513930i
$633$	−0.506729	+	0.292560i	−0.0201407	+	0.0116282i
$634$	−11.2348	+	19.4593i	−0.446192	+	0.772828i
$635$	−16.8276	−	29.1462i	−0.667782	−	1.15663i
$636$	−7.18923	−	4.15071i	−0.285072	−	0.164586i
$637$	−1.07158	−	5.16620i	−0.0424574	−	0.204692i
$638$	−11.7367			−0.464662
$639$	9.60367	−	5.54468i	0.379915	−	0.219344i
$640$	−1.73096	−	2.99811i	−0.0684222	−	0.118511i
$641$			13.0650i			0.516037i	0.966140	+	0.258019i	$0.0830696\pi$
$641$			13.0650i			0.516037i	−0.966140	+	0.258019i	$0.916930\pi$
$642$	3.39817			0.134115
$643$	33.4278	−	19.2995i	1.31826	−	0.761099i	0.334813	−	0.942285i	$-0.391327\pi$
$643$	33.4278	−	19.2995i	1.31826	−	0.761099i	0.983449	+	0.181186i	$0.0579935\pi$
$644$	0.368356	+	0.299792i	0.0145153	+	0.0118135i
$645$			42.0582i			1.65604i
$646$	9.98844	+	6.35059i	0.392990	+	0.249861i
$647$	−42.3375	−	24.4435i	−1.66446	−	0.960975i	−0.970547	−	0.240913i	$-0.922553\pi$
$647$	−42.3375	−	24.4435i	−1.66446	−	0.960975i	−0.693910	−	0.720062i	$-0.744114\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−7.03749	+	12.1893i	−0.276246	+	0.478472i
$650$	−4.55944	−	2.63239i	−0.178836	−	0.103251i
$651$	0.956899	−	5.94692i	0.0375038	−	0.233078i
$652$	−1.89504	+	3.28231i	−0.0742156	+	0.128545i
$653$	−19.8505	−	34.3821i	−0.776811	−	1.34548i	−0.933771	−	0.357871i	$-0.883503\pi$
$653$	−19.8505	−	34.3821i	−0.776811	−	1.34548i	0.156961	−	0.987605i	$-0.449830\pi$
$654$	1.60284	−	2.77621i	0.0626761	−	0.108558i
$655$	−11.8027	−	20.4429i	−0.461171	−	0.798772i
$656$	4.17254			0.162910
$657$			6.04386i			0.235793i
$658$	−0.587942	+	3.65393i	−0.0229204	+	0.142445i
$659$	−36.1865	−	20.8923i	−1.40963	−	0.813848i	−0.414274	−	0.910152i	$-0.635965\pi$
$659$	−36.1865	−	20.8923i	−1.40963	−	0.813848i	−0.995352	+	0.0963042i	$0.969298\pi$
$660$	5.00029	+	2.88692i	0.194636	+	0.112373i
$661$	15.9403	+	27.6094i	0.620005	+	1.07388i	0.989484	+	0.144642i	$0.0462029\pi$
$661$	15.9403	+	27.6094i	0.620005	+	1.07388i	−0.369479	+	0.929239i	$0.620464\pi$
$662$	34.6136			1.34530
$663$	−1.77252	−	1.02337i	−0.0688390	−	0.0397442i
$664$	−8.65416			−0.335847
$665$	−8.02041	+	39.1109i	−0.311018	+	1.51666i
$666$	5.31452			0.205934
$667$	−1.09399	−	0.631616i	−0.0423595	−	0.0244563i
$668$	−12.1647			−0.470666
$669$	11.6970	+	20.2599i	0.452233	+	0.783291i
$670$	1.36299	+	0.786923i	0.0526569	+	0.0304015i
$671$	−0.248481	−	0.143461i	−0.00959251	−	0.00553824i
$672$	1.67008	−	2.05203i	0.0644246	−	0.0791589i
$673$		−	15.4688i		−	0.596279i	−0.954522	−	0.298140i	$-0.903634\pi$
$673$		−	15.4688i		−	0.596279i	0.954522	−	0.298140i	$-0.0963661\pi$
$674$	24.2730			0.934962
$675$	3.49245	+	6.04910i	0.134424	+	0.232830i
$676$	−6.21594	+	10.7663i	−0.239075	+	0.414089i
$677$	−4.78135	−	8.28154i	−0.183762	−	0.318285i	0.759397	−	0.650628i	$-0.225494\pi$
$677$	−4.78135	−	8.28154i	−0.183762	−	0.318285i	−0.943159	+	0.332343i	$0.892161\pi$
$678$	−6.92470	+	11.9939i	−0.265942	+	0.460624i
$679$	−26.8880	−	21.8831i	−1.03186	−	0.839798i
$680$	8.14120	+	4.70032i	0.312201	+	0.180249i
$681$	−13.4047	+	23.2177i	−0.513671	+	0.889704i
$682$		−	3.79701i		−	0.145395i
$683$	33.4628	+	19.3197i	1.28042	+	0.739249i	0.976924	−	0.213585i	$-0.0685140\pi$
