LMFDB - Embedded newform 840.2.bj.b.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40309 - 0.177021i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.93733 + 0.496754i) q^{4} +(-1.27167 + 1.83926i) q^{5} +(-0.866962 - 1.11731i) q^{6} +(0.181931 - 2.63949i) q^{7} +(-2.63031 - 1.03994i) q^{8} +1.00000i q^{9} +(2.10985 - 2.35553i) q^{10} -5.32197i q^{11} +(1.01864 + 1.72115i) q^{12} +(3.09369 + 3.09369i) q^{13} +(-0.722511 + 3.67124i) q^{14} +(-2.19975 + 0.401346i) q^{15} +(3.50647 + 1.92475i) q^{16} +(-1.46510 - 1.46510i) q^{17} +(0.177021 - 1.40309i) q^{18} -2.89036i q^{19} +(-3.37729 + 2.93153i) q^{20} +(1.99505 - 1.73776i) q^{21} +(-0.942101 + 7.46720i) q^{22} +(-4.79525 - 4.79525i) q^{23} +(-1.12456 - 2.59526i) q^{24} +(-1.76572 - 4.67784i) q^{25} +(-3.79308 - 4.88838i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.66364 - 5.02318i) q^{28} +6.46004 q^{29} +(3.15750 - 0.173721i) q^{30} -4.49085i q^{31} +(-4.57918 - 3.32132i) q^{32} +(3.76320 - 3.76320i) q^{33} +(1.79631 + 2.31502i) q^{34} +(4.62334 + 3.69117i) q^{35} +(-0.496754 + 1.93733i) q^{36} +(4.02121 + 4.02121i) q^{37} +(-0.511655 + 4.05543i) q^{38} +4.37514i q^{39} +(5.25759 - 3.51536i) q^{40} -4.24557i q^{41} +(-3.10685 + 2.08506i) q^{42} +(1.38707 - 1.38707i) q^{43} +(2.64371 - 10.3104i) q^{44} +(-1.83926 - 1.27167i) q^{45} +(5.87931 + 7.57703i) q^{46} +(4.86105 + 4.86105i) q^{47} +(1.11845 + 3.84045i) q^{48} +(-6.93380 - 0.960409i) q^{49} +(1.64939 + 6.87601i) q^{50} -2.07196i q^{51} +(4.45669 + 7.53030i) q^{52} +(-2.89836 + 2.89836i) q^{53} +(1.11731 - 0.866962i) q^{54} +(9.78846 + 6.76777i) q^{55} +(-3.22344 + 6.75348i) q^{56} +(2.04379 - 2.04379i) q^{57} +(-9.06402 - 1.14356i) q^{58} +0.671485i q^{59} +(-4.46101 - 0.315199i) q^{60} +11.9048 q^{61} +(-0.794976 + 6.30107i) q^{62} +(2.63949 + 0.181931i) q^{63} +(5.83706 + 5.47072i) q^{64} +(-9.62424 + 1.75594i) q^{65} +(-5.94627 + 4.61394i) q^{66} +(-6.84905 - 6.84905i) q^{67} +(-2.11058 - 3.56617i) q^{68} -6.78151i q^{69} +(-5.83355 - 5.99747i) q^{70} +11.4622 q^{71} +(1.03994 - 2.63031i) q^{72} +(5.02297 - 5.02297i) q^{73} +(-4.93028 - 6.35395i) q^{74} +(2.05918 - 4.55629i) q^{75} +(1.43580 - 5.59957i) q^{76} +(-14.0473 - 0.968230i) q^{77} +(0.774493 - 6.13872i) q^{78} -13.2555i q^{79} +(-7.99917 + 4.00166i) q^{80} -1.00000 q^{81} +(-0.751557 + 5.95693i) q^{82} +(9.55176 + 9.55176i) q^{83} +(4.72829 - 2.37556i) q^{84} +(4.55781 - 0.831573i) q^{85} +(-2.19173 + 1.70064i) q^{86} +(4.56794 + 4.56794i) q^{87} +(-5.53452 + 13.9984i) q^{88} +9.55854 q^{89} +(2.35553 + 2.10985i) q^{90} +(8.72860 - 7.60293i) q^{91} +(-6.90791 - 11.6720i) q^{92} +(3.17551 - 3.17551i) q^{93} +(-5.95999 - 7.68101i) q^{94} +(5.31611 + 3.67557i) q^{95} +(-0.889441 - 5.58649i) q^{96} +(-8.82826 - 8.82826i) q^{97} +(9.55874 + 2.57497i) q^{98} +5.32197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.40309	−	0.177021i	−0.992135	−	0.125173i
$2$	−1.40309	−	0.177021i	−0.992135	−	0.125173i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.93733	+	0.496754i	0.968663	+	0.248377i
$5$	−1.27167	+	1.83926i	−0.568707	+	0.822540i
$5$	−1.27167	+	1.83926i	−0.568707	+	0.822540i
$6$	−0.866962	−	1.11731i	−0.353936	−	0.456139i
$7$	0.181931	−	2.63949i	0.0687634	−	0.997633i
$7$	0.181931	−	2.63949i	0.0687634	−	0.997633i
$8$	−2.63031	−	1.03994i	−0.929955	−	0.367674i
$9$			1.00000i			0.333333i
$10$	2.10985	−	2.35553i	0.667194	−	0.744884i
$11$		−	5.32197i		−	1.60463i	−0.596899	−	0.802316i	$-0.703601\pi$
$11$		−	5.32197i		−	1.60463i	0.596899	−	0.802316i	$-0.296399\pi$
$12$	1.01864	+	1.72115i	0.294056	+	0.496855i
$13$	3.09369	+	3.09369i	0.858036	+	0.858036i	0.991107	−	0.133071i	$-0.0424838\pi$
$13$	3.09369	+	3.09369i	0.858036	+	0.858036i	−0.133071	+	0.991107i	$0.542484\pi$
$14$	−0.722511	+	3.67124i	−0.193099	+	0.981179i
$15$	−2.19975	+	0.401346i	−0.567974	+	0.103627i
$16$	3.50647	+	1.92475i	0.876618	+	0.481187i
$17$	−1.46510	−	1.46510i	−0.355339	−	0.355339i	0.506753	−	0.862091i	$-0.330846\pi$
$17$	−1.46510	−	1.46510i	−0.355339	−	0.355339i	−0.862091	+	0.506753i	$0.830846\pi$
$18$	0.177021	−	1.40309i	0.0417243	−	0.330712i
$19$		−	2.89036i		−	0.663093i	−0.943439	−	0.331547i	$-0.892430\pi$
$19$		−	2.89036i		−	0.663093i	0.943439	−	0.331547i	$-0.107570\pi$
$20$	−3.37729	+	2.93153i	−0.755186	+	0.655511i
$21$	1.99505	−	1.73776i	0.435355	−	0.379209i
$22$	−0.942101	+	7.46720i	−0.200857	+	1.59201i
$23$	−4.79525	−	4.79525i	−0.999879	−	0.999879i	0.000120932	−	1.00000i	$-0.499962\pi$
$23$	−4.79525	−	4.79525i	−0.999879	−	0.999879i	−1.00000		0.000120932i	$0.999962\pi$
$24$	−1.12456	−	2.59526i	−0.229550	−	0.529755i
$25$	−1.76572	−	4.67784i	−0.353145	−	0.935569i
$26$	−3.79308	−	4.88838i	−0.743884	−	0.958690i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.66364	−	5.02318i	0.314398	−	0.949291i
$29$	6.46004			1.19960			0.599800	−	0.800150i	$-0.295247\pi$
$29$	6.46004			1.19960			0.599800	+	0.800150i	$0.295247\pi$
$30$	3.15750	−	0.173721i	0.576478	−	0.0317169i
$31$		−	4.49085i		−	0.806580i	−0.915072	−	0.403290i	$-0.867867\pi$
$31$		−	4.49085i		−	0.806580i	0.915072	−	0.403290i	$-0.132133\pi$
$32$	−4.57918	−	3.32132i	−0.809492	−	0.587131i
$33$	3.76320	−	3.76320i	0.655089	−	0.655089i
$34$	1.79631	+	2.31502i	0.308065	+	0.397023i
$35$	4.62334	+	3.69117i	0.781487	+	0.623922i
$36$	−0.496754	+	1.93733i	−0.0827923	+	0.322888i
$37$	4.02121	+	4.02121i	0.661082	+	0.661082i	0.955635	−	0.294553i	$-0.0951708\pi$
$37$	4.02121	+	4.02121i	0.661082	+	0.661082i	−0.294553	+	0.955635i	$0.595171\pi$
$38$	−0.511655	+	4.05543i	−0.0830013	+	0.657878i
$39$			4.37514i			0.700583i
$40$	5.25759	−	3.51536i	0.831298	−	0.555827i
$41$		−	4.24557i		−	0.663047i	−0.943447	−	0.331524i	$-0.892437\pi$
$41$		−	4.24557i		−	0.663047i	0.943447	−	0.331524i	$-0.107563\pi$
$42$	−3.10685	+	2.08506i	−0.479397	+	0.321732i
$43$	1.38707	−	1.38707i	0.211526	−	0.211526i	−0.593389	−	0.804916i	$-0.702211\pi$
$43$	1.38707	−	1.38707i	0.211526	−	0.211526i	0.804916	+	0.593389i	$0.202211\pi$
$44$	2.64371	−	10.3104i	0.398554	−	1.55435i
$45$	−1.83926	−	1.27167i	−0.274180	−	0.189569i
$46$	5.87931	+	7.57703i	0.866857	+	1.11717i
$47$	4.86105	+	4.86105i	0.709058	+	0.709058i	0.966337	−	0.257279i	$-0.0828261\pi$
$47$	4.86105	+	4.86105i	0.709058	+	0.709058i	−0.257279	+	0.966337i	$0.582826\pi$
$48$	1.11845	+	3.84045i	0.161434	+	0.554322i
$49$	−6.93380	−	0.960409i	−0.990543	−	0.137201i
$50$	1.64939	+	6.87601i	0.233259	+	0.972415i
$51$		−	2.07196i		−	0.290133i
$52$	4.45669	+	7.53030i	0.618032	+	1.04426i
$53$	−2.89836	+	2.89836i	−0.398121	+	0.398121i	−0.877570	−	0.479449i	$-0.840837\pi$
$53$	−2.89836	+	2.89836i	−0.398121	+	0.398121i	0.479449	+	0.877570i	$0.340837\pi$
$54$	1.11731	−	0.866962i	0.152046	−	0.117979i
$55$	9.78846	+	6.76777i	1.31988	+	0.912566i
$56$	−3.22344	+	6.75348i	−0.430750	+	0.902471i
$57$	2.04379	−	2.04379i	0.270707	−	0.270707i
$58$	−9.06402	−	1.14356i	−1.19016	−	0.150157i
$59$			0.671485i			0.0874199i	0.999044	+	0.0437099i	$0.0139177\pi$
$59$			0.671485i			0.0874199i	−0.999044	+	0.0437099i	$0.986082\pi$
$60$	−4.46101	−	0.315199i	−0.575914	−	0.0406920i
$61$	11.9048			1.52425			0.762126	−	0.647429i	$-0.224156\pi$
$61$	11.9048			1.52425			0.762126	+	0.647429i	$0.224156\pi$
$62$	−0.794976	+	6.30107i	−0.100962	+	0.800236i
$63$	2.63949	+	0.181931i	0.332544	+	0.0229211i
$64$	5.83706	+	5.47072i	0.729632	+	0.683840i
$65$	−9.62424	+	1.75594i	−1.19374	+	0.217798i
$66$	−5.94627	+	4.61394i	−0.731936	+	0.567937i
$67$	−6.84905	−	6.84905i	−0.836745	−	0.836745i	0.151684	−	0.988429i	$-0.451530\pi$
$67$	−6.84905	−	6.84905i	−0.836745	−	0.836745i	−0.988429	+	0.151684i	$0.951530\pi$
$68$	−2.11058	−	3.56617i	−0.255946	−	0.432461i
$69$		−	6.78151i		−	0.816398i
$70$	−5.83355	−	5.99747i	−0.697242	−	0.716835i
$71$	11.4622			1.36031			0.680155	−	0.733069i	$-0.261913\pi$
$71$	11.4622			1.36031			0.680155	+	0.733069i	$0.261913\pi$
$72$	1.03994	−	2.63031i	0.122558	−	0.309985i
$73$	5.02297	−	5.02297i	0.587894	−	0.587894i	−0.349167	−	0.937061i	$-0.613535\pi$
$73$	5.02297	−	5.02297i	0.587894	−	0.587894i	0.937061	+	0.349167i	$0.113535\pi$
$74$	−4.93028	−	6.35395i	−0.573133	−	0.738632i
$75$	2.05918	−	4.55629i	0.237774	−	0.526115i
$76$	1.43580	−	5.59957i	0.164697	−	0.642314i
$77$	−14.0473	−	0.968230i	−1.60083	−	0.110340i
$78$	0.774493	−	6.13872i	0.0876941	−	0.695073i
$79$		−	13.2555i		−	1.49137i	−0.666301	−	0.745683i	$-0.732124\pi$
$79$		−	13.2555i		−	1.49137i	0.666301	−	0.745683i	$-0.267876\pi$
$80$	−7.99917	+	4.00166i	−0.894335	+	0.447399i
$81$	−1.00000			−0.111111
$82$	−0.751557	+	5.95693i	−0.0829956	+	0.657832i
$83$	9.55176	+	9.55176i	1.04844	+	1.04844i	0.998765	+	0.0496764i	$0.0158190\pi$