$683$	33.4628	+	19.3197i	1.28042	+	0.739249i	0.303492	+	0.952834i	$0.401847\pi$
$684$	3.86456	−	2.01623i	0.147765	−	0.0770923i
$685$		−	49.0207i		−	1.87298i
$686$	−15.6064	+	9.97198i	−0.595855	+	0.380732i
$687$	20.4578	−	11.8113i	0.780512	−	0.450629i
$688$	12.1488			0.463169
$689$			6.25709i			0.238376i
$690$	0.310721	+	0.538185i	0.0118290	+	0.0204884i
$691$	−16.4981	+	9.52519i	−0.627618	+	0.362355i	−0.779829	−	0.625993i	$-0.784694\pi$
$691$	−16.4981	+	9.52519i	−0.627618	+	0.362355i	0.152211	+	0.988348i	$0.451361\pi$
$692$	9.59558			0.364769
$693$	−0.701003	+	4.35658i	−0.0266289	+	0.165493i
$694$	17.0354	+	9.83540i	0.646655	+	0.373347i
$695$	−25.8048	−	44.6951i	−0.978830	−	1.69538i
$696$	−3.51860	+	6.09439i	−0.133372	+	0.231007i
$697$	−9.81231	+	5.66514i	−0.371668	+	0.214583i
$698$	−12.2294	+	21.1819i	−0.462889	+	0.801748i
$699$	10.1683	−	17.6120i	0.384601	−	0.666148i
$700$	−2.93584	+	18.2456i	−0.110964	+	0.689620i
$701$	2.32278	+	4.02317i	0.0877302	+	0.151953i	0.906551	−	0.422096i	$-0.138705\pi$
$701$	2.32278	+	4.02317i	0.0877302	+	0.151953i	−0.818821	+	0.574049i	$0.805372\pi$
$702$	−0.652756	+	0.376869i	−0.0246367	+	0.0142240i
$703$	10.7153	+	20.5383i	0.404134	+	0.774616i
$704$	0.833907	−	1.44437i	0.0314291	−	0.0544367i
$705$	−2.42130	+	4.19382i	−0.0911916	+	0.157948i
$706$	7.16862	+	12.4164i	0.269795	+	0.467298i
$707$	−10.8443	+	13.3245i	−0.407844	+	0.501120i
$708$	4.21959	+	7.30854i	0.158582	+	0.274672i
$709$	32.4245			1.21773			0.608864	−	0.793274i	$-0.291625\pi$
$709$	32.4245			1.21773			0.608864	+	0.793274i	$0.291625\pi$
$710$	33.2472	+	19.1953i	1.24774	+	0.720385i
$711$	−12.9200	−	7.45937i	−0.484538	−	0.279748i
$712$		−	14.3415i		−	0.537471i
$713$	0.204337	−	0.353922i	0.00765249	−	0.0132545i
$714$	−1.14133	+	7.09315i	−0.0427134	+	0.265454i
$715$		−	4.35197i		−	0.162754i
$716$			15.3186i			0.572485i
$717$	−5.57170			−0.208079
$718$	13.3920	−	7.73185i	0.499783	−	0.288550i
$719$	35.2535	+	20.3536i	1.31473	+	0.759061i	0.982876	−	0.184269i	$-0.0589917\pi$
$719$	35.2535	+	20.3536i	1.31473	+	0.759061i	0.331856	+	0.943330i	$0.392325\pi$
$720$	2.99811	−	1.73096i	0.111733	−	0.0645091i
$721$	20.8916	+	17.0029i	0.778044	+	0.633223i
$722$	15.5837	+	10.8697i	0.579964	+	0.404527i
$723$	5.88826	+	10.1988i	0.218987	+	0.379296i
$724$	−6.26810			−0.232952
$725$		−	49.1541i		−	1.82554i
$726$		−	8.21839i		−	0.305013i
$727$	34.1903	−	19.7398i	1.26805	−	0.732107i	0.293429	−	0.955981i	$-0.405204\pi$
$727$	34.1903	−	19.7398i	1.26805	−	0.732107i	0.974618	+	0.223873i	$0.0718702\pi$
$728$	−1.96888	−	0.316806i	−0.0729715	−	0.0117416i
$729$	1.00000			0.0370370
$730$	−18.1202	+	10.4617i	−0.670657	+	0.387204i
$731$	−28.5696	+	16.4947i	−1.05669	+	0.610078i
$732$	−0.148986	+	0.0860172i	−0.00550669	+	0.00317929i
$733$	40.9484	−	23.6416i	1.51246	−	0.873222i	0.512571	−	0.858645i	$-0.328693\pi$
$733$	40.9484	−	23.6416i	1.51246	−	0.873222i	0.999894	−	0.0145769i	$-0.00464015\pi$
$734$	−28.3807			−1.04755
$735$	−23.7284	+	4.92176i	−0.875235	+	0.181542i
$736$	0.155458	−	0.0897540i	0.00573028	−	0.00330838i
$737$			0.758215i			0.0279292i
$738$			4.17254i			0.153593i
$739$	39.6738			1.45942			0.729712	−	0.683754i	$-0.239654\pi$
$739$	39.6738			1.45942			0.729712	+	0.683754i	$0.239654\pi$
$740$	9.19923	+	15.9335i	0.338170	+	0.585728i
$741$	−2.77254	−	1.76276i	−0.101852	−	0.0647567i
$742$	20.5240	−	7.82055i	0.753458	−	0.287101i
$743$	7.46942	−	4.31247i	0.274027	−	0.158209i	−0.356689	−	0.934223i	$-0.616095\pi$
$743$	7.46942	−	4.31247i	0.274027	−	0.158209i	0.630716	+	0.776014i	$0.282761\pi$
$744$	−1.97162	−	1.13832i	−0.0722833	−	0.0417328i
$745$	14.6692	−	8.46929i	0.537440	−	0.310291i
$746$	31.8536			1.16624
$747$		−	8.65416i		−	0.316639i
$748$			4.52885i			0.165591i
$749$	−5.67520	+	6.97315i	−0.207367	+	0.254793i
$750$	−3.43579	+	5.95095i	−0.125457	+	0.217298i
$751$			37.4692i			1.36727i	0.729824	+	0.683636i	$0.239602\pi$
$751$			37.4692i			1.36727i	−0.729824	+	0.683636i	$0.760398\pi$
$752$	1.21141	+	0.699411i	0.0441757	+	0.0255049i
$753$	10.1039	+	5.83348i	0.368206	+	0.212584i
$754$	5.30420			0.193168
$755$	10.1400	+	17.5631i	0.369034	+	0.639185i
$756$	2.05203	+	1.67008i	0.0746317	+	0.0607401i
$757$	−24.1673	−	41.8590i	−0.878376	−	1.52139i	−0.853123	−	0.521710i	$-0.825294\pi$
$757$	−24.1673	−	41.8590i	−0.878376	−	1.52139i	−0.0252532	−	0.999681i	$-0.508039\pi$
$758$	−13.5940	+	23.5455i	−0.493755	+	0.855209i
$759$	−0.149693	+	0.259276i	−0.00543351	+	0.00941112i
$760$	12.7343	+	8.09638i	0.461921	+	0.293686i
$761$	18.7976	−	10.8528i	0.681412	−	0.393413i	−0.118975	−	0.992897i	$-0.537961\pi$
$761$	18.7976	−	10.8528i	0.681412	−	0.393413i	0.800387	+	0.599484i	$0.204628\pi$
$762$	−4.86076	−	8.41909i	−0.176087	−	0.304991i
$763$	3.02000	+	7.92557i	0.109331	+	0.286925i
$764$	8.25535	−	14.2987i	0.298668	−	0.517309i
$765$	−4.70032	+	8.14120i	−0.169941	+	0.294346i
$766$	14.3483	−	8.28398i	0.518424	−	0.299312i
$767$	3.18046	−	5.50873i	0.114840	−	0.198909i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	15.0434	+	8.68532i	0.542480	+	0.313201i	0.746083	−	0.665853i	$-0.231932\pi$
$769$	15.0434	+	8.68532i	0.542480	+	0.313201i	−0.203604	+	0.979053i	$0.565265\pi$
$770$	−14.2749	+	5.43939i	−0.514433	+	0.196022i
$771$	18.2345			0.656701
$772$	7.75119	−	4.47515i	0.278972	−	0.161064i
$773$	16.7899	+	29.0810i	0.603893	+	1.04597i	0.992225	+	0.124453i	$0.0397177\pi$
$773$	16.7899	+	29.0810i	0.603893	+	1.04597i	−0.388333	+	0.921519i	$0.626949\pi$
$774$			12.1488i			0.436680i
$775$	15.9021			0.571220
$776$	−11.3476	+	6.55154i	−0.407355	+	0.235186i
$777$	−8.87566	+	10.9056i	−0.318413	+	0.391235i
$778$			22.7270i			0.814802i
$779$	−16.1250	+	8.41278i	−0.577739	+	0.301419i
$780$	−2.25979	−	1.30469i	−0.0809135	−	0.0467154i
$781$			18.4950i			0.661803i
$782$	−0.243722	+	0.422138i	−0.00871547	+	0.0150956i
$783$	−6.09439	−	3.51860i	−0.217796	−	0.125744i
$784$	1.42168	+	6.85411i	0.0507744	+	0.244790i
$785$	−9.39237	+	16.2681i	−0.335228	+	0.580632i
$786$	−3.40930	−	5.90509i	−0.121606	−	0.210627i
$787$	−8.89897	+	15.4135i	−0.317214	+	0.549431i	−0.979906	−	0.199462i	$-0.936081\pi$
$787$	−8.89897	+	15.4135i	−0.317214	+	0.549431i	0.662692	+	0.748892i	$0.269414\pi$
$788$	12.5507	+	21.7384i	0.447100	+	0.774400i
$789$	19.1715			0.682524
$790$		−	51.6475i		−	1.83753i