$83$	9.55176	+	9.55176i	1.04844	+	1.04844i	0.0496764	+	0.998765i	$0.484181\pi$
$84$	4.72829	−	2.37556i	0.515899	−	0.259194i
$85$	4.55781	−	0.831573i	0.494364	−	0.0901967i
$86$	−2.19173	+	1.70064i	−0.236340	+	0.183385i
$87$	4.56794	+	4.56794i	0.489734	+	0.489734i
$88$	−5.53452	+	13.9984i	−0.589982	+	1.49224i
$89$	9.55854			1.01320			0.506602	−	0.862180i	$-0.330901\pi$
$89$	9.55854			1.01320			0.506602	+	0.862180i	$0.330901\pi$
$90$	2.35553	+	2.10985i	0.248295	+	0.222398i
$91$	8.72860	−	7.60293i	0.915006	−	0.797003i
$92$	−6.90791	−	11.6720i	−0.720199	−	1.21689i
$93$	3.17551	−	3.17551i	0.329285	−	0.329285i
$94$	−5.95999	−	7.68101i	−0.614726	−	0.792236i
$95$	5.31611	+	3.67557i	0.545421	+	0.377106i
$96$	−0.889441	−	5.58649i	−0.0907782	−	0.570169i
$97$	−8.82826	−	8.82826i	−0.896374	−	0.896374i	0.0987392	−	0.995113i	$-0.468519\pi$
$97$	−8.82826	−	8.82826i	−0.896374	−	0.896374i	−0.995113	+	0.0987392i	$0.968519\pi$
$98$	9.55874	+	2.57497i	0.965579	+	0.260111i
$99$	5.32197			0.534878
$100$	−1.09705	−	9.93964i	−0.109705	−	0.993964i
$101$	−13.5881			−1.35207			−0.676034	−	0.736871i	$-0.736303\pi$
$101$	−13.5881			−1.35207			−0.676034	+	0.736871i	$0.736303\pi$
$102$	−0.366781	+	2.90715i	−0.0363168	+	0.287851i
$103$	−9.76485	+	9.76485i	−0.962159	+	0.962159i	−0.999310	−	0.0371506i	$-0.988172\pi$
$103$	−9.76485	+	9.76485i	−0.962159	+	0.962159i	0.0371506	+	0.999310i	$0.488172\pi$
$104$	−4.92012	−	11.3546i	−0.482457	−	1.11341i
$105$	0.659144	+	5.87925i	0.0643258	+	0.573756i
$106$	4.57974	−	3.55360i	0.444824	−	0.345156i
$107$	−8.55046	−	8.55046i	−0.826604	−	0.826604i	0.160442	−	0.987045i	$-0.448708\pi$
$107$	−8.55046	−	8.55046i	−0.826604	−	0.826604i	−0.987045	+	0.160442i	$0.948708\pi$
$108$	−1.72115	+	1.01864i	−0.165618	+	0.0980186i
$109$	11.6795			1.11869			0.559345	−	0.828935i	$-0.311053\pi$
$109$	11.6795			1.11869			0.559345	+	0.828935i	$0.311053\pi$
$110$	−12.5361	−	11.2286i	−1.19527	−	1.07060i
$111$			5.68684i			0.539771i
$112$	5.71829	−	8.90512i	0.540327	−	0.841455i
$113$	3.21316	+	3.21316i	0.302269	+	0.302269i	0.841901	−	0.539632i	$-0.181437\pi$
$113$	3.21316	+	3.21316i	0.302269	+	0.302269i	−0.539632	+	0.841901i	$0.681437\pi$
$114$	−3.22942	+	2.50583i	−0.302463	+	0.234692i
$115$	14.9177	−	2.72173i	1.39108	−	0.253803i
$116$	12.5152	+	3.20905i	1.16201	+	0.297953i
$117$	−3.09369	+	3.09369i	−0.286012	+	0.286012i
$118$	0.118867	−	0.942154i	0.0109426	−	0.0867323i
$119$	−4.13366	+	3.60056i	−0.378932	+	0.330063i
$120$	6.20341	+	1.23195i	0.566291	+	0.112461i
$121$	−17.3233			−1.57485
$122$	−16.7035	−	2.10740i	−1.51226	−	0.190795i
$123$	3.00207	−	3.00207i	0.270688	−	0.270688i
$124$	2.23085	−	8.70024i	0.200336	−	0.781305i
$125$	10.8492	+	2.70104i	0.970379	+	0.241589i
$126$	−3.67124	−	0.722511i	−0.327060	−	0.0643664i
$127$	−6.36238	+	6.36238i	−0.564570	+	0.564570i	−0.930602	−	0.366032i	$-0.880716\pi$
$127$	−6.36238	+	6.36238i	−0.564570	+	0.564570i	0.366032	+	0.930602i	$0.380716\pi$
$128$	−7.22148	−	8.70920i	−0.638295	−	0.769792i
$129$	1.96161			0.172710
$130$	13.8145	−	0.760053i	1.21161	−	0.0666611i
$131$	11.3331			0.990179			0.495089	−	0.868842i	$-0.335135\pi$
$131$	11.3331			0.990179			0.495089	+	0.868842i	$0.335135\pi$
$132$	9.15993	−	5.42116i	0.797269	−	0.471852i
$133$	−7.62906	−	0.525845i	−0.661524	−	0.0455966i
$134$	8.39742	+	10.8223i	0.725426	+	0.934902i
$135$	−0.401346	−	2.19975i	−0.0345423	−	0.189325i
$136$	2.33005	+	5.37728i	0.199800	+	0.461098i
$137$	6.68283	−	6.68283i	0.570953	−	0.570953i	−0.361442	−	0.932395i	$-0.617715\pi$
$137$	6.68283	−	6.68283i	0.570953	−	0.570953i	0.932395	+	0.361442i	$0.117715\pi$
$138$	−1.20047	+	9.51507i	−0.102191	+	0.809977i
$139$		−	8.40196i		−	0.712645i	−0.934363	−	0.356322i	$-0.884030\pi$
$139$		−	8.40196i		−	0.712645i	0.934363	−	0.356322i	$-0.115970\pi$
$140$	7.12332	+	9.44766i	0.602030	+	0.798473i
$141$			6.87457i			0.578943i
$142$	−16.0825	−	2.02905i	−1.34961	−	0.170274i
$143$	16.4645	−	16.4645i	1.37683	−	1.37683i
$144$	−1.92475	+	3.50647i	−0.160396	+	0.292206i
$145$	−8.21502	+	11.8817i	−0.682221	+	0.986719i
$146$	−7.93685	+	6.15851i	−0.656859	+	0.509682i
$147$	−4.22383	−	5.58205i	−0.348375	−	0.460400i
$148$	5.79284	+	9.78794i	0.476169	+	0.804564i
$149$	−8.72247			−0.714573			−0.357286	−	0.933995i	$-0.616298\pi$
$149$	−8.72247			−0.714573			−0.357286	+	0.933995i	$0.616298\pi$
$150$	−3.69578	+	6.02837i	−0.301759	+	0.492214i
$151$	3.09885			0.252181			0.126090	−	0.992019i	$-0.459757\pi$
$151$	3.09885			0.252181			0.126090	+	0.992019i	$0.459757\pi$
$152$	−3.00579	+	7.60253i	−0.243802	+	0.616647i
$153$	1.46510	−	1.46510i	0.118446	−	0.118446i
$154$	19.5382	+	3.84518i	1.57443	+	0.309853i
$155$	8.25982	+	5.71087i	0.663445	+	0.458708i
$156$	−2.17337	+	8.47608i	−0.174009	+	0.678629i
$157$	−6.41072	+	6.41072i	−0.511631	+	0.511631i	−0.915026	−	0.403395i	$-0.867830\pi$
$157$	−6.41072	+	6.41072i	−0.511631	+	0.511631i	0.403395	+	0.915026i	$0.367830\pi$
$158$	−2.34651	+	18.5987i	−0.186679	+	1.47964i
$159$	−4.09891			−0.325064
$160$	11.9319	−	4.19867i	0.943303	−	0.331934i
$161$	−13.5294	+	11.7846i	−1.06627	+	0.928757i
$162$	1.40309	+	0.177021i	0.110237	+	0.0139081i
$163$	0.883288	−	0.883288i	0.0691844	−	0.0691844i	−0.671668	−	0.740852i	$-0.734422\pi$
$163$	0.883288	−	0.883288i	0.0691844	−	0.0691844i	0.740852	+	0.671668i	$0.234422\pi$
$164$	2.10900	−	8.22507i	0.164686	−	0.642270i
$165$	2.13595	+	11.7070i	0.166283	+	0.911390i
$166$	−11.7111	−	15.0928i	−0.908959	−	1.17143i
$167$	−11.2436	−	11.2436i	−0.870053	−	0.870053i	0.122425	−	0.992478i	$-0.460933\pi$
$167$	−11.2436	−	11.2436i	−0.870053	−	0.870053i	−0.992478	+	0.122425i	$0.960933\pi$
$168$	−7.05475	+	2.49611i	−0.544285	+	0.192579i
$169$			6.14186i			0.472451i
$170$	−6.54223	+	0.359943i	−0.501766	+	0.0276064i
$171$	2.89036			0.221031
$172$	3.37624	−	1.99818i	0.257436	−	0.152360i
$173$	−8.80896	−	8.80896i	−0.669733	−	0.669733i	0.287921	−	0.957654i	$-0.407036\pi$
$173$	−8.80896	−	8.80896i	−0.669733	−	0.669733i	−0.957654	+	0.287921i	$0.907036\pi$
$174$	−5.60061	−	7.21786i	−0.424581	−	0.547184i
$175$	−12.6684	+	3.80956i	−0.957638	+	0.287976i
$176$	10.2434	−	18.6613i	0.772129	−	1.40665i
$177$	−0.474812	+	0.474812i	−0.0356890	+	0.0356890i
$178$	−13.4115	−	1.69207i	−1.00523	−	0.126826i
$179$	−21.6752			−1.62008			−0.810039	−	0.586376i	$-0.800554\pi$
$179$	−21.6752			−1.62008			−0.810039	+	0.586376i	$0.800554\pi$
$180$	−2.93153	−	3.37729i	−0.218504	−	0.251729i
$181$	−22.4165			−1.66620			−0.833101	−	0.553121i	$-0.813437\pi$
$181$	−22.4165			−1.66620			−0.833101	+	0.553121i	$0.813437\pi$
$182$	−13.5929	+	9.12245i	−1.00757	+	0.676201i
$183$	8.41796	+	8.41796i	0.622273	+	0.622273i
$184$	7.62623	+	17.5998i	0.562213	+	1.29747i
$185$	−12.5097	+	2.28239i	−0.919729	+	0.167805i
$186$	−5.01766	+	3.89339i	−0.367913	+	0.285478i
$187$	−7.79720	+	7.79720i	−0.570188	+	0.570188i
$188$	7.00270	+	11.8322i	0.510725	+	0.862952i
$189$	1.73776	+	1.99505i	0.126403	+	0.145118i
$190$	−6.80832	−	6.09823i	−0.493928	−	0.442412i
$191$	16.5721			1.19912			0.599559	−	0.800331i	$-0.295343\pi$
$191$	16.5721			1.19912			0.599559	+	0.800331i	$0.295343\pi$
$192$	0.259038	+	7.99581i	0.0186945	+	0.577048i
$193$	11.8214	+	11.8214i	0.850926	+	0.850926i	0.990247	−	0.139321i	$-0.0444921\pi$
$193$	11.8214	+	11.8214i	0.850926	+	0.850926i	−0.139321	+	0.990247i	$0.544492\pi$
$194$	10.8241	+	13.9496i	0.777122	+	1.00153i
$195$	−8.04700	−	5.56372i	−0.576258	−	0.398427i
$196$	−12.9560	−	5.30502i	−0.925425	−	0.378930i
$197$	8.01054	+	8.01054i	0.570727	+	0.570727i	0.932332	−	0.361604i	$-0.117771\pi$
$197$	8.01054	+	8.01054i	0.570727	+	0.570727i	−0.361604	+	0.932332i	$0.617771\pi$
$198$	−7.46720	−	0.942101i	−0.530671	−	0.0669522i
$199$	−6.10190			−0.432553			−0.216276	−	0.976332i	$-0.569391\pi$
$199$	−6.10190			−0.432553			−0.216276	+	0.976332i	$0.569391\pi$
$200$	−0.220270	+	14.1404i	−0.0155755	+	0.999879i
$201$		−	9.68602i		−	0.683200i
$202$	19.0654	+	2.40538i	1.34143	+	0.169242i
$203$	1.17528	−	17.0512i	0.0824886	−	1.19676i
$204$	1.02926	−	4.01407i	0.0720623	−	0.281041i
$205$	7.80870	+	5.39896i	0.545383	+	0.377080i
$206$	15.4296	−	11.9724i	1.07503	−	0.834155i
$207$	4.79525	−	4.79525i	0.333293	−	0.333293i
$208$	4.89336	+	16.8025i	0.339294	+	1.16505i
$209$	−15.3824			−1.06402
$210$	0.115913	−	8.36580i	0.00799877	−	0.577295i
$211$			15.0084i			1.03322i	0.856220	+	0.516612i	$0.172807\pi$
$211$			15.0084i			1.03322i	−0.856220	+	0.516612i	$0.827193\pi$
$212$	−7.05485	+	4.17531i	−0.484529	+	0.286761i
$213$	8.10498	+	8.10498i	0.555344	+	0.555344i
$214$	10.4835	+	13.5107i	0.716634	+	0.923571i
$215$	0.787285	+	4.31507i	0.0536924	+	0.294285i
$216$	2.59526	−	1.12456i	0.176585	−	0.0765168i
$217$	−11.8535	−	0.817024i	−0.804671	−	0.0554632i