$791$	−13.0472	−	34.2405i	−0.463904	−	1.21745i
$792$	1.44437	+	0.833907i	0.0513234	+	0.0296316i
$793$	0.112297	+	0.0648344i	0.00398777	+	0.00230234i
$794$	−6.84602	−	11.8577i	−0.242956	−	0.420812i
$795$	28.7388			1.01926
$796$	−10.2769	−	5.93337i	−0.364255	−	0.210303i
$797$	−11.8261			−0.418901			−0.209450	−	0.977819i	$-0.567167\pi$
$797$	−11.8261			−0.418901			−0.209450	+	0.977819i	$0.567167\pi$
$798$	−2.31675	+	11.2975i	−0.0820121	+	0.399926i
$799$	−3.79842			−0.134378
$800$	6.04910	+	3.49245i	0.213868	+	0.123477i
$801$	14.3415			0.506732
$802$	−16.0492	−	27.7981i	−0.566719	−	0.981585i
$803$	−8.72957	−	5.04002i	−0.308060	−	0.177858i
$804$	0.393709	+	0.227308i	0.0138850	+	0.00801654i
$805$	−1.62330	−	0.261200i	−0.0572139	−	0.00920609i
$806$			1.71599i			0.0604431i
$807$	7.38072			0.259814
$808$	3.24666	+	5.62338i	0.114217	+	0.197830i
$809$	9.73630	−	16.8638i	0.342310	−	0.592899i	−0.642551	−	0.766243i	$-0.722124\pi$
$809$	9.73630	−	16.8638i	0.342310	−	0.592899i	0.984861	+	0.173344i	$0.0554573\pi$
$810$	1.73096	+	2.99811i	0.0608198	+	0.105343i
$811$	−26.3562	+	45.6502i	−0.925490	+	1.60300i	−0.134719	+	0.990884i	$0.543013\pi$
$811$	−26.3562	+	45.6502i	−0.925490	+	1.60300i	−0.790771	+	0.612112i	$0.790320\pi$
$812$	−6.62956	−	17.3984i	−0.232652	−	0.610564i
$813$	−1.84564	−	1.06558i	−0.0647296	−	0.0373716i
$814$	−4.43182	+	7.67613i	−0.155335	+	0.269048i
$815$		−	13.1210i		−	0.459608i
$816$	2.35164	+	1.35772i	0.0823239	+	0.0475297i
$817$	−46.9498	+	24.4948i	−1.64257	+	0.856963i
$818$			25.8193i			0.902751i
$819$	0.316806	−	1.96888i	0.0110701	−	0.0687982i
$820$	−12.5097	+	7.22250i	−0.436859	+	0.252221i
$821$	−22.6232			−0.789555			−0.394777	−	0.918777i	$-0.629178\pi$
$821$	−22.6232			−0.789555			−0.394777	+	0.918777i	$0.629178\pi$
$822$		−	14.1600i		−	0.493886i
$823$	−18.2327	−	31.5800i	−0.635553	−	1.10081i	−0.986398	−	0.164376i	$-0.947439\pi$
$823$	−18.2327	−	31.5800i	−0.635553	−	1.10081i	0.350845	−	0.936433i	$-0.385894\pi$
$824$	8.81695	−	5.09047i	0.307153	−	0.177335i
$825$	−11.6495			−0.405584
$826$	−22.0444	−	3.54709i	−0.767023	−	0.123419i
$827$	−25.7221	−	14.8507i	−0.894445	−	0.516408i	−0.0190514	−	0.999819i	$-0.506065\pi$
$827$	−25.7221	−	14.8507i	−0.894445	−	0.516408i	−0.875394	+	0.483410i	$0.839398\pi$
$828$	0.0897540	+	0.155458i	0.00311917	+	0.00540256i
$829$	0.656509	−	1.13711i	0.0228015	−	0.0394933i	−0.854400	−	0.519617i	$-0.826075\pi$
$829$	0.656509	−	1.13711i	0.0228015	−	0.0394933i	0.877201	+	0.480123i	$0.159408\pi$
$830$	25.9461	−	14.9800i	0.900604	−	0.519964i
$831$	4.24474	−	7.35210i	0.147248	−	0.255042i
$832$	−0.376869	+	0.652756i	−0.0130656	+	0.0226303i
$833$	−12.6493	−	14.1882i	−0.438271	−	0.491591i
$834$	−7.45388	−	12.9105i	−0.258107	−	0.447054i
$835$	36.4711	−	21.0566i	1.26213	−	0.728694i
$836$	−0.310509	+	7.26320i	−0.0107392	+	0.251203i
$837$	1.13832	−	1.97162i	0.0393460	−	0.0681493i
$838$	1.69739	−	2.93997i	0.0586355	−	0.101560i
$839$	−8.72464	−	15.1115i	−0.301208	−	0.521707i	0.675202	−	0.737633i	$-0.264056\pi$
$839$	−8.72464	−	15.1115i	−0.301208	−	0.521707i	−0.976410	+	0.215926i	$0.930723\pi$
$840$	−1.45509	+	9.04306i	−0.0502053	+	0.312015i