$218$	−16.3873	−	2.06751i	−1.10989	−	0.140030i
$219$	7.10355			0.480013
$220$	15.6015	+	17.9738i	1.05185	+	1.21180i
$221$		−	9.06513i		−	0.609787i
$222$	1.00669	−	7.97916i	0.0675647	−	0.535526i
$223$	−12.3123	+	12.3123i	−0.824491	+	0.824491i	−0.986748	−	0.162258i	$-0.948122\pi$
$223$	−12.3123	+	12.3123i	−0.824491	+	0.824491i	0.162258	+	0.986748i	$0.448122\pi$
$224$	−9.59967	+	11.4824i	−0.641405	+	0.767202i
$225$	4.67784	−	1.76572i	0.311856	−	0.117715i
$226$	−3.93956	−	5.07716i	−0.262056	−	0.337728i
$227$	−1.79701	+	1.79701i	−0.119272	+	0.119272i	−0.764223	−	0.644952i	$-0.776877\pi$
$227$	−1.79701	+	1.79701i	−0.119272	+	0.119272i	0.644952	+	0.764223i	$0.276877\pi$
$228$	4.97475	−	2.94423i	0.329461	−	0.194986i
$229$			19.5718i			1.29334i	0.762769	+	0.646671i	$0.223839\pi$
$229$			19.5718i			1.29334i	−0.762769	+	0.646671i	$0.776161\pi$
$230$	−21.4126	+	1.17809i	−1.41191	+	0.0776809i
$231$	−9.24828	−	10.6176i	−0.608492	−	0.698584i
$232$	−16.9919	−	6.71805i	−1.11557	−	0.441061i
$233$	1.08570	+	1.08570i	0.0711264	+	0.0711264i	0.741775	−	0.670649i	$-0.233984\pi$
$233$	1.08570	+	1.08570i	0.0711264	+	0.0711264i	−0.670649	+	0.741775i	$0.733984\pi$
$234$	4.88838	−	3.79308i	0.319563	−	0.247961i
$235$	−15.1224	+	2.75908i	−0.986474	+	0.179982i
$236$	−0.333563	+	1.30089i	−0.0217131	+	0.0846805i
$237$	9.37309	−	9.37309i	0.608847	−	0.608847i
$238$	6.43727	−	4.32017i	0.417266	−	0.280035i
$239$			7.42640i			0.480374i	0.970727	+	0.240187i	$0.0772088\pi$
$239$			7.42640i			0.480374i	−0.970727	+	0.240187i	$0.922791\pi$
$240$	−8.48587	−	2.82667i	−0.547760	−	0.182461i
$241$			15.6569i			1.00855i	0.863542	+	0.504276i	$0.168241\pi$
$241$			15.6569i			1.00855i	−0.863542	+	0.504276i	$0.831759\pi$
$242$	24.3062	+	3.06660i	1.56246	+	0.197128i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	23.0635	+	5.91375i	1.47649	+	0.378589i
$245$	10.5839	−	11.5317i	0.676182	−	0.736734i
$246$	−4.74361	+	3.68075i	−0.302442	+	0.234676i
$247$	8.94187	−	8.94187i	0.568958	−	0.568958i
$248$	−4.67021	+	11.8123i	−0.296558	+	0.750083i
$249$			13.5082i			0.856049i
$250$	−14.7442	−	5.71034i	−0.932506	−	0.361154i
$251$	4.43083			0.279672			0.139836	−	0.990175i	$-0.455343\pi$
$251$	4.43083			0.279672			0.139836	+	0.990175i	$0.455343\pi$
$252$	5.02318	+	1.66364i	0.316430	+	0.104799i
$253$	−25.5202	+	25.5202i	−1.60444	+	1.60444i
$254$	10.0533	−	7.80072i	0.630798	−	0.489461i
$255$	3.81087	+	2.63485i	0.238646	+	0.165001i
$256$	8.59068	+	13.4982i	0.536918	+	0.843635i
$257$	−4.19884	−	4.19884i	−0.261916	−	0.261916i	0.563916	−	0.825832i	$-0.309294\pi$
$257$	−4.19884	−	4.19884i	−0.261916	−	0.261916i	−0.825832	+	0.563916i	$0.809294\pi$
$258$	−2.75232	−	0.347247i	−0.171352	−	0.0216187i
$259$	11.3455	−	9.88234i	0.704976	−	0.614059i
$260$	−19.5176	−	1.37904i	−1.21043	−	0.0855244i
$261$			6.46004i			0.399867i
$262$	−15.9014	−	2.00620i	−0.982391	−	0.123944i
$263$	17.6896	+	17.6896i	1.09078	+	1.09078i	0.995445	+	0.0953396i	$0.0303937\pi$
$263$	17.6896	+	17.6896i	1.09078	+	1.09078i	0.0953396	+	0.995445i	$0.469606\pi$
$264$	−13.8119	+	5.98488i	−0.850062	+	0.368344i
$265$	−1.64508	−	9.01659i	−0.101056	−	0.553885i
$266$	10.6112	+	2.08832i	0.650613	+	0.128043i
$267$	6.75891	+	6.75891i	0.413639	+	0.413639i
$268$	−9.86656	−	16.6711i	−0.602696	−	1.01835i
$269$		−	16.0070i		−	0.975965i	−0.872853	−	0.487983i	$-0.837733\pi$
$269$		−	16.0070i		−	0.975965i	0.872853	−	0.487983i	$-0.162267\pi$
$270$	0.173721	+	3.15750i	0.0105723	+	0.192159i
$271$			5.71076i			0.346904i	0.984842	+	0.173452i	$0.0554921\pi$
$271$			5.71076i			0.346904i	−0.984842	+	0.173452i	$0.944508\pi$
$272$	−2.31738	−	7.95727i	−0.140512	−	0.482481i
$273$	11.5481	+	0.795974i	0.698925	+	0.0481745i
$274$	−10.5596	+	8.19362i	−0.637930	+	0.494995i
$275$	−24.8953	+	9.39712i	−1.50124	+	0.566668i
$276$	3.36874	−	13.1380i	0.202774	−	0.790815i
$277$	−12.4525	−	12.4525i	−0.748196	−	0.748196i	0.225944	−	0.974140i	$-0.427453\pi$
$277$	−12.4525	−	12.4525i	−0.748196	−	0.748196i	−0.974140	+	0.225944i	$0.927453\pi$
$278$	−1.48732	+	11.7887i	−0.0892038	+	0.707040i
$279$	4.49085			0.268860
$280$	−8.32222	−	14.5169i	−0.497348	−	0.867551i
$281$	−12.5967			−0.751454			−0.375727	−	0.926730i	$-0.622607\pi$
$281$	−12.5967			−0.751454			−0.375727	+	0.926730i	$0.622607\pi$
$282$	1.21694	−	9.64564i	0.0724680	−	0.574390i
$283$	−6.28452	−	6.28452i	−0.373576	−	0.373576i	0.495202	−	0.868778i	$-0.335094\pi$
$283$	−6.28452	−	6.28452i	−0.373576	−	0.373576i	−0.868778	+	0.495202i	$0.835094\pi$
$284$	22.2060	+	5.69388i	1.31768	+	0.337869i
$285$	1.16003	+	6.35808i	0.0687144	+	0.376620i
$286$	−26.0158	+	20.1866i	−1.53835	+	1.19366i
$287$	−11.2061	−	0.772401i	−0.661478	−	0.0455934i
$288$	3.32132	−	4.57918i	0.195710	−	0.269831i
$289$		−	12.7070i		−	0.747469i
$290$	13.6297	−	15.2168i	0.800365	−	0.893563i
$291$		−	12.4850i		−	0.731886i
$292$	12.2263	−	7.23595i	0.715491	−	0.423452i
$293$	1.38895	+	1.38895i	0.0811432	+	0.0811432i	0.746513	−	0.665370i	$-0.231726\pi$
$293$	1.38895	+	1.38895i	0.0811432	+	0.0811432i	−0.665370	+	0.746513i	$0.731726\pi$
$294$	4.93827	+	8.57983i	0.288006	+	0.500386i
$295$	−1.23503	−	0.853905i	−0.0719064	−	0.0497163i
$296$	−6.39521	−	14.7588i	−0.371714	−	0.857839i
$297$	3.76320	+	3.76320i	0.218363	+	0.218363i
$298$	12.2384	+	1.54406i	0.708953	+	0.0894452i
$299$		−	29.6701i		−	1.71586i
$300$	6.25266	−	7.80412i	0.360997	−	0.450571i
$301$	−3.40881	−	3.91351i	−0.196480	−	0.225571i
$302$	−4.34797	−	0.548562i	−0.250197	−	0.0315662i
$303$	−9.60825	−	9.60825i	−0.551979	−	0.551979i
$304$	5.56321	−	10.1350i	0.319072	−	0.581279i
$305$	−15.1389	+	21.8960i	−0.866853	+	1.25376i
$306$	−2.31502	+	1.79631i	−0.132341	+	0.102688i
$307$	−15.4336	+	15.4336i	−0.880844	+	0.880844i	−0.993620	−	0.112776i	$-0.964026\pi$
$307$	−15.4336	+	15.4336i	−0.880844	+	0.880844i	0.112776	+	0.993620i	$0.464026\pi$
$308$	−26.7332	−	8.85381i	−1.52326	−	0.504493i
$309$	−13.8096			−0.785600
$310$	−10.5783	−	9.47503i	−0.600809	−	0.538145i
$311$			11.2050i			0.635376i	0.948195	+	0.317688i	$0.102906\pi$
$311$			11.2050i			0.635376i	−0.948195	+	0.317688i	$0.897094\pi$
$312$	4.54988	−	11.5080i	0.257586	−	0.651511i
$313$	12.3510	−	12.3510i	0.698119	−	0.698119i	−0.265885	−	0.964005i	$-0.585664\pi$
$313$	12.3510	−	12.3510i	0.698119	−	0.698119i	0.964005	+	0.265885i	$0.0856642\pi$
$314$	10.1296	−	7.85998i	0.571649	−	0.443564i
$315$	−3.69117	+	4.62334i	−0.207974	+	0.260496i
$316$	6.58474	−	25.6803i	0.370421	−	1.44463i
$317$	14.3635	+	14.3635i	0.806737	+	0.806737i	0.984139	−	0.177401i	$-0.0567691\pi$
$317$	14.3635	+	14.3635i	0.806737	+	0.806737i	−0.177401	+	0.984139i	$0.556769\pi$
$318$	5.75114	+	0.725593i	0.322508	+	0.0406893i
$319$		−	34.3801i		−	1.92492i
$320$	−17.4848	+	3.77890i	−0.977433	+	0.211247i
$321$		−	12.0922i		−	0.674919i
$322$	21.0691	−	14.1399i	1.17414	−	0.787985i
$323$	−4.23466	+	4.23466i	−0.235623	+	0.235623i
$324$	−1.93733	−	0.496754i	−0.107629	−	0.0275974i
$325$	9.00920	−	19.9344i	0.499741	−	1.10576i
$326$	−1.39569	+	1.08297i	−0.0773003	+	0.0599803i
$327$	8.25863	+	8.25863i	0.456703	+	0.456703i
$328$	−4.41514	+	11.1672i	−0.243785	+	0.616604i
$329$	13.7151	−	11.9463i	0.756137	−	0.658622i
$330$	−0.924536	−	16.8041i	−0.0508940	−	0.925036i
$331$		−	17.9318i		−	0.985619i	−0.870137	−	0.492810i	$-0.835970\pi$
$331$		−	17.9318i		−	0.985619i	0.870137	−	0.492810i	$-0.164030\pi$
$332$	13.7600	+	23.2498i	0.755179	+	1.27600i
$333$	−4.02121	+	4.02121i	−0.220361	+	0.220361i
$334$	13.7854	+	17.7661i	0.754303	+	0.972117i
$335$	21.3069	−	3.88744i	1.16412	−	0.212394i
$336$	10.3403	−	2.25343i	0.564110	−	0.122935i
$337$	12.4993	−	12.4993i	0.680878	−	0.680878i	−0.279320	−	0.960198i	$-0.590109\pi$
$337$	12.4993	−	12.4993i	0.680878	−	0.680878i	0.960198	+	0.279320i	$0.0901089\pi$
$338$	1.08724	−	8.61759i	0.0591381	−	0.468735i
$339$			4.54410i			0.246802i
$340$	9.24305	+	0.653080i	0.501275	+	0.0354183i
$341$	−23.9001			−1.29427
$342$	−4.05543	−	0.511655i	−0.219293	−	0.0276671i
$343$	−3.79646	+	18.1270i	−0.204990	+	0.978764i
$344$	−5.09089	+	2.20596i	−0.274483	+	0.118937i
$345$	12.4729	+	8.62383i	0.671520	+	0.464291i
$346$	10.8004	+	13.9191i	0.580633	+	0.748298i
$347$	23.8793	+	23.8793i	1.28191	+	1.28191i	0.939582	+	0.342325i	$0.111214\pi$
$347$	23.8793	+	23.8793i	1.28191	+	1.28191i	0.342325	+	0.939582i	$0.388786\pi$
$348$	6.58045	+	11.1187i	0.352749	+	0.596027i
$349$			20.9493i			1.12139i	0.828023	+	0.560695i	$0.189466\pi$
$349$			20.9493i			1.12139i	−0.828023	+	0.560695i	$0.810534\pi$
$350$	18.4492	−	3.10259i	0.986153	−	0.165841i
$351$	−4.37514			−0.233528
$352$	−17.6759	+	24.3702i	−0.942130	+	1.29894i
$353$	5.70412	−	5.70412i	0.303600	−	0.303600i	−0.538821	−	0.842421i	$-0.681130\pi$