$841$	10.2611	+	17.7727i	0.353830	+	0.612851i
$842$	28.4183			0.979358
$843$	19.9705	+	11.5299i	0.687819	+	0.397113i
$844$	−0.506729	−	0.292560i	−0.0174423	−	0.0100703i
$845$		−	43.0382i		−	1.48056i
$846$	−0.699411	+	1.21141i	−0.0240462	+	0.0416493i
$847$	16.8644	+	13.7254i	0.579468	+	0.471609i
$848$		−	8.30141i		−	0.285072i
$849$		−	21.7372i		−	0.746020i
$850$	−18.9671			−0.650566
$851$	−0.826187	+	0.477000i	−0.0283213	+	0.0163513i
$852$	9.60367	+	5.54468i	0.329016	+	0.189958i
$853$	14.2949	−	8.25319i	0.489450	−	0.282584i	−0.234896	−	0.972020i	$-0.575475\pi$
$853$	14.2949	−	8.25319i	0.489450	−	0.282584i	0.724346	+	0.689436i	$0.242142\pi$
$854$	0.0723082	−	0.449380i	0.00247434	−	0.0153775i
$855$	−8.09638	+	12.7343i	−0.276890	+	0.435503i
$856$	1.69908	+	2.94290i	0.0580735	+	0.100586i
$857$	−30.9295			−1.05653			−0.528266	−	0.849079i	$-0.677158\pi$
$857$	−30.9295			−1.05653			−0.528266	+	0.849079i	$0.677158\pi$
$858$		−	1.25710i		−	0.0429165i
$859$		−	30.9120i		−	1.05470i	−0.849647	−	0.527352i	$-0.823185\pi$
$859$		−	30.9120i		−	1.05470i	0.849647	−	0.527352i	$-0.176815\pi$
$860$	−36.4235	+	21.0291i	−1.24203	+	0.717087i
$861$	−8.56219	−	6.96846i	−0.291799	−	0.237485i
$862$	26.0758			0.888144
$863$	26.1229	−	15.0821i	0.889234	−	0.513400i	0.0155422	−	0.999879i	$-0.495053\pi$
$863$	26.1229	−	15.0821i	0.889234	−	0.513400i	0.873692	+	0.486480i	$0.161719\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−28.7686	+	16.6096i	−0.978163	+	0.564742i
$866$	−24.1073	+	13.9183i	−0.819199	+	0.472965i
$867$	9.62638			0.326929
$868$	5.62863	−	2.14476i	0.191048	−	0.0727979i
$869$	21.5482	−	12.4408i	0.730971	−	0.422027i
$870$		−	24.3622i		−	0.825957i
$871$		−	0.342661i		−	0.0116106i
$872$	3.20569			0.108558
$873$	−6.55154	−	11.3476i	−0.221736	−	0.384058i
$874$	−0.419814	+	0.660299i	−0.0142004	+	0.0223350i
$875$	−6.47353	−	16.9889i	−0.218845	−	0.574330i
$876$	−5.23414	+	3.02193i	−0.176845	+	0.102102i
$877$	−4.11283	−	2.37454i	−0.138880	−	0.0801826i	0.428950	−	0.903328i	$-0.358884\pi$
$877$	−4.11283	−	2.37454i	−0.138880	−	0.0801826i	−0.567830	+	0.823146i	$0.692217\pi$
$878$	−19.7254	+	11.3884i	−0.665699	+	0.384342i
$879$	−24.9558			−0.841738
$880$			5.77384i			0.194636i
$881$			41.4668i			1.39705i	0.715585	+	0.698526i	$0.246160\pi$
$881$			41.4668i			1.39705i	−0.715585	+	0.698526i	$0.753840\pi$
$882$	−6.85411	+	1.42168i	−0.230790	+	0.0478706i
$883$	−6.68134	+	11.5724i	−0.224845	+	0.389443i	−0.956273	−	0.292476i	$-0.905521\pi$
$883$	−6.68134	+	11.5724i	−0.224845	+	0.389443i	0.731428	+	0.681919i	$0.238854\pi$
$884$		−	2.04673i		−	0.0688390i
$885$	−25.3016	−	14.6079i	−0.850504	−	0.491039i
$886$	−16.6788	−	9.62953i	−0.560336	−	0.323510i
$887$	−13.7321			−0.461077			−0.230539	−	0.973063i	$-0.574049\pi$
$887$	−13.7321			−0.461077			−0.230539	+	0.973063i	$0.574049\pi$
$888$	2.65726	+	4.60251i	0.0891718	+	0.154450i
$889$	25.3941	+	4.08608i	0.851691	+	0.137043i
$890$	24.8246	+	42.9974i	0.832122	+	1.44128i
$891$	−0.833907	+	1.44437i	−0.0279369	+	0.0483882i
$892$	−11.6970	+	20.2599i	−0.391646	+	0.678350i
$893$	−6.09176	−	0.260428i	−0.203853	−	0.00871490i