$353$	5.70412	−	5.70412i	0.303600	−	0.303600i	0.842421	+	0.538821i	$0.181130\pi$
$354$	0.750255	−	0.582152i	0.0398756	−	0.0309410i
$355$	−14.5761	+	21.0819i	−0.773617	+	1.11891i
$356$	18.5180	+	4.74824i	0.981453	+	0.251656i
$357$	−5.46892	−	0.376954i	−0.289446	−	0.0199505i
$358$	30.4122	+	3.83696i	1.60734	+	0.202790i
$359$		−	9.65196i		−	0.509411i	−0.967019	−	0.254705i	$-0.918021\pi$
$359$		−	9.65196i		−	0.509411i	0.967019	−	0.254705i	$-0.0819785\pi$
$360$	3.51536	+	5.25759i	0.185276	+	0.277099i
$361$	10.6458			0.560307
$362$	31.4523	+	3.96819i	1.65310	+	0.208563i
$363$	−12.2494	−	12.2494i	−0.642929	−	0.642929i
$364$	20.6869	−	10.3934i	1.08429	−	0.544762i
$365$	2.85098	+	15.6261i	0.149227	+	0.817906i
$366$	−10.3210	−	13.3013i	−0.539487	−	0.695271i
$367$	−13.8922	−	13.8922i	−0.725165	−	0.725165i	0.244488	−	0.969652i	$-0.421380\pi$
$367$	−13.8922	−	13.8922i	−0.725165	−	0.725165i	−0.969652	+	0.244488i	$0.921380\pi$
$368$	−7.58476	−	26.0441i	−0.395383	−	1.35764i
$369$	4.24557			0.221016
$370$	17.9562	−	0.987923i	0.933499	−	0.0513597i
$371$	7.12290	+	8.17750i	0.369802	+	0.424555i
$372$	7.72945	−	4.57455i	0.400753	−	0.237180i
$373$	−3.22434	+	3.22434i	−0.166950	+	0.166950i	−0.785637	−	0.618687i	$-0.787665\pi$
$373$	−3.22434	+	3.22434i	−0.166950	+	0.166950i	0.618687	+	0.785637i	$0.287665\pi$
$374$	12.3205	−	9.55991i	0.637076	−	0.494331i
$375$	5.76159	+	9.58144i	0.297527	+	0.494784i
$376$	−7.73088	−	17.8413i	−0.398690	−	0.920094i
$377$	19.9854	+	19.9854i	1.02930	+	1.02930i
$378$	−2.08506	−	3.10685i	−0.107244	−	0.159799i
$379$	10.9992			0.564989			0.282495	−	0.959269i	$-0.408838\pi$
$379$	10.9992			0.564989			0.282495	+	0.959269i	$0.408838\pi$
$380$	8.47318	+	9.76158i	0.434665	+	0.500759i
$381$	−8.99776			−0.460969
$382$	−23.2522	−	2.93362i	−1.18969	−	0.150097i
$383$	24.8058	−	24.8058i	1.26752	−	1.26752i	0.320154	−	0.947365i	$-0.396265\pi$
$383$	24.8058	−	24.8058i	1.26752	−	1.26752i	0.947365	−	0.320154i	$-0.103735\pi$
$384$	1.05197	−	11.2647i	0.0536833	−	0.574849i
$385$	19.6443	−	24.6053i	1.00117	−	1.25400i
$386$	−14.4939	−	18.6792i	−0.737720	−	0.950746i
$387$	1.38707	+	1.38707i	0.0705088	+	0.0705088i
$388$	−12.7178	−	21.4887i	−0.645646	−	1.09092i
$389$	−11.7031			−0.593369			−0.296684	−	0.954976i	$-0.595881\pi$
$389$	−11.7031			−0.593369			−0.296684	+	0.954976i	$0.595881\pi$
$390$	10.3058	+	9.23090i	0.521853	+	0.467425i
$391$			14.0510i			0.710591i
$392$	17.2393	+	9.73690i	0.870715	+	0.491788i
$393$	8.01372	+	8.01372i	0.404239	+	0.404239i
$394$	−9.82147	−	12.6575i	−0.494799	−	0.637678i
$395$	24.3803	+	16.8566i	1.22671	+	0.848150i
$396$	10.3104	+	2.64371i	0.518116	+	0.132851i
$397$	17.8317	−	17.8317i	0.894949	−	0.894949i	−0.100035	−	0.994984i	$-0.531895\pi$
$397$	17.8317	−	17.8317i	0.894949	−	0.894949i	0.994984	+	0.100035i	$0.0318953\pi$
$398$	8.56153	+	1.08017i	0.429151	+	0.0541439i
$399$	−5.02273	−	5.76639i	−0.251451	−	0.288681i
$400$	2.81221	−	19.8013i	0.140611	−	0.990065i
$401$	−4.21301			−0.210388			−0.105194	−	0.994452i	$-0.533546\pi$
$401$	−4.21301			−0.210388			−0.105194	+	0.994452i	$0.533546\pi$
$402$	−1.71463	+	13.5904i	−0.0855181	+	0.677826i
$403$	13.8933	−	13.8933i	0.692075	−	0.692075i
$404$	−26.3246	−	6.74994i	−1.30970	−	0.335822i
$405$	1.27167	−	1.83926i	0.0631897	−	0.0913934i
$406$	−4.66745	+	23.7163i	−0.231642	+	1.17702i
$407$	21.4007	−	21.4007i	1.06079	−	1.06079i
$408$	−2.15471	+	5.44990i	−0.106674	+	0.269810i
$409$	−20.1314			−0.995432			−0.497716	−	0.867340i	$-0.665828\pi$
$409$	−20.1314			−0.995432			−0.497716	+	0.867340i	$0.665828\pi$
$410$	−10.0006	−	8.95753i	−0.493893	−	0.442381i
$411$	9.45095			0.466181
$412$	−23.7684	+	14.0670i	−1.17099	+	0.693030i
$413$	1.77238	+	0.122164i	0.0872130	+	0.00601129i
$414$	−7.57703	+	5.87931i	−0.372391	+	0.288952i
$415$	−29.7148	+	5.42147i	−1.45864	+	0.266129i
$416$	−3.89143	−	24.4417i	−0.190793	−	1.19835i
$417$	5.94108	−	5.94108i	0.290936	−	0.290936i
$418$	21.5829	+	2.72301i	1.05565	+	0.133187i
$419$		−	9.05459i		−	0.442345i	−0.975235	−	0.221173i	$-0.929012\pi$
$419$		−	9.05459i		−	0.442345i	0.975235	−	0.221173i	$-0.0709885\pi$
$420$	−1.64356	+	11.7175i	−0.0801975	+	0.571753i
$421$		−	5.84924i		−	0.285075i	−0.989789	−	0.142537i	$-0.954474\pi$
$421$		−	5.84924i		−	0.285075i	0.989789	−	0.142537i	$-0.0455261\pi$
$422$	2.65681	−	21.0582i	0.129332	−	1.02510i
$423$	−4.86105	+	4.86105i	−0.236353	+	0.236353i
$424$	10.6377	−	4.60947i	0.516613	−	0.223856i
$425$	−4.26654	+	9.44046i	−0.206958	+	0.457930i
$426$	−9.93727	−	12.8068i	−0.481462	−	0.620490i
$427$	2.16585	−	31.4226i	0.104813	−	1.52064i
$428$	−12.3176	−	20.8125i	−0.595392	−	1.00601i
$429$	23.2844			1.12418
$430$	−0.340773	−	6.19380i	−0.0164335	−	0.298692i
$431$	5.05090			0.243293			0.121647	−	0.992573i	$-0.461182\pi$
$431$	5.05090			0.243293			0.121647	+	0.992573i	$0.461182\pi$
$432$	−3.84045	+	1.11845i	−0.184774	+	0.0538113i
$433$	14.7693	−	14.7693i	0.709766	−	0.709766i	−0.256720	−	0.966486i	$-0.582642\pi$
$433$	14.7693	−	14.7693i	0.709766	−	0.709766i	0.966486	+	0.256720i	$0.0826417\pi$
$434$	16.4870	+	3.24469i	0.791400	+	0.155750i
$435$	−14.2105	+	2.59271i	−0.681342	+	0.124311i
$436$	22.6269	+	5.80182i	1.08363	+	0.277857i
$437$	−13.8600	+	13.8600i	−0.663013	+	0.663013i
$438$	−9.96692	−	1.25748i	−0.476238	−	0.0600847i
$439$	−4.45853			−0.212794			−0.106397	−	0.994324i	$-0.533931\pi$
$439$	−4.45853			−0.212794			−0.106397	+	0.994324i	$0.533931\pi$
$440$	−18.7086	−	27.9807i	−0.891898	−	1.33393i
$441$	0.960409	−	6.93380i	0.0457338	−	0.330181i
$442$	−1.60472	+	12.7192i	−0.0763288	+	0.604991i
$443$	−6.40064	+	6.40064i	−0.304103	+	0.304103i	−0.842617	−	0.538513i	$-0.818986\pi$
$443$	−6.40064	+	6.40064i	−0.304103	+	0.304103i	0.538513	+	0.842617i	$0.318986\pi$
$444$	−2.82496	+	11.0173i	−0.134067	+	0.522857i
$445$	−12.1553	+	17.5806i	−0.576216	+	0.833401i
$446$	19.4548	−	15.0957i	0.921210	−	0.714802i
$447$	−6.16772	−	6.16772i	−0.291723	−	0.291723i
$448$	15.5018	−	14.4115i	0.732393	−	0.680882i
$449$		−	13.1908i		−	0.622513i	−0.950326	−	0.311257i	$-0.899250\pi$
$449$		−	13.1908i		−	0.622513i	0.950326	−	0.311257i	$-0.100750\pi$
$450$	−6.87601	+	1.64939i	−0.324138	+	0.0777531i
$451$	−22.5948			−1.06395
$452$	4.62880	+	7.82110i	0.217720	+	0.367874i
$453$	2.19122	+	2.19122i	0.102952	+	0.102952i
$454$	2.83947	−	2.20326i	0.133263	−	0.103404i
$455$	2.88385	+	25.7225i	0.135197	+	1.20589i
$456$	−7.50122	+	3.25039i	−0.351277	+	0.152213i
$457$	1.46666	−	1.46666i	0.0686077	−	0.0686077i	−0.671970	−	0.740578i	$-0.734552\pi$
$457$	1.46666	−	1.46666i	0.0686077	−	0.0686077i	0.740578	+	0.671970i	$0.234552\pi$
$458$	3.46463	−	27.4610i	0.161891	−	1.28317i
$459$	2.07196			0.0967109
$460$	30.2524	+	2.13752i	1.41053	+	0.0996626i
$461$	−27.9131			−1.30004			−0.650021	−	0.759916i	$-0.725240\pi$
$461$	−27.9131			−1.30004			−0.650021	+	0.759916i	$0.725240\pi$
$462$	11.0966	+	16.5345i	0.516262	+	0.769257i
$463$	−2.76286	−	2.76286i	−0.128401	−	0.128401i	0.639986	−	0.768387i	$-0.278940\pi$
$463$	−2.76286	−	2.76286i	−0.128401	−	0.128401i	−0.768387	+	0.639986i	$0.778940\pi$
$464$	22.6520	+	12.4340i	1.05159	+	0.577232i
$465$	1.80238	+	9.87876i	0.0835835	+	0.458117i
$466$	−1.33114	−	1.71552i	−0.0616638	−	0.0794700i
$467$	−6.09386	+	6.09386i	−0.281990	+	0.281990i	−0.833902	−	0.551912i	$-0.813898\pi$
$467$	−6.09386	+	6.09386i	−0.281990	+	0.281990i	0.551912	+	0.833902i	$0.313898\pi$
$468$	−7.53030	+	4.45669i	−0.348088	+	0.206011i
$469$	−19.3241	+	16.8319i	−0.892302	+	0.777227i
$470$	21.7065	−	1.19426i	1.00124	−	0.0550869i
$471$	−9.06612			−0.417745
$472$	0.698303	−	1.76621i	0.0321420	−	0.0812965i
$473$	−7.38194	−	7.38194i	−0.339422	−	0.339422i
$474$	−14.8105	+	11.4921i	−0.680270	+	0.527848i
$475$	−13.5206	+	5.10357i	−0.620369	+	0.234168i
$476$	−9.79684	+	4.92206i	−0.449038	+	0.225602i
$477$	−2.89836	−	2.89836i	−0.132707	−	0.132707i
$478$	1.31463	−	10.4199i	0.0601298	−	0.476596i
$479$	−9.22047			−0.421294			−0.210647	−	0.977562i	$-0.567557\pi$
$479$	−9.22047			−0.421294			−0.210647	+	0.977562i	$0.567557\pi$
$480$	11.4061	+	5.46825i	0.520613	+	0.249590i
$481$			24.8807i			1.13446i
$482$	2.77161	−	21.9681i	0.126243	−	1.00062i
$483$	−17.8997	−	1.23377i	−0.814465	−	0.0561383i
$484$	−33.5609	−	8.60542i	−1.52550	−	0.391156i
$485$	27.4640	−	5.01082i	1.24708	−	0.227530i
$486$	0.866962	+	1.11731i	0.0393262	+	0.0506821i
$487$	−8.18028	+	8.18028i	−0.370684	+	0.370684i	−0.867726	−	0.497042i	$-0.834419\pi$
$487$	−8.18028	+	8.18028i	−0.370684	+	0.370684i	0.497042	+	0.867726i	$0.334419\pi$
$488$	−31.3133	−	12.3802i	−1.41749	−	0.560428i
$489$	1.24916			0.0564889
$490$	−16.8916	+	14.3065i	−0.763083	+	0.646300i
$491$			41.0920i			1.85446i	0.374496	+	0.927228i	$0.377816\pi$
$491$			41.0920i			1.85446i	−0.374496	+	0.927228i	$0.622184\pi$
$492$	7.30729	−	4.32471i	0.329438	−	0.194973i
$493$	−9.46460	−	9.46460i	−0.426264	−	0.426264i
$494$	−14.1292	+	10.9634i	−0.635701	+	0.493265i
$495$	−6.76777	+	9.78846i	−0.304189	+	0.439958i
$496$	8.64375	−	15.7470i	0.388116	−	0.707063i
$497$	2.08532	−	30.2543i	0.0935395	−	1.35709i
$498$	2.39124	−	18.9533i	0.107154	−	0.849316i
$499$	−3.09955			−0.138755			−0.0693775	−	0.997590i	$-0.522101\pi$
$499$	−3.09955			−0.138755			−0.0693775	+	0.997590i	$0.522101\pi$
$500$	19.6766	+	10.6222i	0.879965	+	0.475038i
$501$		−	15.9008i		−	0.710396i
$502$	−6.21686	−	0.784351i	−0.277472	−	0.0350073i
$503$	−15.2850	+	15.2850i	−0.681525	+	0.681525i	−0.960344	−	0.278819i	$-0.910057\pi$
$503$	−15.2850	+	15.2850i	−0.681525	+	0.681525i	0.278819	+	0.960344i	$0.410057\pi$
$504$	−6.75348	−	3.22344i	−0.300824	−	0.143583i
$505$	17.2796	−	24.9920i	0.768930	−	1.11213i
$506$	40.3247	−	31.2895i	1.79265	−	1.39099i
$507$	−4.34295	+	4.34295i	−0.192877	+	0.192877i
$508$	−15.4865	+	9.16547i	−0.687104	+	0.406652i
$509$		−	22.7310i		−	1.00753i	−0.863840	−	0.503766i	$-0.831947\pi$
$509$		−	22.7310i		−	1.00753i	0.863840	−	0.503766i	$-0.168053\pi$
$510$	−4.88057	−	4.37153i	−0.216115	−	0.193575i
$511$	−12.3442	−	14.1719i	−0.546077	−	0.626928i
$512$	−9.66405	−	20.4599i	−0.427095	−	0.904207i
$513$	2.04379	+	2.04379i	0.0902356	+	0.0902356i
$514$	5.14807	+	6.63464i	0.227072	+	0.292641i
$515$	−5.54241	−	30.3777i	−0.244228	−	1.33860i
$516$	3.80029	+	0.974439i	0.167298	+	0.0428973i
$517$	25.8704	−	25.8704i	1.13778	−	1.13778i
$518$	−17.6682	+	11.8574i	−0.776294	+	0.520986i
$519$		−	12.4578i		−	0.546835i
$520$	27.1408	+	5.38994i	1.19020	+	0.236365i
$521$			40.6395i			1.78045i	0.455521	+	0.890225i	$0.349453\pi$
$521$			40.6395i			1.78045i	−0.455521	+	0.890225i	$0.650547\pi$
$522$	1.14356	−	9.06402i	0.0500525	−	0.396722i
$523$	−6.15837	−	6.15837i	−0.269287	−	0.269287i	0.559526	−	0.828813i	$-0.310983\pi$
$523$	−6.15837	−	6.15837i	−0.269287	−	0.269287i	−0.828813	+	0.559526i	$0.810983\pi$
$524$	21.9559	+	5.62977i	0.959150	+	0.245937i
$525$	−11.6516	−	6.26411i	−0.508520	−	0.273388i
$526$	−21.6886	−	27.9515i	−0.945669	−	1.21874i
$527$	−6.57954	+	6.57954i	−0.286609	+	0.286609i
$528$	20.4388	−	5.95234i	0.889483	−	0.259042i
$529$			22.9889i			0.999516i
$530$	0.712065	+	12.9423i	0.0309301	+	0.562178i
$531$	−0.671485			−0.0291400
$532$	−14.5188	−	4.80850i	−0.629469	−	0.208475i
$533$	13.1345	−	13.1345i	0.568918	−	0.568918i
$534$	−8.28689	−	10.6798i	−0.358609	−	0.462162i
$535$	26.5998	−	4.85314i	1.15001	−	0.209820i
$536$	10.8925	+	25.1377i	0.470486	+	1.08578i
$537$	−15.3267	−	15.3267i	−0.661394	−	0.661394i
$538$	−2.83358	+	22.4593i	−0.122164	+	0.968289i
$539$	−5.11127	+	36.9015i	−0.220158	+	1.58946i
$540$	0.315199	−	4.46101i	0.0135640	−	0.191971i
$541$			28.3361i			1.21826i	0.793069	+	0.609132i	$0.208482\pi$
$541$			28.3361i			1.21826i	−0.793069	+	0.609132i	$0.791518\pi$
$542$	1.01093	−	8.01271i	0.0434230	−	0.344175i
$543$	−15.8508	−	15.8508i	−0.680224	−	0.680224i
$544$	1.84289	+	11.5750i	0.0790131	+	0.496274i
$545$	−14.8524	+	21.4815i	−0.636207	+	0.920167i
$546$	−16.0622	−	3.16109i	−0.687398	−	0.135282i
$547$	22.3553	+	22.3553i	0.955845	+	0.955845i	0.999066	−	0.0432208i	$-0.0137619\pi$
$547$	22.3553	+	22.3553i	0.955845	+	0.955845i	−0.0432208	+	0.999066i	$0.513762\pi$
$548$	16.2666	−	9.62711i	0.694873	−	0.411250i
$549$			11.9048i			0.508084i
$550$	36.5939	−	8.77801i	1.56037	−	0.374296i
$551$		−	18.6718i		−	0.795447i
$552$	−7.05235	+	17.8375i	−0.300168	+	0.759213i
$553$	−34.9879	−	2.41159i	−1.48784	−	0.102551i
$554$	15.2676	+	19.6763i	0.648657	+	0.835965i
$555$	−10.4596	−	7.23177i	−0.443984	−	0.306972i
$556$	4.17370	−	16.2773i	0.177004	−	0.690313i
$557$	0.233225	+	0.233225i	0.00988206	+	0.00988206i	0.712031	−	0.702148i	$-0.247776\pi$
$557$	0.233225	+	0.233225i	0.00988206	+	0.00988206i	−0.702148	+	0.712031i	$0.747776\pi$
$558$	−6.30107	−	0.794976i	−0.266745	−	0.0336540i
$559$	8.58234			0.362994
$560$	9.10703	+	21.8417i	0.384842	+	0.922982i
$561$	−11.0269			−0.465557
$562$	17.6743	+	2.22988i	0.745543	+	0.0940616i
$563$	−3.22092	−	3.22092i	−0.135745	−	0.135745i	0.635969	−	0.771715i	$-0.280601\pi$
$563$	−3.22092	−	3.22092i	−0.135745	−	0.135745i	−0.771715	+	0.635969i	$0.780601\pi$
$564$	−3.41497	+	13.3183i	−0.143796	+	0.560801i
$565$	−9.99591	+	1.82375i	−0.420531	+	0.0767259i
$566$	7.70526	+	9.93025i	0.323876	+	0.417400i
$567$	−0.181931	+	2.63949i	−0.00764038	+	0.110848i
$568$	−30.1491	−	11.9200i	−1.26503	−	0.500150i
$569$			26.9169i			1.12842i	0.825632	+	0.564208i	$0.190819\pi$
$569$			26.9169i			1.12842i	−0.825632	+	0.564208i	$0.809181\pi$
$570$	−0.502115	−	9.12631i	−0.0210313	−	0.382259i
$571$			43.0137i			1.80007i	0.435818	+	0.900035i	$0.356459\pi$
$571$			43.0137i			1.80007i	−0.435818	+	0.900035i	$0.643541\pi$
$572$	40.0760	−	23.7183i	1.67566	−	0.991714i
$573$	11.7183	+	11.7183i	0.489538	+	0.489538i
$574$	15.5865	+	3.06748i	0.650568	+	0.128034i
$575$	−13.9643	+	30.8985i	−0.582354	+	1.28856i
$576$	−5.47072	+	5.83706i	−0.227947	+	0.243211i
$577$	−20.0391	−	20.0391i	−0.834237	−	0.834237i	0.153856	−	0.988093i	$-0.450831\pi$
$577$	−20.0391	−	20.0391i	−0.834237	−	0.834237i	−0.988093	+	0.153856i	$0.950831\pi$
$578$	−2.24940	+	17.8290i	−0.0935629	+	0.741590i
$579$			16.7180i			0.694778i
$580$	−21.8175	+	18.9378i	−0.905920	+	0.786351i
$581$	26.9495	−	23.4740i	1.11805	−	0.973866i
$582$	−2.21012	+	17.5177i	−0.0916124	+	0.726130i
$583$	15.4250	+	15.4250i	0.638838	+	0.638838i
$584$	−18.4355	+	7.98838i	−0.762868	+	0.330562i
$585$	−1.75594	−	9.62424i	−0.0725993	−	0.397913i
$586$	−1.70295	−	2.19469i	−0.0703480	−	0.0906619i
$587$	3.10705	−	3.10705i	0.128242	−	0.128242i	−0.640073	−	0.768314i	$-0.721096\pi$
$587$	3.10705	−	3.10705i	0.128242	−	0.128242i	0.768314	+	0.640073i	$0.221096\pi$
$588$	−5.41003	−	12.9125i	−0.223106	−	0.532501i
$589$	−12.9802			−0.534838
$590$	1.58170	+	1.41673i	0.0651177	+	0.0583260i
$591$			11.3286i			0.465997i
$592$	6.36043	+	21.8401i	0.261412	+	0.897621i
$593$	25.8276	−	25.8276i	1.06061	−	1.06061i	0.0625732	−	0.998040i	$-0.480069\pi$
$593$	25.8276	−	25.8276i	1.06061	−	1.06061i	0.998040	−	0.0625732i	$-0.0199307\pi$
$594$	−4.61394	−	5.94627i	−0.189312	−	0.243979i
$595$	−1.36572	−	12.1816i	−0.0559891	−	0.499396i
$596$	−16.8983	−	4.33292i	−0.692181	−	0.177483i
$597$	−4.31470	−	4.31470i	−0.176589	−	0.176589i
$598$	−5.25223	+	41.6298i	−0.214780	+	1.70237i
$599$		−	4.23829i		−	0.173172i	−0.996244	−	0.0865860i	$-0.972404\pi$
$599$		−	4.23829i		−	0.173172i	0.996244	−	0.0865860i	$-0.0275957\pi$
$600$	−10.1545	+	9.84303i	−0.414557	+	0.401840i
$601$		−	1.32843i		−	0.0541880i	−0.999633	−	0.0270940i	$-0.991375\pi$
$601$		−	1.32843i		−	0.0541880i	0.999633	−	0.0270940i	$-0.00862534\pi$
$602$	4.09009	+	6.09444i	0.166700	+	0.248391i
$603$	6.84905	−	6.84905i	0.278915	−	0.278915i
$604$	6.00349	+	1.53937i	0.244278	+	0.0626359i
$605$	22.0295	−	31.8620i	0.895626	−	1.29537i
$606$	11.7804	+	15.1821i	0.478545	+	0.616731i
$607$	−14.7286	−	14.7286i	−0.597817	−	0.597817i	0.341914	−	0.939731i	$-0.388925\pi$
$607$	−14.7286	−	14.7286i	−0.597817	−	0.597817i	−0.939731	+	0.341914i	$0.888925\pi$
$608$	−9.59979	+	13.2355i	−0.389323	+	0.536768i
$609$	12.8881	−	11.2260i	0.522251	−	0.454899i
$610$	25.1173	−	28.0421i	1.01697	−	1.13539i
$611$			30.0772i			1.21679i
$612$	3.56617	−	2.11058i	0.144154	−	0.0853152i
$613$	22.4739	−	22.4739i	0.907712	−	0.907712i	−0.0883753	−	0.996087i	$-0.528167\pi$
$613$	22.4739	−	22.4739i	0.907712	−	0.907712i	0.996087	+	0.0883753i	$0.0281675\pi$
$614$	24.3869	−	18.9227i	0.984174	−	0.763659i
$615$	1.70394	+	9.33922i	0.0687096	+	0.376594i
$616$	35.9418	+	17.1550i	1.44813	+	0.691196i
$617$	17.2941	−	17.2941i	0.696233	−	0.696233i	−0.267363	−	0.963596i	$-0.586152\pi$
$617$	17.2941	−	17.2941i	0.696233	−	0.696233i	0.963596	+	0.267363i	$0.0861524\pi$
$618$	19.3761	+	2.44459i	0.779421	+	0.0983358i
$619$			15.8021i			0.635138i	0.948235	+	0.317569i	$0.102867\pi$
$619$			15.8021i			0.635138i	−0.948235	+	0.317569i	$0.897133\pi$
$620$	13.1651	+	15.1669i	0.528722	+	0.609118i
$621$	6.78151			0.272133
$622$	1.98352	−	15.7216i	0.0795318	−	0.630378i
$623$	1.73900	−	25.2297i	0.0696714	−	1.01081i
$624$	−8.42105	+	15.3413i	−0.337112	+	0.614144i
$625$	−18.7644	+	16.5196i	−0.750578	+	0.660782i
$626$	−19.5160	+	15.1432i	−0.780014	+	0.605243i
$627$	−10.8770	−	10.8770i	−0.434385	−	0.434385i
$628$	−15.6042	+	9.23511i	−0.622675	+	0.368521i
$629$		−	11.7829i		−	0.469816i
$630$	5.99747	−	5.83355i	0.238945	−	0.232414i
$631$	13.6955			0.545210			0.272605	−	0.962126i	$-0.412115\pi$
$631$	13.6955			0.545210			0.272605	+	0.962126i	$0.412115\pi$