$894$	4.23731	−	2.44641i	0.141717	−	0.0818203i
$895$	−26.5160	−	45.9270i	−0.886331	−	1.53517i
$896$	2.61215	+	0.420313i	0.0872659	+	0.0140417i
$897$	0.0676510	−	0.117175i	0.00225880	−	0.00391236i
$898$	8.84072	−	15.3126i	0.295018	−	0.510987i
$899$	−13.8747	+	8.01057i	−0.462748	+	0.267167i
$900$	−3.49245	+	6.04910i	−0.116415	+	0.201637i
$901$	11.2710	+	19.5219i	0.375491	+	0.650370i
$902$	−6.02669	−	3.47951i	−0.200667	−	0.115855i
$903$	−24.9298	−	20.2895i	−0.829611	−	0.675191i
$904$	−13.8494			−0.460624
$905$	18.7925	−	10.8498i	0.624683	−	0.360661i
$906$	2.92902	+	5.07321i	0.0973101	+	0.168546i
$907$			46.9498i			1.55894i	0.626437	+	0.779472i	$0.284512\pi$
$907$			46.9498i			1.55894i	−0.626437	+	0.779472i	$0.715488\pi$
$908$	−26.8095			−0.889704
$909$	−5.62338	+	3.24666i	−0.186516	+	0.107685i
$910$	6.45130	−	2.45823i	0.213858	−	0.0814896i
$911$			30.7362i			1.01834i	0.860667	+	0.509168i	$0.170047\pi$
$911$			30.7362i			1.01834i	−0.860667	+	0.509168i	$0.829953\pi$
$912$	3.67838	+	2.33869i	0.121803	+	0.0774419i
$913$	12.4998	+	7.21677i	0.413683	+	0.238840i
$914$		−	24.5101i		−	0.810721i
$915$	0.297785	−	0.515778i	0.00984446	−	0.0170511i
$916$	20.4578	+	11.8113i	0.675944	+	0.390256i
$917$	17.8112	+	2.86595i	0.588179	+	0.0946419i
$918$	−1.35772	+	2.35164i	−0.0448115	+	0.0776157i
$919$	−10.2843	−	17.8129i	−0.339248	−	0.587595i	0.645044	−	0.764146i	$-0.276839\pi$
$919$	−10.2843	−	17.8129i	−0.339248	−	0.587595i	−0.984291	+	0.176551i	$0.943506\pi$
$920$	−0.310721	+	0.538185i	−0.0102442	+	0.0177434i
$921$	1.13626	+	1.96806i	0.0374411	+	0.0648499i
$922$	10.0059			0.329527
$923$		−	8.35848i		−	0.275123i
$924$	−4.12341	+	1.57121i	−0.135650	+	0.0516889i
$925$	−32.1481	−	18.5607i	−1.05702	−	0.610272i
$926$	0.683068	+	0.394370i	0.0224470	+	0.0129598i
$927$	5.09047	+	8.81695i	0.167193	+	0.289587i
$928$	−7.03720			−0.231007
$929$	5.00062	+	2.88711i	0.164065	+	0.0947231i	0.579784	−	0.814770i	$-0.303137\pi$
$929$	5.00062	+	2.88711i	0.164065	+	0.0947231i	−0.415719	+	0.909493i	$0.636470\pi$
$930$	7.88154			0.258446
$931$	−19.3136	−	23.6217i	−0.632978	−	0.774169i
$932$	20.3366			0.666148
$933$	−0.188708	−	0.108951i	−0.00617803	−	0.00356689i
$934$	−1.31926			−0.0431676
$935$	−7.83927	−	13.5780i	−0.256371	−	0.444048i
$936$	−0.652756	−	0.376869i	−0.0213360	−	0.0123183i
$937$	7.85245	+	4.53361i	0.256528	+	0.148107i	0.622750	−	0.782421i	$-0.286015\pi$
$937$	7.85245	+	4.53361i	0.256528	+	0.148107i	−0.366222	+	0.930528i	$0.619349\pi$
$938$	−1.12397	+	0.428282i	−0.0366989	+	0.0139839i
$939$		−	21.4129i		−	0.698784i
$940$	−4.84261			−0.157948
$941$	−4.17141	−	7.22509i	−0.135984	−	0.235531i	0.789989	−	0.613121i	$-0.210086\pi$
$941$	−4.17141	−	7.22509i	−0.135984	−	0.235531i	−0.925973	+	0.377590i	$0.876753\pi$
$942$	−2.71305	+	4.69914i	−0.0883959	+	0.153106i
$943$	−0.374502	−	0.648656i	−0.0121955	−	0.0211232i
$944$	−4.21959	+	7.30854i	−0.137336	+	0.237873i
$945$	−9.04306	−	1.45509i	−0.294171	−	0.0473340i
$946$	−17.5474	−	10.1310i	−0.570514	−	0.329387i
$947$	29.9966	−	51.9557i	0.974760	−	1.68833i	0.294034	−	0.955795i	$-0.405002\pi$
$947$	29.9966	−	51.9557i	0.974760	−	1.68833i	0.680726	−	0.732538i	$-0.261665\pi$
$948$		−	14.9187i		−	0.484538i
$949$	3.94517	+	2.27774i	0.128066	+	0.0739387i
$950$	−30.4187	−	1.30043i	−0.986913	−	0.0421915i
$951$		−	22.4697i		−	0.728629i
$952$	−6.71351	+	2.55815i	−0.217586	+	0.0829101i
$953$	4.08288	−	2.35725i	0.132257	−	0.0763588i	−0.432412	−	0.901676i	$-0.642337\pi$
$953$	4.08288	−	2.35725i	0.132257	−	0.0763588i	0.564669	+	0.825318i	$0.309004\pi$
$954$	8.30141			0.268768
$955$			57.1588i			1.84961i
$956$	−2.78585	−	4.82524i	−0.0901009	−	0.156059i
$957$	10.1643	−	5.86837i	0.328566	−	0.189697i
$958$	10.0305			0.324070
$959$	29.0567	+	23.6482i	0.938291	+	0.763642i
$960$	2.99811	+	1.73096i	0.0967636	+	0.0558665i
$961$	12.9085	+	22.3581i	0.416402	+	0.721229i
$962$	2.00288	−	3.46909i	0.0645754	−	0.111848i
$963$	−2.94290	+	1.69908i	−0.0948336	+	0.0547522i
$964$	−5.88826	+	10.1988i	−0.189648	+	0.328480i
$965$	−15.4926	+	26.8340i	−0.498726	+	0.863818i
$966$	−0.468902	−	0.0754495i	−0.0150867	−	0.00242755i
$967$	16.4025	+	28.4100i	0.527470	+	0.913605i	0.999487	+	0.0320157i	$0.0101926\pi$
$967$	16.4025	+	28.4100i	0.527470	+	0.913605i	−0.472017	+	0.881589i	$0.656474\pi$
$968$	7.11734	−	4.10920i	0.228760	−	0.132075i
$969$	−11.8255	−	0.505553i	−0.379891	−	0.0162407i
$970$	22.6809	−	39.2845i	0.728240	−	1.26135i
$971$	11.7712	−	20.3883i	0.377756	−	0.654293i	−0.612979	−	0.790099i	$-0.710029\pi$
$971$	11.7712	−	20.3883i	0.377756	−	0.654293i	0.990735	+	0.135806i	$0.0433625\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	38.9413	+	6.26592i	1.24840	+	0.200876i
$974$	7.88090	+	13.6501i	0.252520	+	0.437378i
$975$	5.26479			0.168608
$976$	−0.148986	−	0.0860172i	−0.00476893	−	0.00275334i
$977$	38.0719	+	21.9808i	1.21803	+	0.703229i	0.964496	−	0.264098i	$-0.0850743\pi$
$977$	38.0719	+	21.9808i	1.21803	+	0.703229i	0.253532	+	0.967327i	$0.418408\pi$
$978$		−	3.79009i		−	0.121194i
$979$	−11.9595	+	20.7144i	−0.382227	+	0.662036i
$980$	−16.1266	−	18.0885i	−0.515144	−	0.577816i
$981$			3.20569i			0.102350i
$982$		−	19.7276i		−	0.629534i
$983$	−43.6318			−1.39164			−0.695820	−	0.718217i	$-0.744959\pi$
$983$	−43.6318			−1.39164			−0.695820	+	0.718217i	$0.744959\pi$
$984$	−3.61352	+	2.08627i	−0.115195	+	0.0665078i
$985$	−75.2567	−	43.4495i	−2.39788	−	1.38442i
$986$	16.5490	−	9.55455i	0.527026	−	0.304279i
$987$	−1.31779	−	3.45837i	−0.0419458	−	0.110081i
$988$	0.140329	−	3.28247i	0.00446445	−	0.104429i
$989$	−1.09040	−	1.88864i	−0.0346728	−	0.0600551i
$990$	−5.77384			−0.183505
$991$			47.9198i			1.52222i	0.648621	+	0.761111i	$0.275346\pi$
$991$			47.9198i			1.52222i	−0.648621	+	0.761111i	$0.724654\pi$
$992$		−	2.27664i		−	0.0722833i
$993$	−29.9763	+	17.3068i	−0.951268	+	0.549215i
$994$	−27.4168	+	10.4470i	−0.869607	+	0.331359i
$995$	41.0817			1.30238
$996$	7.49472	−	4.32708i	0.237479	−	0.137109i
$997$	−31.1622	+	17.9915i	−0.986917	+	0.569797i	−0.904351	−	0.426789i	$-0.859645\pi$
$997$	−31.1622	+	17.9915i	−0.986917	+	0.569797i	−0.0825660	+	0.996586i	$0.526312\pi$
$998$	−2.59949	+	1.50082i	−0.0822855	+	0.0475076i
$999$	−4.60251	+	2.65726i	−0.145617	+	0.0840720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bc.b.31.1	yes	28
7.5	odd	6		798.2.m.b.145.8	✓	28