$632$	−13.7850	+	34.8662i	−0.548336	+	1.38690i
$633$	−10.6126	+	10.6126i	−0.421812	+	0.421812i
$634$	−17.6107	−	22.6960i	−0.699410	−	0.901374i
$635$	−3.61121	−	19.7929i	−0.143307	−	0.785456i
$636$	−7.94092	−	2.03615i	−0.314878	−	0.0807385i
$637$	−18.4798	−	24.4223i	−0.732198	−	0.967645i
$638$	−6.08601	+	48.2384i	−0.240948	+	1.90978i
$639$			11.4622i			0.453436i
$640$	25.2018	−	2.20695i	0.996188	−	0.0872374i
$641$	−8.27745			−0.326940			−0.163470	−	0.986548i	$-0.552269\pi$
$641$	−8.27745			−0.326940			−0.163470	+	0.986548i	$0.552269\pi$
$642$	−2.14057	+	16.9664i	−0.0844816	+	0.669611i
$643$	25.3683	+	25.3683i	1.00043	+	1.00043i	1.00000		0.000426763i	$0.000135843\pi$
$643$	25.3683	+	25.3683i	1.00043	+	1.00043i	0.000426763		1.00000i	$0.499864\pi$
$644$	−32.0650	+	16.1099i	−1.26354	+	0.634817i
$645$	−2.49452	+	3.60791i	−0.0982216	+	0.142061i
$646$	6.69123	−	5.19198i	0.263263	−	0.204276i
$647$	22.4352	+	22.4352i	0.882020	+	0.882020i	0.993740	−	0.111720i	$-0.0356358\pi$
$647$	22.4352	+	22.4352i	0.882020	+	0.882020i	−0.111720	+	0.993740i	$0.535636\pi$
$648$	2.63031	+	1.03994i	0.103328	+	0.0408526i
$649$	3.57362			0.140277
$650$	−16.1695	+	26.3750i	−0.634222	+	1.03451i
$651$	−7.80400	−	8.95944i	−0.305863	−	0.351148i
$652$	2.14999	−	1.27244i	0.0842002	−	0.0498326i
$653$	26.7390	−	26.7390i	1.04638	−	1.04638i	0.0475057	−	0.998871i	$-0.484873\pi$
$653$	26.7390	−	26.7390i	1.04638	−	1.04638i	0.998871	−	0.0475057i	$-0.0151272\pi$
$654$	−10.1257	−	13.0496i	−0.395944	−	0.510278i
$655$	−14.4120	+	20.8445i	−0.563122	+	0.814462i
$656$	8.17166	−	14.8870i	0.319050	−	0.581239i
$657$	5.02297	+	5.02297i	0.195965	+	0.195965i
$658$	−21.3582	+	14.3339i	−0.832631	+	0.558794i
$659$	43.7385			1.70381			0.851905	−	0.523696i	$-0.175447\pi$
$659$	43.7385			1.70381			0.851905	+	0.523696i	$0.175447\pi$
$660$	−1.67748	+	23.7414i	−0.0652957	+	0.924131i
$661$	22.0188			0.856432			0.428216	−	0.903676i	$-0.359142\pi$
$661$	22.0188			0.856432			0.428216	+	0.903676i	$0.359142\pi$
$662$	−3.17430	+	25.1599i	−0.123373	+	0.977867i
$663$	6.41001	−	6.41001i	0.248944	−	0.248944i
$664$	−15.1908	−	35.0573i	−0.589519	−	1.36049i
$665$	10.6688	−	13.3631i	0.413718	−	0.518199i
$666$	6.35395	−	4.93028i	0.246211	−	0.191044i
$667$	−30.9775	−	30.9775i	−1.19945	−	1.19945i
$668$	−16.1972	−	27.3677i	−0.626688	−	1.05889i
$669$	−17.4122			−0.673194
$670$	−30.5836	+	1.68266i	−1.18155	+	0.0650070i
$671$		−	63.3569i		−	2.44586i
$672$	−14.9073	+	1.33131i	−0.575062	+	0.0513565i
$673$	7.38008	+	7.38008i	0.284481	+	0.284481i	0.834893	−	0.550412i	$-0.185529\pi$
$673$	7.38008	+	7.38008i	0.284481	+	0.284481i	−0.550412	+	0.834893i	$0.685529\pi$
$674$	−19.7502	+	15.3250i	−0.760751	+	0.590296i
$675$	4.55629	+	2.05918i	0.175372	+	0.0792579i
$676$	−3.05099	+	11.8988i	−0.117346	+	0.457646i
$677$	13.7767	−	13.7767i	0.529481	−	0.529481i	−0.390937	−	0.920418i	$-0.627849\pi$
$677$	13.7767	−	13.7767i	0.529481	−	0.529481i	0.920418	+	0.390937i	$0.127849\pi$
$678$	0.804402	−	6.37578i	0.0308929	−	0.244861i
$679$	−24.9082	+	21.6960i	−0.955890	+	0.832615i
$680$	−12.8532	−	2.55255i	−0.492899	−	0.0978857i
$681$	−2.54135			−0.0973849
$682$	33.5341	+	4.23083i	1.28409	+	0.162007i
$683$	4.38792	−	4.38792i	0.167899	−	0.167899i	−0.618156	−	0.786055i	$-0.712120\pi$
$683$	4.38792	−	4.38792i	0.167899	−	0.167899i	0.786055	+	0.618156i	$0.212120\pi$
$684$	5.59957	+	1.43580i	0.214105	+	0.0548990i
$685$	3.79310	+	20.7898i	0.144927	+	0.794337i
$686$	8.53564	−	24.7617i	0.325892	−	0.945407i
$687$	−13.8394	+	13.8394i	−0.528005	+	0.528005i
$688$	7.53348	−	2.19396i	0.287211	−	0.0836440i
$689$	−17.9333			−0.683204
$690$	−15.9741	−	14.3080i	−0.608122	−	0.544696i
$691$	10.6952			0.406865			0.203433	−	0.979089i	$-0.434790\pi$
$691$	10.6952			0.406865			0.203433	+	0.979089i	$0.434790\pi$
$692$	−12.6900	−	21.4417i	−0.482400	−	0.815092i
$693$	0.968230	−	14.0473i	0.0367800	−	0.533612i
$694$	−29.2776	−	37.7319i	−1.11136	−	1.43228i
$695$	15.4533	+	10.6845i	0.586179	+	0.405286i
$696$	−7.26472	−	16.7655i	−0.275368	−	0.635493i
$697$	−6.22019	+	6.22019i	−0.235606	+	0.235606i
$698$	3.70847	−	29.3937i	0.140368	−	1.11257i
$699$			1.53541i			0.0580744i
$700$	−26.4352	+	1.08732i	−0.999155	+	0.0410967i
$701$			8.59363i			0.324577i	0.986743	+	0.162288i	$0.0518875\pi$
$701$			8.59363i			0.324577i	−0.986743	+	0.162288i	$0.948112\pi$
$702$	6.13872	+	0.774493i	0.231691	+	0.0292314i
$703$	11.6227	−	11.6227i	0.438359	−	0.438359i
$704$	29.1150	−	31.0646i	1.09731	−	1.17079i
$705$	−12.6441	−	8.74217i	−0.476204	−	0.329249i
$706$	−9.01316	+	6.99365i	−0.339215	+	0.263210i
$707$	−2.47210	+	35.8657i	−0.0929728	+	1.34887i
$708$	−1.15573	+	0.684001i	−0.0434350	+	0.0257063i
$709$	34.7038			1.30333			0.651665	−	0.758507i	$-0.274071\pi$
$709$	34.7038			1.30333			0.651665	+	0.758507i	$0.274071\pi$
$710$	24.1835	−	26.9995i	0.907590	−	1.01327i
$711$	13.2555			0.497122
$712$	−25.1419	−	9.94030i	−0.942234	−	0.372528i
$713$	−21.5347	+	21.5347i	−0.806483	+	0.806483i
$714$	7.60666	+	1.49702i	0.284672	+	0.0560244i
$715$	9.34507	+	51.2199i	0.349486	+	1.91551i
$716$	−41.9919	−	10.7672i	−1.56931	−	0.402390i
$717$	−5.25126	+	5.25126i	−0.196112	+	0.196112i
$718$	−1.70860	+	13.5426i	−0.0637645	+	0.505404i
$719$	−3.34599			−0.124785			−0.0623923	−	0.998052i	$-0.519873\pi$
$719$	−3.34599			−0.124785			−0.0623923	+	0.998052i	$0.519873\pi$
$720$	−4.00166	−	7.99917i	−0.149133	−	0.298112i
$721$	23.9977	+	27.5507i	0.893720	+	1.02604i
$722$	−14.9371	−	1.88454i	−0.555900	−	0.0701353i
$723$	−11.0711	+	11.0711i	−0.411740	+	0.411740i
$724$	−43.4280	−	11.1355i	−1.61399	−	0.413846i
$725$	−11.4066	−	30.2191i	−0.423632	−	1.12231i
$726$	15.0187	+	19.3555i	0.557395	+	0.718349i
$727$	12.0162	+	12.0162i	0.445657	+	0.445657i	0.893908	−	0.448251i	$-0.147953\pi$
$727$	12.0162	+	12.0162i	0.445657	+	0.445657i	−0.448251	+	0.893908i	$0.647953\pi$
$728$	−30.8655	+	10.9208i	−1.14395	+	0.404753i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.23403	−	22.4295i	−0.0456737	−	0.830152i
$731$	−4.06439			−0.150327
$732$	12.1267	+	20.4900i	0.448215	+	0.757332i
$733$	21.8954	+	21.8954i	0.808727	+	0.808727i	0.984441	−	0.175715i	$-0.0562236\pi$
$733$	21.8954	+	21.8954i	0.808727	+	0.808727i	−0.175715	+	0.984441i	$0.556224\pi$
$734$	17.0327	+	21.9512i	0.628690	+	0.810232i
$735$	15.6381	−	0.670185i	0.576821	−	0.0247202i
$736$	6.03175	+	37.8849i	0.222333	+	1.39645i
$737$	−36.4504	+	36.4504i	−1.34267	+	1.34267i
$738$	−5.95693	−	0.751557i	−0.219277	−	0.0276652i
$739$	−24.6553			−0.906958			−0.453479	−	0.891267i	$-0.649817\pi$
$739$	−24.6553			−0.906958			−0.453479	+	0.891267i	$0.649817\pi$
$740$	−25.3691	−	1.79249i	−0.932586	−	0.0658931i
$741$	12.6457			0.464552
$742$	−8.54648	−	12.7347i	−0.313751	−	0.467505i
$743$	4.80217	+	4.80217i	0.176174	+	0.176174i	0.789686	−	0.613511i	$-0.210244\pi$
$743$	4.80217	+	4.80217i	0.176174	+	0.176174i	−0.613511	+	0.789686i	$0.710244\pi$
$744$	−11.6549	+	5.05024i	−0.427290	+	0.185151i
$745$	11.0921	−	16.0429i	0.406383	−	0.587765i
$746$	5.09482	−	3.95327i	0.186535	−	0.144740i
$747$	−9.55176	+	9.55176i	−0.349481	+	0.349481i
$748$	−18.9790	+	11.2324i	−0.693942	+	0.410699i
$749$	−24.1244	+	21.0132i	−0.881487	+	0.767807i
$750$	−6.38792	−	14.4636i	−0.233254	−	0.528134i
$751$	27.5369			1.00484			0.502418	−	0.864625i	$-0.332444\pi$
$751$	27.5369			1.00484			0.502418	+	0.864625i	$0.332444\pi$
$752$	7.68884	+	26.4015i	0.280383	+	0.962762i
$753$	3.13307	+	3.13307i	0.114175	+	0.114175i
$754$	−24.5035	−	31.5791i	−0.892363	−	1.15004i
$755$	−3.94071	+	5.69958i	−0.143417	+	0.207429i
$756$	2.37556	+	4.72829i	0.0863981	+	0.171966i
$757$	21.5964	+	21.5964i	0.784936	+	0.784936i	0.980659	−	0.195723i	$-0.0627055\pi$
$757$	21.5964	+	21.5964i	0.784936	+	0.784936i	−0.195723	+	0.980659i	$0.562705\pi$
$758$	−15.4328	−	1.94709i	−0.560546	−	0.0707214i
$759$	−36.0910			−1.31002
$760$	−10.1606	−	15.1963i	−0.368565	−	0.551228i
$761$			33.8537i			1.22720i	0.789618	+	0.613598i	$0.210279\pi$
$761$			33.8537i			1.22720i	−0.789618	+	0.613598i	$0.789721\pi$
$762$	12.6247	+	1.59280i	0.457344	+	0.0577009i
$763$	2.12486	−	30.8278i	0.0769250	−	1.11604i
$764$	32.1056	+	8.23227i	1.16154	+	0.297833i
$765$	0.831573	+	4.55781i	0.0300656	+	0.164788i
$766$	−39.1960	+	30.4137i	−1.41621	+	1.09889i
$767$	−2.07737	+	2.07737i	−0.0750094	+	0.0750094i
$768$	−3.47010	+	15.6192i	−0.125217	+	0.563608i
$769$	28.2248			1.01781			0.508907	−	0.860822i	$-0.330050\pi$
$769$	28.2248			1.01781			0.508907	+	0.860822i	$0.330050\pi$
$770$	−31.9184	+	31.0459i	−1.15026	+	1.11882i
$771$		−	5.93806i		−	0.213854i
$772$	17.0297	+	28.7743i	0.612911	+	1.03561i
$773$	18.8947	+	18.8947i	0.679594	+	0.679594i	0.959908	−	0.280314i	$-0.0904386\pi$