19.8	odd	6		798.2.m.b.787.7	yes	28
133.103	even	6	inner	798.2.bc.b.103.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.8	✓	28	7.5	odd	6
798.2.m.b.787.7	yes	28	19.8	odd	6
798.2.bc.b.31.1	yes	28	1.1	even	1	trivial
798.2.bc.b.103.1	yes	28	133.103	even	6	inner

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.99811 - 1.73096i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.47235 - 0.942075i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(1.73096 + 2.99811i) q^{10} +(-0.833907 + 1.44437i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.376869 - 0.652756i) q^{13} +(-2.61215 - 0.420313i) q^{14} +(-2.99811 - 1.73096i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.71544i q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.186177 - 4.35492i) q^{19} -3.46192i q^{20} +(2.47235 - 0.942075i) q^{21} +(1.44437 - 0.833907i) q^{22} +0.179508 q^{23} -1.00000i q^{24} +(3.49245 + 6.04910i) q^{25} +(-0.652756 + 0.376869i) q^{26} +1.00000 q^{27} +(2.05203 + 1.67008i) q^{28} +(-6.09439 - 3.51860i) q^{29} +(1.73096 + 2.99811i) q^{30} +(1.13832 - 1.97162i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.833907 + 1.44437i) q^{33} +(-1.35772 + 2.35164i) q^{34} +(-9.04306 - 1.45509i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.60251 + 2.65726i) q^{37} +(-2.33869 + 3.67838i) q^{38} +(0.376869 - 0.652756i) q^{39} +(-1.73096 + 2.99811i) q^{40} +(-2.08627 - 3.61352i) q^{41} +(-2.61215 - 0.420313i) q^{42} +(-6.07440 - 10.5212i) q^{43} -1.66781 q^{44} +(-2.99811 - 1.73096i) q^{45} +(-0.155458 - 0.0897540i) q^{46} -1.39882i q^{47} +(-0.500000 + 0.866025i) q^{48} +(5.22499 - 4.65827i) q^{49} -6.98490i q^{50} -2.71544i q^{51} +0.753738 q^{52} +(-7.18923 + 4.15071i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(5.00029 - 2.88692i) q^{55} +(-0.942075 - 2.47235i) q^{56} +(0.186177 - 4.35492i) q^{57} +(3.51860 + 6.09439i) q^{58} +8.43918 q^{59} -3.46192i q^{60} +0.172034i q^{61} +(-1.97162 + 1.13832i) q^{62} +(2.47235 - 0.942075i) q^{63} -1.00000 q^{64} +(-2.25979 + 1.30469i) q^{65} +(1.44437 - 0.833907i) q^{66} +(0.393709 - 0.227308i) q^{67} +(2.35164 - 1.35772i) q^{68} +0.179508 q^{69} +(7.10398 + 5.78168i) q^{70} +(9.60367 - 5.54468i) q^{71} -1.00000i q^{72} +6.04386i q^{73} +5.31452 q^{74} +(3.49245 + 6.04910i) q^{75} +(3.86456 - 2.01623i) q^{76} +(-0.701003 + 4.35658i) q^{77} +(-0.652756 + 0.376869i) q^{78} +(-12.9200 - 7.45937i) q^{79} +(2.99811 - 1.73096i) q^{80} +1.00000 q^{81} +4.17254i q^{82} -8.65416i q^{83} +(2.05203 + 1.67008i) q^{84} +(-4.70032 + 8.14120i) q^{85} +12.1488i q^{86} +(-6.09439 - 3.51860i) q^{87} +(1.44437 + 0.833907i) q^{88} +14.3415 q^{89} +(1.73096 + 2.99811i) q^{90} +(0.316806 - 1.96888i) q^{91} +(0.0897540 + 0.155458i) q^{92} +(1.13832 - 1.97162i) q^{93} +(-0.699411 + 1.21141i) q^{94} +(-8.09638 + 12.7343i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-6.55154 - 11.3476i) q^{97} +(-6.85411 + 1.42168i) q^{98} +(-0.833907 + 1.44437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) \) 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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