$773$	18.8947	+	18.8947i	0.679594	+	0.679594i	−0.280314	+	0.959908i	$0.590439\pi$
$774$	−1.70064	−	2.19173i	−0.0611284	−	0.0787800i
$775$	−21.0075	+	7.92960i	−0.754611	+	0.284840i
$776$	14.0402	+	32.4019i	0.504014	+	1.16316i
$777$	15.0104	+	1.03461i	0.538494	+	0.0371165i
$778$	16.4205	+	2.07169i	0.588702	+	0.0742737i
$779$	−12.2712			−0.439662
$780$	−12.8259	−	14.7761i	−0.459240	−	0.529070i
$781$		−	61.0013i		−	2.18280i
$782$	2.48733	−	19.7149i	0.0889468	−	0.705002i
$783$	−4.56794	+	4.56794i	−0.163245	+	0.163245i
$784$	−22.4646	−	16.7135i	−0.802308	−	0.596910i
$785$	−3.63865	−	19.9432i	−0.129869	−	0.711805i
$786$	−9.82538	−	12.6626i	−0.350460	−	0.451659i
$787$	17.9600	−	17.9600i	0.640203	−	0.640203i	−0.310402	−	0.950605i	$-0.600464\pi$
$787$	17.9600	−	17.9600i	0.640203	−	0.640203i	0.950605	+	0.310402i	$0.100464\pi$
$788$	11.5398	+	19.4983i	0.411087	+	0.694598i
$789$			25.0168i			0.890622i
$790$	−31.2238	−	27.9672i	−1.11089	−	0.995030i
$791$	9.06568	−	7.89654i	0.322339	−	0.280769i
$792$	−13.9984	−	5.53452i	−0.497412	−	0.196661i
$793$	36.8297	+	36.8297i	1.30786	+	1.30786i
$794$	−28.1761	+	21.8630i	−0.999934	+	0.775887i
$795$	5.21244	−	7.53894i	0.184866	−	0.267378i
$796$	−11.8214	−	3.03114i	−0.418998	−	0.107436i
$797$	−5.15055	+	5.15055i	−0.182442	+	0.182442i	−0.792419	−	0.609977i	$-0.791179\pi$
$797$	−5.15055	+	5.15055i	−0.182442	+	0.182442i	0.609977	+	0.792419i	$0.291179\pi$
$798$	6.02658	+	8.97990i	0.213339	+	0.317885i
$799$		−	14.2438i		−	0.503911i
$800$	−7.45104	+	27.2852i	−0.263434	+	0.964677i
$801$			9.55854i			0.337735i
$802$	5.91123	+	0.745792i	0.208733	+	0.0263348i
$803$	−26.7321	−	26.7321i	−0.943354	−	0.943354i
$804$	4.81157	−	18.7650i	0.169691	−	0.661790i
$805$	−4.46999	−	39.8702i	−0.157546	−	1.40524i
$806$	−21.9530	+	17.0342i	−0.773260	+	0.600002i
$807$	11.3187	−	11.3187i	0.398436	−	0.398436i
$808$	35.7409	+	14.1308i	1.25736	+	0.497120i
$809$			2.71807i			0.0955622i	0.998858	+	0.0477811i	$0.0152150\pi$
$809$			2.71807i			0.0955622i	−0.998858	+	0.0477811i	$0.984785\pi$
$810$	−2.10985	+	2.35553i	−0.0741326	+	0.0827649i
$811$	−17.0312			−0.598047			−0.299023	−	0.954246i	$-0.596661\pi$
$811$	−17.0312			−0.598047			−0.299023	+	0.954246i	$0.596661\pi$
$812$	10.7472	−	32.4499i	0.377151	−	1.13877i
$813$	−4.03811	+	4.03811i	−0.141623	+	0.141623i
$814$	−33.8155	+	26.2388i	−1.18523	+	0.919668i
$815$	0.501344	+	2.74784i	0.0175613	+	0.0962526i
$816$	3.98801	−	7.26528i	0.139608	−	0.254336i
$817$	−4.00913	−	4.00913i	−0.140262	−	0.140262i
$818$	28.2461	+	3.56368i	0.987602	+	0.124601i
$819$	7.60293	+	8.72860i	0.265668	+	0.305002i
$820$	12.4460	+	14.3385i	0.434635	+	0.500724i
$821$			8.06311i			0.281405i	0.990052	+	0.140702i	$0.0449360\pi$
$821$			8.06311i			0.281405i	−0.990052	+	0.140702i	$0.955064\pi$
$822$	−13.2605	−	1.67302i	−0.462515	−	0.0583533i
$823$	−0.171685	−	0.171685i	−0.00598457	−	0.00598457i	0.704108	−	0.710093i	$-0.251347\pi$
$823$	−0.171685	−	0.171685i	−0.00598457	−	0.00598457i	−0.710093	+	0.704108i	$0.751347\pi$
$824$	35.8394	−	15.5297i	1.24853	−	0.541004i
$825$	−24.2484	−	10.9589i	−0.844222	−	0.381539i
$826$	−2.46518	−	0.485155i	−0.0857746	−	0.0168807i
$827$	24.8846	+	24.8846i	0.865323	+	0.865323i	0.991950	−	0.126628i	$-0.0404153\pi$
$827$	24.8846	+	24.8846i	0.865323	+	0.865323i	−0.126628	+	0.991950i	$0.540415\pi$
$828$	11.6720	−	6.90791i	0.405631	−	0.240066i
$829$		−	4.86782i		−	0.169066i	−0.996421	−	0.0845332i	$-0.973060\pi$
$829$		−	4.86782i		−	0.169066i	0.996421	−	0.0845332i	$-0.0269399\pi$
$830$	42.6523	−	2.34666i	1.48048	−	0.0814538i
$831$		−	17.6104i		−	0.610899i
$832$	1.13333	+	34.9828i	0.0392911	+	1.21281i
$833$	8.75161	+	11.5658i	0.303225	+	0.400731i
$834$	−9.38757	+	7.28418i	−0.325065	+	0.252230i
$835$	34.9779	−	6.38172i	1.21046	−	0.220848i
$836$	−29.8007	−	7.64125i	−1.03068	−	0.264278i
$837$	3.17551	+	3.17551i	0.109762	+	0.109762i
$838$	−1.60285	+	12.7044i	−0.0553697	+	0.438866i
$839$	−41.3167			−1.42641			−0.713205	−	0.700956i	$-0.752757\pi$
$839$	−41.3167			−1.42641			−0.713205	+	0.700956i	$0.752757\pi$
$840$	4.38030	−	16.1497i	0.151135	−	0.557218i
$841$	12.7321			0.439039
$842$	−1.03544	+	8.20702i	−0.0356836	+	0.282832i
$843$	−8.90718	−	8.90718i	−0.306780	−	0.306780i
$844$	−7.45550	+	29.0763i	−0.256629	+	1.00085i
$845$	−11.2965	−	7.81041i	−0.388610	−	0.268686i
$846$	7.68101	−	5.95999i	0.264079	−	0.204909i
$847$	−3.15165	+	45.7247i	−0.108292	+	1.57112i
$848$	−15.7417	+	4.58441i	−0.540571	+	0.157429i
$849$		−	8.88766i		−	0.305024i
$850$	7.65751	−	12.4906i	0.262650	−	0.428423i
$851$		−	38.5654i		−	1.32200i
$852$	11.6758	+	19.7282i	0.400007	+	0.675876i
$853$	−22.0624	−	22.0624i	−0.755403	−	0.755403i	0.220079	−	0.975482i	$-0.429369\pi$
$853$	−22.0624	−	22.0624i	−0.755403	−	0.755403i	−0.975482	+	0.220079i	$0.929369\pi$
$854$	−8.60134	+	43.7053i	−0.294332	+	1.49556i
$855$	−3.67557	+	5.31611i	−0.125702	+	0.181807i
$856$	13.5984	+	31.3823i	0.464784	+	1.07262i
$857$	5.01954	+	5.01954i	0.171464	+	0.171464i	0.787622	−	0.616158i	$-0.211312\pi$
$857$	5.01954	+	5.01954i	0.171464	+	0.171464i	−0.616158	+	0.787622i	$0.711312\pi$
$858$	−32.6701	−	4.12182i	−1.11534	−	0.140717i
$859$			33.7766i			1.15244i	0.817293	+	0.576222i	$0.195474\pi$
$859$			33.7766i			1.15244i	−0.817293	+	0.576222i	$0.804526\pi$
$860$	−0.618299	+	8.75079i	−0.0210838	+	0.298399i
$861$	−7.37777	−	8.47011i	−0.251434	−	0.288661i
$862$	−7.08688	−	0.894117i	−0.241380	−	0.0304538i
$863$	−28.6141	−	28.6141i	−0.974034	−	0.974034i	0.0256373	−	0.999671i	$-0.491838\pi$
$863$	−28.6141	−	28.6141i	−0.974034	−	0.974034i	−0.999671	+	0.0256373i	$0.991838\pi$
$864$	5.58649	−	0.889441i	0.190056	−	0.0302594i
$865$	27.4040	−	4.99986i	0.931764	−	0.170001i
$866$	−23.3371	+	18.1082i	−0.793028	+	0.615341i
$867$	8.98519	−	8.98519i	0.305153	−	0.305153i
$868$	−22.5583	−	7.47113i	−0.765680	−	0.253587i
$869$	−70.5456			−2.39309
$870$	20.3976	−	1.12224i	0.691543	−	0.0380476i
$871$		−	42.3777i		−	1.43591i
$872$	−30.7206	−	12.1459i	−1.04033	−	0.411313i
$873$	8.82826	−	8.82826i	0.298791	−	0.298791i
$874$	21.9003	−	16.9933i	0.740790	−	0.574807i
$875$	9.10317	−	28.1448i	0.307743	−	0.951469i
$876$	13.7619	+	3.52871i	0.464971	+	0.119224i
$877$	8.33092	+	8.33092i	0.281315	+	0.281315i	0.833633	−	0.552318i	$-0.186257\pi$
$877$	8.33092	+	8.33092i	0.281315	+	0.281315i	−0.552318	+	0.833633i	$0.686257\pi$
$878$	6.25572	+	0.789255i	0.211120	+	0.0266361i
$879$			1.96427i			0.0662531i
$880$	21.2967	+	42.5713i	0.717911	+	1.43508i
$881$			40.9847i			1.38081i	0.723423	+	0.690405i	$0.242568\pi$
$881$			40.9847i			1.38081i	−0.723423	+	0.690405i	$0.757432\pi$
$882$	−2.57497	+	9.55874i	−0.0867038	+	0.321860i
$883$	1.65748	−	1.65748i	0.0557788	−	0.0557788i	−0.678667	−	0.734446i	$-0.737442\pi$
$883$	1.65748	−	1.65748i	0.0557788	−	0.0557788i	0.734446	+	0.678667i	$0.237442\pi$
$884$	4.50314	−	17.5621i	0.151457	−	0.590678i
$885$	−0.269497	−	1.47710i	−0.00905906	−	0.0496522i
$886$	10.1137	−	7.84762i	0.339777	−	0.263646i
$887$	−19.9148	−	19.9148i	−0.668675	−	0.668675i	0.288735	−	0.957409i	$-0.406765\pi$
$887$	−19.9148	−	19.9148i	−0.668675	−	0.668675i	−0.957409	+	0.288735i	$0.906765\pi$
$888$	5.91397	−	14.9582i	0.198460	−	0.501963i
$889$	15.6359	+	17.9509i	0.524412	+	0.602055i
$890$	20.1671	−	22.5154i	0.676003	−	0.754719i
$891$			5.32197i			0.178293i
$892$	−29.9691	+	17.7367i	−1.00344	+	0.593870i
$893$	14.0502	−	14.0502i	0.470171	−	0.470171i
$894$	7.56205	+	9.74569i	0.252913	+	0.325945i
$895$	27.5636	−	39.8662i	0.921350	−	1.33258i
$896$	−24.3016	+	17.4766i	−0.811861	+	0.583851i
$897$	20.9799	−	20.9799i	0.700499	−	0.700499i
$898$	−2.33506	+	18.5079i	−0.0779218	+	0.617617i
$899$		−	29.0111i		−	0.967573i
$900$	9.93964	−	1.09705i	0.331321	−	0.0365683i
$901$	8.49278			0.282935
$902$	31.7026	+	3.99976i	1.05558	+	0.133177i
$903$	0.356878	−	5.17766i	0.0118762	−	0.172302i
$904$	−5.11012	−	11.7931i	−0.169960	−	0.392233i
$905$	28.5063	−	41.2296i	0.947581	−	1.37052i
$906$	−2.68659	−	3.46237i	−0.0892558	−	0.115030i
$907$	−25.1708	−	25.1708i	−0.835783	−	0.835783i	0.152518	−	0.988301i	$-0.451262\pi$
$907$	−25.1708	−	25.1708i	−0.835783	−	0.835783i	−0.988301	+	0.152518i	$0.951262\pi$
$908$	−4.37406	+	2.58872i	−0.145158	+	0.0859098i
$909$		−	13.5881i		−	0.450689i
$910$	0.507137	−	36.6015i	0.0168114	−	1.21333i
$911$	−44.7962			−1.48417			−0.742083	−	0.670308i	$-0.766162\pi$
$911$	−44.7962			−1.48417			−0.742083	+	0.670308i	$0.766162\pi$
$912$	11.1003	−	3.23271i	0.367567	−	0.107046i
$913$	50.8341	−	50.8341i	1.68236	−	1.68236i
$914$	−2.31749	+	1.79823i	−0.0766559	+	0.0594802i
$915$	−26.1876	+	4.77793i	−0.865736	+	0.157954i
$916$	−9.72237	+	37.9170i	−0.321236	+	1.25281i
$917$	2.06184	−	29.9136i	0.0680881	−	0.987835i
$918$	−2.90715	−	0.366781i	−0.0959503	−	0.0121056i
$919$		−	18.8636i		−	0.622254i	−0.950368	−	0.311127i	$-0.899293\pi$
$919$		−	18.8636i		−	0.622254i	0.950368	−	0.311127i	$-0.100707\pi$
$920$	−42.0685	−	8.35446i	−1.38696	−	0.275438i
$921$	−21.8265			−0.719206
$922$	39.1646	+	4.94121i	1.28982	+	0.162730i
$923$	35.4604	+	35.4604i	1.16719	+	1.16719i
$924$	−12.6426	−	25.1638i	−0.415912	−	0.827828i
$925$	11.7102	−	25.9109i	0.385030	−	0.851945i
$926$	3.38746	+	4.36563i	0.111319	+	0.143463i
$927$	−9.76485	−	9.76485i	−0.320720	−	0.320720i
$928$	−29.5817	−	21.4558i	−0.971066	−	0.704323i
$929$	19.6948			0.646164			0.323082	−	0.946371i	$-0.395281\pi$
$929$	19.6948			0.646164			0.323082	+	0.946371i	$0.395281\pi$
$930$	−0.780154	−	14.1799i	−0.0255823	−	0.464976i
$931$	−2.77593	+	20.0412i	−0.0909773	+	0.656823i
$932$	1.56403	+	2.64267i	0.0512314	+	0.0865636i
$933$	−7.92311	+	7.92311i	−0.259391	+	0.259391i
$934$	9.62899	−	7.47150i	0.315070	−	0.244475i
$935$	−4.42560	−	24.2565i	−0.144733	−	0.793273i
$936$	11.3546	−	4.92012i	0.371137	−	0.160819i
$937$	2.00932	+	2.00932i	0.0656415	+	0.0656415i	0.739165	−	0.673524i	$-0.235220\pi$
$937$	2.00932	+	2.00932i	0.0656415	+	0.0656415i	−0.673524	+	0.739165i	$0.735220\pi$
$938$	30.0930	−	20.1960i	0.982572	−	0.659422i
$939$	17.4669			0.570012
$940$	−30.6676	−	2.16686i	−1.00027	−	0.0706751i
$941$	40.0324			1.30502			0.652510	−	0.757780i	$-0.273716\pi$
$941$	40.0324			1.30502			0.652510	+	0.757780i	$0.273716\pi$
$942$	12.7206	+	1.60490i	0.414459	+	0.0522903i
$943$	−20.3586	+	20.3586i	−0.662967	+	0.662967i
$944$	−1.29244	+	2.35454i	−0.0420653	+	0.0766338i
$945$	−5.87925	+	0.659144i	−0.191252	+	0.0214419i
$946$	9.05077	+	11.6643i	0.294266	+	0.379239i
$947$	−12.5079	−	12.5079i	−0.406453	−	0.406453i	0.474047	−	0.880500i	$-0.342793\pi$
$947$	−12.5079	−	12.5079i	−0.406453	−	0.406453i	−0.880500	+	0.474047i	$0.842793\pi$
$948$	22.8148	−	13.5026i	0.740992	−	0.438545i
$949$	31.0790			1.00887
$950$	19.8741	−	4.76733i	0.644802	−	0.154673i
$951$			20.3131i			0.658698i
$952$	14.6172	−	5.17185i	0.473745	−	0.167621i
$953$	−1.52100	−	1.52100i	−0.0492699	−	0.0492699i	0.682043	−	0.731312i	$-0.261092\pi$
$953$	−1.52100	−	1.52100i	−0.0492699	−	0.0492699i	−0.731312	+	0.682043i	$0.761092\pi$
$954$	3.55360	+	4.57974i	0.115052	+	0.148275i
$955$	−21.0742	+	30.4804i	−0.681946	+	0.986322i
$956$	−3.68909	+	14.3874i	−0.119314	+	0.465321i
$957$	24.3104	−	24.3104i	0.785844	−	0.785844i
$958$	12.9372	+	1.63222i	0.417980	+	0.0527346i
$959$	−16.4235	−	18.8551i	−0.530341	−	0.608862i
$960$	−15.0357	−	9.69157i	−0.485276	−	0.312794i
$961$	10.8323			0.349429
$962$	4.40442	−	34.9099i	0.142004	−	1.12554i
$963$	8.55046	−	8.55046i	0.275535	−	0.275535i
$964$	−7.77765	+	30.3326i	−0.250501	+	0.976948i
$965$	−36.7756	+	6.70971i	−1.18385	+	0.215993i
$966$	24.8965	+	4.89972i	0.801033	+	0.157646i
$967$	−33.2049	+	33.2049i	−1.06780	+	1.06780i	−0.0702702	+	0.997528i	$0.522386\pi$
$967$	−33.2049	+	33.2049i	−1.06780	+	1.06780i	−0.997528	+	0.0702702i	$0.977614\pi$
$968$	45.5657	+	18.0152i	1.46454	+	0.579030i
$969$	−5.98871			−0.192385
$970$	−39.4216	+	2.16891i	−1.26575	+	0.0696396i
$971$	30.3477			0.973905			0.486952	−	0.873429i	$-0.338109\pi$
$971$	30.3477			0.973905			0.486952	+	0.873429i	$0.338109\pi$
$972$	−1.01864	−	1.72115i	−0.0326729	−	0.0552061i
$973$	−22.1769	−	1.52858i	−0.710958	−	0.0490039i
$974$	12.9258	−	10.0296i	0.414168	−	0.321369i
$975$	20.4662	−	7.72529i	0.655444	−	0.247407i
$976$	41.7438	+	22.9137i	1.33619	+	0.733451i
$977$	13.5302	−	13.5302i	0.432870	−	0.432870i	−0.456734	−	0.889603i	$-0.650981\pi$
$977$	13.5302	−	13.5302i	0.432870	−	0.432870i	0.889603	+	0.456734i	$0.150981\pi$
$978$	−1.75268	−	0.221127i	−0.0560446	−	0.00707087i
$979$		−	50.8702i		−	1.62582i
$980$	26.2330	−	17.0831i	0.837981	−	0.545699i
$981$			11.6795i			0.372897i
$982$	7.27416	−	57.6558i	0.232128	−	1.83987i
$983$	−31.5723	+	31.5723i	−1.00700	+	1.00700i	−0.00702388	+	0.999975i	$0.502236\pi$
$983$	−31.5723	+	31.5723i	−1.00700	+	1.00700i	−0.999975	+	0.00702388i	$0.997764\pi$
$984$	−11.0184	+	4.77441i	−0.351252	+	0.152203i
$985$	−24.9202	+	4.54669i	−0.794023	+	0.144869i
$986$	11.6043	+	14.9551i	0.369555	+	0.476268i
$987$	18.1453	+	1.25070i	0.577573	+	0.0398101i
$988$	21.7652	−	12.8814i	0.692445	−	0.409813i
$989$	−13.3027			−0.423001
$990$	11.2286	−	12.5361i	0.356867	−	0.398422i
$991$	−54.1158			−1.71904			−0.859522	−	0.511098i	$-0.829239\pi$
$991$	−54.1158			−1.71904			−0.859522	+	0.511098i	$0.829239\pi$
$992$	−14.9155	+	20.5644i	−0.473569	+	0.652920i
$993$	12.6797	−	12.6797i	0.402377	−	0.402377i
$994$	−8.28155	+	42.0803i	−0.262675	+	1.33471i
$995$	7.75959	−	11.2230i	0.245996	−	0.355792i
$996$	−6.71026	+	26.1699i	−0.212623	+	0.829224i
$997$	−25.5492	+	25.5492i	−0.809152	+	0.809152i	−0.984505	−	0.175354i	$-0.943893\pi$
$997$	−25.5492	+	25.5492i	−0.809152	+	0.809152i	0.175354	+	0.984505i	$0.443893\pi$
$998$	4.34895	+	0.548687i	0.137664	+	0.0173684i
$999$	−5.68684			−0.179924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.13.4	yes	184
5.2	odd	4	inner	840.2.bj.b.517.48	yes	184
7.6	odd	2	inner	840.2.bj.b.13.3	✓	184
8.5	even	2	inner	840.2.bj.b.13.47	yes	184
35.27	even	4	inner	840.2.bj.b.517.47	yes	184
40.37	odd	4	inner	840.2.bj.b.517.3	yes	184
56.13	odd	2	inner	840.2.bj.b.13.48	yes	184
280.237	even	4	inner	840.2.bj.b.517.4	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.3	✓	184	7.6	odd	2	inner
840.2.bj.b.13.4	yes	184	1.1	even	1	trivial
840.2.bj.b.13.47	yes	184	8.5	even	2	inner
840.2.bj.b.13.48	yes	184	56.13	odd	2	inner
840.2.bj.b.517.3	yes	184	40.37	odd	4	inner
840.2.bj.b.517.4	yes	184	280.237	even	4	inner
840.2.bj.b.517.47	yes	184	35.27	even	4	inner
840.2.bj.b.517.48	yes	184	5.2	odd	4	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40309 - 0.177021i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.93733 + 0.496754i) q^{4} +(-1.27167 + 1.83926i) q^{5} +(-0.866962 - 1.11731i) q^{6} +(0.181931 - 2.63949i) q^{7} +(-2.63031 - 1.03994i) q^{8} +1.00000i q^{9} +(2.10985 - 2.35553i) q^{10} -5.32197i q^{11} +(1.01864 + 1.72115i) q^{12} +(3.09369 + 3.09369i) q^{13} +(-0.722511 + 3.67124i) q^{14} +(-2.19975 + 0.401346i) q^{15} +(3.50647 + 1.92475i) q^{16} +(-1.46510 - 1.46510i) q^{17} +(0.177021 - 1.40309i) q^{18} -2.89036i q^{19} +(-3.37729 + 2.93153i) q^{20} +(1.99505 - 1.73776i) q^{21} +(-0.942101 + 7.46720i) q^{22} +(-4.79525 - 4.79525i) q^{23} +(-1.12456 - 2.59526i) q^{24} +(-1.76572 - 4.67784i) q^{25} +(-3.79308 - 4.88838i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.66364 - 5.02318i) q^{28} +6.46004 q^{29} +(3.15750 - 0.173721i) q^{30} -4.49085i q^{31} +(-4.57918 - 3.32132i) q^{32} +(3.76320 - 3.76320i) q^{33} +(1.79631 + 2.31502i) q^{34} +(4.62334 + 3.69117i) q^{35} +(-0.496754 + 1.93733i) q^{36} +(4.02121 + 4.02121i) q^{37} +(-0.511655 + 4.05543i) q^{38} +4.37514i q^{39} +(5.25759 - 3.51536i) q^{40} -4.24557i q^{41} +(-3.10685 + 2.08506i) q^{42} +(1.38707 - 1.38707i) q^{43} +(2.64371 - 10.3104i) q^{44} +(-1.83926 - 1.27167i) q^{45} +(5.87931 + 7.57703i) q^{46} +(4.86105 + 4.86105i) q^{47} +(1.11845 + 3.84045i) q^{48} +(-6.93380 - 0.960409i) q^{49} +(1.64939 + 6.87601i) q^{50} -2.07196i q^{51} +(4.45669 + 7.53030i) q^{52} +(-2.89836 + 2.89836i) q^{53} +(1.11731 - 0.866962i) q^{54} +(9.78846 + 6.76777i) q^{55} +(-3.22344 + 6.75348i) q^{56} +(2.04379 - 2.04379i) q^{57} +(-9.06402 - 1.14356i) q^{58} +0.671485i q^{59} +(-4.46101 - 0.315199i) q^{60} +11.9048 q^{61} +(-0.794976 + 6.30107i) q^{62} +(2.63949 + 0.181931i) q^{63} +(5.83706 + 5.47072i) q^{64} +(-9.62424 + 1.75594i) q^{65} +(-5.94627 + 4.61394i) q^{66} +(-6.84905 - 6.84905i) q^{67} +(-2.11058 - 3.56617i) q^{68} -6.78151i q^{69} +(-5.83355 - 5.99747i) q^{70} +11.4622 q^{71} +(1.03994 - 2.63031i) q^{72} +(5.02297 - 5.02297i) q^{73} +(-4.93028 - 6.35395i) q^{74} +(2.05918 - 4.55629i) q^{75} +(1.43580 - 5.59957i) q^{76} +(-14.0473 - 0.968230i) q^{77} +(0.774493 - 6.13872i) q^{78} -13.2555i q^{79} +(-7.99917 + 4.00166i) q^{80} -1.00000 q^{81} +(-0.751557 + 5.95693i) q^{82} +(9.55176 + 9.55176i) q^{83} +(4.72829 - 2.37556i) q^{84} +(4.55781 - 0.831573i) q^{85} +(-2.19173 + 1.70064i) q^{86} +(4.56794 + 4.56794i) q^{87} +(-5.53452 + 13.9984i) q^{88} +9.55854 q^{89} +(2.35553 + 2.10985i) q^{90} +(8.72860 - 7.60293i) q^{91} +(-6.90791 - 11.6720i) q^{92} +(3.17551 - 3.17551i) q^{93} +(-5.95999 - 7.68101i) q^{94} +(5.31611 + 3.67557i) q^{95} +(-0.889441 - 5.58649i) q^{96} +(-8.82826 - 8.82826i) q^{97} +(9.55874 + 2.57497i) q^{98} +5.32197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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